Methods for Biological Modeling Subgroup (MFBM)

Ad hoc subgroup meeting room
(reserved for subgroup activities)
Senate Chamber in The Ohio Union

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Sub-group minisymposia

Recent advances in the mathematics of biochemical reaction networks

Organized by: Tung Nguyen, Matthew Johnson, Jiaxin Jin
Note: this minisymposia has multiple sessions. The other session is MS02-MFBM-1.

  • Hyukpyo Hong Institute for Basic Science (Biomedical Mathematics Group)
    "Network translation allows for revealing long-term dynamics of stochastic reaction networks"
  • Long-term behaviors of biochemical systems are described by steady states in deterministic models and stationary distributions in stochastic models. Their analytic solutions can be obtained for limited cases, such as linear or finite-state systems. Interestingly, analytic solutions can be easily obtained when underlying networks have special topologies, called weak reversibility (WR) and zero deficiency (ZD). However, such desired topological conditions do not hold for the majority of cases. Thus, we propose a method of translating networks to have WR and ZD while preserving the original dynamics was proposed. Additionally, we prove necessary conditions for having WR and ZD after translation. Our method provides a valuable tool for analyzing and understanding the long-term behavior of biochemical systems, and we demonstrate its efficacy with several examples.
  • Angelyn Lao De La Salle University (Department of Mathematics and Statistics)
    "A Reaction Network Analysis of Insulin Signaling"
  • The insulin signaling system is an important metabolic system that initiates the uptake of glucose into the cell. This reduced ability of cells to use available insulin for energy metabolism is viewed as a common factor in diseases such as obesity, type 2 diabetes, metabolic syndrome, and cancer, and more recently to brain insulin resistance in connection with mild cognitive impairment and Alzheimer’s disease (AD). The complexity of the insulin signaling system, both in terms of the number of molecular components involved as well as the intricate combination of positive and negative feedback loops, clearly warrants the application of mathematical modeling and computational tools. This talk presents the construction of the insulin signaling reaction network and the analysis of its robustness and stability using Chemical Reaction Network Theory.
  • M. Ali Al-Radhawi Northeastern University (Department of Electrical and Computer Engineering)
    "Contraction and entrainment in reaction networks"
  • In previous work, we have developed an approach to understanding the long-term dynamics of classes of chemical reaction networks, based on “rate-dependent Lyapunov functions”, and developed an effective computational package. In this talk, we show that stronger notions of convergence can be established by proving contraction with respect to non-standard norms. This enables us to show that such networks entrain to periodic inputs. We illustrate our theory with examples from signalling pathways and genetic circuits.
  • Jinsu Kim POSTECH (Mathematics / Mathematical biology)
    "Recent studies about mixing times of stochastically modeled reaction networks"
  • Molecular counts of small-size biological systems can be modeled with continuous-time Markov chains on infinite positive integer grids with polynomial rates. In this talk, we will discuss recent studies about mixing times of continuous-time Markov chains modeling chemical reaction systems. The mixing time, which indicates the time for the distance between the distribution of the stochastic process and its stationary distribution, is typically investigated with the Lyapunov function method and canonical path method. Recently, we discovered examples that do not lend themselves easily to analysis via those two methods but are shown to have either fast mixing or slow mixing with our new technique.

Integration of data and modeling for multiscale biology

Organized by: Yuchi Qiu, Heyrim Cho

  • Jianhua Xing University of Pittsburgh (Computational and Systems Biology)
    "Reconstructing cellular dynamics from single cell data"
  • A grand challenge in single cell studies is to construct a quantitative, predictive, and genome-wide mathematical model describing cellular dynamics. Single-cell (sc)RNA-seq, together with RNA velocity and metabolic labeling, reveals cellular states and transitions at unprecedented resolution. A frontier of research is how to extract dynamical information from the snapshot data. In this talk I will first discuss our recently developed dynamo framework (Qiu et al. Cell, 2022), focusing on the underlying mathematical framework. Then I will discuss our recent efforts of reconstructing full dynamical equations using discrete calculus on graphs (Zhang et al. to be submitted). I will conclude with an example of applying the formalism, together with transition path analyses originally developed in chemical physics, to study how epithelial-to-mesenchymal transition couples with cell cycle (Wang et al. Sci Adv 2020, eLife 2022, Hu et al., in preparation).
  • Aden Forrow University of Maine (Mathematics and Statistics)
    "Trajectory inference with lineage tracing"
  • Over the past decade, rapid advances in experimental techniques have produced a flood of data on biological systems at single cell resolution. A key goal for the field is to understand dynamic processes by inferring the trajectories of cell states over time. Time-dependent information typically cannot be recovered directly because standard high-throughput measurements destroy the measured cells. That experimental constraint leads to strict mathematical limits on what it is possible to learn from the data. To get around those limits, we need different measurements, such as recording the history of cell divisions with lineage tracing. In this talk, I will show how lineage tracing helps disentangle complex trajectories that could not be resolved from traditional single-cell data, including identifying disparate ancestry among nearly identical cells.
  • Yuchi Qiu Michigan State University (Department of Mathematics)
    "Interpretable AIs in data-driven biology: from topological data analysis to multiscale modeling"
  • Artificial intelligence (AI) has become increasingly prominent in analyzing biological data on both large-scale and single-cell levels, leading to a revolution in deciphering functions and dynamics of complex biological systems. Despite its success, traditional black-box AIs often struggle to provide comprehensive understanding and interpretation of the multiscale processes in complex, heterogeneous, and noisy data. To address these challenges, we combine topological data analysis (TDA) and multiscale modeling to enhance AI interpretability. Our TDA-driven models capture the intricate patterns in complex data. Additionally, data-driven multiscale modeling infers temporal dynamics within biological systems. By incorporating these innovative techniques, we aim to accelerate protein design and understand cell fate dynamics from single-cell omics data, ultimately improving the applicability and interpretability of AI models in the analysis of complex biological data.

Recent advances in the mathematics of biochemical reaction networks

Organized by: Tung Nguyen, Matthew Johnson, Jiaxin Jin
Note: this minisymposia has multiple sessions. The other session is MS01-MFBM-1.

  • James Brunner Los Alamos National Laboratory (Biosciences)
    "Inferring microbial interactions with their environment from genomic and metagenomic data"
  • Microbial communities organize through a complex set of interactions between microbes and their environment, and the resulting metabolic impact on the host ecosystem can be profound. Microbial activity has been shown to impact human health, leading to a myriad of treatments meant to manipulate the resident microbiota of the human gut. Additionally, microbes of plant rhizospheres have a strong influence on plant growth and resilience. Finally, microbial communities impact decomposition in terrestrial ecosystems, influencing the way that carbon is stored in soil and removed from the atmosphere. In order to understand, predict, and influence these processes, genome-scale modeling techniques have been developed to translate genomic data into inferred microbial dynamics. However, these techniques have a strong dependence on unknown parameters and initial community compositions, and are often difficult to analyze qualitatively. With the goal of understanding microbial community metabolic dynamics, we infer the series of interaction networks underlying the resource-mediated community model defined by individual genome-scale models. I will present our tool, MetConSIN, for inferring these networks as well as our current efforts to analyze and simplify the model. Finally, I will discuss our future goals for the prediction of microbial community metabolic impact on their host ecosystem.
  • Tung Nguyen Texas A&M University (Department of Mathematics)
    "Absolute concentration robustness in multi-site phosphorylation networks with a bifunctional enzyme"
  • Shinar and Feinberg in 2010 introduced the concept of absolute concentration robustness (ACR) to mean the concentration of a certain species (called ACR species) is invariant across all positive steady states. Biological networks with ACR have been observed experimentally in certain signaling systems in E. coli, and recently have also been proposed as synthetic controllers by Kim and Enciso in 2020. Shinar and Feinberg gave a sufficient condition for the existence of an ACR species; that is the network must have a deficiency of one and there are two non-terminal complexes differing in the ACR species. While the condition is easily checked, many biologically important networks do not have a deficiency of exactly one. In this work, we present a large class of biological networks with arbitrary deficiency and capable of exhibiting ACR. Notably, this class contains multi-site phosphorylation cycles with a ``bifunctional' enzyme. We provide the necessary and sufficient conditions for ACR in such a class of networks, and highlight the essential role of bifunctionality for the existence of ACR.
  • Jiaxin Jin The Ohio State University (Mathematics)
    "Weakly reversible deficiency one realizations of polynomial dynamical systems: an algorithmic perspective"
  • Given a dynamical system with a polynomial right-hand side, can it be generated by a reaction network that possesses certain properties? This question is important because some network properties may guarantee specific {em dynamical} properties, such as existence or uniqueness of equilibria, persistence, permanence, or global stability. Here we focus on this problem in the context of weakly reversible deficiency one networks. In particular, we describe an algorithm for deciding if a polynomial dynamical system admits a weakly reversible deficiency one realization, and identifying one if it does exist. In addition, we show that weakly reversible deficiency one realizations can be partitioned into mutually exclusive Type I and Type II realizations, where Type I realizations guarantee existence and uniqueness of positive steady states, while Type II realizations are related to stoichiometric generators, and therefore to multistability.
  • Aidan S. Howells University of Wisconsin–Madison (Mathematics)
    "Stochastic reaction networks within interacting compartments"
  • Stochastic reaction networks, which are typically modeled as continuous-time Markov chains on $mathbb Z^d_{ge0}$, have proven to be a useful tool for the understanding of processes, chemical and otherwise, in homogeneous environments. There are multiple avenues for generalizing away from the assumption that the environment is homogeneous, with the proper modeling choice dependent upon the context of the problem being considered. One such generalization, introduced by Duso and Zechner in 2020, involves a varying number of interacting compartments, or cells, each of which contains an evolving copy of the stochastic reaction system. The novelty of the model is that these compartments also interact via the merging of two compartments (including their contents), the splitting of one compartment into two, and the appearance and destruction of compartments. We will discuss results pertaining to explosivity, transience, recurrence, and positive recurrence of the model, and explore a number of examples demonstrating some possible non-intuitive behaviors. Based on join work with David F. Anderson

Stochastic methods for biochemical reaction networks

Organized by: Wasiur KhudaBukhsh, Hye-Won Kang
Note: this minisymposia has multiple sessions. The other session is MS04-MFBM-1.

  • Grzegorz A. Rempala The Ohio State University (Biostatistics)
    "Agent-based, aggregated dynamics for chemical reaction networks"
  • In this talk I will present a modeling framework for approximating stochastic dynamics of a single tagged molecule in a large biochemical network (CRN). This framework is based on approximating the dynamics of the CRN representing a biological system with hybrid dynamics combining the stochastic laws of individually-tagged molecules with the mean-field laws of the remaining species comprising the CRN. The approximation is well-defined over the entire process evolution time and leads to efficient and fully parallelizable simulation techniques. Moreover, it also allow for principled and efficient statistical inference for model parameters, which is difficult or even impossible in traditional agent-based models (ABM). As part of the development of the ABA approach, one could also consider how to incorporate different individual features (e.g., when molecules of the same species have individual characteristics or spatial features). I will present some molecular examples illustrating potential applications, including the HIV virus dendritic cell invasion models and models of multi-stage transcriptional bursting.
  • Hye-Won Kang University of Maryland, Baltimore County (Department of Mathematics and Statistics)
    "Stochastic oscillations in the enzyme-catalyzed chemical reaction network in glycolysis"
  • We consider a simple chemical reaction network in glycolysis. In a large volume limit of this system, species concentrations can exhibit a steady or an oscillatory behavior depending on the choice of the parameter values. To investigate how the inherent fluctuations affect the oscillatory behavior of the species copy numbers, we compare stochastic and deterministic dynamics of the system with selected parameter values near a separatrix. Due to the inherent fluctuations, a parameter region of the stochastic model cannot be separated clearly by the system behavior. We test several chemical reaction networks modified from the original system in glycolysis and investigate how the effects of the inherent fluctuations can be regulated. This is joint work with Luan Nguyen at UMBC.
  • Yi Fu University of California, San Diego (Bioinformatics and Systems Biology PhD Program)
    "Comparison Theorems for Stochastic Chemical Reaction Networks"
  • Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. Our proof also yields a method for simultaneously simulating the sample paths of two comparable SCRNs. Our tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. We illustrate our results with applications to models of chromatin regulation and enzymatic kinetics.
  • Arnab Ganguly Louisiana State University (Mathematics)
    "Statistical inference of stochastic differential equations with applications to biochemical reactions"
  • Stochastic differential equations (SDES) are potent tools in modeling temporal evolution of a variety of systems. For the model to be accurate it is necessary to learn or estimate certain key parameters of the underlying SDE or sometimes the entire driving functions from the available data. Although computational methods for these types of learning problems have been studied in the literature, there is a critical lack of theoretical results on limiting behavior of the underlying estimators even for one-dimensional SDEs. The complexity of the SDE dynamics hinders usage of standard statistical tools in deriving the relevant properties. The goal of this talk is to partly fill this gap in theoretical understanding of these types of inference problems. In particular, we will discuss recent results on desirable asymptotic properties including consistency and central limit theorem of some of the estimators. We will specifically illustrate these results for SDEs that are used to model biochemical reaction systems.

Inference, analysis, and control of Boolean network models

Organized by: David Murrugarra

  • Elena Dimitrova California Polytechinc State University, San Luis Obispo (Mathematics)
    "A unified approach to reverse engineering and data selection for unique network identification"
  • Due to cost concerns, it is optimal to gain insight into the connectivity of biological and other networks using as few experiments as possible. Data selection for unique network connectivity identification has been an open problem since the introduction of algebraic methods for reverse engineering for almost two decades. In this talk we determine what data sets uniquely identify the unsigned wiring diagram corresponding to a system that is discrete in time and space. Furthermore, we answer the question of uniqueness for signed wiring diagrams for Boolean networks. Computationally, unsigned and signed wiring diagrams have been studied separately, and in this talk we also show that there exists a polynomial ideal capable of encoding both unsigned and signed information. This provides a unified approach to studying reverse engineering that also gives significant computational benefits.
  • Brandilyn Stigler Southern Methodist University (Mathematics)
    "Computational Algebraic Methods for Boolean Network Modeling"
  • Biological data science is a field replete with many substantial data sets from laboratory experiments and myriad diverse methods for modeling, simulation, and analysis. As a data set can have a large number of associated models, model selection is often required as a post-processing step. In parallel experimental design can be utilized as a preprocessing step to minimize the number of resulting models, many of which may be biologically irrelevant. In this talk we focus on the problem of inferring Boolean models of biological networks from data. We will outline theoretical results and computational algorithms related to model construction and model selection. This work draws from algebraic geometry and algebraic combinatorics, and has been used to model a variety of biological processes including tissue development and tumor progression.
  • Claus Kadelka Iowa State University (Department of Mathematics)
    "A modular design of gene regulatory networks emerges naturally in response to an evolutionary multi-objective optimization problem"
  • Building complicated structures from simpler building blocks is a widely observed principle in both natural and engineered systems. In molecular systems biology, it is also widely accepted, even though there has not emerged a clear definition of what constitutes a simple building block, or module. For a Boolean network, we recently proposed to define its modules as the strongly connected components of its wiring diagram. This structure-based definition of modularity implies a decomposition of the dynamics of a Boolean network. In this talk, I show through simulation studies that modularity allows Boolean networks to maximize both their phenotypical robustness and their dynamical complexity. The former is biologically desirable as gene regulatory networks need to robustly maintain a phenotype in the presence of perturbations. At the same time, meaningful biological networks must harbor multiple phenotypes (corresponding to attractors of the Boolean network), allowing the network to dynamically shift from one phenotype to another based on its current need. These findings provide evidence that modularity, defined using the graph-theoretical concept of strong connectedness, is evolutionarily advantageous.
  • Daniel R. Plaugher University of Kentucky (Department of Toxicology and Cancer Biology)
    "Phenotype control techniques for gene regulatory networks"
  • Modeling cell signal transduction pathways with Boolean networks (BNs) has become an established method for analyzing intracellular communications over the last few decades. What's more, BNs provide a course-grained approach, not only to understanding molecular communications, but also for targeting pathway components that alter the long-term outcomes of the system. This has come to be known as phenotype control theory. In this presentation we discuss the interplay of various approaches for controlling gene regulatory networks. We will also explore comparisons between the methods on a specific cancer model, and highlight some challenges facing each technique.

Stochastic methods for biochemical reaction networks

Organized by: Wasiur KhudaBukhsh, Hye-Won Kang
Note: this minisymposia has multiple sessions. The other session is MS03-MFBM-1.

  • Wasiur R. KhudaBukhsh University of Nottingham (School of Mathematical Sciences)
    "Multiscale approximations for a simple transfection process"
  • The talk will focus on chemical reaction networks (CRNs) that describe creation, annihilation, combination or binding, and changes in the physical state of a collection of chemical species. Many prominent examples of intracellular dynamics, genetic switches, and dynamics of population interactions can be modelled by CRNs, where the interacting particles exhibit vastly different intrinsic scales in terms of abundance, or the reactions operate at different time scales varying over many orders of magnitude. The traditional deterministic approach to multiscale approximations used in such situations employs singular perturbation theory, often invoking Tikhonov’s theorem and Fenichel theory. In this talk, I will take a stochastic viewpoint and consider a probabilistic way to derive multiscale approximations. The talk will be fairly nontechnical, and no prior knowledge biology is required.
  • Ruth Baker University of Oxford (Mathematical Institute)
    "Efficient approaches for simulating and calibrating stochastic models of biological processes"
  • With the advent of a host of new experimental technologies, the last ten years has seen an explosion in the amount and types of data now being generated. As such, increasingly larger and more complicated processes are now being explored, including large signalling or gene regulatory networks, and the development, dynamics and disease of entire cells and tissues. Detailed mathematical models of these processes have the potential to provide vital insights where data alone cannot, but to achieve this goal requires meeting significant mathematical challenges in efficiently simulating models and calibrating them to experimental data. In this talk, I will outline some methods we have developed that leverage both low- and high-fidelity models and variance-reducing Monte Carlo approaches to make progress.
  • Jae Kyoung Kim KAIST (Mathematical Sciences)
    "Inference of non-Markovian systems from cell signaling to infectious diseases"
  • The complex processes involved in cell signaling and infectious diseases often include multiple hidden intermediate steps. However, it is possible to simplify these systems by replacing them with a single time delay distribution, such as a gamma distribution. This simplification reduces the number of variables, making it easier to infer parameters based on limited observations. Although this approach offers advantages, it presents a challenge. Since the model is non-Markovian, traditional inference techniques based on the Markov property (where dynamics depend only on the current state, not the past) cannot be directly applied. In my presentation, I will introduce a Bayesian inference framework specifically designed for non-Markovian systems. This framework enables us to identify the properties of the cell signaling network that reduce cell-to-cell heterogeneity in response to antibiotics. Additionally, I will discuss how our framework can be used to infer both the reproduction number and the distribution of infectious periods solely from confirmed case time series. This resolves the biased estimation issues associated with the conventional SEIR ODE model. 
  • Boseung Choi & Eunjin Eom Korea University (Division of Big Data Science; Department of Economics Statistics)
    "A Bayesian model for the relationship SARS-CoV-2 wastewater and community-wide seroprevalence with mutation and vaccination effect"
  • Since early in the COVID-19 pandemic, SARS-CoV-2 wastewater concentration has been measured as a surrogate for community prevalence. However, our knowledge remains limited regarding wastewater concentration and the effects of the COVID-19 vaccination on the overall disease burden as measured by hospitalization rates. We used weekly SARS-CoV-2 wastewater concentration, antibody test results, and spatially linked vaccination and hospitalization data, from April to August 2021. Our susceptible (S), vaccinated (V), variant-specific infected (I1 and I2), recovered (R), and seropositive (T) model (SVI2RT) tracked prevalence longitudinally. This was related to wastewater concentration for spatial analysis of strain mutation, vaccination effect, and overall hospitalization burden. To construct the SVI2RT compartment model, we utilized the dynamical survival analysis (DSA) framework for using survival analysis methods to build approximate models of individual-level ecological dynamics based on mean-field approximations and the Markov Chain Monte Carlo (MCMC) method based on the Bayesian approaches. We used the Bayesian linear regression model to identify the effect of the estimated prevalence according to the Alpha and Delta mutations on the community wastewater concentration and the hospitalization burden. We found strong linear association between wastewater concentration and estimated community prevalence. During the study period, the estimated effect of SARS-CoV-2 Delta variant emergence was seen as large as the increase in infection counts, corresponding to the increase in wastewater concentration. Hospitalization burden and wastewater concentration had the strongest correlation at 1 week lag time. Therefore, the wastewater samples can be used to estimate the effects of vaccination and hospitalization burden.

Data-driven methods for biological modeling

Organized by: John Nardini, Erica Rutter, Kevin Flores

  • Natalia Kravtsova The Ohio State University (Department of Mathematics)
    "Scalable Gromov-Wasserstein based comparison of biological time series"
  • A time series is an extremely abundant data type arising in many areas of scientific research, including the biological sciences. Any method that compares time series data relies on a pairwise distance between trajectories, and the choice of distance measure determines the accuracy and speed of the time series comparison. This work introduces an optimal transport type distance for comparing time series trajectories that are allowed to lie in spaces of different dimensions and/or with differing numbers of points possibly unequally spaced along each trajectory. The construction is based on a modified Gromov-Wasserstein distance optimization program, reducing the problem to a Wasserstein distance on the real line. The resulting program has a closed-form solution and can be computed quickly due to the scalability of the one-dimensional Wasserstein distance. We discuss theoretical properties of this distance measure, and empirically demonstrate the performance of the proposed distance on several datasets with a range of characteristics commonly found in biologically relevant data. We also use our proposed distance to demonstrate that averaging oscillatory time series trajectories using the recently proposed Fused Gromov-Wasserstein barycenter retains more characteristics in the averaged trajectory when compared to traditional averaging, which demonstrates the applicability of Fused Gromov-Wasserstein barycenters for biological time series. Fast and user friendly software for computing the proposed distance and related applications is provided. The proposed distance allows fast and meaningful comparison of biological time series and can be efficiently used in a wide range of applications.
  • Yordan P. Raykov University of Nottingham (Statistics and Probability)
    "Digital disease progression biomarkers for Parkinson's disease: algorithms for passive monitoring"
  • In order to facilitate truly passive monitoring of long-term diseases such as Parkinson’s disease (PD), there is a need for models which can reliably quantify symptom-related characteristics of the disease in the highly variable context of daily life, rather than reflect the spurious correlation between sensor-based measurements and desired clinical outcomes. Toward that end, we develop scalable Bayesian nonparametric latent variable models with the capacity to capture a sparser representation of IMU data in free-living and detect statistical fluctuations reflective of different PD symptomatics. We propose the use of Bayesian radial basis function layers as an augmentation mechanism in off-the-shelf symptom detection methods and demonstrate their applicability as a mediator learning framework in the detection of PD resting tremors. We outline formally some of the fundamental challenges in doing causal inference in digital monitoring clinical trials for PD and propose theoretically justified strategies for dealing with different types of observed and unobserved confounding in free-living digital biomarkers. Furthermore, we propose novel latent variable models for quantifying time-of-day symptom fluctuations in free-living and a framework for temporal causal estimation of variable time horizon causes and outcomes.

Algebra, Combinatorics, and Topology in Modern Biology

Organized by: Daniel A. Cruz,Margherita Maria Ferrari

  • Lina Fajardo Gomez University of South Florida (Mathematics)
    "Homology for Directed Graphs with Applications to DNA Recombination"
  • We propose custom made cell complexes, in particular prodsimplicial complexes, in order to analyze data consisting of directed graphs. These are constructed by attaching cells that are products of simplices and are suited to study data of acyclic directed graphs, called here consistently directed graphs. We investigate possible values of the first and second Betti numbers and the types of cycles that generate nontrivial homology. We apply these tools to graphs associated with DNA recombination processes in certain species of ciliates and we study the effects of changes in the directed graphs on the homology.
  • Puttipong Pongtanapaisan Arizona State University (Mathematics and statistics)
    "On the scarcity of split links spanning a lattice tube"
  • Frisch, Wasserman, and Delbrück conjectured that as the length of a polymer chain tends to infinity, the probability of knotting approaches 1. Similar questions regarding the entanglement complexity of multiple closed curves can also be addressed with lattice models. In this talk, I will show that all but exponentially few sufficiently large spanning pairs of self-avoiding polygons in the (2x1)-tube are linked.
  • Caitlin Lienkaemper Boston University (Department of Mathematics and Statistics)
    "Combinatorial coexpression in mosquito olfaction"
  • Across species, the olfactory system follows a stereotyped organization: each olfactory receptor neuron expresses a single type of olfactory receptor, and responses of olfactory sensory neurons which express the same receptor are pooled before they are sent to higher regions of the brain. Mosquitoes have recently been shown to violate this organization: olfactory sensory neurons coexpress multiple receptor types, thus mixing information about activation of different receptors from the start. We describe the properties of this pattern of receptor expression as a combinatorial code, consider from an information-theoretic perspective how coexpression helps mosquitoes perform as olfactory-guided predators, and investigate how the pattern of coexpression must be tuned to the pattern of stimulus statistics.
  • Radmila Sazdanovic NC State University (Mathematics)
    "Categorified chromosome aberration model"
  • Graphs are ubiquitous in mathematics and widely used to model physical phenomena in science and engineering. One such model was developed by Sachs and collaborators to analyze exchange type chromosome aberrations. In this talk we introduce a 'categorification' of this model where chromosomes (and their aberrant versions) are modeled as objects and the aberrations causing exchange processes as morphisms in a thin-surface cobordism category. This new framework allows for interpreting and analyzing patterns of chromosome aberrations observed in radiation experiments.
  • Margherita Maria Ferrari University of Manitoba (Department of Mathematics)
    "Graph theory for DNA self-assembly"
  • The chemical and physical properties of DNA strands contain a high degree of information which allows DNA to serve as building material for assembling nanostructures. These complexes have a wide range of applications, including drug delivery and molecular scaffolding. In this talk, we focus on assembling graph-like structures using branched junction DNA molecules which are star-shaped molecules that join together through adhesion sites at the end of their arms. We describe a combinatorial representation of these molecules and consider the problem of optimally building a target graph under different laboratory settings. We show how this question give rises to new graph invariants and how these invariants can be studied through edge-colorings and graph decompositions.

Data-driven multiscale modeling of cancer

Organized by: Heber Rocha, John Metzcar, Paul Macklin

  • Alexander Browning University of Oxford (Mathematical Institute)
    "Drawing biological insight from non-identifiabile models of tumour growth using simple surrogates"
  • Models are now routine in the interpretation of biological data, however are often limited by parameter non-identifiabilities. Indeed, simple goodness-of-fit metrics including the likelihood and residual error give only limited information about where a model does and doesn’t fit. In the talk, we demonstrate a new framework for the study non-identifiability of complex models of tumour growth using simple surrogate models, that lie in between a model of interest and the data. For example, the traditional one-dimensional line of constant goodness-of-fit, studied in traditional likelihood-based identifiability analysis, might lie at the intersection of two higher dimensional surfaces, each representing features in the data (in this case, the maximum size and initial growth rate of the tumour). One can move along this intersection in parameter space and achieve only a minimal change to the model predictions; hence, parameter non-identifiability. Overall, we demonstrate a novel technique for gaining insight from the complex biological models that are often essential for the elucidation of important biological processes.
  • Jeanette Johnson Johns Hopkins University (Immunology)
    "Integrating Omics Data and Agent-Based Models for Comprehensive Digital Biology"
  • Agent-based modeling for biological systems currently suffers from limited ability to systematically integrate experimental data into model parameters. To facilitate the wider use of ABMs in these contexts, we sought ways to address this issue. Here we present two models built in the PhysiCell agent based modeling framework using results from high-throughput analyses. We show a method for generation of model agents directly from standard 10x Visium spatial transcriptomics data into an initial state of the ABM, preserving spatial relationships between cells when translating data to model. In future work we hope to build a general purpose “digital tissue” pipeline, capable of constructing spatially-resolved ABMs in 2d and 3d. We then show a model built upon more qualitative observations from a pancreatic cancer single-cell atlas and a separate set of clinical trial results from a matched biological context. The model simulates hypotheses of tumor progression among a group of epithelial and immune cells under three therapy conditions, exploring the tumor-immune logic of the system and attempting to understand what could have led to the results of the clinical trial. These integrations are proof-of-concept for more general integration of omics with agent-based models, and will empower life science investigators to make use of ABMs, which are ultimately very powerful hypothesis building and visualization tools, in their research.
  • Adam MacLean University of Southern California (Department of Quantitative and Computational Biology)
    "Learning gene regulatory networks that control cell state transitions from multi-modal single-cell genomics"
  • Single-cell genomics offer unprecedented resolution with which to study cell fate decision-making in cancer. We present new tools to infer gene regulatory networks (GRNs) controling cell fate decisions and model their multiscale dynamics. We introduce popInfer, single-cell multi-modal GRN inference via regularized regression, and demonstrate its potential for network discovery Through application to hematopoiesis, we discover new gene interactions regulating early fate decisions during stem cell differentiation that are profoundly affected by diet and age.
  • Matthew Simpson Queensland University of Technology (School of Mathematical Sciences)
    "A stochastic mathematical model of 4D tumour spheroids with real-time fluorescent cell cycle labelling"
  • In vitro tumour spheroids have been used to study avascular tumour growth and drug design for over 50 years. Tumour spheroids exhibit heterogeneity within the growing population that is thought to be related to spatial and temporal differences in nutrient availability. The recent development of real-time fluorescent cell cycle imaging allows us to identify the position and cell cycle status of individual cells within the growing spheroid, giving rise to the notion of a four-dimensional (4D) tumour spheroid. We develop the first stochastic individual-based model (IBM) of a 4D tumour spheroid and show that IBM simulation data compares well with new experimental data using a primary human melanoma cell line. The IBM provides quantitative information about nutrient availability within the spheroid, which is important because it is difficult to measure these data experimentally.

Stochastic Methods in Oncology and Population Dynamics

Organized by: Linh Huynh, Deena Schmidt

  • Heyrim Cho University of California Riverside (Mathematics)
    "Modeling of CAR T-cell and neural stem cell therapy for brain cancer"
  • Recent advances in cell and gene engineering technologies enabled a variety of cell based treatments to be used as part of a treatment for a variety of diseases and conditions. Many different types of cells are available to be transplanted to replace or repair damaged tissue and/or cells. In this talk, I will discuss chimeric antigen receptor (CAR) T-cell therapy and neural stem cell (NSC) therapy for brain diseases, and the potential of how mathematical models can help increase the treatment efficacy. A hybrid stochastic agent based and partial differential equation model of CAR T-cell therapy is developed to understand the effect of timing in a combination treatment for heterogeneous brain cancer. Similarly, a hybrid model of NSC treatment is developed to study the effect of injection location and to predict its migration path. I will also present results using ordinary differential equation models on better understanding of the cellular dynamics in a population level.
  • Alexandru Hening Texas A&M (Mathematics)
    "Population dynamics under random switching"
  • An important question in ecology is the relationship between the coexistence of species and environmental fluctuations. A natural way to model environmental fluctuations is to use stochastic differential equations (SDE) or piecewise deterministic Markov processes (PDMP). In a PDMP, the environment switches between a fixed finite number of states to each of which we associate an ordinary differential equation (ODE). In each state the dynamics is given by the flow of its associated ODE. After a random time, the environment switches to a different state, and the dynamics is governed by the ODE associated to the new state. I will look at two and three species examples of SDE and PDMP and explain how the randomness can lead to some very interesting and counterintuitive behavior.
  • Khanh Ngoc Dinh Columbia University (Irving Institute for Cancer Dynamics)
    "Modeling and simulation of cancer evolution in bulk and single-cell DNA-sequencing data"
  • We explain how models of population genetics can be used to provide quantitative inference of clonal evolution of cancer. The talk has two parts. Part 1 is devoted to the definition and mathematical properties of the Site Frequency Spectrum (SFS), one of the commonly used characteristics of cell populations undergoing growth and mutation. We explore the basic consistency of the approaches based on Wright-Fisher or Moran coalescents versus those based on birth-death processes. This provides building blocks for Part 2, which introduces the heuristic estimation equations, which employ the observable characteristics of the SFS, and allow an exact solution providing estimates of the growth and mutation rates and origin times of the clones. Examples based on simulations and available tumor data are presented. Accuracy of the estimates and their possible applications are discussed. Contributions of Emmanuel Asante, Khanh Dinh, Roman Jaksik, Andrew Koval, Paweł Kuś, and Simon Tavaré are acknowledged.
  • James MacLaurin New Jersey Institute of Technology (Mathematics)
    "From blips to puffs: estimating the probability of noise-induced calcium waves"
  • Intracellular calcium signalling is widely hypothesized to be a stochastic phenomenon that bridges scales. Microscopic calcium channels open and close stochastically, producing small blips in the local calcium concentration. If enough of them open, then the local elevation in calcium concentration can be sufficient to initiate a cell-wide calcium wave or 'puff'. We estimate the probability / frequency of calcium puffs using the theory of Large Deviations: this theory facilitates accurate estimates for the most probable way that numerous microscopic channels (coupled by the concentration of calcium and other signalling molecules) can organize to produce a cell-wide puff.

Sub-group contributed talks

MFBM Subgroup Contributed Talks

  • Connor McShaffrey Indiana University Bloomington
    "Decomposing Viability Space"
  • When trying to model how an organism will fare in a particular environment, we need to be able to capture the potential dynamics of the system as well as the survival outcomes they lead to. A growing body of work has been approaching this problem by building dynamical systems models with imposed viability limits, which separate living and terminal states. Since the viability limits are not implicit in the equations that govern the dynamics, there is no guaranteed correspondence between the phase portrait and which initial conditions will remain viable. This means that the topology demands a richer set of analyses, which we refer to as characterizing viability space. Here we will set the groundwork for this methodology, including criteria for novel bifurcations, using a simple mass-action protocell model.
  • Holly Huber University of Southern California
    "Systematic Bayesian Posterior Analysis Facilitates Hypothesis Formation and Guides Investigation of Pancreatic Beta Cell Signaling"
  • Intracellular protein dynamics can be simulated with a system of ordinary differential equations, where parameters represent reaction rate constants and initial protein concentrations. Such mechanistic models formalize the biological hypotheses they’re based on. Bayesian inference fits the posterior distribution of model parameters to data; evidence of alternative hypotheses can manifest in the posterior and serve as a starting point for hypothesis refinement. However, existing approaches to search for such evidence are largely ungeneralizable and unsystematic, limiting their scalability. Here, we show that ranking marginal posteriors by information gained from experimental data provides a systematic and generalizable way to search for alternative hypothesis evidence. Rather than searching for evidence at random, one can search per the ranking. We subsequently use this approach to refine our understanding of pancreatic beta cell signaling dynamics, which regulate beta cell proliferation.
  • Nathaniel Linden University of California San Diego
    "Multimodel modeling for blood glucose and insulin measurements in diabetes"
  • Uncertainty in a model formulation due to differing assumptions or unknown system mechanisms is often overlooked when applying mathematical models in biology and medicine. In diabetes diagnostics, mathematical models have long been used to make inferences about a patient’s metabolic health using available clinical data such as blood glucose measurements over time. These approaches often rely on a phenomenological model to approximate the physiological system, ignoring possible uncertainty in the model structure. However, there are usually several possible phenomenological models, each of which uses different formulations to represent the same biological processes. Given a family of phenomenological models, one typically chooses a single model based on a priori assumptions. In this work, we instead focus on leveraging the whole family of models to develop robust predictors in the face of uncertainty in the models describing the biological process. We explore several approaches to average the predictions from all available models, including Bayesian model averaging and probability distribution fusion. These methods allow us to construct robust predictors using the entire model family and reduce biases associated with choosing a single best model. As a test case, we chose the prediction of beta cell insulin regulation and associated diagnostic metrics from blood glucose measurements. Our results show that working with a family of models instead of a single model improves the certainty of modeling-based predictions, reduces biases associated with selecting one model, and explicitly accounts for model uncertainty.
  • Robert DeJaco National Institute of Standards and Technology
    "Reducing Bias and Quantifying Uncertainty in Fluorescence Produced By PCR"
  • We present a new approach for relating nucleic-acid content to fluorescence in a real-time Polymerase Chain Reaction (PCR) assay. By coupling a two-type stochastic branching process for PCR with a fluorescence analog of Beer’s Law, the approach reduces bias and quantifies uncertainty in fluorescence. As the two-type branching process distinguishes between complementary strands of DNA, it allows for a stoichiometric description of reactions between fluorescent probes and DNA and can capture the initial conditions encountered in assays targeting RNA. Analysis of the expected copy-number identifies additional dynamics occurring at short times (or, equivalently, low cycle numbers), while investigation of the variance reveals the contributions from liquid volume transfer, imperfect amplification, and strand-specific amplification (i.e., if one strand is synthesized more efficiently than its complement). Linking the branching process to fluorescence by the Beer’s Law analog allows for a more objective and a priori description of background fluorescence. It also enables uncertainty quantification (UQ) in fluorescence which, in turn, leads to analytical relationships between amplification efficiency (probability) and limit of detection. This work sets the stage for UQ-PCR, where both the input copy-number and its uncertainty are quantified from fluorescence measurements.

MFBM Subgroup Contributed Talks

  • Anna Konstorum Institute for Defense Analyses
    "A decomposition as a model: extracting mechanistic information from high-throughput time-course data using tensor dictionary learning"
  • Matrix decomposition methods such Principal Components Analysis (PCA) and Non-Negative Matrix Factorization (NMF), as well as non-linear analogues such as t-SNE and UMAP, have become increasingly popular in bioinformatics to perform data dimension reduction. For data that includes a time-course, a more natural representation is as a tensor (a multi-index array). We show that one can reframe the tensor decomposition of sample-by-feature-by-time-course data as a tensor dictionary learning problem, which effectively models each subject as a sum of rank-one matrices we term 'Feature Canonical Trajectories' (FCTs). The benefits of the FCT representation is that it provides not only an embedding and clustering of subjects, but also a model for the data by representing subject gene expression data as a linear combination of canonical trajectories of feature-sets. We show that by reframing the decomposition as a data model we can also identify new metrics to choose a decomposition algorithm and approximation for improved interpretability, and provide an example of this in action by identifying a novel age-specific FCT associated with platelet vaccination response data.
  • Dewayne A. Dixon Howard University
    "Core Epigenetic Module Biomarkers among Various PTSD Subtypes"
  • Posttraumatic stress disorder (PTSD) is a debilitating condition triggered by traumatic events. Notable symptom differences exist between combat-exposed veterans, active-duty personnel, and civilian PTSD cases. However, the underlying biological mechanisms remain elusive. This study aims to uncover the shared biological core modules associated with PTSD by leveraging extensive omics data among various PTSD subtypes. To achieve this, we employed the 'COre Module Biomarker Identification with Network ExploRation' (COMBINER) approach on DNA methylation data to identify key network modules of epigenetic modification across PTSD subtypes. These findings not only enhance our knowledge of PTSD's diverse symptomatology but also pave the way for the development of biomarkers and personalized treatments.
  • Heber L Rocha Indiana University
    "Multiscale Modeling and Data Assimilation: A Path to Personalized Medicine"
  • In recent years, a growing interest in personalized medicine has emerged as a result of significant advancements in the fields of biology, data science, and computational modeling. One emerging concept that has obtained attention from the scientific community is the patient digital twin (DT), which aims to develop a comprehensive model to enable clinicians to systematically analyze the complexity of each patient, simulate treatment outcomes, and select the optimal treatment option. Constructing a patient digital twin (DT) involves creating a detailed computational model that can capture the unique characteristics of an individual patient. The model should include information about the patient's medical history, current health status, genetic makeup, and other relevant factors that can affect treatment outcomes. However, obtaining all this information can be challenging, as clinical data on individual patients is often limited. To overcome this limitation, researchers can use mechanistic models to replicate observed phenomena across various scenarios. In this study, we developed a mechanistic model of cancer-immune interactions in pulmonary micrometastasis. We found that the model could express a wide range of patient trajectories, from complete tumor elimination to uncontrollable growth. Using high-throughput computing platforms, we analyzed 100k virtual patient trajectories by exploring the parameter space of this model. Initially, we analyzed patient data at a single time point using clustering methods, but the results did not clearly identify patient trajectories. Further investigation revealed that the same patient could have completely different trajectories, making it challenging to categorize patients. The mechanistic model helped us understand this issue, showing that early or non-interactions between macrophages and invading tumor cells were responsible. This also explained the limitations of traditional patient stratification based on data alone. Additionally, it highlighted the need for digital twins that are patient-specific, dynamical, and continuously updated with new patient data instead of one-time calibration.
  • Hyun Kim Institute for basic science
    "Enhancing dimensionality reduction in single-cell RNA sequencing: a novel tool for improved preprocessing and noise filtering"
  • Single-cell RNA sequencing (scRNA-seq) has enabled various analyses, including cellular phenotyping and gene regulatory network reconstruction. However, the sparsity, high dimensionality, bias, skewness in data distribution, and technical noise in scRNA-seq data present challenges for downstream analyses. In order to tackle these issues, conventional packages depend on log-normalization for preprocessing and require users to select the reduced dimension when employing various dimensionality reduction methods. Nonetheless, these approaches can result in signal distortion and subjectivity when determining reduced data dimensions. To overcome the limitation of conventional methods, we developed a new tool that corrects signal distortion during preprocessing and effectively filters out noise in data, enhancing the reliability of the outcome of dimensionality reduction. Our tool demonstrated superior performance compared to 9 widely used packages, including Seurat, Scanpy, and Monocle3 when tested on 53 real and simulated datasets.

MFBM Subgroup Contributed Talks

  • Hyeontae Jo Institute for Basic Science (IBS)
    "Density Physics-Informed Neural Network infers an arbitrary density distribution for non-Markovian system"
  • In this talk, we have developed Density-PINN (Physics-Informed Neural Networks), a method capable of estimating the probability density function embedded within a differential equation. While conventional PINNs have focused on determining the solutions or parameters of differential equations that can explain observed data, we introduce a specialized approach for estimating the probability density function contained within the equation. Specifically, when dealing with a limited number of stochastic time series as observed data, and where only the average of the data satisfies the solution of the differential equation, we have constructed a mean-generating model using Variational Autoencoders. By applying our method to single-cell gene expression data from 16 promoters in response to antibiotic stress, we discovered that promoters with slower signaling initiation and transduction exhibit greater cell-to-cell heterogeneity in response intensity.
  • Luigi Frunzo University of Naples Federico II
    "Mathematical modelling of phototrophic-heterotrophic biofilm system"
  • The presentation will concerns a mathematical model for the analysis and prediction of microbial interactions within mixotrophic biofilms composed of microalgae and heterotrophic bacteria. The model combines equations for biomasses growth and decay, diffusion-reaction of substrates, and detachment process. In particular, the colonization of external species invading the biofilm is considered. The biofilm growth is governed by nonlinear hyperbolic PDEs while substrate and invading species dynamics are dominated by semilinear parabolic PDEs. It follows a complex system of PDEs on a free boundary domain. The equations are numerically integrated by using the method of characteristics. The model has been applied to simulate the ecology of a mixotrophic biofilm formed by phototrophic and heterotrophic species. The comparison of numerical and experimental data will confirm the accuracy of the proposed model.
  • Samantha Linn University of Utah
    "First passage times under frequent stochastic resetting"
  • Stochastic search processes with stochastic resetting have recently received substantial attention in mathematical biology. Much of the existing work concerns only the study of mean first passage times (FPTs) of such processes due to their analytical tractability. In our work, we forgo the standard analytical approach of defining the FPT in terms of a last renewal equation of its density and instead reformulate it as a sum over failed and successful attempts. This method allows us to determine the full distribution and moments of the FPT for a broad class of stochastic search processes in the limit of frequent stochastic resetting. Our results apply to any system whose short-time behavior of the search process without resetting can be approximated. In addition to the typical case of exponentially distributed resetting times, we prove our results for a wide array of resetting time distributions. Finally, we show that the errors of our approximations vanish exponentially fast in typical scenarios of diffusive search.
  • Silvia Berra University of Genova, Italy
    "Drug dosage in cancer: a mathematical approach for computing steady states of chemical reaction networks"
  • During the G1-S transition phase of life of colorectal cells many proteins interact in chemical reactions, some of which are crucial since mutations altering the function of the corresponding proteins may cause cancer. The set of these interactions can be described through a properly designed Chemical Reaction Network (CRN). In turn, the latter can be represented by a mathematical model consisting in a system of autonomous ordinary differential equations. Computing the steady state of this system is a key step for understanding the global (and local) effects of each mutation and of some specific targeted drugs used to contrast the corresponding functional alterations. The most common approach for computing the steady state consists in simulating the system's dynamical evolution in time; however, this is a very time-consuming process. Here I propose a different method, consisting in recasting the steady state computation problem as a root-finding one. To solve the latter, an algorithm that combines the Newton method and the gradient descent approach is introduced, where the non-negativity constraints on the steady state concentrations are assured by defining and applying a suitable operator P at the end of every iterative step [1]. Such an algorithm, which is convergent under specific assumptions, turns out to be more precise and faster than the dynamic approach. Starting from a CRN previously introduced for modeling the G1-S transition phase of colorectal cells [2], the method is validated in simulation mimiking both physiological and mutated status and also in the presence of targeted drugs applied individually or together in a combined therapy. [1] Berra, Silvia, et al. 'A fast and convergent combined Newton and gradient descent method for computing steady states of chemical reaction networks.' arXiv preprint arXiv:2212.14252 (2022). [2] Sommariva, Sara, et al. 'Computational quantification of global effects induced by mutations and drugs in signaling networks of colorectal cancer cells.' Scientific reports 11.1 (2021): 19602.

MFBM Subgroup Contributed Talks

  • Jordan Collignon University of California, Merced
    "[PSI]-CIC: A Deep-Learning Pipeline for the Annotation of Sectored Saccharomyces cerevisiae Colonies"
  • The [PSI^+] prion phenotype in yeast manifests as a white, pink, or red color pigment related to the fraction of soluble Sup35. Experimental manipulations destabilize prion phenotypes, and allow colonies to exhibit [psi^-] (red) sectored phenotypes within otherwise completely white colonies. The mechanisms governing both size and quantity of sectors remain unknown. Images of experimental yeast colonies exhibiting sectored phenotypes offer an abundance of data to help uncover mechanisms of sectoring. However, the structure of sectored colonies is ignored in traditional biological pipelines. This is both because colony counting is labor intensive and procedures for characterizing sectored colonies do not exist. In this study, we present [PSI]-CIC, the first computational pipeline designed to identify and characterize features of sectored yeast colonies. We develop a neural network architecture that we train on synthetic images of sectored yeast colonies and apply to real images of [PSI^+], [psi^-], and sectored colonies. Our pipeline correctly predicts the colony state and frequency of sectors in approximately 89.2% of colonies detected in hand annotated experimental images. With this information, the scope of our pipeline can be later extended toward categorizing colonies grown under different experimental conditions, allowing for more meaningful and detailed comparisons between experiments performed on yeast. Our approach aims to streamline the analysis of sectored yeast colonies providing a rich set of quantitative metrics to compare with mathematical models of sector formation and provide insights into mechanisms driving the curing of prion phenotypes.
  • Md Masud Rana University of Kentucky
    "Differential geometry and graph theory-based machine-learning model for drug design"
  • The fundamental step in the drug design and discovery process is understanding and accurately predicting the binding affinity between a drug candidate (ligand) and its receptor protein. Machine learning-based methods have become increasingly popular in this regard due to their efficiency and accuracy, as well as the growing availability of data on the structure and binding affinity of protein-ligand complexes. In molecular and biomolecular studies, differential geometry and graph theory are widely used to analyze vast, diverse, and complex datasets. Using molecular surface representation, crucial chemical and biological data can be encoded in differentiable manifolds that can reduce dimensionality. Graph theory is extensively used in biomolecular research because molecules or molecular complexes can be naturally modeled as graphs. Here, we will present several models based on differential geometry and graph theory that can be combined with advanced machine learning techniques to predict protein-ligand binding affinity with high accuracy. Our proposed models have demonstrated superior performance compared to numerous state-of-the-art models on established benchmark datasets.
  • Theo Loureaux University of California Merced
    "Automating the Generation of Synthetic Training Data for Biological Image Segmentation"
  • Image segmentation, the identification of specific objects from a larger image, is an important topic in computer vision and is critical to the study of biological and medical images. Common deep-learning approaches for image segmentation require large sets of labeled training-data. For many biological applications, annotated training data is not available and, as such, developing synthetic data sets - where the true labels are known - has become a standard approach in these methods. However, most methods of synthetic data generation often require substantial human intervention to create. This work takes a first step towards a fully-automated method for the segmentation of complex biological images. In this talk, we present an iterative greedy algorithm that automates the selection of boundary points on a particular object, regardless of the complexity of its shape, by calculating the approximate solution to an optimization problem. We first demonstrate on a large set of curated shapes of various complexity that our algorithm generally does a better job than a naive approach, especially when the boundary of the shape is complex. We then apply our approach to the image segmentation in two biological contexts: identification of prion oligomers in AFM images, the identification of sectored yeast colonies. We show that our approach provides improvements to standard pipelines, and that greater improvements are possible by adding image artifacts - such as pixellization and sector coloring. Our work demonstrates that significant improvements can be made in biological image segmentation through the computational efficient generation of realistic synthetic samples. Keywords : Image segmentation, deep learning, synthetic images, automation, prions, yeast

Sub-group poster presentations

MFBM Posters

Ahmed Fathi University of Naples Federico II, Naples, Italy
Poster ID: MFBM-01 (Session: PS01)
"An upscaled model of heavy metal biosorption in homogeneous porous media"

A field scale model for heavy metals biosorption in homogeneous soils is constructed while considering the influence of biofilm and heavy metals interactions at the pore scale. The biofilm processes at the mesoscale are described by the Wanner-Gujer model for biofilm growth and then upscaled using the volume averaging approach to distinguish its effective parameters at the field scale [Gaebler et. al., 2022]. A laminar and convection-dominated regime is assumed for the flow within the soil. Within the soil pores, two separately growing bacteria species are assumed in the biofilm phase. Dissolved substrates and suspended bacteria are injected in the soil at a constant rate.  A generic heavy metal is assumed to be transported in the soil and diffuse within the biofilm, affecting its overall growth rate. In turn, the biofilm retains this toxic metal through biosorption, and prevents it from reaching the underground water. The resulting macroscale model is described by a stiff system of hyperbolic equations to be solved numerically by the uniformly accurate central scheme of order 2 (UCS2) and using MATLAB platform. Different simulation scenarios have been investigated by varying the biofilm growth and biosorption parameters. The upscaled model accurately capture the mesoscale biosorption processes after a rigorous mathematical derivation.

Alessandro Maria Selvitella Purdue University Fort Wayne
Poster ID: MFBM-02 (Session: PS01)
"On the variability of human leg stiffness across strides during running gait and some consequences for the analysis of kinematic and kinetic data"

In this presentation, we discuss a recent analysis of the variability of human leg stiffness across strides during running. We analyze the effects of speed, mass, and age on the dependence of the stiffness across strides. The major finding of our analysis is that the time series of several measurements of human leg stiffness show autocorrelation at large lags. Our results hint at the fact that feedforward strategies might be preferred at higher velocities. Furthermore, our analysis questions the common practice in biomechanics that researchers consider each stride as independent. We recommend caution in doing so, without first confirming the independence of any biomechanical measurements across strides with rigorous statistical tests such as those developed in our work. This is a joint work with Prof. Kathleen Lois Foster, Department of Biology, Ball State University.

ANUPAM KUMAR PANDEY Indian Institute of Technology (Banaras Hindu University), Varanasi
Poster ID: MFBM-03 (Session: PS01)
"Oesophageal catheterisation under the influence of dilating amplitude with peristaltically driven Newtonian fluid: A mathematical model"

We presented a mathematical model of swallowing in a catheterized oesophageal tube by duly considering the peripheral and core layers. We adequately account for the fluid mass conservation in both these layers. According to Kahrilas et al. (1995) and Pandey et al. (2017), peristaltic waves that govern the flow are thought to have gradually dilating amplitudes so that the distal oesophagus experiences higher pressure to ensure smooth delivery of gradually globular getting bolus into the abdomen through the cardiac sphincter. The technique of long wavelength and low Reynolds number is used to get the solutions in terms of stream function. Mass conservation in the two layers is taken care of by resolving the interface as a streamline from a fourth-order algebraic equation. The previous researchers' attempt to uniform wave amplitude had ignored mass conservation identically in the two layers by a wrong assumption of a fixed ratio between the layers. Due to unrealistic assumptions, those results cannot be accepted. Pressure, flow rate, and forces expressions are obtained for the tube with the catheter. The findings are accepted, and the interface between the two layers is explored. One wavelength's worth of pressure variation with flow rate is investigated. It is found that pressure and flow rate have a linear relationship even when the tube is catheterized. With pressure, the flow rate rises. It has been discovered that pressure rises as the peripheral layer viscosity does. Moreover, it has been found that when peripheral viscosity increases, the flow rate rises. Additionally, it has been found that as the flow rate in a catheterized oesophagus increases for a given difference in pressure, the peripheral layer thins down.

Ari Barnett (Roldan) Moffitt Cancer Center
Poster ID: MFBM-04 (Session: PS01)
"Approaches for Dealing with Data Disparity and Complex Dynamics"

Data disparity remains a persistent challenge for the broader translational science community. At present, models working with observational data frequently encounter difficulties stemming from inconsistent measurement frequencies and insufficiently diverse patient populations. Approaching this as a compounded problem we seek to develop a novel framework that utilizes the concept of Time series Generative Adversarial Networks (TGAN) originally proposed by Yoon [1]. While generative frameworks have been introduced, none can fully provide a sound solution for the temporal dynamics involved with time series observations. TGAN specifically aims to address temporal dynamics by utilizing a jointly optimized embedding space. Here we propose utilizing TGAN to generate both synthetic patients and semi-synthetic time series. Previously TGAN has been shown to outperform similar approaches, both qualitatively (tSNE) and quantitatively (discriminative and predictive scoring) on a variety of real-world datasets. For this research we aim to provide a conceptual methodology for aiding in the discovery of underlying mechanistic models via the integration of SINDy [2].By utilizing synthetic data that capture underlying dynamics we hypothesize that we can train models while holding out all real observation data for testing. Similarly with semi-synthetic time series we anticipate a better overall capture of disease dynamics. References [1] J. Yoon, D. Jarrett, and M. van der Schaar, “Time-series Generative Adversarial Networks,” in Advances in Neural Information Processing Systems, Curran Associates, Inc., 2019. Accessed: Feb. 14, 2023. [Online]. Available: [2] S. L. Brunton, J. L. Proctor, and J. N. Kutz, “Discovering governing equations from data by sparse identification of nonlinear dynamical systems,” Proc. Natl. Acad. Sci. U.S.A., vol. 113, no. 15, pp. 3932–3937, Apr. 2016, doi: 10.1073/pnas.1517384113.

Candan Celik Institute for Basic Science
Poster ID: MFBM-05 (Session: PS01)
"Reducing gene expression noise: The role of RNA stem-loops in translation regulation"

Stochastic modelling is key to understanding the dynamics of intracellular events in most biochemical systems, including gene-expression models. The stochasticity in the levels of gene products, e.g., messenger RNA (mRNA) and protein, is referred to as noise, which leads to cell-to-cell variability. The contributions to noise can emerge from different sources, such as structural elements. Recent studies have demonstrated that mRNA structure can be more complex than the most straightforward assumptions. Here, we study a structuration/generalisation of a stochastic gene-expression model in which mRNA molecules can be found in one of its finite number of different states and can transition among these states. In addition to characterising and deriving non-trivial analytical expressions for the steady-state protein distribution, we provide two different examples, which can be readily obtained from the structured/generalised model. The main example pertains to the formation of stem-loops; here, we reinterpret previous data and provide additional insights. Our analysis reveals that stem loops that restrict translation can reduce noise.

Dongju Lim KAIST
Poster ID: MFBM-06 (Session: PS01)
"Mood Prediction for Bipolar Disorder Patient with Sleep Pattern Information"

Mood episode prediction is an essential task for the treatment of bipolar disorder patients. Recent studies revealed that sleep patterns and circadian rhythm misalignment are valuable information to predict mood episodes. However, the specific contributions of different sleep and circadian rhythm information to mood prediction are less understood. Here, we employed the XGBoost model and compare the importance of sleep and circadian rhythm features in predicting mood episodes. Additionally, we used SHAP value analysis to show the circadian rhythm and mood relationship difference between depressive episodes and hypomanic episodes.

Dylan T. Casey University of Vermont, Burlington, VT
Poster ID: MFBM-07 (Session: PS01)
"An agent-based model of fibrosis on lung architecture"

Idiopathic pulmonary fibrosis (IPF) is a disease characterized by remodeling and stiffening of fibrous collagen leading to septal thickening, alveolar destruction, and a stiffer lung. Little is known about how healthy parenchyma transitions to the characteristic IPF pattern seen on computed tomography (CT) scans. We investigate the morphogenesis of IPF with an agent-based model (ABM) that simulates cells interaction with extracellular matrix to imitate the progression of tissue accumulation. We incorporate alveolar architecture so that the model can simulate the conversion of real lung structure into a fibrotic environment. Lungs from mice with bleomycin-induced fibrosis and control mice were fixed at constant pressure and scanned with micro-CT at 4.9-micron slices. The lung architecture from the control serves as the scaffolding our agents traverse. Agents representing pro-fibrotic phenotypes increased tissue density by a fixed amount and were allowed to build off this tissue into airspaces while anti-fibrotic agents removed a fraction of tissue density. The ABM was run until the control lung architecture resembled the fibrotic lung architecture. The addition of agents acting on anatomically realistic alveolar architectures results in tissue remodeling reminiscent of that seen in pulmonary fibrosis, and thus can provide insight into emergent structures arising in fibrosis.

Juliano Ferrari Gianlupi Indiana University
Poster ID: MFBM-08 (Session: PS01)
"PhenoCellPy: A Python package for biological cell behavior modeling"

PhenoCellPy is an open-source Python package that defines methods for modeling sequences of cell behaviors and states (e.g., the cell cycle, or the Phases of cellular necrosis). PhenoCellPy defines Python classes for the Cell Volume (which it subdivides between the cytoplasm and nucleus) and its evolution, the state of the cell and the behaviors the cell displays in each state (called the Phase), and the sequence of behaviors (called the Phenotype). PhenoCellPy's can extend existing modeling frameworks as an embedded model. It supports integration with modeling frameworks in a number of ways, e.g. by messaging the main simulation when a change in behavior occurs. PhenoCellPy can function with any python-based modeling framework that supports Python 3, NumPy and SciPy.

Megan Haase University of Virginia
Poster ID: MFBM-09 (Session: PS01)
"A Cellular Potts Model of skeletal muscle regeneration to reveal novel interventions that improve recovery from muscle injury"

Muscle regeneration is a complex process due to dynamic and multiscale biochemical and cellular interactions, making it difficult to determine optimal treatments for muscle injury using experimental approaches alone. To understand the degree to which individual cellular behaviors impact endogenous mechanisms of muscle recovery, we developed an agent-based model (ABM) using the Cellular Potts framework to simulate the dynamic microenvironment of a cross-section of murine skeletal muscle tissue. We referenced more than 200 published studies to define over 100 parameters and rules that dictate the behavior of muscle fibers, satellite stem cells (SSC), fibroblasts, neutrophils, macrophages, microvessels, and lymphatic vessels, as well as their interactions with each other and the microenvironment. We utilized parameter density estimation to calibrate the model to temporal biological datasets describing cross-sectional area (CSA) recovery, SSC, and fibroblast cell counts at multiple time points following injury. The calibrated model was validated by comparison of other model outputs (macrophage, neutrophil, and capillaries counts) to experimental observations. Predictions for eight model perturbations that varied cell or cytokine input conditions were compared to published experimental studies to validate model predictive capabilities. Latin hypercube sampling and partial rank correlation coefficient were used to identify optimal therapeutic strategies which guided in-silico perturbations of cytokine diffusion coefficients and decay rates. This analysis suggests a new hypothesis that a combined alteration of specific cytokine decay and diffusion parameters results in greater fibroblast and SSC proliferation and increased fiber recovery at 28 days (97% vs 82%, p<0.001) as compared to the baseline condition. Future work will explore this new hypothesis through novel coupled in-vivo and in-silico experiments to understand treatment responses with various injury types and microenvironmental conditions.

Randy Heiland Indiana University
Poster ID: MFBM-10 (Session: PS01)
"PhysiCell Studio: a graphical tool to create, execute, and visualize a multicellular model"

Defining a multicellular model can be challenging. There may be hundreds of parameters that specify the attributes and behaviors of multiple cell types and diffusible substrates in a model. If the model can be defined using a format specification, e.g., a markup language, then it can be readily shared in a minimal first step towards reproducibility. However, specifying the parameters of cell behaviors and substrates by hand is time consuming, error-prone, and ultimately a limiting factor in rapidly developing and refining sophisticated multicellular models. PhysiCell is an open source physics-based multicellular simulation system with an active and growing user community. It uses XML (extensible markup language) to define a model. To date, users needed to manually edit the XML to modify a model. PhysiCell Studio is a graphical tool to simplify this task. It provides a multi-tabbed GUI (graphical user interface) that allows graphical editing of the model and its associated XML, including the creation/deletion of fundamental objects, e.g., cell types and substrates/signals in the microenvironment. It also lets users run their model and interactively visualize results, allowing for more rapid model refinement. Using PhysiCell Studio in the classroom and training workshops has significantly reduced the training time for new learners, allowing them to develop sophisticated modeling. Conversely, frequent classroom and workshop use of the Studio has driven substantial improvements to the GUI. Like PhysiCell, the Studio is open source software, and contributions from the community are encouraged.

Rholee Xu Worcester Polytechnic Institute
Poster ID: MFBM-11 (Session: PS01)
"Experimental measurement of elastic moduli in the moss Physcomitrium patens informs modeling of plant cell tip growth"

Plant cell morphology and growth are essential for plant development and adaptation. Some key cell types, such as pollen tubes, root hairs, and moss protonemata, develop specifically by tip growth. Cell wall material deposition and internal structure rearrangement (wall loosening) are the major contributing factors to the growth and morphogenesis of tip cells. As the cell wall is physically extended due to turgor pressure, we must understand the wall mechanical response against turgor pressure in order to elucidate this complex process. Studies into this process include theoretical modeling of tip growing cells, which are mostly based on the classical Lockhart theory, where the wall extends irreversibly in response to turgor pressure. These models predict that the shape of growing cells is critically dependent on a dramatic gradient of elastic moduli or effective viscosities from the tip domain to the shank region. While the elastic moduli have been measured experimentally in yeast and other tip-growing cells in simplified settings, the dramatic gradient transcending a difference in the order of several magnitudes has never been found. We argue the previous prediction is biased because these models do not distinguish wall deformation due to active processes, such as wall material deposition and wall loosening, from its elastic properties. Our research attempts to address these concerns by first measuring elastic moduli using our model organism, the moss Physcomitrium patens. We use a novel technique of measuring the elastic property by quantifying wall deformation from fluorescent bead tracking and surface region triangulation; and quantifying the wall tension from wall surface shape analysis. We find that there does exist a gradient of moduli between the tip and shank, but with a difference within an order of magnitude. Additional samples and improvement of error analysis will allow us to confirm this and investigate further into differences between cell types in P. patens. We will then apply this technique on other experiments to study how these elastic moduli differ during growth, or when cell wall composition is modified. This novel method will help bring advancements to the field of cell wall mechanics and the understanding of tip cell growth.

Thomas Dombrowski Moffitt Cancer Center
Poster ID: MFBM-12 (Session: PS01)
"Tumor-immune ecosystem dynamics exploration via a high-resolution agent-based model"

BACKGROUND: Radiation therapy is the single most utilized therapeutic agent in oncology, yet in the biology-driven medicine era, advances in radiation oncology have primarily focused on improving physical dose properties. As a result, the field of radiation oncology currently does not individualize radiation dose prescription based on the intrinsic biology of a patient’s tumor. METHODS: We develop a high resolution, 3D multiscale agent-based model that simulates the interactions of cancer cells with antitumor immune effector T-cells and immune-inhibitory suppressor cells. The immune cells and cancer cells are treated to be on a staggered lattice, where the immune cells are located at the cell vertices and the cancer cells are located at the centroid of the 3D unit lattice. Each cell is considered as an individual agent, and their behavior at any time is determined by a stochastic decision-making process based on biological-driven mechanistic rules. The absolute numbers of effector and suppressor immune cells in conjunction with the cancer cell burden were used to define the tumor-immune ecosystem (TIES). RESULTS: Simulations of tumor growth in various TIES reveal that in our model, the tumor-immune ecosystem yields 2 functional phenotypes: where tumors evade immune predation and where tumors are eradicated by the immune system. The immune cells are seen to dynamically move via chemokinesis with components of Brownian motion (exploration) and of directed motion toward the highest gradient of dead cancer cells (exploitation). Mechanistic rules are defined at a local and individual level to impose spatial restrictions on the immune cells and prevent immediate infiltration to the center of the tumor. The resulting movement and spatial rules lead to an emergent local immune swarming and formation of tertiary lymphoid structures. CONCLUSION: This is the first clinically and biologically validated computational model to simulate and predict pan-cancer response and outcomes via the perturbation of the TIES by radiotherapy. This work was supported by the NIH/NCI 1U01CA244100

Yun Min Song KAIST
Poster ID: MFBM-13 (Session: PS01)
"Noisy delay denoises biochemical oscillators"

Genetic oscillators arise from delayed transcriptional negative feedback loops, wherein repressor proteins inhibit their own synthesis after a temporal production delay. This delay, generated by sequential processes involved in gene expressions such as transcription, translation, folding, and translocation, is distributed due to the inherent noise of the processes. Because the delay determines repression timing and therefore the oscillation period, it has been commonly believed that delay noise weakens oscillatory dynamics. However, in this talk, we demonstrate that noisy delay can actually denoise genetic oscillators by improving the temporal peak reliability.

Xiaojun Wu University of Southern California
Poster ID: MFBM-14 (Session: PS01)
"Single-cell Ca2+ parameter inference reveals how transcriptional states inform dynamic cell responses"

Single-cell genomic technologies offer vast new resources with which to study cells, but their potential to inform parameter inference of cell dynamics has yet to be fully realized. Here we develop methods for Bayesian parameter inference with data that jointly measure gene expression and Ca2+ dynamics in single cells. We propose to share information between cells via transfer learning: for a sequence of cells, the posterior distribution of one cell is used to inform the prior distribution of the next. In application to intracellular Ca2+ signaling dynamics, we fit the parameters of a dynamical model for thousands of cells with variable single-cell responses. We show that transfer learning accelerates inference with sequences of cells regardless of how the cells are ordered. However, only by ordering cells based on their transcriptional similarity can we distinguish Ca2+ dynamic profiles and associated marker genes from the posterior distributions. Inference results reveal complex and competing sources of cell heterogeneity: parameter covariation can diverge between the intracellular and intercellular contexts. Overall, we discuss the extent to which single-cell parameter inference informed by transcriptional similarity can quantify relationships between gene expression states and signaling dynamics in single cells.

Anna-Dorothea Heller Max Planck Institute of Colloids and Interfaces, Potsdam, Germany
Poster ID: MFBM-01 (Session: PS02)
"A stochastic Cellular Automaton Model to simulate Bone Remodeling"

Bone remodeling is a very complex and fine-tuned process, which is necessary to ensure a healthy bone structure. If this process gets out of balance – e.g., because of hormonal disbalance or the impact of bone metastases – pathologies like osteoporosis can appear. In this contribution we introduce a novel computational approach to investigate this balance by connecting the bone remodeling process with its microenvironment. Our goal is to better understand the well-balanced and complex dynamic of the subprocesses involved in healthy bone remodeling. We implement a 3D stochastic cellular automaton (SCA), where voxels interact only with their nearest neighbors in a scaffold representing bone tissue. At each time point, each voxel can take one of four different states that stand for the different phases of bone remodeling: formation, quiescent bone, resorption, and environment. To create a compact representation of the frequency-dependent interaction of those voxel states we make use of methods borrowed from evolutionary game theory for the update rule of the cellular automaton [1]. This representation encodes knowledge about the mutual impact the different actors of bone remodeling (osteocytes, osteoclasts and osteoblasts) have on each other. Each parameter in the model has therefore a direct connection to the biological processes. First, we set up simulations of the model with either only resorption or only formation. This choice reduced the model complexity and allowed us to determine parameter spaces for a self-regulating behavior for each of them. The self-regulating behavior is defined by resorption or formation starting and ending without further parameter tuning. Parameters outside the range of self-regulation will lead to either osteolytic lesions (resorption) or heterotopic ossification (formation). Further analyses supported the approach of a spatial model with a small neighborhood to simulate the local phenomena observed in bone remodeling. Next, we coupled the two processes of resorption and formation. In the limit of separation of time scales, our model showed that self-regulating resorption followed by self-regulating formation reproduces the physiological bone remodeling behavior. Further analysis will create a more fluid coupling of the two processes while involving more parameters. The model has the potential to use the role of the microenvironment to evaluate the impact of additional factors, such as drugs or bone metastases. We are planning on using experimental in vivo data from a breast cancer bone metastasis mouse model [2], which includes spatial and temporal dynamic of early osteolytic lesions, to fit additional parameters. Hopefully, these findings will add to the discussion, how pathological behavior might be controlled, if not even reversed. [1] M. D. Ryser and K.A. Murgas, Bone remodeling as a spatial evolutionary game, Journal of Theoretical Biology, 2017 [2] S. A. E. Young, A.-D. Heller et al., From breast cancer cell homing to the onset of early bone metastasis: dynamic bone (re)modeling as a driver of osteolytic disease, bioRxiv preprint

Brock Sherlock University of New South Wales
Poster ID: MFBM-02 (Session: PS02)
"An Algorithmic Approach for Constraining Stochastic Models with Multiple Data Sets"

Mean-field models of protein translocation in mammalian cell metabolism in response to insulin have previously been used to identify dominant processes at the macroscopic scale (J. Biol. Chem., 289(25): 17280-17298). These mean field models do not take the stochasticity and variance of the data fully into account, however. These models also do not provide explanatory mechanisms for the response to the insulin signal. We have developed a candidate stochastic queuing network model that may provide further insight into mechanisms at the molecular scale for glucose transporter translocation in insulin regulated metabolism. To test the efficacy of the model as an explanation of the biological mechanisms, an assessment of the ability of the model to represent all the different observations needs to be quantified. For each particular experimental protocol the data set consists of small numbers of repeated samples at discrete time points of the system under that experimental condition. The stochastic model then aims to describe all the different time evolving distributions corresponding to the different experimental protocols. Not only do the distributions of the data and model need to be compared at each time point in the data set for each protocol, but also a comparison needs to be made across time as each of the distributions evolve. Additionally, the correspondence of the stochastic model and observations across the different experimental protocols needs to be quantified. In systems where data is sparse, robustness can be given to inference when independent data sets from multiple sources are combined, given that the model parameters constrained by the different protocols overlap. In this investigation, different distance measures and comparators of evolving distributions are explored for the candidate model of glucose transporter translocation with a view to building a practical algorithm for inference of stochastic models with multiple stochastic data sets from different experimental protocols. The efficacy and implications of different approaches and for the candidate model is discussed.

Eduardo A. Chacin Ruiz University at Buffalo, The State University of New York, Buffalo, NY
Poster ID: MFBM-03 (Session: PS02)
"Mathematical Modeling of Drug Release from Bi-Layered Drug Delivery Systems in the Eye"

Wet age-related macular degeneration (AMD) is a blinding chronic eye disease commonly treated with monthly intravitreal injections. Drug delivery systems (DDS) aim to reduce injection frequency. Here, we developed mathematical models of drug release from bi-layered prototype chitosan-polycaprolactone (PCL) DDS to help optimize their design and improve wet AMD treatments. Fick’s second law is used to model the unsteady-state drug release from DDS into phosphate buffer saline. For drug-loaded chitosan-PCL microspheres, we solved the diffusion equation numerically using finite differences in MATLAB, and finite elements in COMSOL. We then use COMSOL for modeling a more complicated geometry consisting of a chitosan-PCL cylindrical device with a hollow core for drug loading. Furthermore, we use ordinary least squares objective functions in both software to estimate relevant parameters from the DDS using experimental data. Our MATLAB and COMSOL models accurately simulated the cumulative drug release behavior from the microspheres for 160 days compared to in vitro experimental data. For the cylindrical device, we observed large deviations in the initial 50 days, with more accurate predictions after that, implying other drug-release mechanisms, like erosion, need to be considered for the initial phase. The models can help optimize the design of bi-layered DDS to improve wet AMD treatments and provide insights into the mechanisms involved in the drug release from these DDS.

Eui Min Jeong Institute for Basic Science (IBS)
Poster ID: MFBM-04 (Session: PS02)
"Combined multiple transcriptional repression mechanisms generate ultrasensitivity and robust oscillations"

Transcriptional repression can occur via various mechanisms, such as blocking, sequestration and displacement. For instance, the repressors can hold the activators to prevent binding with DNA or can bind to the DNA-bound activators to block their transcriptional activity. Although the transcription can be completely suppressed with a single mechanism, multiple repression mechanisms are used together to inhibit transcriptional activators in many systems, such as circadian clocks and NF-κB oscillators. This raises the question of what advantages arise if seemingly redundant repression mechanisms are combined. Here, by deriving equations describing the multiple repression mechanisms, we find that their combination can synergistically generate a sharply ultrasensitive transcription response and thus strong oscillations. This rationalizes why the multiple repression mechanisms are used together in various biological oscillators. The critical role of such combined transcriptional repression for strong oscillations is further supported by our analysis of formerly identified mutations disrupting the transcriptional repression of the mammalian circadian clock. The hitherto unrecognized source of the ultrasensitivity, the combined transcriptional repression, can lead to robust synthetic oscillators with a previously unachievable simple design.

Farjana Tasnim Mukta University of Kentucky
Poster ID: MFBM-05 (Session: PS02)
"An Extended Atom Type System for Algebraic Graph-Based Machine Learning Model in Drug Design"

Drug discovery is a highly complicated and time-consuming process. One of the main challenges in drug development is predicting whether a drug-like molecule will interact with a specific target protein. This prediction is crucial in expediting the validation and discovery of targets, and it enables biochemists and pharmacists to accelerate the drug development process. In recent studies of biomolecular sciences, the application of algebraic graph-based models to accurately represent molecular complexes and predict drug-target binding affinity has generated significant interest among researchers. Here, we present algebraic graph-based molecular representations to form data-driven scoring functions (SF) named AGL-EAT-Score featuring extended atom types to capture wide-range interactions between the target and drug candidate. Our model applies multiscale weighted colored subgraphs for the protein-ligand complex where the graph coloring is based on SYBYL atom-type and ECIF atom-type interactions. Furthermore, combined with the gradient-boosting decision tree (GBDT) machine-learning algorithm, our newly developed SF has outperformed numerous state-of-the-art models in PDBbind benchmarks for binding affinity scoring power, and the D3R dataset, a worldwide grand challenge in drug design.

Furkan Kurtoglu Indiana University
Poster ID: MFBM-06 (Session: PS02)
"Multiscale Agent-Based Modeling of Metabolic Crosstalk Between Colorectal Cancer Cells and Cancer-Associated Fibroblasts"

Understanding altered metabolism in different conditions requires consideration of various connections across multiple scales. This project aims to understand the metabolic relationship between Colorectal Cancer Cells and Cancer-Associated Fibroblast (CAF). Firstly, an experimental workflow is designed to measure the effect of CAF presence on CRC metabolism. The Flux Balance Analysis (FBA) model is created using growth and metabolomic data. Next, 3-D multiscale agent-based model (ABM) is built to scale from a single cell level to dozens of organoids. We integrated the metabolic model as an FBA model to be employed as a chemical network in each agent. The multiscale model provides the spatial information, which is local substrate availabilities and cellular pressures, to be used as input to FBA. The metabolic model yields a biomass creation rate used as cellular volume growth in agents. Individual agents proliferate with adequate cellular volume and exchange rates for essential chemicals. The distribution of important metabolites in the 3-D domain is calculated by 3-D reaction-diffusion equations. However, the whole computational framework is expensive; therefore, we enhanced our framework with a surrogate model and multiple domains. The metabolic model portion of the simulation is speeded up with a deep neural network (DNN) which is trained by high throughput pre-run FBA model screens. Other acceleration is gained by coarsening the microenvironment domain, which does not contain cells. Multiscale simulations have matched with experimental growth rates. Overall, we combine multiple scales from the molecular level to the 3-D experimental well-containing hundreds of thousands of cells. High-throughput simulations with multiscale knockdowns will help us understand the altered metabolism and discover important targets to diminish this metabolic relationship.

Jabia M. Chowdhury University at Buffalo, The State University of New York, Buffalo, NY
Poster ID: MFBM-07 (Session: PS02)
"Computational Simulation of Pharmacokinetic Modeling of Drug Bevacizumab in AMD Treatment"

Age-related macular degeneration (AMD) is an irreversible disease caused by macular deterioration and responsible for vision loss. AMD is caused by the growth of abnormal leaky blood vessels due to the high presence of vascular endothelial growth factor (VEGF) in the macular region of the eye. Anti-VEGF drugs have been proven most stable medication in AMD treatment that inhibits the action of vascular endothelial growth factor in the macula. One of the most suggested anti-VEGF drugs used in AMD treatment is Bevacizumab using intravitreal injection. In our study, we developed a 3D spherical region of vitreous for the human and rabbit eye to computationally simulate the pharmacokinetic effect of the intravitreally injected drug Bevacizumab. The model is simulated in COMSOL under time-dependent conditions to observe the spatial drug distribution and calculate the concentration profile in the vitreous and near macula regions. The vitreous is treated as a Darcy porous medium, and the drug transport through the porous medium is solved using mass transport physics coupled with Darcy’s law, including the convection-diffusion effect. The model includes the drug elimination route both anteriorly and posteriorly. Both models are validated against the experimental pharmacokinetic model data using the drug Bevacizumab, and our drug concentration-time plots in vitreous for both the human and rabbit eye are in good agreement with the experimental data. The drug concentration near the macula is also explained with experimental validation.

Jnanajyoti Bhaumik SUNY Buffalo
Poster ID: MFBM-08 (Session: PS02)
"Fixation dynamics for switching networks"

Population structure has been known to substantially affect evolutionary dynamics. Networks that promote the spreading of fitter mutants are called amplifiers of natural selection, and those that suppress the spreading of fitter mutants are called suppressors. Research in the past two decades has found various families of amplifiers while suppressors still remain somewhat elusive. It has also been discovered that most networks are amplifiers under the birth-death updating combined with uniform initialization, which is a standard condition assumed widely in the literature. In the present study, we extend the birth-death processes to temporal (i.e.,time-varying) networks. For the sake of tractability, we restrict ourselves to switching temporal networks, in which the network structure alternates between two static networks at constant time intervals. We show that, in a majority of cases, switching networks are less amplifying than both of the two static networks constituting the switching networks. Furthermore, most small switching networks are suppressors, which contrasts to the case of static networks.

Joel Vanin Indiana University Bloomington
Poster ID: MFBM-09 (Session: PS02)
"Towards a virtual cornea - an agent-based model to study interactions between the cells and layers of the cornea under homeostasis and following chemical exposure."

Corneal injuries following chemical exposure differ in severity and reversibility. Various in vivo, ex vivo, and in vitro experimental methods attempt to predict whether exposure will lead to severe (corrosive), moderate, mild, or no irritancy but differ in their ability to prognosticate human-relevant eye irritation outcome. A detailed computational model of corneal injury at the multi-cellular level (depicting individual cells and biochemical processes in detail) which could predict these adverse outcomes would enable limitless virtual experiments. To improve the spatial and dynamic understanding of corneal chemical hazard, we built a multicellular agent-based model in the CompuCell3D modeling environment that aims to recapitulate complex cell behaviors underlying homeostasis and wound healing of the stratified epithelial layer and the stroma. The model represents a two-dimensional sagittal section of the limbal area with stem and transit-amplifying cells and a stratified epithelium layer keeping the same structure seen in its biological archetype, with a bilayer of superficial cells, two to three layers of wing cells, a single layer of basal cells attached to the basement membrane, and immune cells, bounded by virtual spaces to represent the tear layer and Bowman's membrane. Beneath this epithelial membrane lies an area representing the stroma with keratinocyte cells. Homeostasis in the epithelial layer implements signal information (cytokines, growth factors) and other factors can be added to more completely simulate the emergent wound-healing behavior where tear composition changes after injury, having higher levels of EGF (proliferation and migration), TGF-α (mitogen), HGF (proliferation and migration, promotes wound healing), KGF (proliferation), and IGF (proliferation), in the regulation of composite cellular behavior and multicellular interactions on proliferation and cell migration to the wounded site. These changes in the microenvironment activate quiescent limbal stem cells to proliferate and differentiate into transient-amplifying cells, which also proliferate and consequently differentiate into the other cell types present in the stratified epithelium layer. This mechanism is enough to heal mild and moderate wounds that avoid damaging the basement membrane. In cases of severe injury, other systems, including vascular and myeloid, participate in the repair of the Bowman's membrane and the stroma. This prototype virtual corneal model aims to define a more mechanistic human-relevant classification scheme, predict the time of recovery from each of those injuries, and offer potential explanations for the corneal anomalies (erosions and corneal ulcers) after severe damage and simulated responses to bioactivity data from various in vitro models of corneal toxicity. This will help toxicologists better understand critical events in cornea-chemical exposures as well as predict human-relevant adverse outcomes. Disclaimer: this abstract does not necessarily reflect USEPA policy.

Liam D. O'Brien The Ohio State University
Poster ID: MFBM-10 (Session: PS02)
"Changes in Approximate Symmetries of a Parametrized Turing Pattern"

Organisms exhibit a dazzling array of symmetries, from the rotational symmetries of flowers to the fractal symmetries of trees and even bilateral symmetries in humans. Symmetry is fundamental and is often a predictor of survivability, fecundity, and evolvability. Although it is intuitively clear that symmetry exists in nature, the symmetries are typically imperfect, making it difficult to apply mathematical tools that were built to understand idealized versions of symmetry. In 2021, Gandhi et al. proposed a real-valued operator that can quantify approximate symmetries by evaluating how much an object changes under a transformation. When one parametrizes the transformation and considers the operator’s graph on the parameter space, the symmetries of the object appear as local minima. I consider the rotational symmetries of a Turing pattern, showing that if we treat minima and maxima of the graph as stable and unstable equilibria (respectively), the changes in extrema are qualitatively similar to changes in equilibria that we observe in classical local bifurcations. Studying relevant properties of the operator may allow us to apply the tools of bifurcation theory to understand how approximate symmetries form in development.

Mohammad Nooranidoost Florida State University
Poster ID: MFBM-11 (Session: PS02)
"Modeling Biofilm Spatio-temporal Organization as a Viscoelastic Gel-mix"

Biofilms are complex heterogeneous substances that can be viewed from the perspective of soft matter physics and continuum mechanics. Biofilm structure can be modeled as a multiphase system where each component has its own rheological characteristics. From the biophysics point of view, the biofilm components create a gel-mix consisting of a polymeric network (polysaccharides) and fluid solvent. The biological and mechanical interactions between these components govern biofilm physics and its spatial variation. We developed a mathematical model to describe the spatiotemporal organization of the biofilm components as a multiphase system where each volume in space is fractionally occupied by the polymeric network and the fluid solvent. The polymeric network is modeled as a viscoelastic fluid that induces viscoelastic stresses due to the rheological behavior of polysaccharides. This viscoelastic stress is a function of the biofilm viscoelastic properties, which are estimated using a Markov Chain Monte Carlo method based on experimental data. The fluid solvent is modeled as a Newtonian fluid, creating viscous stresses within the computational domain. The dynamics of the phases are governed by the conservation of mass and momentum. Each phase moves with its own velocity, introducing a drag force between the phases that is proportional to the velocity difference between the phases. The motion and interaction of the gel-mix components are formulated as a set of equations in an incompressible Navier-Stokes form. These equations are discretized in integral form for infinitesimal control volumes on a two-dimensional staggered grid. This model helps us understand the motion of the biofilm components and can help future researches elucidate the dynamics of polymeric network that forms the backbone of the biofilm.

Nicholas O. Glover University at Buffalo, The State University of New York, Buffalo, NY
Poster ID: MFBM-12 (Session: PS02)
"Simulating solute transport through the kidney glomerulus using FEBio"

Chronic kidney disease (CKD) is a family of kidney diseases with various root causes that lead to eventual kidney failure and are characterized by dysfunction of the glomeruli, the functional subunits of the kidneys where blood is filtered. A glomerulus includes the glomerular filtration barrier (GFB) made of the endothelial layer, basement membrane, podocyte epithelial layer, and glycocalyx. The deterioration of the filtration barrier means that the kidney cannot effectively filter solutes from the capillaries, such as proteins, excess water, and other waste products. The functionality of the GFB is measured by the glomerular filtration rate or the rate at which fluid from the capillaries in the kidney is filtered to be excreted. Assessing glomerular dysfunction during CKD requires quantifying the effect of damage in the anatomical ultrastructure of GFB and the unwanted transport of protein through the GFB. Though various methods of assessing glomerular dysfunction exist, current computational models often neglect the glycocalyx as well as the effect of solute and GFB charge. We use open-source software FEBio (Finite Elements for Biomechanics) to simulate fluid transport in different layers of the GFB. FEBio applies continuum biphasic (fluid dynamics/solid biomechanics) theory to describe viscous fluid interactions with porous-hydrated biological tissues. The biphasic fluid-solid interactions (BFSI) solver in FEBio is used to model structures of the glycocalyx, glomerular basement membrane, porous medium, and fluid-solid interactions through the intricate small channels that form the fenestrated endothelial layer and the GBM. Transport equations describe the movement of fluids and solutes from the blood vessel lumen through the GFB. The anatomical ultrastructural parameters for the proposed model were estimated from high-resolution electron microscopy of the glomerular capillary wall. With the information gathered from the electron microscopy images, a “subunit” consisting of the averaged parameterized features of the filter was used to simulate GFB. In addition, ultrastructural parameters were used to design the 3D fluid domain for the simulation using MATLAB and GIBBON, a dedicated biomechanics add-on. The volumetric domain was exported to FEBio, where material properties, boundary conditions, and an analysis step were included for the model. The conditions of the simulation were analogous to the physiological conditions of the in vivo environment. Our simulations showed the flux of solutes (e.g., albumin, glucose, signaling molecules) through the GFB, which can be used to find the glomerular filtration rate (GFR). We intend to simulate the dynamic effects of biomolecular reactions on kidney ultrastructure as it relates to CKD. We use the model to analyze important dynamic phenomena during disease progression, including the widening of the filtration slit, thickening of the glomerular basement membrane, and detachment of the podocyte food processes. By recreating the human anatomy in a computational platform and applying the correct transport phenomena in each tissue layer, the physiological effects on the transport of solutes and glomerular filtration rate can be determined. Understanding the glomeruli’s fluid transport and chemical and physical interactions is critical to provide insights into human development, disease progression, and wound healing possibilities.

Richard C. Windecker, PhD N/A (retired from Bell Labs)
Poster ID: MFBM-13 (Session: PS02)
"An Agent-Based Model for Step Lengths in a Random Walk"

As an animal searching for prey performs a random walk, processes in the animal’s nervous system make decisions that produce a distribution of step lengths. I will describe in detail an Agent-Based Model for how an animal’s nervous system might make these decisions. The “agents,” that I call “Simple Abstract Neurons,” are NON-deterministic generalizations of well-known digital logic gates. I will use a simple version of the model, with carefully-chosen, made-up parameters to illustrate central concepts. I will give a detailed example of how the model parameters can be adjusted to fit a set of empirical data; in this case, from a diving marine predator: an individual blue shark. The SAN model fits the shark data much more closely than the “best fit” of a theoretical, analytical model. Theoretical studies suggest that when prey is plentiful, an exponential distribution of step lengths is effective. Otherwise, a power-law distribution is optimum. Animals follow such distributions only to the degree that evolutionary pressures may have resulted in an approximation that gives an acceptable balance of cost vs. benefit. But theory provides no insight as to how an animal might produce the observed behavior. The SAN model suggests some answers and makes testable predictions. For example, the model easily and naturally explains how an animal can follow an approximate power-law distribution while avoiding the implied infinities at very short and very long step lengths. Because the underlying processes are stochastic, any set of empirical data is a sample from a range of possible sets. Model-generated “synthetic data” can be used to characterize this range. The model can also be used to perform very insightful “What if?” experiments. SANs are compatible with digital logic; the number of possible pure and hybrid networks is huge. The potential is very large for the SAN model to be adapted to other animal behaviors besides random walks.

Saikanth Ratnavale University of Notre Dame
Poster ID: MFBM-14 (Session: PS02)
"Optimal controls of the mosquito-borne disease, Dengue with vaccination and control measures"

Dengue is one of the most common mosquito-borne diseases in the world, and a person can get infected by one of the four serotypes of the virus named DENV-1, DENV-2, DENV-3, and DENV-4. After infection with one of these serotypes, an individual will maintain permanent immunity to that serotype, and partial immunity to the other three serotypes. Therefore, there is a risk of getting infected by this virus a maximum of four times, and the symptoms may vary from mild fever to high fever, bleeding, enlarged liver, and severe shock, and sometimes these symptoms may lead to death. It is obvious that the increase in the number of infected individuals makes a negative impact on a country’s economy. Hence, the use of different control measures such as mosquito repellents and the introduction of a vaccine against the virus is important in controlling the spread of the virus. In this study, I am presenting a methodology on how to estimate the optimal rate of vaccinations based on the QDENGA dengue vaccine and the optimal rate of control measures to reduce the number of new and severe dengue cases while minimizing the overall cost. In addition, this vaccine claims high protection against symptomatic disease and waning protection over time for some DENV serotypes. However, the extent to which protection against disease conditional on infection is unknown. I consider different scenarios subject to the possible combinations of vaccine protection and control measures to investigate the most effective parameter values to control the transmission of the virus. Disease forecasts including the number of newly infected individuals in each serotype, the optimal rate of control measure, and vaccinations for a period of ten years are performed with the help of computer software.

Torkel Loman Massachusetts Institute of Technology
Poster ID: MFBM-15 (Session: PS02)
"Catalyst: Fast Biochemical Modeling with Julia"

We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high performance simulation of chemical reaction networks (CRNs). Catalyst acts as both a domain-specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying reaction networks; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for use in numerical solvers. Currently, Catalyst supports conversion to symbolic discrete stochastic chemical kinetics (jump process), chemical Langevin (stochastic differential equation), and mass-action reaction rate equation (ordinary differential equation) models. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in a broad variety of numerical solvers. The performance of the numerical solvers Catalyst targets is illustrated across a variety of reaction networks by benchmarking stochastic simulation algorithm and ODE solver performance. These benchmarks demonstrate significant performance improvements compared to several popular reaction network simulators. Finally, Catalyst combines with a range of packages within the Julia package ecosystem, enabling functions such as steady state finding, bifurcation analysis, parameter fitting, and much more.

Zainab Almutawa University of Maryland Baltimore County
Poster ID: MFBM-16 (Session: PS02)
"Switching off activity in minimal three-cell topologies of coupled heterogenous beta cells"

Beta cells are cells in the pancreas that produce and release insulin in response to blood glucose levels. Interactions between beta cells within their local network of an islet is important for the regulation of insulin secretion and to enhance the glucose stimulated response. Beta cells are coupled through gap junctions and generate synchronous threshold-based oscillations of their membrane potential. Dysfunction of coupling has been associated with diabetes. Experiments have suggested individual beta cells can control synchronization. We have previously shown in specific conditions a 'switch' cell can serve this purpose. However, the cellular and network conditions are not fully understood. To test a minimal model representation of this behavior we use a mathematical model of bursting in two triplet configurations, chain and triangle. Biological heterogeneity is introduced by varying the gap junctional coupling and the rate of calcium extrusion parameters for each of the cells, which permits varying types of frequencies. We measure the amplitude of a patched steady cell, and we investigate how the bursting of a high frequency cell and coupling can lead to change of the behavior of the patched steady cell. To demonstrate a switch cell exists, we effect the second intermediate frequency cell by (a) silencing it setting the voltage to rest or (b) ablating it disconnecting this cell from other cells, and observe under what conditions there is a loss of activity. We have found the range of coupling strength and calcium extrusion parameters that support switch cell behavior in the simplified system.

Caroline Tatsuoka The Ohio State University
Poster ID: MFBM-17 (Session: PS02)
"Data Driven Modeling of Biological Systems with Deep Neural Networks"

We will present methods to uncover the unknown dynamics and features of several biological systems via deep neural network (DNN). We will show how DNNs can be used as approximations to flow maps of the true underlying biological system utilizing residual networks. Further, we will demonstrate its extension to systems with only partially observed data and systems with uncertain parameters. Once an accurate DNN model is constructed, it can be used as a predictive model for the unknown system, allowing us to conduct further system analysis. We will further explore its extension to the inverse problem, or recovering parameters on the system given the available data.

Shawn Means University of Auckland
Poster ID: MFBM-18 (Session: PS02)
"Reduction of order for uterine smooth muscle cell model: Relevance and Reproducability"

We apply a reduction method to a published uterine smooth muscle cell (uSMC) by Tong, et al. 2011, using both a representative ion channel and steady-state approximation approach. Although an extensive catalogue of potassium channels are known to reside in the uSMC, we hypothesise not all are functionally relevant to reproduce the data given. Further, the Tong model incorporates a vast range of time scales for the Hodgkin-Huxley type activation and inactivataion variables ranging over six orders of magnitude. We demonstrate effective use of a reduced suite of potassium channels and deployment of steady-state approximations that not only reproduces the same data set as the Tong model but additional data a later expanded Tong model with even more potassium channels. Moreover, our reduced model increases computational performance by 200%.

Dae Wook Kim University of Michigan
Poster ID: MFBM-19 (Session: PS02)
"Wearable data assimilation to estimate the circadian phase"

The circadian clock is an internal timer that coordinates the daily rhythms of behavior and physiology, including sleep and hormone secretion. Accurately tracking the state of the circadian clock, or circadian phase, holds immense potential for precision medicine. Wearable devices present an opportunity to estimate the circadian phase in the real world, as they can non-invasively monitor various physiological outputs influenced by the circadian clock. However, accurately estimating circadian phase from wearable data remains challenging, primarily due to the lack of methods that integrate minute-by-minute wearable data with prior knowledge of the circadian phase. To address this issue, we propose a framework that integrates multi-time scale physiological data to estimate the circadian phase, along with an efficient implementation algorithm based on Bayesian inference and a new state space estimation method called the level set Kalman filter. Our numerical experiments indicate that our approach outperforms previous methods for circadian phase estimation consistently. Furthermore, our method enables us to examine the contribution of noise from different sources to the estimation, which was not feasible with prior methods. We found that internal noise unrelated to external stimuli is a crucial factor in determining estimation results. Lastly, we developed a user-friendly computational package and applied it to real-world data to demonstrate the potential value of our approach. Our results provide a foundation for systematically understanding the real-world dynamics of the circadian clock.

Organizing committee
  • Laura Kubatko, chair
  • Adriana Dawes
  • Mary Ann Horn
  • Janet Best
  • Adrian Lam
  • Grzegorz Rempala
  • Will Gehring
Scientific organizing committee
  • Adriana Dawes
  • Mary Ann Horn
  • Jane Heffernan
  • Hayriye Gulbudak
  • Jeffrey West
SMB 2023 is being held on the campus of The Ohio State University. As visitors to campus, all SMB participants must follow The Ohio State University Policy on Non-Discrimination, Harassment, and Sexual Misconduct.

Organizing committee
  • Laura Kubatko, chair
  • Adriana Dawes
  • Mary Ann Horn
  • Janet Best
  • Adrian Lam
  • Grzegorz Rempala
  • Will Gehring
Scientific organizing committee
  • Adriana Dawes
  • Mary Ann Horn
  • Jane Heffernan
  • Hayriye Gulbudak

  • Jeffrey West

SMB 2023 is being held on the campus of The Ohio State University. As visitors to campus, all SMB participants must follow The Ohio State University Policy on Non-Discrimination, Harassment, and Sexual Misconduct.