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.

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.

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 https://arxiv.org/abs/2303.14093

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.

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.

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.

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.

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.

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.

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.

• 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.

• 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.

• 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.

• 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