Epidermal wound closure is a complex process involving the coordination of many mechanisms across multiple spatial scales. In this work we use cell-based modelling to investigate wound closure mechanisms acting on whole-wound and localised scales. We begin by exploring spatial effects on wound closure - specifically tissue compression due to cell division events and individual cellular compression. We then consider two key wound healing mechanisms: purse-string closure and cell crawling. The purse-string mechanism involves contraction of the acto-myosin cables in cells adjacent to the wound edge whereas the cell crawling mechanism describes active cellular migration due to lamellipodial protrusions. Previous cell-based models of wound healing have attempted to describe the purse-string mechanism at a cellular level scale. However, it has been established that purse-string behaviour occurs on a whole-wound scale. In particular, an actomyosin cable forms around the entire wound edge and contracts ‘globally’ during closure. In this work, we formulate a wound-scale model for purse-string closure and compare it to a locally acting model. Finally, we propose two models for cell crawling: one where cells respond to their local environment and another in which cells actively migrate in response to a global cue. We compare the two models and discuss the relative benefits of each. We conclude by summarising the overall differences between globally and locally acting mechanisms and propose more realistic extensions of each model.

To function and survive, cells need to be able to sense and respond to their local environment in a process called mechanotransduction. Crucially, mechanical and biochemical perturbations to a cell can initiate signaling cascades which can induce, among other responses, cell growth, apoptosis, proliferation and differentiation - focal adhesions and actomyosin stress fibres are at the heart of this process. The formation and maturation of these structures (connected by a positive feedback loop) is pivotal in non-motile cells, where stress fibres are generally of ventral type, interconnecting focal adhesions and producing isometric tension. We have formulated a one-dimensional bio-chemo-mechanical continuum model to describe the coupled formation and maturation of ventral stress fibres and focal adhesions. We use a set of reaction-diffusion-advection equations to describe three sets of biochemical events: the polymerisation of actin and bundling and activation of the resultant fibres; the formation and maturation of adhesions between the cell and substrate; and the upregulation of certain signaling proteins in response to focal adhesion and stress fibre formation. The evolution of these key proteins is then coupled to a Kelvin-Voigt viscoelastic description for the cell cytoplasm and for the ECM. We employ this model to understand how cells respond to external and intracellular cues in vitro. We are able to replicate various experimentally observed phenomena including demonstrating that stress fibres exhibit non-uniform striation, cells form weaker stress fibres and focal adhesions on compliant surfaces and myosin II inhibition leads to disruption of focal adhesions. The model hence provides a platform for systematic investigation into how the cell biochemistry and mechanics influence the growth and development of the cell and facilitates prediction of internal cell measurements that are difficult to ascertain experimentally, such as stress distribution.

Many cells adjust the direction of polarized growth or migration in response to external directional cues. The yeast Saccharomyces cerevisiae orient their cell fronts (also called the polarity sites) up pheromone gradients in the course of mating. However, the initial polarity site often misaligns with the pheromone gradient. Therefore, to track pheromone gradients requires reorientation of the polarity site. During this reorientation phase, the polarity site displays erratic assembly-disassembly behavior as it moves around the cell cortex. The mechanisms underlying this dynamic behavior remain poorly understood. Particle-based simulations of the core polarity circuit revealed that molecular-level fluctuations are insufficient to overcome the strong positive feedback required for polarization and generate relocating polarity sites. Inclusion of a pheromone-sensing pathway that acts over longer time scales than the pathways associated with the core polarity circuit generated a mobile polarity site with properties similar to those observed experimentally. This sensing pathway couples polarity establishment to the gradient sensing and, surprisingly, it also has a positive feedback architecture because polarity factors direct secretion of new pheromone receptors to the cell membrane. This second positive feedback loop also allows cells to stabilize their polarity site once the site is aligned with the pheromone gradient.

Epithelial shape change is of major importance in early development across the animal kingdom. Using a new particle-based simulation framework, Tissue Forge (https://compucell3d.org/TissueForge), we set out to model the epithelial morphogenesis of zebrafish epiboly, in which the blastoderm epithelium, sitting atop a large yolk cell, gradually stretches downward over the yolk to completely engulf it. The forces driving this extension and shape change are believed to be generated within the yolk cell and act on the epithelial margin. We use single particles to represent cells, and global potentials and bonds to represent cellular interactions such as adhesion and tissue tension. Tissue extension occurs when exogenous force from the yolk cell is strong enough to overcome the internal tension of the epithelial layer. Dynamic, stochastic remodeling of intercellular bonds, with constraints on the neighborhood topology, allows for viscoelastic tissue deformation and cell rearrangement in response to exogenous forces, while maintaining tissue integrity. Stress and strain patterns within the epithelium show a spatial and temporal dependence on model parameters and may help to distinguish between hypothesized force generation mechanisms.

In the real world, mutations of genetic sequences are often accompanied by their recombinations. Such joint phenomena are modeled by phylogenetic networks. These networks are typically generated or reconstructed from coalescent processes that may arise from optimal merging or fitting together a given set of phylogenetic trees. L. Nakkleh formulated the phylogenetic network reconstruction problem (PNRP) as follows: Given a family of phylogenetic trees over a common set of taxa, is there a unique minimal phylogenetic network whose set of spanning trees contains the family? There are different answers to PNRP, since there are different ways to define what a “minimal network” is (based on different optimization criteria). Inspired by ideas from topological data analysis (TDA) (i.e. filtered simplicial complexes), we devise a simplicial lattice-model for modeling phylogenetic networks, called the cluttergram, that generalizes the dendrogram (filtered partition) model of phylogenetic trees. We show that the collection of all cluttergrams over the same set of taxa (leaves) forms a lattice. This lattice-model allows us to solve the PNRP in a mathematically rigorous way and in a way that is free of choosing optimization criteria for the reconstruction process. The solution to the phylogenetic network reconstruction process is obtained by taking the join operation of the dendrograms on the lattice of cluttergrams (by viewing dendrograms as cluttergrams). Furthermore, we show that computing the join-cluttergram from a given set of dendrograms is polynomial in the size and the number of the input trees (dendrograms). Moreover, motivated by the tool of persistence diagram in topological data analysis, we introduce an invariant of cluttergrams, called the mergegram, by extending the corresponding construction that was defined by Elkin and Kurlin on dendrograms. Then, we show that the mergegram is a 1-Lipschitz stable invariant of cluttergrams. This new TDA-signature of phylogenetic networks enable us to utilize standard statistical pipelines (vectorization and machine learning) to study phylogenetic networks. To illustrate the utility of these new TDA-tools to Phylogenetics, in this work we provide Python implementations of the introduced concepts and also experiments with certain benchmark biological datasets. This is joint work with Pawel Dlotko and Jan Senge.

Phylogenetic networks are a generalization of phylogenetic trees allowing for the representation of speciation and reticulate evolutionary events such as hybridization or horizontal gene transfer. Traditionally, two types of phylogenetic networks were considered in the literature: unrooted (undirected) ones that are often used to represent conflict in data and rooted (directed) ones that explicitly depict evolution as a directed process. Recently, however, semi-directed phylogenetic networks have emerged as a class of phylogenetic networks sitting between rooted and unrooted phylogenetic networks since they contain directed and undirected edges. For example, software such as PhyloNetworks, NANUQ, and PhyNEST reconstructs semi-directed level-1 networks from biological data. However, in contrast to rooted and unrooted phylogenetic networks, little is known about searching spaces of semi-directed phylogenetic networks to find an optimal network. In this talk, we introduce semi-directed phylogenetic networks and related concepts. We then discuss a rearrangement move, called cut edge transfer (CET), and show that the space of semi-directed level-1 networks with a fixed leaf set and number of reticulations is connected under CET. Hence, every semi-directed level-1 network in this space can be transformed into any other such network by a sequence of CETs. By introducing two additional moves that allow for the addition and deletion of reticulations, we extend our results to semi-directed (level-1) network on a fixed leaf set. As a byproduct, we also obtain connectedness results for rooted level-1 networks under a rooted version of CET.

Understanding the spatial and temporal dynamics of plant populations has important implications for the fields of ecology and conservation. A rich body of mathematical approaches have been developed to mechanistically model population spread based on species demography and seed dispersal patterns. However, with over 390,000 plant species on Earth, it is not feasible to collect complete information on all species for the purpose of making generalized conclusions. This problem may be addressed through trait-based modeling, which seeks to represent realistic combinations of organismal traits rather than focusing on individual species. In this work, I use a Bayesian multivariate approach to synthesize sparse datasets and estimate key demographic and dispersal parameters for a population of virtual species. I then use integrodifference equations to estimate population spreading speeds for virtual species and investigate links between movement-related extinction risk and easy-to-measure plant functional traits. This work demonstrates an example of how empirical data, statistical modeling, and mathematical modeling may be synthesized to advance understanding and inform decision-making in complex fields such a spatial ecology.

The Antibody Mediated Prevention (AMP) trials demonstrated that passive administration of the broadly neutralizing monoclonal antibody VRC01 could prevent some HIV acquisition events. Here we used mathematical modeling to demonstrate that VRC01 influenced viral loads in AMP participants who acquired HIV. Instantaneous inhibitory potential (IIP), which integrates VRC01 serum concentration and VRC01 sensitivity of acquired viruses in terms of both IC50 and IC80, had a dose-response relationship with first positive viral load (p=0.03), which was particularly strong above a threshold of IIP=1.6 (r=-0.6, p=2e-4). Next, combined pharmacokinetic, pharmacodynamic and viral load kinetic modeling revealed that VRC01 neutralization predicted from in vitro IC80s and serum VRC01 concentrations overestimated in vivo neutralization by 600-fold (95% CI: 300-1200). We show how the trained model can be naturally conducive for informing design and projecting efficacy in coming preventive and therapeutic HIV trials of combination monoclonal antibodies.

Management of human immunodeficiency virus (HIV) infection requires strict adherence to a daily drug regiment to prevent viral rebound. Red blood cells (RBCs) that lack nuclei and other organelles required for viral replication have been proposed as viral traps for HIV-1 as an alternative treatment for HIV-1. RBCs persistence in-host would require less frequent treatment offering a promising long-lasting augmentation to the existing highly active antiretroviral therapy (HAART). We develop an in-vitro model to assess the neutralization potential of RBCs targeting HIV-1 by expressing CD4, CCR5, or a CD4-glycophorin A (CD4-GpA) fusion protein and seek to elucidate the requirements for successful use of red blood cell viral traps for both treatment of HIV-1 and prophylaxis against both HIV-1 and SARS-CoV-2 infection.

SARS-CoV-2 viral loads have been linked with COVID-19 severity and transmission risk, and their kinetics vary across individuals. We clustered data from 1355 infections in the National Basketball Association cohort to identify six distinct patterns of viral shedding, which differ according to peak, duration, expansion rate and clearance rate. We then developed a mechanistic mathematical model that recapitulated observed viral trajectories, including viral rebound. Our results suggest that more rapid viral elimination occurs following vaccination and during omicron infection due to enhanced innate and acquired immune responses. We extended this model to include nirmatrelvir pharmacokinetics. In a published randomized double-blinded clinical trial, ritonavir-boosted nirmatrelvir decreased hospitalization and death by 95% and decreased nasal viral load by 0.5 log relative to placebo when given early during symptomatic infection to high-risk individuals. Our results from simulating this trial demonstrate niramtrelvir IC50 (50% inhibitory concentrations) estimates from in vitro assays are 100-fold less than plasma concentration required to reduce viral infection by 50% in humans. A maximally potent agent would reduce viral load by 3 orders of magnitude. We also project modifications to the treatment regimen that can reduce the frequency of viral rebound.

Patient-specific premorbidity, age, and sex are significant heterogeneous factors that influence the severe manifestation of lung diseases, including COVID-19 fibrosis. The renin-angiotensin system (RAS) plays a prominent role in regulating effects of these factors. Recent evidence suggests that patient-specific alteration of RAS homeostasis with premorbidity and the expression level of angiotensin converting enzyme 2 (ACE2), depending on age and sex, is correlated with lung fibrosis. However, conflicting evidence suggests decreases, increases, or no changes in RAS after SARS-CoV-2 infection. In addition, detailed mechanisms connecting the patient-specific conditions before infection to infection-induced fibrosis are still unknown. Here, a mathematical model is developed to quantify the systemic contribution of heterogeneous factors of RAS in the progression of lung fibrosis. Three submodels are connected—a RAS model, an agent-based COVID-19 in-host immune response model, and a fibrosis model—to investigate the effects of patient-group-specific factors in the systemic alteration of RAS and collagen deposition in the lung. The model results indicate cell death due to inflammatory response as a major contributor to the reduction of ACE and ACE2, whereas there are no significant changes in ACE2 dynamics due to viral-bound internalization of ACE2. Reduction of ACE reduces the homeostasis of RAS including angiotensin II (ANGII), while the decrease in ACE2 increases ANGII and results in severe lung injury and fibrosis. The model explains possible mechanisms for conflicting evidence of RAS alterations in previously published studies. Also, the results show that ACE2 variations with age and sex significantly alter RAS peptides and lead to fibrosis with around 20% additional collagen deposition from systemic RAS with slight variations depending on age and sex. This model may find further applications in patient-specific calibrations of tissue models for acute and chronic lung diseases to develop personalized treatments.

The recent geographical expansion of Aedes mosquito-borne diseases (ABDs) is a global health threat. Quantifying these pathogens’ epidemiology and identifying at-risk populations are key steps toward preparing for future ABD outbreaks. Data from past outbreaks should be central to informing these efforts, but leveraging these data toward generalizable conclusions is often difficult. Outbreak data are context-dependent and take various forms (e.g., a time-series of cases or retrospective serology data), precluding straightforward comparisons. In this presentation, we approach this problem from two angles, using chikungunya virus (CHIKV) as an example. First, we show how outbreaks with different types of data can be compared directly through the framework of Bayesian inference and mathematical modeling. We use this approach to estimate several measurements of outbreak risk and potential size, such as the basic reproduction number (R0), for 87 CHIKV outbreaks. Second, we test whether these risk estimates can be predicted using local, pre-outbreak information, including demographic factors and previously published climate-based indices of suitability for ABD transmission. Our results suggest that climate-based indices may approximate where outbreaks can occur, but do not predict R0, outbreak risk, or potential outbreak size. More broadly, we illustrate the importance of combining a biologically realistic model with various data sources when quantifying the risk of ABD transmission.

Antimicrobial Resistant Organisms (ARO) pose a significant threat to human and animal health. Adherence to biosecurity measures is critical in preventing the spread of infectious diseases and minimizing the emergence of AROs. This study aims to develop a modeling framework to quantify the effects of biosecurity adherence on the dynamics of antimicrobial-resistant bacteria in cattle farms. A deterministic Susceptible-Infected-Recovered-Susceptible (SIRS) model is formulated, accounting for drug-susceptible and drug-resistant pathogen strains capable of growth and survival within and between hosts. First, the possible outcomes of the SIRS model are analytically derived and numerically verified as a benchmark. Then, the SIRS model is further extended by stochastically incorporating cattle-farmworker-environment interactions. Using numerical simulations and sensitivity analysis, the likelihood of ARO emergence is investigated under different degrees of compliance with biosecurity measures, such as cattle quarantine, hand hygiene, equipment disinfection, animal health check-ups, and proper use of antibiotics. The present work is the first step toward understanding the influence of biosecurity adherence on human and animal health.

The Eastern Equine Encephalitis virus (EEEV) is an erratic and deadly neurological disease that spans the northeastern coast of the United States and Canada. An analysis of the migration patterns of both the mosquito vector and the avian host species was conducted to determine the rate at which the virus is spread between the Black-Tailed Mosquito (Culiseta melanura) and select avian species. It was found that certain species of avians shared similar, or even identical, migration patterns with the Black-Tailed Mosquito. A system of ordinary differential equations (ODEs) was developed and analyzed to gain insight into the transmission dynamics of EEE between the two host classes. A host stage-structured model was incorporated where the avian host group is split into two categories, adults, and hatch-year avians. By using this, the extent to which fluctuations occurred in transmission rates according to host/vector abundances, mosquito biting rate, and type of host was explored. Elasticity analysis was then conducted on all parameters that form the basic reproductive number (ℛ0­) to find the parameters that cause the greatest change in ℛ0. The hypothesis that is evaluated is that hatch-year avians are more readily exposed to the mosquito vector as they lack a defense mechanism, unlike their adult counterpart, allowing for a better understanding of how hatch-year avians drive the infection.

Transmission heterogeneity plays a critical role in the dynamics of an epidemic. During an outbreak of an emerging infectious disease, efforts to characterize transmission heterogeneity are generally limited to quantifications during a small outbreak or a limited number of generations of a larger outbreak. Understanding how transmission heterogeneity itself varies over the course of a large enduring outbreak not only improves understanding of observed disease dynamics but also informs public health strategy and response. In this study, we employ a simple method, adaptable to other emerging infectious disease outbreaks, to quantify the spatiotemporal variation in transmission heterogeneity for the 2022 mpox outbreak in the United States. In line with past research on mpox and following reports of potential superspreading events early in this outbreak, we expected to find high transmission heterogeneity as quantified by the dispersion parameter of the offspring distribution, k. Our methods use maximum likelihood estimation to fit a negative binomial distribution to transmission chain offspring distributions informed by a large mpox contact tracing dataset. We find that, while estimates of transmission heterogeneity varied across the outbreak with spatiotemporal pockets of high heterogeneity, overall transmission heterogeneity was low. When testing our methods on simulated data from an outbreak with high transmission heterogeneity, k estimate accuracy depended on the contact tracing data accuracy and completeness. Since the actual contact tracing data had high incompleteness, our values of k estimated from the empirical data may therefore be artificially high. However, it is also possible that our estimates accurately reflect low transmission heterogeneity for the United States mpox outbreak, which could differ substantially from the patterns observed elsewhere.

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.

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.

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.

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.

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.

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.

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

Temporal difference learning models, once developed as computer algorithms, have transformed how we study human decision-making and related brain activity. These models describe how a person updates their valuation of a decision according to an error in predicted rewards. While these valuations have conventionally been one-dimensional, recent experiments and theories suggest that these valuations might be multi-dimensional. In this talk, I will give a brief introduction to conventional modeling of human decision-making and discuss recent work to extend current reinforcement learning models to capture multi-dimensional valuations. Further, I will demonstrate the advantage of these extended models, from the perspective of what a person learns and the decisions they make, and connect these models to recent experiments. Last, I will discuss how these ideas can inform the design of future experiments

The circadian (~24h) clock is based on a negative feedback loop centered around the PERIOD protein (PER) that is translated in the cytoplasm and then enters the nucleus to repress its own transcription at the right time of day. Such precise nucleus entry is mysterious because thousands of PER molecules transit through crowded cytoplasm and arrive at the perinucleus across several hours. To understand this, we developed a mathematical model describing the complex spatiotemporal dynamics of PER as a single random time delay. We find that the spatially coordinated bistable phosphoswitch of PER, which triggers the phosphorylation of accumulated PER at the perinucleus, leads to the synchronous and precise nuclear entry of PER. This leads to robust circadian rhythms even when PER arrival times are heterogenous and perturbed due to changes in cell crowdedness, cell size, and transcriptional activator levels. This shows how the circadian clock compensates for spatiotemporal noise.

Perfusion imaging is valuable because it is used to help grade tumors; differentiate between tumor types; differentiate tumors from nonneoplastic lesions; guide intraoperative sampling; most importantly, determine the efficacy of treatment. Computational techniques combined with the imaged data can help identify important biological parameters. For example, key parameters include cerebral blood flow (CBF), cerebral blood volume (CBV) and mean transit time (MTT) . These parameters can help distinguish between the likely salvageable tissue and irreversiblydamaged infarctcore.Theparametersarecalculateddeconvolvingcontrast-time curves with the arterial inlet input function. A common approach employed with the deconvolution method is a singular value decomposition (SVD). However, these algorithms are very sensitive to noise and artifacts in the source image which may introduce additional distortions in the output parameters. For this reason, we will employ machine learning algorithms to aid in the measurements of perfusion parameters from CT imaging and compare to parameter measurement using SVD with regularization.

Nowadays graphs have become of significant importance given their use to describe complex system dynamics, with important applications to real world problems, e.g. graph representation of the brain, social networks, biological networks, spreading of a disease, etc.. In this work, [4], we introduce a novel graph wavelet packets construction, to our knowledge different from the ones known in literature. We get inspired by the Spectral Graph Wavelet Transform defined by Hammond et all. in [1], based on a spectral graph wavelet at scale s > 0, centered on vertex n, and a spectral graph scaling function, respectively. Moreover, after defining the wavelet packet spaces, and the associated tree, we obtain a dictionary of frames for R^N; with known lower and upper bounds. We will give some concrete examples on how the wavelet packets can be used for compressing, denoising and reconstruction by considering a signal, given by the fRMI (functional magnetic resonance imaging) data, on the nodes of voxel-wise brain graph G with 900760 nodes (representing the brain voxels) defined in [2]-[3]. References [1] D. K. Hammond, P. Vandergheynst , and R. Gribonval, Wavelets on graphs via spectral graph theory, Appl. Comput. Harmon. Anal. 30 (2011) 129-150. [2] A. Tarun, D. Abramian, M. Larsson, H. Behjat, and D. Van De Ville, Voxel-Wise Brain Graphs from Diffusion-Weighted MRI: Spectral Analysis and Application to Functional MRI, preprint (2021). [3] A. Tarun, H. Behjat, T. Bolton, D. Abramian, D. Van De Ville, Structural mediation of human brain activity revealed by white-matter interpolation of fMRI, NeuroImage 213 (2020) 116718.[4] I.M. Bulai, S. Saliani, Spectral graph wavelet packets frames, Applied and Computational Harmonic Analysis (2023).

One of the main obstacles to treating cancer is its ability to evolve and resist treatment. In this project, we mathematically model how the cancer microenvironment interacts with cancer cells and affects response to therapy in the context of estrogen-receptor positive (ER+) breast cancer, endocrine therapy, and cancer-associated fibroblasts (CAFs). The system is described with ordinary differential equations (ODEs) to investigate the impacts that cancer cells and CAFs have on each other’s population dynamics. We explore two different proposed scenarios of cancer-CAF dynamics: 1) cancer cells can recruit CAFs from an endless supply of fibroblasts, 2) a constant total population of fibroblasts that can switch between healthy and cancer-associated. In each scenario, we analyze stability of fixed points to determine the impacts of endocrine treatment and CAFs on the long-term behavior of cancer to address the questions: What role does estrogen/endocrine therapy play in resistance acquisition? Is resistance inevitable? If not, what can we do to prevent it? If resistance is inevitable, can we reverse it? and how? Both systems exhibit vastly different long-term outcomes dependent on estrogen availability in the system. For example, the models predict that a mere 20-hour difference in the initiation of endocrine therapy dictates the difference between the population of cancer dying off or growing infinitely. Furthermore, constant lower levels of available estrogen or constant small populations of CAFs prolong the systems' periods of slow growth. In the recruitment model, we also find that the existence of enough CAFs is necessary for the cancer population to grow exponentially under endocrine therapy or survive. Thus, the model suggests rapid tumor growth can be delayed by increasing the death rate of CAFs. By including CAFs in our model, we hope to provide new insights into how ER+ breast cancer develops resistance to endocrine therapy.

This talk will describe our recent modeling effort to understand the stochastic dynamics of cancer dormancy, which refers to the ability of cancer cells to remain inactive below detection thresholds for prolonged time periods despite therapeutic interventions. There are different types of cancer dormancy, including cellular and immune-mediated dormancy. The balance between pro-tumor and anti-tumor immunity plays a critical role in cancer elimination or progression, resulting in cancer escape, elimination, or equilibrium. This equilibrium phase is associated with immune-mediated dormancy, where T cell killing matches the cancer division rate. Previous mathematical models that have been proposed to study dormancy, such as those using ordinary differential equations (ODEs), have limitations like neglecting the distributional behavior of cells and failing to make predictions with equilibrium population sizes close to zero, which may overlook the extinction probability of this absorbing state. To address these limitations, this talk will present a new stochastic model based on non-linear birth-death processes to more accurately describe dormancy dynamics. The model assumes a cancer population undergoing stochastic birth and death with an exponential growth rate, modified by an immunomodulation function that depends on the population size and an inhibitory element. This modeling framework can be used to identify the immunomodulatory effects of cancer therapy and the tumor microenvironment on the timing and likelihood of cancer elimination.

The identification of optimal cancer therapies is significantly complicated by the dynamic interplay between tumor immune evasion and T-cell exhaustion. Cytotoxic T-cell immunosurveillance plays a vital role in immunoediting cancers, and understanding the effects of immunoediting on cancer progression to escape is an ongoing work in progress. One critical factor that remains poorly understood is how the spatial and geometric cues of the extracellular matrix (ECM) in the tumor microenvironment affect the tumor-T-cell interaction. This is further complicated by ECM remodeling by primary cancer en route to metastasis. To address these challenges, we have developed a dual-agent-based model (ABM) to explore the relationship between ECM fiber geometry, tumor spatial growth, and the adaptive process of T-cell recognition of tumor-associated antigens. Using this model, we demonstrate the influence of ECM fiber orientation on cancer spatiotemporal progression. We compare and contrast the spatial dependence of tumor progression in the setting of circumferentially versus radially packed ECM fibers. By studying the balance of T cell accessibility on tumor recognition and antigen loss. Immune microenvironmental factors, including hypoxia and nutrient concentration, can explain cancer progression secondary to T-cell dysfunction. Overall, our preliminary findings provide a more detailed description of cancer spatiotemporal progression, and our model provides a computational means by which ECM geometry and microenvironmental parameters can be integrated for predicting the outcome of tumor-immune evolution across a number of contexts.

Despite recent improvements in cancer therapy, phenotypic adaptation persists as a significant barrier in overcoming therapeutic resistance. Recent experimental efforts have attempted to minimize cancer cell growth by using increasingly sophisticated drug cycling strategies. However, this search has been slowed owing to the sheer complexity in the number of allowable temporally varying policies, thereby necessitating more efficient computational identification of optimal dosing strategies. In this study, we develop a stochastic description of cellular adaptation wherein temporally adaptive cells select their phenotype based on their prior encounter with an uncertain environmental landscape. We first apply this model to explain distinct growth phenotypes observed experimentally in bacterial systems navigating fluctuating nutrient landscapes. We then extend and apply our stochastic model in experimental collaboration to study prostate cell line-specific optimal adaptation to temporally varying enzalutamide therapy. Using this approach, we predict that under specific drug cycling frequencies, adaptive cells' nutrient availability is universally reduced compared to cells in constant ones, which confirms empirical observations about cancer cell growth.

Introduction: Neoadjuvant therapy (NAT) is considered the standard-of-care for locally advanced breast cancer. Recent studies indicated that magnetic resonance imaging (MRI) data acquired after the first 1-3 cycles of NAT can provide early prediction of breast cancer patient response. However, it remains to be determined when the best times are to collect the longitudinal images to maximize both predictive accuracy and patient convenience. In this study, we seek to establish an in silico framework to address this unmet need by integrating mechanism-based mathematical modeling with Bayesian-based data assimilation. Methods: A TNBC cohort (n = 139) from the ARTEMIS trial was used for this study. For each patient, longitudinal MRIs were collected before (MRI1), during (MRI2), and after (MRI3) the Adriamycin/Cyclophosphamide (A/C) NAT regimen. We have developed a mechanism-based mathematical model to make patient-specific predictions of TNBC response to the A/C therapy. In particular, the model is a reaction-diffusion equation describing the spatiotemporal change in tumor cellularity due to cell migration, proliferation, and treatment-induced death. We implemented the model with a Bayesian-based scheme: Using MRI1 for initialization and MRI2 for calculating the posterior distributions of model parameters, then making predictions at the end of A/C. The standard derivation (SD) of the predicted tumor volume was defined as the uncertainty. The difference between the mean of the predicted tumor volume and the MRI3 measurement was defined as the error. We then optimized to find the optimal day for collecting MRI2 that reduced the uncertainty and error of the model prediction at the completion of A/C. In particular, we generated synthetic data at candidate time points (termed MRI2*; i.e., time points at which we may want to collect additional MRI data) by fitting the model to all collected MRIs, recalibrated the model with the synthetic data MRI2* to make prediction at the completion of A/C, and then evaluated the corresponding prediction uncertainty and error. The date for MRI2* that minimized the prediction uncertainty and error is determined to be the optimal time point for the second imaging session. Results: Preliminary implementation and tests were performed on one patient with tumor volumes derived from the imaging data. The Bayesian-based scheme calibrated the model using the clinically measured MRI1 and MRI2 (i.e., MRI2 at day 30). Comparing the model prediction of the residual tumor volume to the measurement of MRI3, the prediction uncertainty and error were 24.72% and 32.64%, respectively. The identified optimal time point for the mid-treatment imaging session, MRI2* at day 38, provided a minimal prediction uncertainty and error of 13.02% and 7.55%, respectively. Thus, the optimized date for the second MRI resulted in a 47.33% decrease in uncertainty and a 76.87% decrease in error for predicting the residual tumor volume at the end of A/C. Conclusion: These preliminary results demonstrate that our approach has the potential to identify the optimal time point for the second MRI scan of a longitudinal MRI protocol to improve the precision and accuracy of early prediction of TNBC patient response to NAT. Ongoing efforts include extending the implementation to 3D and applying it to more patients. Acknowledgments: NCI U01CA142565, U01CA174706, U24CA226110. CPRIT RR160005. Clinical trial NCT02276443. MDACC Moon Shot Program. MDACC-TACC-Oden Institute Consortium Pilot Project.

Gene drives (GDs) allow scientists to spread a genetic cargo into a target population, even if the cargo is harmful to the carrier organism. GD technology has immense promise in everything from conservation efforts to the control of mosquito-borne diseases. To spread, GDs exploit DNA repair mechanisms to duplicate themselves at the expense of a target gene. However, repair does not always occur as intended, and can produce alleles that are resistant to the GD. Resistance is one of the greatest threats to GD use in the wild and is difficult to study at appropriate scales within laboratory experiments. Current approaches to studying resistance have predominantly relied on a binary paradigm: resistant alleles are either functional or non-functional. Neither resistant allele can be targeted by the GD construct but only the former restores proper genetic functioning to the organism. In this study, we consider the contribution of resistant alleles that are partially functional, and therefore fall outside this paradigm. Partially functional resistance occurs when a resistant allele restores some—but not all—genetic functioning to the organism. Organisms carrying such alleles do not spread the GD as efficiently but may still incur heavy fitness costs. Using a coupled genetic population dynamics model, we study GD performance in a target population with partially functional resistance. In addition to extending the current theoretical framework used to study resistance, we also study the roles played by certain DNA repair mechanisms, making our work generalizable to many target organisms. We pay particular attention to GD performance in certain mosquito species of interest, such as the malaria mosquito Anopheles gambiae, and the dengue mosquito Aedes aegypti. This work provides a key next step in understanding how the mechanisms behind resistance can help or hinder GD success. Furthermore, our work can inform the development of GDs going forward so as to mitigate the risk of control failure due to resistance arising in target populations.

The origin of chromosomes was a major transition in the evolution of complex cellular life. In this talk, we model the origin of chromosomes by considering a simple protocell composed of two types of genes: a “fast gene' with an advantage for gene-level self-replication and a “slow gene' that replicates more slowly at the gene level, but which confers an advantage for protocell-level reproduction. Using a PDE to describe the effects of within-cell and between-cell competition, we find that the gene-level advantage of fast replicators casts a long shadow on the multilevel dynamics of protocell evolution: no level of between-protocell competition can produce coexistence of the fast and slow replicators when the two genes are equally needed for protocell-level reproduction. We find that introducing a “dimer replicator', a linked pair of the slow and fast genes, can allow for long-time coexistence under multilevel competition between fast, slow, and dimer replicators. Our results suggest that the formation of a simple chromosome-like dimer replicator can help to overcome the shadow of lower-level selection and work in concert with multilevel selection to promote coexistence of genes that compete under gene-level replication but are synergistic at a higher level of selection.

Over the past two decades, there has been growing recognition of the need for discipline-situated computational modeling and simulation pedagogy in post-secondary STEM curricula. However, current research in this area remains largely definitional and aspirational in nature, as there are limited empirical studies on how to best support the development of computational expertise in undergraduate students. Outside of computer science programs, a student's exposure to computing education often remains siloed within introductory programming courses that lack meaningful integration with disciplinary content. Furthermore, current practice in early undergraduate computational education in engineering programs tends to focus heavily on the procedural and technical aspects of programming knowledge rather than on the application of computation to problem-solving and design. Because the field of discipline-based computation is under-theorized, traditional instructional approaches have typically defaulted to teaching the cognitive aspects of computation. To build transferable skills and expertise, however, instructors can draw upon constructivist traditions by situating computation within disciplinary contexts. This talk presents computational apprenticeship (an application of the cognitive apprenticeship framework) as a constructivist research and practice framework for developing transferable computational expertise in the undergraduate STEM curriculum. Aspects of the computational apprenticeship model in practice are illustrated using examples from computational biology.