Wednesday, June 16 at 09:30am (PDT)
Wednesday, June 16 at 05:30pm (BST)
Thursday, June 17 01:30am (KST)


Lattice Models and Agent-Based Models in Biology: Linking Individual Properties to Population Properties

Organized by: Bhargav Karamched (Florida State University, United States of America)
Note: this minisymposia has multiple sessions. The second session is MS12-CBBS.

  • Tom Chou (University of California - Los Angeles, United States of America)
    "RNA polymerase and ribosome interactions in transcriptional error correction and translation-transcription coupling"
  • Backtracking of RNA polymerase (RNAP) is an important pausing mechanism during DNA transcription that is part of the error correction process. We model the backtracking mechanism of RNA polymerase which usually happens when the polymerase tries to incorporate a mismatched nucleotide. Previous models have made simplifying assumptions such neglecting the trailing polymerase behind the backtracking polymerase or assuming that the trailing polymerase is stationary. We derive exact analytic solutions of a discrete stochastic model that includes interacting (exclusionary) RNAPs by explicitly showing how a trailing RNAP influences the probability that an error is corrected or incorporated by the leading backtracking RNAP. Moments of conditional first passage times to error correction or error incorporation are also computed. We also develop a very similar model for describing translation-transcriptional coupling during which a ribosome simultaneously elongates (and produces a polypeptide) while interacting with the leading RNAP.
  • Claudia Neuhauser (University of Houston, United States of America)
    "Fighting Cancer with Viruses--Mathematical Models to Guide Therapy"
  • Virotherapy of cancer relies on engineered viruses that selectively attack and kill cancer cells but leave healthy cells unaffected. The success of this therapy relies on the successful establishment of an infection that results in the death of cancer cells. To gain a better understanding of the dynamics, we developed spatially explicit, stochastic models of multi-species interactions to map out under what conditions the symbiont (virus) effectively eliminates the host (cancer cells). I will present rigorous results and conjectures based on simulations. I will report on an experimental system (in vitro and in vivo) that was developed by Dr. David Dingli (Mayo Clinic) and uses this mathematical framework to predict the effectiveness of virotherapy in cancer.
  • James Glazier (Indiana University, United States of America)
    "Multicellular modeling of viral infection and immune response in epithelial tissues and response to drug therapy"
  • Simulations of tissue-specific effects of viral infections like COVID-19 are essential for understanding disease outcomes and optimizing therapies. Such simulations need to support continuous updating in response to rapid advances in understanding, and parallel development by multiple groups. We present an open-source platform for multiscale spatiotemporal simulation of an epithelial tissue, viral infection, cellular immune response and tissue damage. We studied the effects on progression of treatment potency and time of first treatment for an antiviral. We also show an extended version of the simulation with additional immune cell types calibrated to match extensive existing data on the progression of murine influenza infection. Simulations suggest that the microenvironment in which a virus spreads plays a dominant role in disease onset and progression, and that spatially-resolved models may be important to better understand and more reliably predict future health states based on susceptibility of potential lesion sites using spatially resolved patient data on the state of an infection.
  • Joanna Wares (University of Richmond, United States of America)
    "Developing a computational modeling course in the time of COVID-19"
  • What happens when you decide, in January, that you will teach Computational Modeling in Public Health in the coming fall (2020), and then COVID-19 breaks out? You turn your class into a COVID-19 modeling class! Here, I describe efforts to teach upper-level undergraduate mathematics students how to create and analyze their own mathematical models, both differential-equations and agent-based types. I will explain my first attempt at the course design, and how I utilized the wealth of papers and examples provided by the scientific community in 2020 to answer questions about COVID-19. I will also describe some of the research my students developed in the course and then continued in the following semester. In their research, one focus was on understanding the underlying socio-economic inequities in COVID-19 outcomes.

Combining modeling and inference in cell biology

Organized by: Maria-Veronica Ciocanel (Duke University, United States), John Nardini (North Carolina State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS14-CDEV.

  • Alexandria Volkening (Northwestern University, United States)
    "Topological methods for quantitatively describing cell-based patterns"
  • Self-organization is present at many scales in biology, and here I will focus specifically on elucidating how brightly colored cells interact to form skin patterns in zebrafish. Wild-type zebrafish are named for their dark and light stripes, but mutant zebrafish feature variable skin patterns, including spots and labyrinth curves. All of these patterns form as the fish grow due to the interactions of tens of thousands of pigment cells, making agent-based modeling a natural approach for describing pattern formation. By identifying cell interactions that may change to create mutant patterns, the longterm motivation for my work is to help link genes, cell behavior, and visible animal characteristics in fish. However, agent-based models are stochastic and have many parameters, so comparing simulated patterns and fish images is often a qualitative process. Developing analytically tractable continuum models from agent-based systems is one means of addressing these challenges and better understanding the roles of different parameters in pattern formation. Alternatively, methods from topological data analysis can be applied to cell-based systems directly. In this talk, I will overview our models and present quantitative comparisons of in silico and in vivo cell-based patterns using our topological methods.
  • Fiona Macfarlane (University of Saint Andrews, United Kingdom)
    "A hybrid discrete-continuum approach to model Turing pattern formation"
  • We have developed a hybrid discrete-continuum modelling framework to investigate the formation of cellular patterns through the Turing mechanism. In this framework, a stochastic individual-based model of cell migration and proliferation is combined with a reaction-diffusion system for the concentrations of some interacting chemical species. As an illustrative example, we consider a model in which the dynamics of the morphogens are governed by an activator-inhibitor system that gives rise to Turing pre-patterns. The cells then interact with the morphogens in their local area through either of two forms of chemically-dependent cell action: Chemotaxis or chemically-controlled proliferation. We consider both the case of static spatial domains and additionally investigate the case of growing domains. In all cases we are able to derive the corresponding deterministic continuum limits, inferring an appropriate system of PDEs to model the dynamics of the hybrid model. We investigate parameter situations in which the numerical simulations of the PDE models give an accurate description of the hybrid models, and cases where they do not qualitatively match the hybrid models. This framework is intended to present a proof of concept for the ideas underlying the models, with the aim to then apply the related methods to the study of specific patterning and morphogenetic processes in the future.
  • Suzanne Sindi (University of California Merced, United States)
    "Multi-Scale Modeling and Parameter Inference in Yeast Protein Aggregation"
  • Unlike a disease caused by a virus or a bacteria, in prion diseases the infectious agent is created by the host organism itself. Prion proteins are responsible for a variety of neurodegenerative diseases in mammals such as Creutzfeldt-Jakob disease in humans and “mad-cow disease” (Bovine Spongiform Encephalopathy or BSE) in cattle. While these diseases are fatal to mammals, prions are harmful to yeast, making yeast an ideal model organism for prion diseases. Most mathematical approaches to modeling prion dynamics have focused on either the protein dynamics in isolation, absent from a changing cellular environment, or modeling prion dynamics in a population of cells by considering the “average” behavior. However, such models have been unable to recapitulate in vivo properties of yeast prion strains. My group develops physiologically relevant mathematical models by considering both the prion aggregates (which evolve inside individual yeast cells) and the yeast cells (which grow and divide). In this talk, I will present a stochastic biochemical reaction system for protein aggregation and demonstrate that the standard computational assumption - fixed protein monomer mass - leads to incorrect biological conclusions. We relax the mass conservation restriction through the use of an additional “slack” species and discover new regimes of biologically relevant behavior. These regimes necessarily correspond to the biologically feasible regions of parameter space for prion aggregation.
  • Adam MacLean (University of Southern California, United States)
    "Bayesian inference of Calcium signaling dynamic provides a map from single-cell gene expression to cellular phenotypes"
  • Since single-cell RNA sequencing technologies have become widespread, great efforts have been made to develop appropriate computational methods to learn biological features from high dimensional datasets. Much less effort has gone into the important yet challenging task of learning about dynamic processes from genomic data. Here we employ spatial transcriptomic data (MERFISH) linked to dynamic Ca2+ responses in single cells for parameter inference. We quantify cell-cell similarity -- learnt via nonnegative matrix factorization of transcriptomic signatures -- and use it to define informative cell-specific priors. We show that these informative priors dramatically speed up Bayesian parameter inference for an ODE model of Ca2+ dynamics. Analysis of posterior parameter distributions across hundreds of single cells allows us to identify genes driving phenotypic changes and link these genes to specific Calcium pathway parameters that are sensitive to outputs. Finally, we test our ability to predict Ca2+ responses using only the cell-cell similarity. This allows us to quantify the amount of information on a dynamic cell phenotype that is contained in the gene expression data alone.

Numerical methods in biomedical sciences

Organized by: Yifan Wang (University of California, Irvine, USA), Pejman Sanaei (New York Institute of Technology, USA)
Note: this minisymposia has multiple sessions. The second session is MS14-DDMB.

  • Feng Fu (Dartmouth University, USA)
    "Mathematical Modeling of Combination Cancer Immunotherapy"
  • It is of fundamental importance to understand the key mechanisms that govern the progression of cancer and elucidate the often-unknown factors that account for treatment failures. Immunotherapies have had a significant impact, but only in a minority of late-stage lung cancer and melanoma patients. While potentially curative immunotherapies are being rapidly developed and tested, a major barrier is the lack of quantitative models to describe and evaluate their efficacy. We investigate clinically relevant mathematical and in-silico models of cancer cell dynamics for personalized immunotherapy that boost anti-tumor activities of effector immune cells using single-agent checkpoint blockade and their potential combinations. Our work can be used to interpret lab and clinical results and to guide the design of future lab experiments and clinical trials, all with an eye toward model-informed personalized immunotherapy.
  • Pejman Sanaei (Mathematical modeling in tissue engineering, USA)
    "Mathematical modeling in tissue engineering"
  • Cell proliferation within a fluid-filled porous tissue-engineering scaffold depends on a sensitive choice of pore geometry and flow rates: regions of high curvature encourage cell proliferation, while a critical flow rate is required to promote growth for certain cell types. When the flow rate is too slow, the nutrient supply is limited; when it is too fast, cells may be damaged by the high fluid shear stress. As a result, determining appropriate tissue-engineering-construct geometries and operating regimes poses a significant challenge that cannot be addressed by experimentation alone. In this work, we present a mathematical theory for the fluid flow within a pore of a tissue-engineering scaffold, which is coupled to the nutrient concentration as well as the growth of cells on the pore walls. We exploit the slenderness of a pore that is typical in such a scenario, to derive a reduced model that enables a comprehensive analysis of the system to be performed. We derive analytical solutions in a particular case of a nearly piecewise constant growth law and compare these with numerical solutions of the reduced model. Qualitative comparisons of tissue morphologies predicted by our model, with those observed experimentally, are also made. We demonstrate how the simplified system may be used to make predictions on the design of a tissue-engineering scaffold and the appropriate operating regime that ensures a desired level of tissue growth.
  • Yifan Wang (University of California Irvine, USA)
    "Lattice Boltzmann approach to study the evolutionary dynamics of stem-cell driven cancer"
  • We propose a new approach based on the Lattice Boltzmann Method to simulate tumor cell growth dynamics in the crowded intracellular system. The main advantage of this approach is that it resolves the cell-growth process at the mesoscopic level and thereby provides a more accurate and detailed description than the standard continuous approaches. It is also more computationally efficient than agent-based approaches. Moreover, our method can treat non-regular boundary surfaces efficiently and can capture the heterogeneous property of the intercellular micro-environment and the stochasticity in the tumor growth and other phenomena such as cell confinement from the tissue/extracellular matrix structure.
  • Min-jhe Lu (Department of Mathematics, Illinois institute of technology, Chicago, Illinois, USA)
    "Nonliner simulation of vascular tumor growth with a necrotic core and chemotaxis"
  • In this work, we develop a sharp interface tumor growth model to study the effect of both the intratumoral structure using a fixed necrotic core and the extratumoral nutrient supply from vasculature. We first show that our model extends the one by Cristini et al. (Cristini et al., J. Math. Biol., 2003 Mar;46(3):191-224) using linear stability analysis. Then we solve the generalized model using a spectrally accurate boundary integral method in an annular domain with a Robin boundary condition that models tumor vasculature. Our nonlinear simulations reveal the effects of angiogenesis, chemotaxisand necrosis in the development of morphological instabilities. The values of the nutrient concentration with its fluxes and the hydrostatic pressure with its gradients are solved accurately on the boundaries to better understand the balance in the controlling of the necrosis.

Ecological models at the interface of empirical and theoretical research

Organized by: Amanda Laubmeier (Texas Tech University, United States), Kyle Dahlin (University of Georgia, United States)

  • Annabel Meade (North Carolina State University, United States)
    "Population model for the invasive insect Homalodisca vitripennis and the egg parasitoid Cosmocomoidea ashmeadi"
  • The glassy-winged sharpshooter, Homalodisca vitripennis, is an invasive pest which presents a major economic threat to the grape industries in California by spreading a disease-causing bacteria, Xylella fastidiosa. Recently a common enemy of H. vitripennis, certain mymarid parasitoid species including Cosmocomoidea ashmeadi and Cosmocomoidea morrilli, have been studied to use in place of insecticides as a control method. We create a time and temperature dependent mathematical model to analyze data and answer the question: Does the implementation of C. ashmeadi as a biological control method cause a significant decrease in the population of H. vitripennis?
  • Sofya Zaytseva (University of Georgia, United States)
    "Pattern Formation in Intertidal Oyster Reefs"
  • The Eastern oyster population has plummeted over the last century due to unregulated harvesting, effects of pollution and prevalence of disease, making reef restoration of critical importance. While various aspects of reef development have been studied in the past, the importance of water flow and geophysical processes on oyster reef development remains not well understood. This becomes particularly important in reef restoration and can help determine suitable locations and optimal configurations for the construction of artificial reefs. We use drone imagery of an extensive intertidal reef network to investigate the relationships between topography, flow, and reef geometry. This talk will focus on some recent results from our analysis exploring these relationships.
  • Shandelle Henson (Andrews University, United States)
    "Climate Change and Tipping Points for Seabird Colonies in the North American Pacific Northwest"
  • Changes in sea surface temperatures in the Pacific Northwest are associated with changes in reproductive and feeding tactics in colonial seabirds. Warm years in the El Niño–Southern Oscillation are associated with short-term “lifeboat” tactics such as egg cannibalism that are not sustainable over the long term. Mathematical models suggest that prolonged rises in SST can create tipping points that allow colony collapse.

Recent Perspectives on Mathematical Education

Organized by: Stacey Smith? (The University of Ottawa, Canada)
Note: this minisymposia has multiple sessions. The second session is MS14-EDUC.

  • Kara Allum (Oxford University, United Kingdom)
    "Maths is for everyone: why interdisciplinary and DEI focused approaches should be the basis of high school outreach"
  • Mathematics is one of the most abstract topics we learn at high school and whilst the joy of problem-solving appeals to some of us, questions like “why do I need to know this?” or “how is this useful?” are typically asked by everyone else. Mathematics is inherently interdisciplinary within academia, a fact that is often not communicated within high schools or outreach projects, and leads to misinformation around the idea of what a mathematician is and where their work applies. This disconnect continues when we try to ask the question of who can be a mathematician? The primary and high schools we work with and the researchers we send both have big impacts on future engagement, and, when combined with the academic stereotype (and often reality) that every mathematician is a cisgender straight white man, we can disenfranchise a lot of young people before they get to make up their own minds. In this talk, I will describe my experiences working on different types of outreach programs, mathematical or otherwise, and put forward ideas I have learned from these projects that I believe should form the basis of mathematical outreach. I will discuss the power of storytelling, the need to protect curiosity and why we must strive to be more proactive participants within our local communities. Interdisciplinary topics and DEI work are integral factors to outreach and are key to moving the current narrative away from mathematics being exclusive to one where mathematics belongs to everyone.
  • Kathleen Hoffman (University of Maryland, Baltimore County, USA)
    "Extending Quantitative Reasoning in the Biological Sciences"
  • About a decade ago, a call to transform the curriculum in the biological sciences along with the change in the MCAT focus from courses to competencies spurred a flurry of activity surrounding interdisciplinary education, particularly quantitative reasoning in the biological sciences. Funded by HHMI, UMBC, in a joint project with three other universities, set out to develop validated competency-based modules to facilitate quantitative reasoning in the first two biology courses. Results showed a modest increase in quantitative competencies, but a discrepancy in achievement gains between direct entry and transfer students. To mediate this effect, UMBC, along with four community college partners, developed a consortium of faculty and administrators to facilitate quantitative module development in four core biology courses and to facilitate large-scale implementation. Funded by an NSF IUSE grant, the consortium will track student achievement with the intention of both mitigating the achievement gap between direct entry and transfer students, as well as understanding the effect of increased exposure to quantitative modules.
  • Shelby Scott (University of Tennessee at Knoxville, USA)
    "Things I learned as an interdisciplinary graduate student"
  • Graduate school is a confusing and difficult experience for all students, but there are particular challenges that come from being an interdisciplinary early career researcher. In this talk, I will share some of my struggles faced as a biomathematician/ecologist/statistician/data scientist and give insight to some of the positive and negative feelings many of us seem to have during our time as interdisciplinary graduate students. The goal is to open up an honest conversation about the difficulties of wearing multiple hats as an academic and to de-stigmatize some of these experiences.
  • Glenn Ledder (University of Nebraska, Lincoln, USA)
    "A Teaching Module for Mathematical Epidemiology Using Matlab or R"
  • With the enormous impact COVID-19 is having on our students’ lives, there is no better subject to motivate mathematics students than mathematical epidemiology. Add to that the significant amount of misinformation promulgated on the internet and by political actors, and it is clear we have a moral duty, as well as a mathematical one, to teach this subject. The main pedagogical problem we face is that the standard teaching materials on mathematical epidemiology focus on the theory of simple endemic disease models. This is fine as far as it goes, but the crisis we face concerns a complicated disease on an epidemic time scale. Instead of equilibrium analysis of the simplest models, we need a focus on modeling, simulation, and experiment on more realistic models as well as the simplest ones. In particular, we need to address questions about how public health measures impact the progress of an epidemic and “call bullshit” on false or misleading public statements. Our pedagogical challenges are to create materials that allow a student with minimal programming experience to set up virtual experiments in a program-based model implementation and to create meaningful modeling questions that use those experiments. To that end, I have created educational modules for the SIR, SEIR, and SEAIHRD (COVID-19) models, each of which is centered on a suite of programs that encode the model and are carefully designed to have a minimal “model-user interface”, so that students with the barest minimum of programming experience can modify the programs to address specific questions. This presentation will focus on the Matlab version of the SEIR and COVID-19 modules. I will show the programs and how easy they are for novices to use, and I will highlight a few of the experiments and accompanying questions.

Social Networks and Opinion Dynamics

Organized by: Daniel Simonson (University of California, Irvine, USA), Samuel Lopez (University of California, Irvine, USA)

  • Maxi San Miguel ( Institute for Cross-Disciplinary Physics and Complex Systems - Campus Universitat de les Illes Balears, Spain)
    "Coevolution dynamics of opinion and social network"
  • Modeling opinion dynamics of a set of interacting agents requires specifying the social network of interactions and the state (opinion) of the agents, represented as nodes of the network. The links of the network can also have a state, representing for instance attractive or repulsive interactions. In addition, the network might not be fixed, but adaptive with a time dependent topology in which agents can choose and change their neighbors. We introduce such a general dynamical model for binary opinions including the coupled dynamics of the states of the nodes, the states of the links and the topology of the network. We find a transition from a dynamical state of coexisting opinions to a consensus state showing network fragmentation at the transition line. Our results contribute to the description of processes of emergence of social fragmentation and polarization.
  • Tomasz Raducha ( IFISC, Institute for Cross-disciplinary Physics and Complex Systems (UIB-CSIC), Spain)
    "Vulnerabilities of democratic electoral systems: zealot and media-susceptibility"
  • The vulnerability of democratic processes is under scrutiny after scandals related to Cambrige Analytica (2016 U.S. elections, the Brexit referendum, and elections in Kenya). The deceptive use of social media in the US, the European Union and several Asian countries, increased social and political polarization across world regions. Finally, there are straightforward frauds like Crimea referendum and Belarus elections. These challenges are eroding democracy, the most frequent source of governmental power, and raises multiple questions about its vulnerabilities. Democratic systems have countless ways of performing elections, which create different electoral systems (ES). It is therefore in citizens' interest to study and understand how different ESs relate to different vulnerabilities and contemporary challenges. These systems can be analyzed using network science in various layers -- they involve a network of voters in the first place, a network of electoral districts connected by commuting flow for instance, or a network of political parties to give a few examples. It is essential to provide new tools and arguments to the discussion on the evaluation of electoral systems. We aim at comparing different ESs in a dynamical framework. Our novel approach of analyzing electoral systems in such way with all its aspects included, from opinion dynamics in the population of voters to inter-district commuting patterns to seat appointment methods, will help answering questions like: Which electoral systems are more predictable/stable under fluctuations? Which electoral systems are the most robust (or vulnerable) under external and internal influences? Which features of electoral systems make them more (less) stable?
  • Daniel Simonson (University of California, Irvine, USA)
    " The effects of opinion weighting, (dis)agreement, and external influence on social group formation"
  • Opinion dynamics can be modeled by using agent-based simulations, where agents in a population are characterized by binary opinions on a number of different issues. They engage in pairwise interactions, whereby if the agreement level is high, the interlocutor is recognized as an ``ally' and the individual will flip one of their opinions to coincide with the interlocutor; if the agreement is low, they will switch away from the interlocutor. While it is usually assumed that all issues in the opinion vector are equally important, here we investigate how breaking this symmetry influences the dynamics. We find that the model outcomes can be predicted by a single Agreement-Disagreement Score (ADS) in [-1,1]. ADS characterizes how likely individuals in the population are to regard an interlocutor as an ally; low-ADS (very ``cautious') populations tend to converge to a two-faction system with exponentially high convergence times, while high-ADS (very ``trusting') populations tend to converge to a single-faction system relatively fast. In heterogeneous populations characterized by individual issue weighting, individuals that are more ``trusting' are more likely to join the majority group compared to those that are more ``cautious'. In the presence of an influencer, for ADS both near -1 and 1, a single faction tends to emerge, but in the former case it coincides with the influencer's opinions, while in the latter case it is the opposite. Time to fixation is also affected by the presence of an influencer, especially for negative-ADS populations, where it no longer experiences such a large increase near -1. One can say that an influencer unifies the population to align with the source of influence if ADS>1 and to disagree with it if ADS<1, and consensus is reached relatively fast for both extremely ``trusting' and extremely ``cautious' populations.
  • Gyorgy Korniss ( Rensselaer Polytechnic Institute, USA)
    "The Impact of Heterogeneous Thresholds on Social Contagion and Influencing with Multiple Initiators"
  • The threshold model is a simple but classic model of contagion spreading in complex social systems. To capture the complex nature of social influencing we investigate the transition in the behavior of threshold-limited cascades in the presence of multiple initiators as the distribution of thresholds is varied between the two extreme cases of identical thresholds and a uniform distribution. We observe a non-monotonic change in the cascade size as we vary the standard deviation. Further, for a sufficiently large spread in the threshold distribution, the tipping-point behavior of the social influencing process disappears and is replaced by a smooth crossover governed by the size of initiator set. P.D. Karampourniotis, S. Sreenivasan, B.K. Szymanski, and G. Korniss, The Impact of Heterogeneous Thresholds on Social Contagion with Multiple Initiators', PLoS ONE 10(11): e0143020 (2015); P. D. Karampourniotis, B.K. Szymanski, G. Korniss, 'Influence Maximization for Fixed Heterogeneous Thresholds', Scientific Reports 9, 5573 (2019);

Immunobiology and Infection Subgroup mini-symposium

Organized by: Stanca Ciupe (Virginia Tech, United States), Jessica Conway (Penn State University, USA), Amber Smith (University of Tennessee Health Science Center, USA), Jonathan Forde (Hobart and William Smith Colleges, USA)
Note: this minisymposia has multiple sessions. The second session is MS14-IMMU.

  • James Faeder (University of Pittsburg, USA)
    "Multiscale Modeling of Viral Replication and Interferon-mediated Immune Responses"
  • Most intrahost models of viral infections track virus are built on ordinary differential equations that track viral and cell population but that simplify processes at the intracellular level. While these models have yielded key insights into the factors that affect viral load kinetics and have identified how factor such as timing and mechanism can determine treatment efficacy, there are several questions that require more detailed modeling of interactions at the molecular level. In particular, viral replication products and host signaling pathways interact in numerous ways that determine both the quantitative and qualitative outcomes of infection. For example, type I interferon (IFN) responses elicited by virus infection of cells in lymphoid tissues near the sites of infection not only mediate resistance of the infected cells to viral replication, but also may provide systemic resistance. In particular, with encephalitic alphaviruses, the antiviral state is stimulated in the brain early after peripheral infection. It is important to understand the characteristics and cell types involved in this early interferon stimulation as they may be protective from fatal disease. We have developed an experimental model in which the encephalitic alphavirus, eastern equine encephalitis virus (EEEV), infects various types of immune cells in an in vitro culture system. Using this system we are able to measure the kinetics of various steps in viral replication and host cell response, including induction of Type I IFNs and induction of IFN-regulated genes. We will use data from this experimental model to build and calibrate a computational model that will predict cell type specific IFN responses to viral infection and the potentially distal effects of this induction on mitigating viral infections. We will used this integrated experimental and model-based approach to identify key control mechanisms in viral and host dynamics that could be utilized for design of therapies to mitigate the effects of viral infection.
  • Hana Dobrovolny (Texas Christian University, USA)
    "An ODE model of syncytia formation during viral infections"
  • Several viral infections are known to form syncytia, which are multinuclear cells created by cells that have fused together. Little is known, however, about how the syncytia alter viral dynamics. We use an ODE model to study how different assumptions about the viral production of syncytia and lifespan of syncytia change the resulting infection time course. We find that the effect of syncytia on viral titer is only apparent when the basic reproduction number for infection via syncytia formation is similar to the reproduction number for cell free viral transmission. When syncytia fusion rate is high, we find the presence of syncytia can lead to long-lasting infections if viral production is suppressed in syncytia.
  • Daniel Reeves (Fred Hutchinson Cancer Research Center, USA)
    "Merging viral dynamics and phylogenetics reveals host-mediated selection may be sufficient, but not necessary, to explain within-host HIV evolution"
  • Modern HIV research depends crucially on both viral sequencing and population size measurements. To directly link mechanistic biological processes and evolutionary dynamics during HIV infection, we developed multiple within-host phylodynamic (wi-phy) models of HIV primary infection for comparative validation against viral load and evolutionary dynamics data. The most parsimonious and accurate model required no explicit immune selection, suggesting that the host adaptive immune system reduces viral load, but does not drive observed viral evolution. Rather, genetic drift primarily dictates fitness changes. These results hold during early infection. Moreover, during chronic infection — a setting in which adaptive immune selection has been observed -- viral fitness distributions are not largely different from in vitro distributions that emerge without adaptive immunity. Simulations highlight how phylogenetic inference must consider complex viral and immune-cell population dynamics to gain accurate mechanistic insights.
  • Jessica Conway (Penn State University, USA)
    "Unified model of short- and long-term HIV viral rebound"
  • Antiretroviral therapy (ART) effectively controls HIV infection, suppressing HIV viral loads. Typically suspension of therapy is rapidly followed by rebound of viral loads to high, pre-therapy levels. Indeed, a recent study showed that approximately 90% of treatment interruption study participants show viral rebound within at most a few months of therapy suspension, but the remaining 10%, showed viral rebound some months, years, or maybe permanently, after ART suspension. Design of therapeutic interventions to expand this latter group are underway. However, an understanding of the heterogeneity in rebound dynamics, crucial in design of clinical trials to test these interventions, is lacking. We will discuss our branching process model to gain insight into these post-treatment dynamics. Specifically we provide theory that explains both short- and long-term viral rebounds, and post-treatment control, via a branching process model with time-inhomgeneous rates, validated with data from Li et al. (2016). We will discuss the associated biological interpretation and implications. Finally we will provide an example of how our modeling can be used to inform HIV treatment suspension study design.

Vector-borne Diseases: Data, Modeling, and Analysis

Organized by: Jing Chen (Nova Southeastern University, United States), Shigui Ruan (University of Miami, United States), Xi Huo (University of Miami, United States)
Note: this minisymposia has multiple sessions. The second session is MS06-MEPI.

  • Rongsong Liu (University of Wyoming, United States)
    "Using Multiple Dose Pharmacokinetic Models to Predict Bioavailability of Toxins in Vertebrate Herbivores"
  • In the presented work, compartmental pharmacokinetic models are built to predict the concentration of toxic phytochemical in the gastrointestinal tract and blood following oral intake by an individual vertebrate herbivore. The existing single and multiple dose pharmacokinetic models are extended by inclusion of impulsive differential equations which account for an excretion factor whereby unchanged toxins are excreted in the feces due to gastrointestinal mobility. An index α is defined to measure the fraction of bioavailability attributed to the excretion factor of gastrointestinal motility. Sensitivity analysis was conducted and suggests, for any toxin, the bioavailability index α depends mostly on absorption rate of toxin from gastrointestinal tract into the blood, frequency of elimination due to gastrointestinal motility, and the frequency of toxin intake, under the model assumptions.
  • Yanyu Xiao (University of Cincinnati, United States)
    "Examine the dehydration effects on the behaviours of insects"
  • Current insights into the mosquito dehydration response rely on studies that examine specific responses but ultimately fail to provide an encompassing view of mosquito biology. Here, we examined underlying changes in the biology of mosquitoes associated with dehydration. Specifically, we show that dehydration increases blood feeding in the northern house mosquito, Culex pipiens, which was the result of both higher activity and a greater tendency to land on a host. Similar observations were noted for Aedes aegypti and Anopheles quadrimaculatus. RNA-seq and metabolome analyses in C. pipiens following dehydration revealed that factors associated with carbohydrate metabolism are altered, specifically the breakdown of trehalose. Suppression of trehalose breakdown in C. pipiens by RNA interference reduced phenotypes associated with lower hydration levels. Lastly, mesocosm studies for C. pipiens confirmed that dehydrated mosquitoes were more likely to host feed under ecologically relevant conditions. Disease modeling indicates dehydration bouts will likely enhance viral transmission. This dehydration-induced increase in blood feeding is therefore likely to occur regularly and intensify during periods when availability of water is low.
  • William Fitzgibbon (University of Houston, United States)
    "Mathematical Models for the Spatio Temporal Spread of Vector Born Disease in Highly Heterogeneous Domains: Part I"
  • This is a sequenced pair of talks. Part I will be given by the first alphabetically listed author and Part II will be given by the second alphabetically listed author. We are witnessing a global resurgence of vector-borne disease. The term vector-borne disease (VBD) refers to infectious disease that is transmitted between humans or and various animal species and vector arthropods (typically, mosquito, ticks, flies, mites). Among humans they can be potentially fatal and frequency feature a high level of morbidity. They also pose a major threat to livestock and wildlife. Common VBD’s affecting humans are malaria, dengue, yellow fever, Lyme disease, Zika, West Nile Virus, and of course the infamous plague. VBD’, perhaps less widely known than their human counterparts, include screwworm, blue tongue disease, cattle fever, equine encephalitis, and akabane. In these talks we will present a suite of distributed parameter models that describe the spatio-temporal spread of vector born disease. We will pay particular attention issues modelling and analytical issues associated with the incorporation of a high degree of spatial heterogeneity. Part I will focus primarily upon the development of the models while Part II will focus upon analytical issues and challenges presented by models involving this level of complexity.
  • Jeffrey Morgan (University of Houston, United States)
    "Mathematical Models for the Spatio Temporal Spread of Vector Born Disease in Highly Heterogeneous Domains: Part II"
  • This is a sequenced pair of talks. Part I will be given by the first alphabetically listed author and Part II will be given by the second alphabetically listed author. We are witnessing a global resurgence of vector-borne disease.  The term vector-borne disease (VBD) refers to infectious disease that is transmitted between humans or and various animal species and vector arthropods (typically, mosquito, ticks, flies, mites).  Among humans they can be potentially fatal and frequency feature a high level of morbidity.  They also pose a major threat to livestock and wildlife.  Common VBD’s affecting humans are malaria, dengue, yellow fever, Lyme disease, Zika,  West Nile Virus, and of course the infamous plague.  VBD’, perhaps less widely known than their human counterparts, include screwworm, blue tongue disease, cattle fever, equine encephalitis, and akabane. In these talks we will present a suite of distributed parameter models that describe the spatio-temporal spread of vector born disease. We will pay particular attention issues modelling and analytical issues associated with the incorporation of a high degree of spatial heterogeneity. Part I will focus primarily upon the development of the models while Part II  will focus upon analytical issues and challenges presented by models involving this level of complexity. 

Data-driven methods for biological modeling in industry

Organized by: Kevin Flores (North Carolina State University, USA)
Note: this minisymposia has multiple sessions. The second session is MS14-MFBM.

  • Anna Sher (Pfizer, USA)
    "Quantitative Systems Pharmacology (QSP) in cardiovascular disease: Preclinical case studies with real-world data"
  • Many pharmaceutical companies are starting to utilize mechanistic modeling of physiological systems, in particular Quantitative Systems Pharmacology (QSP) modeling, at all stages of drug discovery and development, including exploratory, preclinical, and clinical studies. At Pfizer, ongoing efforts in cardiovascular and metabolic programs involve investigating target rationale, preclinical to clinical translation, drug efficacy and safety using systems modeling and simulations of various aspects of cardiometabolic abnormalities. I will discuss modeling and simulation techniques used in these efforts and highlight challenges related to the incorporation of real-world data preclinically. Examples will include Metabolic Flux Analysis as well as translation from cellular to whole heart mechanical function studies.
  • Doris Fuertinger (Fresenius Medical Care, Germany)
    "1 year of precision therapy: Experiences in optimal drug administration based on an individualized biomathematical anemia model"
  • The majority of patients suffering from end-stage kidney disease develop anemia at some point. Management of anemia with erythropoiesis stimulating agents (ESA) has been established more than three decades ago, however, it remains difficult to stabilize hemoglobin levels within the desired target range. We developed a comprehensive mathematical model that describes the reproduction of red blood cells and the effect of ESAs on it. The resulting system of hyperbolic partial differential equations is adapted to individual patients using routine clinical data by estimating a set of key parameters on the individual level. A nonlinear model predictive controller was designed around the PDE model incorporating several techniques used to create robust and adaptive feedback control systems. The resulting software solution is currently used in a randomized clinical trial. Challenges around adapting a complex PDE system to noisy and missing data will be addressed and interim results from the clinical study presented.
  • Alhaji Cherif (Renal Research Institute, USA)
    "Bone and mineral disturbances in uremic patients"
  • Reduced renal function has a significant impact on a myriad of interlinked secondary pathophysiological abnormalities, including metabolic acidemia, and mineral and bone disorder (CKD-MBD), which comprise secondary hyperparathyroidism (SHPT) and vascular calcification. These sequelae contribute to increased morbidity and mortality in patients with chronic kidney and end-stage renal diseases. We developed a multi-scale comprehensive physiology-based mathematical model describing bone remodeling and mineral homeostasis that enables in silico exploration of the ramifications of disease- and therapy-induced disturbances Using a multi-scale mechanistic physiology-based model quantitating the interrelations of osteoclasts, osteoblasts, and osteocytes on bone remodeling, we incorporate intercellular and intracellular signaling pathways, cytokines, parathyroid hormone (PTH), sclerostin, and endocrine and paracrine feedbacks (Cherif et al., ΝDΤ 2018, 33 (Suppl. 1): 165–166). The predictions of the model are demonstrated by comparing model results of different pathologies (e.g., primary hyperparathyroidism (PHPT) and SHPT, chronic metabolic acidemia, uremia) to clinical observations. In addition, we explore the effect of altered PTH (teriparatide) administration regimen (e.g., dosing frequency and amplitude) on bone catabolism and anabolism, respectively. Our model correctly predicts clinically observed responses to induced primary and secondary hyperparathyroidism, metabolic acidosis, and their impact on extracellular calcium (Ca) and phosphate (PO4) levels and bone mineral density (BMD). In particular, the model predicts the catabolic effect of metabolic acidosis on bone remodeling, including decreased bone mineral density, and increased efflux of Ca and PO4 from the bone. The model shows the differential responses of osteo-anabolic and catabolic effects of continuously and intermittently elevated levels of PTH (teriparatide), respectively. Furthermore, we observe that intermittent administration of PTH with a high frequency and amplitude induces bone catabolism similar to that seen in pathologies with continuously elevated PTH (i.e., PHT, or SHPT). Low PTH frequency with high dosing amplitude induces both osteoclastic and osteoblastic activities, but the net result is bone anabolism. Our results suggest that both frequency and amplitude of PTH (teriparatide) cycling affect the balance of osteo-catabolic and -anabolic effects, and there exists optimal PTH (teriparatide) frequency-amplitude combinations that enhance anabolic gains. The model provides an opportunity to investigate the effects of reduced renal function on the complex interlinked pathophysiological processes of CKD-MBD. The in-silico assessment can serve as a complementary tool for (1) gaining further insights into the features of bone and mineral metabolism, (2) exploring optimal therapeutic modalities for patients with metabolic bone diseases, and minimize unintended disease-specific outcomes, and (3) performing virtual clinical trials for newly emerging and off-label therapeutic options.
  • Malidi Ahamadi (Amgen, USA)
    "Disease progression platform for Leucine-Rich Repeat Kinase 2 in Parkinson's Disease to Inform Clinical Trial Designs"
  • Drug discovery and development of new therapeutics for Parkinson’s Disease (PD) has a high attrition rate which has been attributed to incomplete understanding of the complex pathophysiology of neurodegenerative disorders and difficulties in designing efficient clinical trials to develop new disease modifying agents among other several factors. Clinical assessments (e.g., disability or quality of life scales) are affected/confounded by symptomatic effects of therapy and are unable to differentiate this effect from disease-modification, at least in the short-term. A quantitative assessment of patient characteristics and patient enrichment is one of valuable tools to improve clinical trial efficiency. A disease progression model1,2, identifying relevant patient characteristics impacting the temporal change in disease status assessed using Movement Disorder Society-Unified Parkinson's disease rating scale, was developed to evaluate optimal study designs. Results showed that the progression rate in motor symptoms in individuals with PD who carry a leucine-rich repeat kinase 2 (LRRK2) mutation was slightly slower (~0.170 points/month) compared to idiopathic PD patients (~0.222 points/month). Trial simulations showed that for a non-enriched placebo-controlled clinical trial approximately 70 subjects/arm would be required to detect a drug effect of 50% reduction in the progression rate with 80% probability. Whereas 85, 93 and 100 subjects/arm would be required for an enriched clinical trial with 30%, 50% and 70% subjects with LRRK2 mutations, respectively, to detect a 50% drug effect with 80% power. These findings are expected to play an important role in designing long-term trials for PD programs. Reference 1. Malidi Ahamadi et al., Development of a Disease Progression Model for Leucine-Rich Repeat Kinase 2 in Parkinson's Disease to Inform Clinical Trial Designs, Clin Pharmacol Ther, Volume 107, Number 3, March 2020. 2. Malidi Ahamadi et al., A disease progression model to quantify the non‐motor symptoms of Parkinson’s disease in participants with leucine‐rich repeat kinase 2 mutation, Clin Pharmacol Ther., 2021 Apr 24. doi: 10.1002/cpt.2277.

Dynamics of hematopoiesis in health and disease - from governing principles to clinical implications

Organized by: Peter Ashcroft (ETH Zurich, Switzerland), Tony Humphries (McGill University, Canada), Morten Andersen (Roskilde University, Denmark)
Note: this minisymposia has multiple sessions. The second session is MS12-MMPB.

  • Lora Bailey (Grand Valley State University, USA)
    "The resilience of hematopoietic feedback networks against mutations"
  • In hematopoietic systems, cell fate decisions such as stem cell differentiation or differentiated cell death may be controlled by cell populations through cell-to-cell signaling to keep the system in a state of homeostasis. By examining different feedback networks mathematically, we can determine not only which feedback networks are possible, but which have greater resilience against mutations. While networks with exactly one feedback loop are sufficient for maintaining homeostasis, they are all equally vulnerable to dangerous mutations that alter the present feedback and can lead to unlimited growth of cancerous populations. Therefore, a network with multiple, redundant feedback loops appears evolutionarily advantageous. We discovered that these redundant networks have varying degrees of resilience against mutations. For some redundant networks, any mutation that weakens or eliminates one of the existing feedback loops results in the growth of the cancerous stem cell population, while for other redundant networks this same type of alteration can lead to a depletion of the cancerous stem cell population and may slow down further unwanted evolution.
  • Mia Brunetti (Université de Montréal, Centre de recherche du CHU Sainte-Justine, Canada)
    "Mathematical modelling of the pre-leukemic phase of AML to evaluate clonal reduction therapeutic strategies"
  • Acute myeloid leukemia (AML) is an aggressive blood cancer subtype characterized by the uncontrolled proliferation of myeloblasts in the bone marrow and the blood. While rare, this disease has one of the highest mortality rates of any leukemias. The inefficiency of standard therapies, which target leukemic cells directly, highlights the need for a new approach to treating AML. Previous studies identified a premalignant phase preceding the onset of AML orchestrated by pre-leukemic stem cells (pre-LSCs). Pre-LSCs outcompete healthy hematopoietic stem cells and allow for AML to develop through their clonal expansion and the acquisition of secondary mutations. More recently, studies have suggested that different approved medications target pre-LSCs. These clonal reduction strategies could completely prevent the evolution of AML; however a better understanding of their impact on hematopoiesis is required. In response, we developed a Moran model of hematopoietic stem cells dynamics in the pre-leukemic phase. To this model, we integrated population pharmacokinetic-pharmacodynamics (PK-PD) models to investigate the clonal reduction potential of several candidate drugs. Our results suggest that three cardiac glycosides (proscillaridin A, digoxin and ouabain) reduce the expansion of premalignant stem cells through a decrease in pre-LSC viability, underlining the prospect of these treatments for AML.
  • Derek Park (Department of Integrated Mathematical Oncology, Moffitt Cancer Center, USA)
    "Deep Reinforcement Learning of Optimal Chemotherapy Scheduling Demonstrates a Robustness vs. Performance Tradeoff in Patient Outcomes"
  • Hematopoietic and immune dynamics are a complex system that often underpins success or failure for cancer chemotherapy. While multiple mathematical models exist for simulating cancer treatment and response, there remains a significant deficit in regards to optimization and getting cohesive, generalizable strategies. Here, we present a deep reinforcement learning framework to optimize previously established models of hematopoietic and immune dynamics during chemotherapy. By testing differing reward mechanisms and training on biased cohorts, we demonstrate a robustness-performance trade-off when it comes to treating aggressive versus less-aggressive tumors. Finally, we present how this framework can be generalized to other hematopoietic models in cancer treatment settings.
  • John Higgins (Department of Systems Biology, Harvard Medical School; Department of Pathology, Massachusetts General Hospital, USA)
    "Population dynamics of circulating blood cells in the pathogenesis and diagnosis of some common diseases"
  • Circulating populations of red (RBC) and white blood cells and platelets in humans are tightly regulated, and rates of production, maturation, and turnover are modulated in response to disease. Anemia or low red blood cell count is a common early finding in diseases ranging from infection to cancer to malnutrition, and persistence of anemia is associated with poor patient outcomes. The age distribution of the circulating cell populations provides a history of disease-induced perturbations and homeostatic responses, but it is not currently feasible to measure these distributions. Standard clinical blood counts (CBCs) report only a handful of blood cell population statistics, but CBCs usually involve thousands of single-cell measurements. Building on existing theory and analysis, we have developed models of the RBC age distribution that use these and other routine clinical data sets to enable inferences about the RBC age distribution and how it is altered in common disease states. These models suggest for instance that the healthy response to blood loss often entails not only the recognized compensatory increase in production of new cells but also an unappreciated decrease in turnover of old cells, a response which would also serve to mitigate the effects of the loss.

Mathematical modeling approaches to understanding pain processing and chronic pain therapies

Organized by: Jennifer Crodelle (Middlebury College, USA), Kevin Hannay (University of Michigan, USA), Victoria Booth (University of Michigan, USA)

  • Jennifer Crodelle (Middlebury College, USA)
    "Firing-rate models for analyzing spinal circuit motifs underlying chronic pain"
  • Neuronal circuitries underlying the processing of pain signaling in the dorsal horn of the spinal cord are complex and not yet completely understood. In addition, changes induced in those circuitries due to nerve injury in chronic pain patients have been attributed to multiple pathologies at the cellular and synaptic levels. Using a firing-rate model formalism for activity of projection and interneuron neuronal populations, we construct models of multiple identified microcircuits that process mechanical sensory and nociceptive input to analyze how their parallel filtering of incoming signals affects projection neuron responses. We use the model to investigate how different proposed chronic pain pathologies disrupt and distort microcircuit processing to result in allodynia and hyperalgesia.
  • Warren Grill (Department of Biomedical Engineering, Duke University, USA)
    "Network Models to Analyze and Design Spinal Cord Stimulation for Chronic Pain"
  • Spinal cord stimulation (SCS) is an established treatment for chronic pain, but neither the neural mechanisms underlying SCS nor the relationship between the applied parameters of SCS and its clinical efficacy have been fully characterized. We developed and validated biophysical models of dorsal column axons as well as the dorsal horn neural circuit that processes peripheral sensory inputs, including nociceptive information. We simulated the effects of SCS across a range of frequencies and amplitudes on the activity of model dorsal column axons and model wide dynamic range projection neurons. SCS applied at amplitudes as low as 60% of the predicted sensory threshold activated model dorsal column axons, and the pattern of resulting activity was irregular and strongly dependent on the stimulation amplitude. These model-based predictions were validated with in vivo recordings from single dorsal column axons in anesthetized rats. The increased activity in dorsal column axons generated by SCS drove activity in model inhibitory interneurons and subsequently reduced model wide dynamic range neuron firing rates. Changes in model wide dynamic range neuron firing rate varied non-monotonically with stimulation amplitude and rate, and maximum inhibition occurred at 75-85% of sensory threshold and at rates between 50-90 Hz. Further in vivo recordings showed that net inhibition of putatively excitatory neurons was maximal at 80% of the predicted sensory threshold. The new understanding resulting from the implementation and validation of biophysically-based computations models provides a platform to guide the design of novel methods of stimulation
  • Steven A Prescott (Neurosciences and Mental Health, The Hospital for Sick Children; Department of Physiology and Institute of Biomedical Engineering, University of Toronto , Canada)
    "Altered processing of tactile input due to chloride dysregulation in the spinal dorsal horn "
  • Synaptic inhibition in the dorsal horn of the spinal cord plays a key role in processing somatosensory input. Weakened inhibition can cause light touch to be mistakenly perceived as painful – a phenomenon known as mechanical allodynia, which is common after nerve injury. Nerve injury induces many changes in the spinal dorsal horn, including weakened inhibition. This disinhibition is due primarily to chloride dysregulation caused by downregulation of the potassium-chloride co-transporter KCC2. KCC2 normally keeps intracellular chloride at a low concentration, thus maintaining the chloride driving force that GABAA and glycine receptors rely on to mediate inhibition. Weakened inhibition causes receptive fields to expand, which in turn affects spatial summation. Weakened inhibition also ungates polysynaptic pathways, allowing low-threshold inputs to activate projection neurons that are normally activated exclusively by high-threshold inputs. In this talk, I will discuss experimental data and our efforts to incorporate those data into a circuit-level model of the spinal dorsal horn. 
  • Scott Lempka (Department of Biomedical Engineering, University of Michigan; Department of Anesthesiology, University of Michigan; Biointerfaces Institute, University of Michigan, USA)
    "Computational modeling of neural recruitment during spinal cord stimulation for pain"
  • Spinal cord stimulation (SCS) is a popular neurostimulation therapy for severe chronic pain. To improve stimulation efficacy, multiple modes are now used in the clinic. Clinical observations have produced speculation that these modes target different neural elements and/or work via distinct mechanisms of action. However, in humans, these hypotheses cannot be conclusively answered via experimental methods. Therefore, we utilized computational modeling to assess the response of primary afferents, interneurons, and projection neurons to multiple forms of SCS. We used this modeling approach to understand how various technical and physiological factors, such as neuron geometry and waveform patterns (e.g., burst and kilohertz-frequency SCS), affect the cellular response to SCS. In our simulations, local cell thresholds were always higher than afferent thresholds, arguing against direct recruitment of these interneurons and projection neurons. Furthermore, all of the clinical SCS waveforms had the same relative neural recruitment order, albeit with different absolute thresholds. This result suggests that these SCS modalities do not exert differential effects through distinct recruitment profiles. These results motivate future work to contextualize clinical observations across conventional and emerging SCS paradigms.

Frontiers in Mathematical Oncology

Organized by: Kasia Rejniak & Heiko Enderling (Moffitt Cancer Center, USA)

  • Thomas E. Yankeelov (The University of Texas at Austin, USA)
    "Imaging-based mathematical modeling of brain cancer across scales"
  • Our lab is focused on developing tumor forecasting methods by integrating advanced imaging technologies with predictive, mathematical models to forecast tumor growth and treatment response. In this presentation, we will provide an overview of three vignettes in mathematical oncology that span the in vitro (cells), in vivo pre-clinical (rats), and in vivo clinical (human) scales in brain cancer. Each project employs quantitative imaging to calibrate an appropriate mathematical model to predict how the tumors grow, how they respond to therapy, or how the therapy is delivered. The first vignette employs time resolved microscopy data to calibrate a system of ordinary differential equations to predict the response of glioma cells to single- and multi-fraction radiation therapy in vitro. We then move to in vivo, pre-clinical studies where we make use of quantitative magnetic resonance imaging (MRI) data reporting on cellularity and perfusion to calibrate a system of reaction diffusion models to predict the response of glioma cells to single- and multi-fraction radiation therapy in a murine model of brain cancer. The final vignette is focused on employing MRI, x-ray computed tomography (CT), and single photon emission computed tomography (SPECT) to calibrate a reaction-diffusion-advection equation to predict and optimize the spatio-temporal distribution of radiolabeled liposomes for the treatment of recurrent glioblastoma multiforme in patients. The long-term goal of these studies is to provide a rigorous, but practical, experimental-computational approach describing tumor development, informed and validated by readily available imaging data.
  • Arne Traulsen (Max Planck Institute for Evolutionary Biology, Germany)
    "Measuring cancer heterogeneity and possibilities of exploiting it in treatment"
  • Evolving populations naturally diversify. For populations of cancer cells, this has been extensively explored on the genotypic level and recognized as a potential problem in treatment. Phenotypic diversity, on the other hand, is typically harder to measure, but it may also be directly relevant for treatment, especially when different treatment options are available. Theoretical models show that cancer progression could be delayed substantially if the current phenotypic state can be taken into account in the choice of therapy.
  • Angélique Stéphanou (University of Grenoble, France)
    "Cell metabolism and intracellular acidity regulation in cancer cells, from experimental characterization to computational models with therapeutic perspectives"
  • The metabolism of cancer cells is characterized by increased glycolysis due to local hypoxic conditions. Glycolysis in turn induces an increase in acidity which is detrimental to cells. Cancer cells, however, exhibit a higher resistance to acidity than normal cells due to a better ability to regulate their intracellular pH. We have experimentally characterized the regulatory capacity of two glioma cell lines using fluorescence microscopy. We observed that the regulation of acidity is not the same for the two cell lines. This has consequences for cellular aggressiveness, metastatic potential and treatment planning since the main drug used against glioblastoma is highly pH dependent. Theoretically, we revised a model of cellular metabolism to specifically take into account the influence of pH on cellular metabolic adaptation. The model suggests that the Warburg effect, often described as a hallmark of cancer, can actually be viewed as a transient adaptation mechanism to a disturbed environment rather than an inherent characteristic of the cancer cell. As such, targeting the acidic environment rather than targeting the cancer cell could offer a good alternative therapeutic strategy.
  • Elizabeth Wayne (Carnegie Mellon University, USA)
    "Developing experimental and mathematical models to measure changes in tumor associate macrophage polarization in response to immunotherapy"
  • Tumor associated macrophages (TAMs) are a significant player in cancer microenvironment. They can comprise 50%-80% of a solid tumor mass and M2, anti-inflammatory polarized TAMs are correlated with poorer clinical outcomes. Numerous therapeutic strategies attempt to modulate TAM polarization to decrease tumor growth. However, macrophage polarization is dependent on a number of intrinsic and extrinsic factors. Understanding the factors government TAM polarization can help us understand therapeutic response heterogeneity. Here the talk will discuss experimental models for deciphering the interplay of TAM polarization, drug accumulation, and tumor growth. Moreover, this talk will discuss ideas for developing models that work in tandem with experimental data. Being able to experimentally and mathematically model the effect of immunomodulatory drugs on TAM polarization could enhance decision making in personalized cancer treatment.