Organized by: Bogdan Kazmierczak (Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland), Je-Chiang Tsai (Department of Mathematics, National Tsing Hua University, Taiwan)

• Hirofumi Izuhara (University of Miyazaki, Japan)
  "On the spreading front arising in mathematical models of population dynamics"
Understanding the invasion processes of biological species is a fundamental issue in ecology. Several mathematical models have been proposed to estimate the spreading speed of species. In recent decades, it was reported that some mathematical models of population dynamics have an explicit form of the evolution equations for the spreading front, which are represented by free boundary problems such as the Stefan-like problem. To understand the formation of the spreading front, we consider the singular limit of reaction-diffusion models and give some interpretations for spreading front from the viewpoint of modeling.
• Dariusz Wrzosek (University of Warsaw, Poland)
  "Chemical signalling and pattern formation in predator-prey models"
Chemical signalling is an ubiquitous mechanism which impacts distribution of species in space and time . Its role seems to be crucial in the case of patterning in homogeneous landscapes. Many chemicals (e.g. pheromones, kairomones) released by plants and animals are used as means of inter and intraspecific communication. Olfaction is a primary means by which prey detect predators and trigger anti-predator responses. In this talk based on joint papers with Purnedu Mishra we consider the role of repulsive chemotaxis in predator-prey models and using qualitative analytical methods and simulations show complex behaviour of solutions depending on model structure and parameters.
• Tomasz Lipniacki (Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland)
  "Traveling and standing fronts on curved surfaces"
We analyze heteroclinic traveling waves propagating on two dimensional manifolds to show that the geometric modification of the front velocity is proportional to the geodesic curvature of the front line. As a result, on surfaces of concave domains, stable standing fronts can be formed on lines of constant geodesic curvature. These lines minimize the geometric functional describing the system’s energy, consisting of terms proportional to the front line-length and to the inclosed surface area. Front stabilization at portions of surface with negative Gaussian curvature, provides a mechanism of pattern formation. In contrast to the mechanism associated with the Turing instability, the proposed mechanism requires only a single scalar bistable reaction–diffusion equation and connects the intrinsic surface geometry with the arising pattern. By considering a system of equations modeling boundary-volume interactions, we show that polarization of the boundary may induce a corresponding polarization in the volume.
• Tilmann Glimm (Western Washington University, USA)
  "Modeling interplay of pattern formation and cell phenotype transitions during limb cartilage formation"
A regulatory network consisting of two  galactoside-binding proteins, galectins  Gal-1A and Gal-8 and their counterreceptors, mediates the spatial patterning  of the avian limb skeleton through the patterned morphogenesis of mesenchymal  condensations. Formation of the pattern can be modeled as a reaction-diffusion-adhesion process, wherein the galectins form a mutually self-enhancing expression network via the respective counterreceptors, while their diffusion, Gal-1A-mediated cell adhesion and its antagonism  by Gal-8 determines the spatial separation of mesenchymal protocondensations. A mathematical consists of a system of parabolic PDEs with nonlocal advection terms that model cell-cell adhesion. Apart from generating spatial patterns, the dynamical system of the underlying galectin reaction network is interesting in its own right and can be completely examined with analytical means. We identify two stable steady states: where the concentrations of both the galectins are respectively, negligible and very high.  We give an explicit Lyapunov function, which shows that there are no periodic solutions. Our model therefore predicts that the galectin network may exist in low expression and high expression states separated in space or time without any intermediate states.  We verify these predictions in experiments  performed with high density micromass cultures of chick limb mesenchymal cells and observe that cells inside and outside the precartilage protocondensations exhibit distinct behaviors with respect to galectin expression, motility, and spreading. The interactional complexity of the Gal-1 and -8-based  patterning network is therefore sufficient to partition the mesenchymal cell population into two discrete cell-types, which can be spatially patterned when incorporated into a diffusion-enabled system.

Organized by: Magdalena Stolarska (University of St. Thomas, United States), Lisanne Rens (Delft University of Technology, Netherlands)
Note: this minisymposia has multiple sessions. The second session is MS06-CDEV.

• Qiyao Peng (Delft University of Technology, Netherlands)
  "A cell shape evolution model for wound contraction and cancer cell metastasis using morphoelasticity"
Cells may attain various shapes and sizes. It has been widely documented that cell geometry influences cellular activities like cell growth and death, cell mobility and adhesion to the direct environment. The shape of a motile cell is determined by its boundaries, which dynamically vary with a local balance between retraction and protrusion. During wound healing, epidermal cells alter their shape for re-epithelialization and fibroblasts (spindle shape) differentiate into myofibroblasts (dendric shape) to regenerate collagen bundles in the extracellular matrix, while they exert traction forces causing skin contraction. For cancer cell metastasis, which is the main reason of death of cancer patients, cancer cells need to deform in order to migrate through and around obstacles during invasion and they are observed to apply traction forces on their immediate environment. We developed a phenomenological model to simulate cell shape evolution during cell migration, based on the work in [1] and [2], where the traction forces exerted by the cells were not yet considered. Plastic deformations of the direct environment of the cells are modeled by morphoelasticity theory and point forces, which result into partial differential equations describing the momentum balance with Dirac Delta distributions for point forces over the boundary elements of the cells. The partial differential equations are solved by finite-element methods. In our model, the cell membrane is split into line segments by nodal points, and each point is connected to the cell center by an elastic spring to maintain the cell cytoskeleton (see Figure 1). Together with chemotaxis/mechanotaxis, passive convection and random walk, the displacement of the nodal point is determined. Hence, the cell shape evolves over time during cell migration. To validate the model, we managed to reproduce the most important trends observed in the experiment in [3]. The model can be applied to mimic various (microscopic) biological observations with several equilibrium shapes of cell, for instance, circular, elliptic and hypercloid-shaped. These equilibrium shapes are characteristic for the phenotype of the cell. Furthermore, the current model provides a basis that can be expanded to describe more experimentally observed phenomena in cell geometry. For more details about this part of work, we refer to [4]. References: [1] Chen J, Weihs D, Dijk MV, Vermolen FJ (2018) A phenomenological model for cell and nucleus deformation during cancer metastasis. Biomechanics and Modeling in Mechanobiology 17(5):1429–1450, DOI 10.1007/s10237-018-1036-5, URL https://doi.org/10.1007/s10237-018-1036-5 [2] Vermolen FJ, Gefen A (2012) A phenomenological model for chemico-mechanically induced cell shape changes during migration and cell–cell contacts. Biomechanics and Modeling in Mechanobiology 12(2):301–323, DOI 10.1007/s10237-012-0400-0, URL https://doi.org/10.1007/s10237-012-0400-0 [3] Mak M, Reinhart-King CA, Erickson D (2013) Elucidating mechanical transition effects of invading cancer cells with a subnucleus-scaled microfluidic serial dimensional modulation device. Lab Chip 13(3):340–348, DOI 10.1039/c2lc41117b, URL https://doi.org/10.1039/c2lc41117b [4] Peng Q, Vermolen FJ and Weihs D (2021) A Formalism for Modelling Traction forces and Cell Shape Evolution during Cell Migration in Various Biomedical Processes. Journal Biomechanics and Modeling in Mechanobiology. Online from April 2021.
• Haryana Thomas (University at Buffalo, The State University of New York, United States)
  "Excess Collagen Deposition in Diabetic Kidney Disease Enhances Cellular Communication: A Mathematical Model"
Diabetic kidney disease is a significant health burden in the US and worldwide. During diabetic kidney disease collagen deposition occurs in the mesangium, a tissue located at the center of the filtration unit of the kidney. The collagen deposition that occurs in the mesangium changes the transport property of the matrix, and, therefore, the ability of signaling molecules to traverse through that medium. The extent to which collagen deposition impacts the ability of glomerular cells to communicate has not been previously investigated. Using established models, we investigated whether collagen deposition impacts glomerular cell communication. We hypothesize that the pathological deposition of collagen decreases the ability of glomerular cells to communicate. Our model predicted that collagen deposition enhances the signaling range of the mesangial cell. This enhancement can disrupt the controlled, localized inter-cellular signaling that occurs in health and thus contribute to the exacerbation of diabetic kidney damage. Previously, many models have been developed to study the parameters that impact the signaling range of cells, however, the mathematical interrogation of inter-cellular signaling in the context of diabetic kidney damage has not been previously done. The novel insight gained from this mathematical study enhances our understanding of how pathological tissue damage induced by diabetes contributes to the disruption of cellular function.
• Robyn Shuttleworth (University of Saskatchewan, Canada)
  "Cell-scale degradation of peritumoural extracellular matrix fibre network and its role within tissue-scale cancer invasion"
Local cancer invasion of tissue is a complex, multiscale process which plays an essential role in tumour progression. During the interaction between cancer cell population and the extracellular matrix (ECM), of key importance is the role played by both bulk two-scale dynamics of ECM fibres within collective movement of the tumour cells and the multiscale leading-edge dynamics driven by proteolytic activity of the matrix-degrading enzymes (MDEs) that are secreted by the cancer cells. We focus on understanding the cell-scale cross talk between the micro-scale parts of these two multiscale subsystems which get to interact directly in the peritumoural region, with immediate consequences both for MDE micro-dynamics occurring at the leading edge of the tumour and for the cell-scale rearrangement of the naturally oriented ECM fibres in the peritumoural region, ultimately influencing the way a tumour progresses in the surrounding tissue.
• Katarzyna Rejniak (H. Lee Moffitt Cancer Center & Research Institute, United States)
  "ECM mechanical and metabolic architecture during early ductal invasions"
Progression from a ductal carcinoma in situ (DCIS) to an invasive tumor is a major step initiating a devastating and often lethal metastatic cascade. One sentinel event that initiate this process is the development of ductal microinvasions, i.e., small cohorts of tumor cells that breach the basement membrane surrounding the duct and migrate through the extracellular matrix (ECM) leading to irreversible changes in tumor and stromal architecture. We used a combination of advanced image analysis techniques applied to patients’ histology data to extract features which identify specific properties of individual tumor cells inside the duct and on the invasive front. By integrating these histology-based data with a hybrid agent-based mathematical model, we investigated the biomechanical interactions between the cells and the ECM fiber architecture, and microenvironmental physical and metabolic features that define tumor niche prone to microinvasions.

Organized by: Elisenda Feliu (University of Copenhagen, Denmark), Casian Pantea (West Virginia University, USA)
Note: this minisymposia has multiple sessions. The second session is MS06-DDMB.

• Anne Shiu (Texas A&M University, USA)
  "Absolute concentration robustness in networks with many conservation laws"
The concept of absolute concentration robustness (ACR) was introduced by Shinar and Feinberg in their investigations into how biochemical systems maintain their function despite changes in the environment. A reaction system exhibits ACR in some species if the positive steady-state value of that species does not depend on initial conditions. Mathematically, this means that the positive part of the variety of the steady-state ideal lies entirely in a hyperplane of the form x_i=c, for some c>0. Deciding whether a given reaction system -- or those arising from some reaction network -- exhibits ACR is difficult in general, but this talk describes how for many simple networks, assessing ACR is straightforward. Indeed, our criteria for ACR can be performed by simply inspecting a network or its standard embedding into Euclidean space. Our main results pertain to networks with many conservation laws, so that all reactions are parallel to one other. Such 'one-dimensional' networks include those networks having only one species. We also consider networks with only two reactions, and show that ACR is characterized by a well-known criterion of Shinar and Feinberg. Finally, up to some natural ACR-preserving operations -- relabeling species, lengthening a reaction, and so on -- only three families of networks with two reactions and two species have ACR.
• Stefan Mueller (University of Vienna, Austria)
  "Monomial parametrizations of positive equilibria"
We consider positive steady states of chemical reaction networks with (generalized) mass-action kinetics that allow a monomial parametrization. The latter is often a prerequisite in applications where one studies phenomena such as multistationarity and absolute concentration robustness. In particular, we review results on complex-balanced equilibria (special equilibria given by binomial equations) and toric steady states (where all steady states are binomial). For example, a recent result states that a network with mass-action kinetics has toric steady states if it is dynamically equivalent to a network with generalized mass-action kinetics that has zero effective and kinetic-order deficiencies and hence complex-balanced (and no other) equilibria. Finally, we discuss steps towards a characterization of networks with monomial parametrizations.
• Badal Joshi (California State University San Marcos, USA)
  "Preserving Robust Output despite highly variable reactant supplies"
A cell/biochemical network must produce a consistently robust, easily readable output when interacting with its environment. However, the internal conditions of the cell and the available supplies of reactants are highly variable. To overcome this, the biochemical network must have architecture which is capable of producing the same output despite variations in reactant supplies, a property we will refer to as output robustness. As a possible means of achieving a robust system output, Shinar and Feinberg suggested the property of ACR (absolute concentration robustness), which requires that all steady states be in a hyperplane parallel to a coordinate hyperplane. However, ACR is neither necessary nor sufficient for output robustness, a fact that can be noticed in simple biochemical systems. To develop a stronger connection with output robustness, we define dynamic ACR, a property related to dynamics, rather than only to equilibrium behavior, and one that ensures convergence to a robust value. We illustrate the definition, and certain natural sub-types of dynamic ACR, with a rich body of examples of reaction networks. Towards the end, we will give a brief description of certain minimal motifs of dynamic ACR networks.
• Jiaxin Jin (University of Wisconsin, Madison, USA)
  "Uniqueness of weakly reversible and deficiency zero realization"
Weakly reversible, deficiency zero mass-action systems, being complex-balanced for any choice of rate constants, are remarkably stable. Here we show that if a dynamical system is generated by a weakly reversible network that has deficiency equal to zero, then this network must be unique. Moreover, we show that both weak reversibility and deficiency zero are necessary for uniqueness. We also describe an algorithm that can determine whether or not a system of differential equations can admit a weakly reversible, deficiency zero realization.

Organized by: Rebecca Tyson (University of British Columbia, Canada), Maria Martignoni (Memorial University of Newfoundland, Canada), Frithjof Lutscher (University of Ottawa, Canada)
Note: this minisymposia has multiple sessions. The second session is MS08-ECOP.

• Jimmy Garnier (CNRS - Universite de Savoie-Mont Blanc, France)
  "Genetic diversity in age-structured populations"
In many population, the individuals behavior might differ according to their age. The emerging structure have profound influence on the population dynamics as well as its genetic diversity. I will investigate the dynamics of the genetic diversity in metapopulations. I show that the duration of the juvenile stage or the reproduction strategy might have profound influence on the local diversity of sub--population composing the metapopulation.
• Maria Martignoni (Memorial University of Newfoundland, Canada)
  "Mechanisms for coexistence and competitive exclusion among mutualist guilds."
Mutualistic interactions are gaining increasing attention in the scientific literature, especially as pollination and plant-microbe symbioses play a key role in agricultural productivity. In particular, the widespread symbiosis between plants and arbuscular mycorrhizal (AM) fungi, offers a promising sustainable alternative for maintaining productivity in farmland. Despite the potential benefits for soil quality and crop yield associated with the use of AM fungi, experiments assessing the effective establishment of the fungi in the field have given inconsistent results. Additionally, it is not clear whether the introduction of commercial AM fungi could lead to a biodiversity loss in the native fungal community, and ultimately have a negative impact on plant growth. We developed a series of mathematical models for plant and AM fungal growth to assess the establishment, spread and impact of an introduced species of AM fungi on the native fungal community and on plant productivity. Our models provide a theoretical framework to determine the circumstances under which the inoculated fungal species can coexist with the native fungal community and effectively boost productivity, versus when inoculation constitutes a biodiversity risk and, ultimately, a detriment to crop yield. Overall, our results show that diversity within mutualistic communities promotes productivity and reduces the risk of invasion and biodiversity loss posed by the introduction of a less mutualistic, or even parasitic, species. Although my analysis focuses on plant-fungal interactions, my findings provide valuable criteria to assess the impact of species introduction in mutualistic communities in general, such as other beneficial microbes or pollinator communities.
• Frithjof Lutscher (University of Ottawa, Canada)
  "A seasonal hybrid model for the evolution of flowering onset in plants"
In temperate climates with strong seasonal changes, plants need to decide how to allocate resources to vegetative growth or to reproduction during a potentially short favorable season. Many plants switch from mostly vegetative growth early in the season to mostly reproduction late in the season. The onset of flowering marks the transition between the two phases. Later onset of flowering typically implies a larger size at maturity and higher reproductive capacity. At the same time, it limits the remaining time in the favorable season for pollination and seed development. Hence, plants face a trade-off for some optimal flowering onset. In this talk, I will present a seasonal hybrid model for the density of a plant population, structured by onset of flowering as a trait. I will apply two complementary approaches to analyze the system. Overall, I find that evolution favours some intermediate flowering times.
• Kelsey Marcinko (Whitworth University, USA)
  "Host-Parasitoid Dynamics and Climate-Driven Range Shifts"
Climate change has created new and evolving environmental conditions that cause the habitat ranges of many species to shift upward in elevation and/or towards the poles. To investigate the impact of climate-driven range shifts on host and parasitoid insect species, I consider an integrodifference equation (IDE) model. Using this IDE model, I determine criteria for coexistence of the host and parasitoid species as the habitat shifts spatially. I compare several methods of determining the critical habitat speed, beyond which the parasitoid cannot survive. To make the analysis tractable, I determine the critical speed from a spatially-implicit model that uses an approximation of the dominant eigenvalue of an integral operator. Because the kernel is asymmetric, classical methods for determining the dominant eigenvalue perform poorly. Instead, I approximate the dominant eigenvalue with a method known as geometric symmetrization. The critical speed for parasitoid survival, as computed from the spatially-implicit model, is a good lower bound for the critical speed as determined from simulations of the full IDE model. This framework allows for further exploration of how biological factors impact the coexistence of the host and parasitoid species.

Organized by: Vanessa Rivera Quinones (Latinxs and Hispanics in the Mathematical Sciences (LATHISMS), Puerto Rico), Alicia Prieto Langarica (Youngstown State University, United States of America)

• Vanessa Rivera Quinones (Latinxs and Hispanics in the Mathematical Sciences (LATHISMS), Puerto Rico)
  "Life is a cooperative game: The interplay of individual behavior in group cooperation"
The evolution of cooperation has been a long-standing question both from a sociological and mathematical perspective. This in part, because of the common narrative that the world operates under a 'survival of the fittest' framework. However, cooperation is not only observed in many biological systems, it can also emerge in social dilemmas under certain conditions. We explore cooperative game theory as the mathematical lens to study the emergence of cooperation as an optimal strategy in social dilemmas. In particular,  we focus on predicting when coalitions will form, what are the joining actions or behaviors that groups can take, and what is the resulting pay-off. In this talk,  we provide an overview of common examples of the evolution of cooperation in social dilemmas, and interesting directions of future study.
• Malena Espanol (School of Mathematical and Statistical Sciences, Arizona State University, United States of America)
  "An Edge-preserving Iterative Method for Electrical Impedance Tomography"
Electrical impedance tomography (EIT) is a low-cost, portable, and noninvasive imaging system that does not use ionizing radiation. It has many potential applications including the continuous monitoring of patients with acute respiratory distress syndrome, which in particular is affecting many patients during the current Covid-19 pandemic. In this talk, we present an efficient numerical method that improves the reconstructed image of a human torso.
• Selenne Bañuelos (California State University Channel Islands, United States of America)
  "A Mathematical Model with Combination Phage-Antibiotic Therapy and Immune System Response"
Antimicrobial resistance (AMR) is a serious threat to global health today. A renewed interest in phage therapy – the use of bacteriophages to treat pathogenic bacterial infections – has emerged given the spread of AMR and lack of new drug classes in the antibiotic pipeline. There are few mathematical models that consider the effect of phage-antibiotic combination therapy. Moreover, some biological details such as the immune system response on phage have been neglected. To address these limitations, we utilized a mathematical model to examine the role of the immune response in concert with phage-antibiotic combination therapy compounded with the effects of the immune system on the phages being used for treatment. We explore the effect of phage-antibiotic combination therapy by adjusting the phage and antibiotics dose or altering the timing. The model results show that it is important to consider the host immune system in the model and that frequency and dose of treatment are important considerations for the effectiveness of treatment.
• Alejandra Herrera Reyes (Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, United United Kingdom)
  "Identifying unique observations in super-resolution microscopy with a spatiotemporal model"
Fluorescence microscopy has provided cellular biologists with quantifiable data, that can be paired with mathematical models to discover the mechanics of the imaged processes. Moreover, super-resolution microscopy achieves nanometer resolution images, allowing us to visualize the organization of proteins at nano-scales. dSTORM is a super-resolution technique that relies on the use of photo-switchable fluorophores. One known problem with dSTORM is that images obtained with this technique can suffer from recording a single photo-switchable fluorophore multiple times, possibly creating artificial features. This is especially relevant in the analysis of membrane B-cell receptors clustering, where spatial clustering might relate to immune activation. We developed a protocol to estimate the number of unique fluorophores present in the experiment by coupling their temporal (with a Markov-chain model) and spatial (with a Gaussian mixture model) dynamics within a maximum likelihood framework. Previous studies have used the temporal information, but they have not coupled it with the spatial information (both localization and localization estimation error). We present the results of our estimation protocol on simulated data, well-characterized DNA origami data, and B-cell receptor data with positive results. Our model is general enough to apply to other biological systems besides B-cell data and will enhance a microscopy technique that is widely used in biological applications.

Organized by: Anna Miller (Department of Integrated Mathematical Oncology, Moffitt Cancer Center, United States), Nancy Huntly (Ecology Center and Department of Biology, Utah State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS06-EVOP.

• Peter Adler (Department of Wildland Resources and the Ecology Center, Utah State University, USA)
  "Challenges in quantifying fluctuation-dependent coexistence mechanisms in nature"
Although modern coexistence theory is 20 yrs old, empirical tests remain scarce. We review the formidable challenges in conducting invasibility analyses in natural ecosystems that make such tests rare. Theory asks, how quickly would each species in a community increase from low abundance in the presence of competitors near their stochastic equilibrium abundances, and how do various features of the environment or the species themselves affect this invasion growth rate? Answering these questions experimentally requires removing a focal species from a community, allowing the remaining species to approach equilibrium, reintroducing the focal species at low abundance, and then repeating these steps under different experimental treatments and for all species in the community. Logistical problems make this approach impractical for macroscopic species growing in nature. An alternative approach is building a model that captures the essential dynamics of the community, and then simulating invasion experiments using the model. The challenges for this approach include naïve application of statistical conventions that may predetermine results, and uncertainty about whether models fit to observational data can accurately project dynamics outside the range of conditions that were directly observed.
• Robin Snyder (Department of Biology, Case Western Reserve University, USA)
  "Quantifying fluctuation-dependent coexistence mechanisms for populations of spatially-structured, discrete individuals"
We traditionally analyze coexistence by asking when each species in a system could invade a community made up of the others. To do this, we assume that the invader is rare enough that it does not compete with itself and yet is common enough that we can ignore demographic stochasticity. Spatially extended systems with discrete individuals cause these assumptions to break down. Local dispersal and competition create clumpy invader distributions, so that invaders are common over the scale with which they interact, yet populations are small within the limited scale of interaction, so that discreteness cannot be ignored. Here we present a simulation-based method for quantifying how much different processes or traits contribute to coexistence in spatially structured community models with discrete individuals. We demonstrate our method using simulations of the lottery model and consider contributions from environmental fluctuations (E), competition fluctuations (C), demographic stochasticity, and their interactions. As the spatial scales of competition and dispersal decrease, invaders become more clustered and invader-invader competition increases. This weakens the positive contribution of Cov(E, C) and strengthens the negative effects of fluctuations in C. The effect of demographic stochasticity is small and the trend with increased invader clustering is not statistically significant.
• Virginia Turati (Department of Integrated Mathematical Oncology, Moffitt Cancer Center, USA)
  "An integrated approach to understanding the clonal dynamics of childhood B-cell precursor acute lymphoblastic leukemia during treatment to relapse"
Comparison of intratumor genetic heterogeneity at diagnosis and relapse suggests that chemotherapy induces bottleneck selection of subclonal genotypes. However, evolutionary events after chemotherapy could also explain changes in clonal dominance seen at relapse. We investigated mechanisms of selection in BCP-ALL during induction chemotherapy where maximal cytoreduction occurs. To distinguish stochastic versus deterministic events, individual leukemias were transplanted into xenografts and chemotherapy administered. We subsequently leveraged the Hybrid Automata Library (HAL) to implement a mathematical model and, based on the experimental data, infer the evolutionary trajectories leading from initial treatment response to relapse. Analyses of the immediate post-treatment leukemic residuum at single-cell resolution revealed that chemotherapy has little impact on genetic heterogeneity. Instead, treatment acts on the extensive transcriptional and epigenetic heterogeneity of untreated BCP-ALL, selecting a phenotypically uniform population with hallmark signatures of deep quiescence and primitive developmental stage. The mathematical model further suggests that in those leukemias in which most subclones display similar fitness, subclonal selection happens later and not as a direct result of treatment. Instead, in those rarer leukemias in which genotype and phenotypes broadly related to treatment resistance (i.e., proliferation potential) co-segregate, only a few lineages survive through relapse.
• Jeff Maltas (Cleveland Clinic, USA)
  "Reversibility of evolution in tunably correlated environments"
Naturally evolving populations constantly face changing environmental conditions. One interesting question is to explore if adaptations that occur as a result of a new environment can be reversed by returning to the previous environment. Using simulations we quantify the genotypic and phenotypic reversibility of an asexually reproducing population. We show that the interlandscape correlation between landscape pairs can dramatically impact the reversibility of this population. Finally, we show that slowly vs quickly switching between landscapes can significantly impact reversibility.

Organized by: Roya Zandi (University of CA, Riverside, USA), Amber Smith (University of Tennessee, USA), Reidun Twarock (University of York, UK)

• Carolyn Teschke (Department of Molecular and Cell Biology, University of Connecticut, USA)
  "Using a scaffold to build a viral capsid"
Many dsDNA viruses, including the herpesviruses and tailed bacteriophages, build a precursor capsid called a procapsid into which the dsDNA is subsequently packaged. These viruses require an internal scaffolding protein to assemble coat proteins into procapsids of the proper size and shape. How a scaffolding protein affects the conformation of a coat protein so that it is competent for assembly is not understood. We have used single molecule fluorescence experiments to demonstrate a surprisingly high affinity interaction between bacteriophage P22’s monomeric scaffolding protein and coat protein. This interaction shifts coat protein into a conformation consistent with the procapsid configuration of the protein. Thus, scaffolding protein directly activates coat protein for assembly.
• Siyu Li (Northwestern University, China)
  "The physical mechanism of virus self-assembly"
Understanding the basic mechanism of virus self-assembly is fundamental in deciphering the formation and evolution of viruses and exploring their applications to drug delivery, gene therapy and vaccination. While considerable progress has been achieved in determining the virus structures, kinetic pathways by which hundreds or thousands of proteins assemble to form structures with icosahedral order (IO) is still elusive. To decipher the assembly pathway, we developed a computational model to simulate the virus growth. We proposed two mechanisms of small virus assembly: en-mass and nucleation-growth, and studied the role of elasticity and genome in the disorder-order transition process. Moreover, we study the growth of large viruses and discover the universal role of scaffolding proteins in the formation of viral capsids. Using continuum elasticity theory, we show that a nonspecific template not only selects the radius of the capsid, but also leads to the error-free assembly of protein subunits into capsids with universal IO. The mechanism we study will help us deeply understand the correlation between protein building blocks and virus macrostructures, and guide the experiments to explore the possibility of antiviral drugs that inhibit the virus self-assembly.
• Trevor Douglas (Department of Chemistry, Indiana University, Bloomington IN 47405, USA)
  "Directed Assembly of Virus-Based Nanoreactors Across Multiple Lengthscales"
The virus like particles (VLP) derived from the bacteriophage P22 provide an opportunity for constructing catalytically functional nano-materials by directed encapsulation of enzyme cargos into the interior volume of the capsid. Directed enzyme encapsulation is achieved by genetically fusing the enzyme of interest to a truncated version of the scaffolding protein, which directs capsid assembly and is encapsulated within the capsid. This approach affords the packing of the desired enzymes within the roughly 60 nm diameter P22 capsid at very high packing density. The self-assembly of these nanoreactors is dependent on the multivalent nature of the cargo and this can be used to control the density of encapsulated cargo. We have explored the molecular level porosity of capsid and determined the range of substrates that can access the encapsulated enzyme and the dependence of this gating on molecular size and charge. Using these P22 nanoreactors as individual building blocks we can extend their utility towards the fabrication of hierarchically complex systems by further manipulation of their exterior surfaces. Superlattice materials, with long-range order, can be assembled through the directed hierarchical assembly of individual P22 particles, mediated by interparticle electrostatic interactions or through interactions of surface bound decoration proteins. In this way we can create ordered 3D materials that exhibit complex coupled behavior through communication between individual P22 nanoreactors.
• Giuliana Indelicato (Department of Mathematics, The University of York, UK)
  "The role of surface stress in non-quasi-equivalent viral capsids"
We focus here on viruses in the PRD1-adenovirus lineage which do not always conform to the Caspar and Klug classification. Instead of being built from one type of capsid protein (CP), they either code for multiple distinct structural proteins that break the local symmetry of the capsomers in specific positions, or exhibit auxiliary proteins that stabilize the capsid shell. We investigate the hypothesis that this occurs as a response to mechanical stress. We construct a coarse-grained model of a viral capsid, derived from the experimentally determined atomistic positions of the CPs. For T = 28 viruses in this lineage, which have capsids formed from two distinct structural proteins, we show that the tangential shear stress in the viral capsid concentrates at the sites of local symmetry breaking. In the T = 21, 25 and 27 capsids, we show that stabilizing proteins decrease the tangential stress. These results suggest that mechanical properties can act as selective pressures on the evolution of capsid components, counterbalancing the coding cost imposed by the need for such additional protein components.

Organized by: Miranda Teboh-Ewungkem (Lehigh University, United States), Calistus N. Ngonghala, (University of Florida, Gainsville, FL, United States), Jude D. Kong (York University, Toronto, ON, Canada,, Canada)
Note: this minisymposia has multiple sessions. The second session is MS14-MEPI.

• Philip Maini (Mathematical Institute, Oxford, UK)
  "Modelling collective leader-follower behaviour"
Collective movement is a very common occurrence in biology and ecology. I will review work in which I have been involved for the past few years on (i) angiogenesis (formation of new blood vessels) in wound healing and cancer growth; (ii) cranial neural crest migration in normal development. The models will range from coupled systems of partial differential equations to discrete cell-based systems. I will show how we have derived a new model for the classical snail-trail system and also how, working with experimental colleagues, we have generated new biological insights.
• Nakul Chitnis (Swiss Tropical and Public Health Institute, Switzerland)
  "Modelling Mosquitoes and Malaria"
We present mathematical models of mosquito population dynamics and mosquito foraging behaviour and combine these with models of malaria transmission. We use these models to explore the dynamics of mosquito behaviour on malaria transmission and investigate the impact of vector control interventions on malaria transmission and disease burden.
• Divine Wanduku (Department of Mathematics, Georgia Southern University, United States)
  "A Stochastic Multi-Population Behavioral Model to Assess the Roles of Education Campaigns, Random Supply of Aids, and Delayed ART Treatment in HIV/AIDS Epidemic"
The successful reduction in prevalence rates of HIV in many countries is attributed to control measures such as information and education campaigns (IEC), antiretroviral therapy (ART), and national, multinational and multilateral support providing official developmental assistance (ODAs) to combat HIV. However, control of HIV epidemics can be interrupted by limited random supply of ODAs, high poverty rates and low living standards. This study presents a stochastic HIV/AIDS model with treatment assessing the roles of IEC, the supply of ODAs and early treatment in HIV epidemics. The supply of ODAs is assessed via the availability of medical and financial resources leading more people to get tested and begin early ART. The basic reproduction number ( $mathfrak{R}_{0}$) for the dynamics is obtained, and other results for HIV control are obtained by conducting stability analysis for the stochastic SITRZ disease dynamics. Moreover, the model is applied to Uganda HIV/AIDS data, wherein linear regression is applied to predict the $mathfrak{R}_{0}$ over time, and to determine the importance of ART treatment in the dynamics.
• Jacek Banasiak (Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa)
  "Beyond the Next Generation Matrix Method"
The Next Generation Matrix method has been one of the most popular methods for establishing the stability of the disease-free equilibrium. It has, however, some drawbacks - for instance it is not directly applicable for problems with the immigration of infectives. In this talk, we shall discuss some ways of dealing with such problems, based on perturbation techniques.

Organized by: Erica Rutter (University of California, Merced, United States), Suzanne Sindi (University of California, Merced, United States)
Note: this minisymposia has multiple sessions. The second session is MS08-MFBM.

• Emilia Kozlowska (Departement of Systems Biology and Engineering, Silesian University of Technology, Poland)
  "Application of mechanistic and machine learning modeling to predict long-term response to treatment for cancer patients"
The most common subtype of lung cancer is non-small cell lung cancer (NSCLC) that constitutes 80% of all lung cancer cases. NSCLC is usually diagnosed at an advanced stage because of non-specific symptoms, leading to high mortality. The standard treatment for NSCLC patients is a combination of chemotherapy and radiotherapy and, as an emerging type of treatment, immunotherapy. We collected clinical data from over 500 patients with non-small cell lung cancer. From the cohort, we extracted 50 patients who were treated only with platinum-based chemotherapy with palliative intent i.e., under the assumption of failed cure. The clinical data including, among others, short and long-term response to chemotherapy and amount of chemotherapy cycles, were applied to calibrate the mechanistic model using a machine learning approach. We developed a computational platform to find the best protocol for the administration of platinum-doublet chemotherapy in the palliative setting. The core of the platform is the mathematical model, in the form of a system of ordinary differential equations, describing dynamics of platinum-sensitive and platinum-resistant cancer cells and interactions reflecting competition for space and resources. The model is simulated stochastically by sampling the parameter values from a joint probability distribution. The model simulations faithfully reproduce the clinical cohort at three levels, long-term response (OS), initial response, and the relationship between the number of chemotherapy cycles and time between two consecutive chemotherapy cycles. In addition, we investigated the relationship between initial and long-term responses. We showed that these two variables do not correlate, which means that we cannot predict patient survival based solely on the initial response. We also tested several chemotherapy schedules to find the best one for patients treated with palliative intent. We found that optimal treatment schedule depends, among others, on the strength of competition among sensitive and resistant subclones in a tumor.
• Sara Ranjbar (Mathematical NeuroOncology Lab, Precision Neurotherapeutics Program, Mayo Clinic, Arizona, United States)
  "MRI-based estimation of the abundance of immunohistochemistry markers in GBM brain using deep learning"
Glioblastoma (GBM) is a devastating primary brain tumor known for its heterogeneity and invasion. Despite uniformly aggressive therapies including surgery, radiation, and chemotherapy, the median survival rate remains about 15 months. There are many targeted therapies in clinical trials; however, the eloquence of the location makes both the drug delivery and the local efficacy of any drug difficult to assess. Clinical imaging remains the primary modality to assess tumor response, but it is an obscured lens through which it is nearly impossible to distinguish between actual tumor growth and tumor cell death from a large immune response. Over the past decade, MRI has been suggested by many studies to reflect the underlying tumor biology. In this talk, we will discuss our groups’ approach to building a robust deep learning model to connect MRI patterns at GBM biopsied locations with cell proliferation abundance measured by immunohistochemistry staining. If successful, this model can provide a non-invasive readout of cell proliferation and reveal the effectiveness of a given cytotoxic therapy including standard-of-care radiotherapy that targets cell proliferation.
• Joan Ponce (UCLA, United States)
  "An integrated framework for building trustworthy data-driven epidemiological models: Application to the COVID-19 outbreak in New York City"
Epidemiological models can provide the dynamic evolution of a pandemic but they are based on many assumptions and parameters that have to be adjusted over the time when the pandemic lasts. However, often the available data are not sufficient to identify the model parameters and hence infer the unobserved dynamics. Here, we develop a general framework for building a trustworthy data-driven epidemiological model, consisting of a workflow that integrates data acquisition and event timeline, model development, identifiability analysis, sensitivity analysis, model calibration, model robustness analysis, and forecasting with uncertainties in different scenarios. In particular, we apply this framework to propose a modified susceptible–exposed–infectious–recovered (SEIR) model, including new compartments and model vaccination in order to forecast the transmission dynamics of COVID-19 in New York City (NYC). We find that we can uniquely estimate the model parameters and accurately predict the daily new infection cases, hospitalizations, and deaths, in agreement with the available data from NYC's government's website. In addition, we employ the calibrated data-driven model to study the effects of vaccination and timing of reopening indoor dining in NYC.
• Emily Zhang (North Carolina State University, USA)
  "Deep Learning and Regression Approaches to Forecasting Blood Glucose Levels for Type 1 Diabetes"
Controlling blood glucose in the euglycemic range is the main goal of developing sensor-augmented pump therapy for type 1 diabetes patients. The pump therapy delivers the amount of insulin dose determined by glucose predictions through the use of computational algorithms. A computationally efficient and accurate model that can capture the physiological nonlinear dynamics is critical for developing an accurate therapy device. Four data-driven models are compared, including different neural network architectures, a reservoir computing model, and a novel linear regression approach. Model predictions are evaluated over continuous 30 and 60 minute time horizons using real-world data from wearable sensor measurements, a continuous glucose monitor, and self-reported events through mobile applications. The four data-driven models are trained on 12 data contributors for around 32 days, 8 days of data are used for validation, with an additional 10 days of data for out-of-sample testing. Model performance was evaluated by the root mean squared error and the mean absolute error. A neural network model using an encoder-decoder architecture has the most stable performance and is able to recover missing dynamics in short time intervals. Regression models performed better at long-time prediction horizons (i.e., 60 minutes) and with lower computational costs. The performance of several distinct models was tested for individual-level data from a type 1 diabetes data set. These results may enable a feasible solution with low computational costs for the time-dependent adjustment of pump therapy for diabetes patients.

Organized by: Karin Leiderman (Colorado School of Mines, United States), Anna Nelson (University of Utah, USA)
Note: this minisymposia has multiple sessions. The second session is MS01-MMPB.

• Amandeep Kaur (University of California Merced, USA)
  "A new view of an old mechanism: mathematical modeling of TFPI inhibition in coagulation"
Blood coagulation is a complex network of biochemical reactions necessary to form a blood clot. The process occurs in three, overlapping stages: initiation, amplification, and propagation, with inhibitory mechanisms occurring at each stage to help avoid the system over clotting. Initiation in the tissue factor pathway begins when clotting factor VIIa (FVIIa) in the plasma binds its cofactor, tissue factor (TF), in the subendothelium and forms an active enzyme complex. Next, clotting factor X (FX) in the plasma can bind TF:VIIa, form an intermediate complex where it is enzymatically cleaved into activated FX (FXa). FXa is necessary for further events in coagulation. It has long been recognized that tissue factor pathway inhibitor (TFPI) is a strong inhibitor of TF:VIIa activity during initiation, with the primary mechanism of action reportedly being TFPI binding to FXa in the plasma, forming a complex, and then rebinding to TF:VIIa to form the newly inhibited, quaternary complex TF:VIIa:TFPI:Xa. However, previous mathematical models of this type of inhibition, for small injuries under flow, show that flow itself is a more important inhibitor of the system than TFPI. The goal of this study was to revisit previous experimental studies of TFPI where additional inhibitory reactions were suggested to be at play and use mathematical models and constrained optimization to fit these reactions schemes to multiple sets of data simultaneously. Our preliminary results suggest that the alternative reaction scheme for TFPI better describes the experimental data. Next, we highlight the ramifications of using one scheme versus the other when interpreting results from mathematical models of coagulation.
• Jamie Madrigal (Colorado School of Mines, USA)
  "Estimating lipid-dependent reaction velocities"
Blood coagulation is a network of biochemical reactions whereby dozens of proteins act collectively to initiate a rapid clotting response. It is known that many of the coagulation reactions require a cellular (lipid) surface on which to occur and, in addition, the enzymatic rates are thought to be enhanced on lipid surfaces; surface diffusion and near-surface concentrations of substrates are thought to play important roles in this enhancement. Experimental data shows that at both low and high lipid concentration, rates of enzymatic reactions are low while there is some optimal intermediate lipid concentration where the rate is the fastest; this is known as the template effect. To our knowledge, this effect has never been accounted for in previous mathematical models of coagulation reactions and thus these models all result in enzyme generation that increases monotonically as lipid concentration increases. We have developed a mathematical model of lipid-mediated enzyme reactions in which the association rates between lipid-bound reactants are modified by an interaction probability. The interaction probability is derived by considering the fraction of the lipid surface that is occupied by any lipid-bound species. Preliminary model results agree with experiment ones and show the template effect. Next, for an enzymatic reaction where the experimentally measured reaction velocities are considerably different for varying lipid concentrations, we used the model with constrained optimization to estimate the intrinsic kinetic rate constants that can be fixed across lipid concentrations.
• Anastasiia Mozokhina (Peoples Friendship University of Russia (RUDN University), Russia)
  "The influence of microthrombi in small vessels on the pulmonary blood flow"
Blood coagulation is an important physiological mechanism aimed to stop bleeding if the integrity of blood vessel walls is violated due to an injury. However, if the fragile balance between pro- and anticoagulant factors is not preserved, this can lead to different pathological states including thrombosis, possibly leading to heart attack, stroke, pulmonary embolism, or deep vein thrombosis. On the other side, various bleeding disorders including hemophilia can appear in the case of insufficient blood coagulation. During the ongoing COVID-19 epidemic, multiple microthrombi are observed in small pulmonary vessels leading to reduced pulmonary blood circulation and to decrease of oxygen saturation level, representing the main mortality cause of the coronavirus disease. In the current work, the model of thrombi growth is combined with the quasi-one-dimensional blood flow model of pulmonary circulation. The model is used to estimate the influence of blood vessel obstruction on the total blood flow through the lungs. The modelling results can be used as a first approximation for a non-invasive estimation of oxygen level during the coronavirus disease. The work is supported by the Ministry of Science and Higher Education of the Russian Federation: agreement no. 075-03-2020-223/3 (FSSF-2020-0018)
• Dmitry Nechipurenko (Lomonosov Moscow State University, Russia)
  "Initiation and confinement of coagulation reactions under the shear flow"
Under conditions of the high shear rate, formation of the hemostatic plug relies on platelet adhesion, activation and aggregation, and the platelet plug is additionally stabilized by fibrin mesh. It is generally considered, that coagulation reactions are significantly inhibited under flow conditions due to dilutional effects of the blood flow. However, in vitro experiments suggest that fibrin formation in platelet free plasma is possible even under arterial blood flow conditions and critically depends on the tissue factor density, the size of the “damaged” region with tissue factor and the shear rate itself. However, the exact mechanisms, which a) protect initial stages of coagulation reactions from dilution by arterial flow and b) further confine fibrin polymerization in space - are poorly understood. Here we describe both experimental and theoretical framework to address these questions. In vitro experiments were based on perfusion of recalcified platelet free plasma through microfluidic flow chambers combined with fluorescent microscopy and address the dynamics of fibrin propagation in 4D under controlled shear rate. In silico models are focused on the primary stages of coagulation process under defined shear rate and serve as important tool for elucidation and investigation of the possible mechanisms. Using in vitro model we have inferred the critical spatiotemporal parameters of fibrin polymerization process under arterial shear rate. In silico model was further used to study the kinetics of thrombin generation depending on critical internal parameters and correlated with experimental data. Our results suggest a novel mechanism, which might be important for the protection of the primary coagulation reactions from the blood flow. This work was supported by the Russian Foundation for Basic Research grant 19-51-15004 to F.A. and performed within the framework of the Development Program of the Interdisciplinary Scientific and Educational School of Lomonosov Moscow State University

Organized by: Zahra Aminzare (University of Iowa, United States), Vaibhav Srivastava (Michigan State University, United States)
Note: this minisymposia has multiple sessions. The second session is MS06-NEUR.

• Zack Kilpatrick (University of Colorado Boulder, United States)
  "Heterogeneity Improves Speed and Accuracy in Social Networks"
How does temporally structured private and social information shape collective decisions? To address this question we consider a network of rational agents who independently accumulate private evidence that triggers a decision upon reaching a threshold. When seen by the whole network, the first agent’s choice initiates a wave of new decisions; later decisions have less impact. In heterogeneous networks, first decisions are made quickly by impulsive individuals who need little evidence to make a choice but, even when wrong, can reveal the correct options to nearly everyone else. We conclude that groups comprised of diverse individuals can make more efficient decisions than homogenous ones. In addition, we extend this analysis to the groups of agents receiving correlated observations, showing the first agent to decide is less accurate in this case.
• Hermann Riecke (Northwestern University, United States)
  "Paradoxical Phase Response and Enhanced Synchronizability of Gamma-Rhythms by Desynchronization"
Neurons are often observed to form large ensembles that fire coherently and rhythmically, constituting a macroscopic collective oscillation. The synchronization of such γ -rhythms arising in different brain areas is thought to be relevant for the communication between these brain areas and has been implicated in various cognitive functions. What determines whether these collective oscillations can synchronize with each other or with periodic external inputs? We show that, surprisingly, both uncorrelated noise and heterogeneity in the neuronal properties can enhance the synchronizability of γ -rhythms. They do that by reducing the within-network synchrony. This allows external inputs to conspire with the within-network inhibition to change the number of neurons that participate in the rhythm, which changes the frequency of the rhythm substantially and enhances its synchronizability. A characteristic feature of this mechanism is a paradoxical phase response of the collective oscillation: external input can advance the rhythm although they directly delay each individual neuron and vice versa. We demonstrate this for various types of neuron models in networks supporting ING- and PING-rhythms. We use direct numerical simulations of spiking networks as well as the adjoint method for the phase-response curve within the exact mean-field theory of Lorentzian networks of quadratic-integrate-fire neurons.
• James MacLaurin (New Jersey Institute of Technology, United States)
  "Stochastic Oscillations Emerging from the Stochastic Pulling Forces of Microtubules"
Following early work of Grill and Kruse, it is well known that the mitotic spindle pole can oscillate during cell division. The oscillation arises due to the growth of cytoskeletal microtubules - these radiate outwards and attach to two poles. This oscillatory behavior can arise during asymmetric cells divisions that result in daughter cells of unequal sizes. The spindle is essential to organize chromosome segregation during mitosis but also to define the constriction place at which the original cell is divided. The original model due to Grill and Kruse assumes that the microtubules and motors can be well-approximated as a continuum, and thereby modeled using PDEs and ODEs. In this work we develop a finite-size microscopic model, with microtubules detaching and reattaching in a stochastic manner. Furthermore, in our model the binding of individual microtubules is affected by the density of microtubules that are already attached. We perform stochastic simulations, and use analytic methods to project the cumulative effects of the stochasticity onto the limit cycle. We also demonstrate that the continuum model arises in the large size limit of this finite size system.
• Jonathan Touboul (Brandeis University, United States)
  "Noise-induced synchronization and anti-resonance in interacting excitable systems; Applications to Deep Brain Stimulation in Parkinson’s Disease"
In large networks of excitable elements driven by noise, a surprising regime of orderly, perfectly synchronized periodic solutions arises for intermediate levels of noise, as the network transitions from clamping around the stable equilibrium at low noise, to asynchrony at high noise. I will present a theory for the emergence of these synchronized oscillations due to noise. This noise-induced synchronization, distinct from classical stochastic resonance, is fundamentally collective in nature. Indeed, I show that, for noise and coupling within specific ranges, an asymmetry in the transition rates between a resting and an excited regime progressively builds up, leading to an increase in the fraction of excited neurons eventually triggering a chain reaction associated with a macroscopic synchronized excursion and a collective return to rest where this process starts afresh, thus yielding the observed periodic synchronized oscillations. We further uncover a novel antiresonance phenomenon in this regime: noise-induced synchronized oscillations disappear when the system is driven by periodic stimulation with frequency within a specific range (high relative to the spontaneous activity). In that antiresonance regime, the system is optimal for measures of information transmission. This observation provides a new hypothesis accounting for the efficiency of high-frequency stimulation therapies, known as deep brain stimulation, in Parkinson’s disease, a neurodegenerative disease characterized by an increased synchronization of brain motor circuits. We further discuss the universality of these phenomena in the class of stochastic networks of excitable elements with specific coupling and illustrate this universality by analyzing various classical models of neuronal networks. Altogether, these results uncover some universal mechanisms supporting a regularizing impact of noise in excitable systems, reveal a novel antiresonance phenomenon in these systems, and propose a new hypothesis for the efficiency of high-frequency stimulation in Parkinson’s disease.

Organized by: Russell Rockne (Beckman Research Institute, City of Hope National Medical Center, USA), Andrea Bild (Beckman Research Institute, City of Hope National Medical Center, USA)

• Jessica Leete (Pfizer Inc, Cambridge MA, USA)
  "Towards virtual populations for human efficacy prediction in lung cancer: preclinical to clinical translation of anti-PD-(L)1 treatments"
Objectives: Immune checkpoint inhibitors such as anti-PD-1 and anti-PD-L1 are promising new therapeutic options that cease tumor cells’ immunosuppressive properties; however, low response rates to these therapeutics indicate an unmet medical need in treating non-small cell lung cancer (NSCLC). NSCLC is a highly heterogenous disease both spatially and genetically, and provides unique challenges to predicting treatment outcome. We propose a model of anti-PD-(L)1 in both preclinical mouse models and human NSCLC. We use this model to explore the effect of parameters on model outcome in preparation for implementation of virtual population methods to explore inter-patient variability. Methods: We present a drug and target focused model of anti-PD-(L)1 treatment in CT26 BALB/c mice and NSCLC in humans. The model includes the mechanisms of action of anti-PD-1 and anti-PD-L1. We translate the model structure to that of a 'typical' NSCLC patient using published popPK and binding affinities of approved anti-PD-(L)1 treatments. Parameter sensitivity is explored through both local and global sensitivity analyses. Results: Pre-clinical simulations show the model's ability to match a wide variety of responses to treatment by allowing tumor growth parameters and tumor PD-1+ CD8+ T cell concentration to vary between individuals. Model simulations are sensitive to parameters that determine PD-(L)1 abundance and the speed and magnitude of T cell proliferation after treatment. Conclusions: Focus on modeling a 'typical' human patient may lead to an incomplete characterization of treatment efficacy in situations where there is high inter-patient variability in responses. Immuno-oncology treatments in particular may benefit from methods that can quantify the effect of patient variability on treatment outcome.
• Nataly Kravchenko-Balasha (The Institute of Biomedical and Oral Research, The Hebrew University of Jerusalem, Israel, Israel)
  "Computational quantification and characterization of independently evolving cellular subpopulations within tumors is critical to inhibit anti-cancer therapy resistance"
Drug resistance continues to be a principle limiting factor across diverse anti-cancer therapies. Contributing to the complexity of this challenge is cancer plasticity where one cancer subtype switches to another in response to treatment (e.g. Triple Negative Breast Cancer (TNBC) to Her2-positive breast cancer). For optimal treatment outcomes, accurate tumor diagnosis and subsequent therapeutic decisions are vital. In this study an information-theoretic single-cell quantification strategy was developed to provide a high resolution and individualized assessment of tumor composition for a customized treatment approach. Briefly, this single-cell quantification strategy computes a barcode based on at least 100, 000 tumor cells and reveals a set of ongoing processes in each cell. Using these cell-specific barcodes, distinct subpopulations evolving within the tumor in response to an outside influence (e.g. anticancer treatments) are revealed and mapped. Barcodes, are further applied to assign targeted drug combinations to each individual tumor to optimize tumor response to therapy. This unique strategy was validated using TNBC models and patient-derived tumors known to switch phenotypes in response to radiotherapy (RT). We show that a barcode-guided targeted cocktail significantly enhances tumor response to RT and prevents regrowth of once resistant tumors. The strategy presented herein has the potential to significantly reduce the occurrence of cancer treatment resistance, with a broad applicability in clinical use.
• Alexander R. A. Anderson (Integrated Mathematical Oncology Department H. Lee Moffitt Cancer Center & Research Institute, USA)
  "Exploiting evolution to design better cancer therapies"
Our current approach to cancer treatment has been largely driven by finding molecular targets, those patients fortunate enough to have a targetable mutation will receive a fixed treatment schedule designed to deliver the maximum tolerated dose (MTD). These therapies generally achieve impressive short-term responses, that unfortunately give way to treatment resistance and tumor relapse. The importance of evolution during both tumor progression, metastasis and treatment response is becoming more widely accepted. However, MTD treatment strategies continue to dominate the precision oncology landscape and ignore the fact that treatments drive the evolution of resistance. Here we present an integrated theoretical/experimental/clinical approach to develop treatment strategies that specifically embrace cancer evolution. We will consider the importance of using treatment response as a critical driver of subsequent treatment decisions, rather than fixed strategies that ignore it. We will also consider using mathematical models to drive treatment decisions based on limited clinical data. Through the integrated application of mathematical and experimental models as well as clinical data we will illustrate that, evolutionary therapy can drive either tumor control or extinction using a combination of drug treatments and drug holidays. Our results strongly indicate that the future of precision medicine shouldn’t be in the development of new drugs but rather in the smarter evolutionary, and model informed, application of preexisting ones.
• Andrew Gentles (Departments of Medicine and Biomedical Informatics, Stanford University, USA)
  "Building an atlas of cell states and cellular ecosystems across human solid tumors"
Determining how cells vary with their local signaling environment and organize into distinct cellular communities is critical for understanding processes as diverse as development, aging, and cancer. We have developed EcoTyper, a new machine learning framework for large-scale identification and validation of cell states and multicellular communities from bulk, single-cell, and spatially-resolved gene expression data. When applied to 12 major cell lineages across nearly 6,000 tumor specimens from 16 types of human carcinoma, EcoTyper identified 69 transcriptionally-defined cell states. Most cell states were specific to neoplastic tissue, ubiquitous across tumor types, and significantly prognostic. By analyzing cell state co-occurrence patterns, we discovered 10 clinically-distinct multicellular communities with unexpectedly strong conservation, including four with unique myeloid and stromal elements, one enriched in normal tissue, and two associated with early cancer development. This work elucidates fundamental units of cellular organization in human carcinoma and provides a framework for large-scale profiling of cellular ecosystems in any tissue.