Organized by: Andreas Buttenschoen (University of Massachusetts Amherst), Calina Copos (Northeastern University)

1. Jupiter Algorta University of British Columbia
   "A Data-Driven Model of Polarity Reversal in Migrating Cells"
We study how motile cells can reverse their polarity when exposed to changing stimuli, using mathematical modeling alongside extensive experimental data from optogenetic assays carried out by our collaborators in the Orion Weiner lab (UCSF). These experiments revealed an unexpected phenomenon: when a localized input is followed by a global stimulus, cells often reverse their direction of turning. To explain this, our collaborators hypothesized the existence of a slow-acting, locally produced inhibitor downstream of Rac, a signaling molecule known to promote actin assembly and front-edge protrusion. We test this idea by adapting an existing reaction diffusion model that, under certain conditions, produces a stable spatial pattern: a polarized distribution with a clear front and back. This modeling framework, often referred to as wave-pinning, has not previously been fitted directly to experimental data. Here, we calibrate the model’s reaction terms to time-dependent Rac activity data, introducing a novel approach that embraces cellular heterogeneity by fitting a distribution of parameters across multiple cells. While the Rac-inhibitor circuit captures several key features of the response, it fails to reproduce reversal. Incorporating PIP3, an upstream regulator of Rac, allows the model to recover reversal dynamics and reproduce the full range of observed behaviours. In this presentation, we will show the development of our modeling framework from its earliest steps, including how data fitting informed model refinement. Our results validate the experimental hypothesis and yield new predictions about the molecular timing and feedback logic underlying flexible polarity control.
2. Mariya Savinov New York University
   "Modeling mechanically driven tumor cluster coattraction on ECM"
Authors: Mariya Savinov (1), Jeremy Garcia (2), Alex Mogilner (1,2), Carlos Carmona-Fontaine (2) (1): Courant Institute of Mathematical Sciences, New York University, New York, NY. (2): Department of Biology, New York University, New York, NY Collective cell migration is essential for morphogenesis, playing a key role in processes such as embryonic development and cancer metastasis. The ability of cells to collectively migrate in a directional manner depends on coordination cues, both local between cells and extracellular (e.g. chemotaxis). How cells in cancer clusters coordinate their movements, particularly in early metastasis, is still not well understood. Here we tackle this question using a combined experimental and modeling approach. Our experimental efforts employed a model system of multicellular tumor structures, which we refer to as cell clusters, on extracellular matrix (ECM). We found that when two cell groups are within a threshold distance, they “coattractâ€, spontaneously migrating collectively towards each other. Surprisingly, the tumor cell clusters also detect and then migrate toward biologically inert beads, suggesting that the coattraction is a consequence of a mechanical cue of the ECM. To uncover the mechanisms underlying the robust coattraction threshold, we developed a mathematical model of the ECM as a 2D deformable elastic, cable-network material. As experiments have shown that cell clusters pull and concentrate the ECM, the model ECM is subjected to isotropic contractile stresses by the tumor cell clusters. Through analysis and numerical simulation, our model reveals how the mechanical force distribution of the underlying ECM acts as a symmetry-breaking cue to initiate cell cluster coattraction. We reproduce key experimental results and, notably, our model predicts a lower coattraction threshold between a single cluster and bead as compared to a pair of cell clusters. This work demonstrates how mechanical forces in the ECM can efficiently guide tumor cell cluster migration, and has broad implications regarding the survival of tumor cells during the metastatic journey.
3. Wei Wang Johns Hopkins University
   "Statistics of fracture in collective cell migration"
When cells migrate collectively, individual cells or small groups can detach from the main body. These fracture events play an important role in cancer invasion and other biological processes, but their statistics and physical control mechanisms remain unclear. We present a theoretical and experimental study that quantifies the statistics of fracture events in collectively migrating tissues and connects them to physical models of active matter with growth and breakup. We analyze experiments where human carcinoma cells migrate along chemotactic gradients in microchannels and sometimes rupture away from the invading strand. Most rupture events involve single cells, but larger clusters also occur. The rupture probability shows little dependence on the degree of geometric confinement. To understand these observations, we construct a phase-field model of deformable cells that incorporates chemotaxis, heterogeneous cell states (followers, guided cells, and leader cells), and cell-cell and cell-wall adhesion. This model recapitulates key features of the experiments, including the distribution of rupture sizes and times. Our results show that cell-channel adhesion is necessary for cells in narrow channels to invade, and strong cell-cell adhesion leads to fewer but larger ruptures. Chemotaxis also influences the rupture behavior: Strong chemotaxis strength leads to larger and faster ruptures. We also examine the connection between biological jamming transitions and fracture. Our results suggest unjamming is necessary but not sufficient to create ruptures. To generalize this picture, we study how cell groups control their cluster sizes using a one-dimensional active particle model of growing and fragmenting chains. In this model, rupture is driven by random cell motility, and cluster size is set by the balance between growth and breakup. We compute the rupture rate analytically and solve for the exact steady-state size distributions. We show that these statistics depend only on the ratio of break to division rates, and that size variability can be reduced by restricting division to cluster edges or localizing rupture to the interior. Our theory also suggests that the observed drop in fracture rate in experiments can be explained by relatively small changes in cell motility. Together, these results provide a physical framework for understanding the statistics of fracture in collective migration, with implications for both tissue size regulation and cancer cell metastasis.
4. Eric Cytrynbaum University of British Columbia
   " A model for root zone regulation by brassinosteroid and CLASP"
The root apical meristem of the plant A. thaliana is organized into distinct zones, each of which plays an important developmental role. The plant hormone brassinosteroid and the protein CLASP influence the size and dynamics of the elongation and division zones thereby controlling the rate of root growth. This regulation allows plant growth to be responsive to environmental conditions. In this talk, I will describe a model for a mechanism by which brassinosteroid and CLASP modulate cell elongation and cell division. The model is able to match measured root growth data for wild type and two mutants under the condition that CLASP has a biphasic influence on the rate of cell cycle progression, with a maximum cell division rate for intermediate levels of CLASP. This result suggests that CLASP, a regulator of microtubule dynamics, must be finely tuned to allow microtubules to efficiently relocalize through the cell cycle.

Organized by: Keisha Cook, Anna Nelson (Clemson University), Alessandra Bonfanti (Politecnico di Milano) Giulia Celora (University of Oxford) Kelsey Gasior (University of Notre Dame) Qixuan Wang (University of California, Riverside)

Note: this minisymposia has multiple sessions. The other session is: and Part-1.

1. Merlin Pelz University of Minnesota
   "Effect of compartmentalization: synchronization and symmetry-breaking of diffusively coupled cells in 2-D and 3-D"
The Kuramoto model has been used in the last decades to gain insight into the behaviour of coupled discrete oscillators, as it is simple enough to be analyzed and exhibits a breadth of possible behaviours, such as synchronization, oscillation quenching, and chaos. However, the question arises how one can derive precise coupling terms between spatially localized oscillators, e.g., cells, that interact through a time-dependent diffusion field. We focus on a compartmental-reaction diffusion system with nonlinear intracellular kinetics of two species inside each small and well-separated cell with reactive boundary conditions. For the case of one bulk-diffusing species in ℝ² and ℝ³, we derive new memory-dependent integro-ODE systems that characterize how intracellular oscillations in the collection of cells are coupled through the PDE bulk-diffusion field. By using a fast numerical approach relying on the ``sum-of-exponentials'' method to derive a time-marching scheme for this nonlocal system, diffusion induced synchrony (in-phase, anti-phase, mixed-mode etc.) is examined for various spatial arrangements of cells. This theoretical modelling framework, relevant when spatially localized nonlinear oscillators are coupled through a PDE diffusion field, is distinct from the traditional Kuramoto paradigm for studying oscillator synchronization on networks or graphs. It opens up new avenues for characterizing synchronization phenomena associated with various discrete oscillatory systems in the sciences, such as quorum-sensing behaviour. Allowing for two bulk-diffusing species, our systems show that cell group symmetry-breaking can be achieved due to an exceeding cell membrane permeability ratio of the two species while their diffusivities in the bulk are on the same order. This behaviour cannot be obtained with standard two-species reaction-diffusion systems that were mentioned first in Turing's pioneering work on morphogenesis. Our systems expose a simple way through which cell specialization may emerge robustly. (This is joint work with Michael J. Ward.)
2. Sharon Lubkin North Carolina State University
   "Geometry, pattern, and mechanics of notochords"
Chordocytes, in early zebrafish and other teleost notochords, have been shown to pack in a small number of stereotyped patterns. Mutations or treatments which disrupt the typical patterning are associated with developmental defects, including scoliosis. The dominant WT “staircase” pattern is the only regular pattern displaying transverse eccentricity. Morphometry and pattern analysis have established a length ratio governing which patterns will be observed. Physical models of cell packing in the notochord have established relationships between this geometric ratio, a mechanical tension ratio, the transverse aspect ratio, pattern, pressure, and taper. Since a major function of the early notochord is to act as both a column and a beam, we aim to understand the overall resistance to compression and bending in terms of these mesoscale cell/tissue properties. To frame the relationships between these properties, we have developed a model of the notochord as an elastic closed-cell foam, packed in either the “staircase” or “bamboo” pattern. A pressure study reveals a surprising lack of shape change as internal notochord pressure is varied, and determines the tension ratio between different surfaces in the notochord in terms of the relative stiffnesses and internal pressure. A bending study reveals that deformations of the model notochords are well described by classical beam theory, and determines the flexural rigidity of the model notochords in terms of relative stiffnesses and pressure. We find that the staircase pattern is more than twice as stiff as the bamboo pattern. Moreover, the staircase pattern is more than twice as stiff in lateral bending as in dorsoventral bending. This biomechanical difference may provide a specific developmental advantage to regulating the cell packing pattern in early-stage notochords. Partially funded by Simons Foundation grant 524764.
3. Anna Nelson University of New Mexico
   "Modeling mechanisms of microtubule growth and nucleation in living neurons"
The stability and polarity of the microtubule cytoskeleton is required for long-range, sustained transport within neuronal cells. In particular, the healthy microtubule cytoskeleton is comprised of tubulin protein and is stable with a particular orientation. However, when injured, these microtubules are dynamic, rearrange their orientation, and the appearance of microtubules is up-regulated. It is unknown what mechanisms are involved in this balance between dynamic rearrangement and sustained function. Using a stochastic mathematical model that incorporates experimental data, we seek to understand how nucleation can impact microtubule growth dynamics in dendrites of fruit fly neurons. In the stochastic model, we assume two mechanisms limit microtubule growth: limited tubulin availability and the dependence of shrinking events on microtubule length. To better understand our stochastic model, we develop a partial differential equation (PDE) model that describes microtubule growth and nucleation dynamics, and we compare analytical results to results from the complex stochastic model. Insights from these models can then be used to understand what mechanisms are used organize into polarized structures in neurons, and how microtubule dynamics, like nucleation, may impact cargo localization post-injury.
4. Julio Belmonte North Carolina State University
   "Brillouin Microscopy and Physical Modelling Reveal the Role of Dynamic Changes in Cell Material Properties During Gastrulation"
During animal development, the acquisition of three-dimensional morphology is a direct consequence of the dynamic interaction between cellular forces and cell/tissue compliance. While the generation and transmission of cellular forces has been widely explored, less is known about cell material properties, which are often assumed to be uniform and constant during morphogenesis. Using line-scan Brillouin microscopy we found that cells in the Drosophila embryo undergo rapid and spatially varying changes in their material properties along their apical-basal axis during gastrulation. We identify microtubules as potential effectors of cell mechanics in this system, which show progressive enrichment and alignment along the apical-basal axis of central mesodermal cells during furrow formation. We corroborate our experimental findings with a novel agent-based physical model of gastrulation using the Cellular Potts model. Our model highlights for the first time the importance of cell's longitudinal (apical-basal) stiffness in translating actin-driven apical constriction into cell shape changes; shows that only variation in cells' sub-apical compartment stiffness contributes to furrow formation; and predicts that, while stiffer mesoderm correlates with deeper furrows, better outcomes are achieved if cells are initially softer and stiffen over time, as seen in our Brillouin measurements. Our work provides the first spatio-temporal description of the rapidly evolving material properties of cell populations during morphogenesis, highlights the potential of Brillouin microscopy in studying the dynamic changes in cell material properties, and suggests a new role for microtubules during gastrulation.

Organized by: Fabian Spill (University of Birmingham), Anotida Madzvamuse, University of British Columbia

Note: this minisymposia has multiple sessions. The other session is: and Part-1.

1. Gulsemay Yigit The University of British Columbia
   "Reaction-Diffusion Systems in Bilayer Geometries with Variable Width"
In this talk, we study reaction-diffusion systems when the width of the bilayer geometry is varied. Our aim is to understand the influence of bilayer geometries, and their role in pattern formation. Bilayer geometries are fundamental in cellular and developmental biology; bilayer structures of the cytosol-cortex mechanism significantly affect the diffusion and reaction rates of molecules which are essential in cell signaling. As the width of the thin layer geometries becomes smaller and smaller, the Laplace operator representing classical planar diffusion becomes the Laplace-Beltrami operator representing surface diffusion. Furthermore, we exploit the thin-layer approximation to explore and understand conditions for the diffusion-driven instabilities. Finally, we present bulk- and surface-finite element simulations of the reaction-diffusion systems on bilayer geometries with variable width sizes.
2. Maryam Parvizi University of Birmingham
   "A Mathematical Energy-Based Framework for Modeling Single-Cell Epithelial Migration"
We propose a comprehensive energy-based mathematical framework for modeling singlecell epithelial migration, integrating key intracellular mechanisms that drive motility. This model unifies the dynamic interactions among endoplasmic reticulum (ER) morphology, cytoskeletal architecture, cell shape regulation, and migratory polarization. Specifically, our framework accounts for (i) structural transitions in the ER between sheet-like and tubular states, (ii) stochastic polymerization and depolymerization of actin filaments and microtubules, and (iii) the establishment and maintenance of front–rear polarity. These transitions are represented as metastable states within a global free-energy landscape, where mechanical coupling between the ER and cytoskeleton governs intracellular force distribution, organelle positioning, and shape adaptation. Central to this model is an extension of the Ginzburg–Landau theory , which we apply to describe key biophysical transitions: actin filament polymerization and depolymerization, microtubule instability, structural shifts in ER morphology (tubules versus sheets), and the establishment of spatial polarity. These phenomena are treated as transitions between metastable states governed by a global free energy functional. The ER–cytoskeleton interaction is modeled as a mechanically coupled system that influences force generation, intracellular trafficking, and front–rear organization.
3. Stephanie Portet University of Manitoba
   "Transport of intermediate filaments in cells"
Intermediate filaments are key components of the cytoskeleton, playing essential roles in cell mechanics, signalling and migration. Their organization into networks is a major determinant of their cellular functions. The spatiotemporal organization of intermediate filaments results from the interplay between assembly and disassembly processes, along with various modes of intracellular transport. In this talk, I will provide an overview of mathematical models used to investigate different aspects of the intracellular transport mechanisms of intermediate filaments. Co-authors – John C. Dallon (Department of Mathematics, Brigham Young University, Provo, Utha, USA) Sandrine Etienne-Manneville (CPMC, Institut Pasteur, Paris, France) and Youngmin Park (Department of Mathematics, University of Florida, Gainesville, Florida, USA)
4. Vijay Rajagopal The University of Melbourne
   "MitoMimics: Synthetic microscopy timelapse data for zero-annotation AI segmentation and tracking of mitochondrial dynamics"
Mitochondrial dynamics—the motion, fusion, division, and turnover of mitochondria—govern their capacity to produce energy and execute signaling roles. The growing interest in live imaging and tracking of these dynamics is hampered by current mitochondrial segmentation methods, which show limited accuracy, especially with low signal-to-noise ratio data. To address this challenge, we introduce MitoMimics, a software program that generates synthetic time-lapse movies of mitochondrial dynamics. AI models trained on MitoMimics-generated data outperform existing methods in mitochondria image segmentation. Furthermore, MitoMimics offers advanced capabilities: it segments individual mitochondria, tracks fusion and fission events, and maps emergent mitochondrial network dynamics by automated graph network construction and analysis.

Organized by: Daozhou Gao (Cleveland State University), Xingfu Zou, University of Western Ontario

Note: this minisymposia has multiple sessions. The other session is: and Part-2.

1. Sebastian Schreiber University of California, Davis
   "Impacts of the Tempo and Mode of Environmental Fluctuations on Population Growth"
Populations consist of individuals living in different states and experiencing temporally varying environmental conditions. Individuals may differ in their geographic location, stage of development (e.g. juvenile versus adult), or physiological state (infected or susceptible). Environmental conditions may vary due to abiotic (e.g. temperature) or biotic (e.g. resource availability) factors. As survival, growth, and reproduction of individuals depend on their state and the environmental conditions, environmental fluctuations often impact population growth. Here, we examine to what extent the tempo and mode of these fluctuations matter for population growth. We model population growth for a population with $d$ individual states and experiencing $N$ different environmental states. The models are switching, linear ordinary differential equations $x'(t)=A(sigma(omega t))x(t)$ where $x(t)=(x_1(t),dots,x_d(t))$ corresponds to the population densities in the $d$ individual states, $sigma(t)$ is a piece-wise constant function representing the fluctuations in the environmental states $1,dots,N$, $omega$ is the frequency of the environmental fluctuations, and $A(1),dots,A(n)$ are Metzler matrices representing the population dynamics in the environmental states $1,dots,N$. $sigma(t)$ can either be a periodic function or correspond to a continuous-time Markov chain. Under suitable conditions, there exists a Lyapunov exponent $Lambda(omega)$ such that $lim_{ttoinfty} frac{1}{t}logsum_i x_i(t)=Lambda(omega)$ for all non-negative, non-zero initial conditions $x(0)$ (with probability one in the random case). For both random and periodic switching, we derive analytical first-order and second-order approximations of $Lambda(omega)$ in the limits of slow ($omegato 0$) and fast ($omegatoinfty$) environmental fluctuations. When the order of switching and the average switching times are equal, we show that the first-order approximations of $Lambda(omega)$ are equivalent in the slow-switching limit, but not in the fast-switching limit. Hence, the mode (random versus periodic) of switching matters for population growth. We illustrate our results with applications to a simple stage-structured model and a general spatially structured model. When dispersal rates are symmetric, the first order approximations suggest that population growth rates increase with the frequency of switching -- consistent with earlier work on periodic switching. In the absence of dispersal symmetry, we demonstrate that $Lambda(omega)$ can be non-monotonic in $omega$. In conclusion, our results show that population growth rates often depend both on the tempo ($omega$) and mode (random versus deterministic) of the environmental fluctuations. This work is in collaboration with Pierre Monmarch'{e} (Institut universitaire de France) and '{E}douard Strickler (Universit'{e} de Lorraine).
2. Adrian Lam Ohio State University
   "Can Spatial Heterogeneity Alone Lead to Selection for Dispersal?"
In a seminal paper, A. Hastings showed by pairwise invasbility analysis that in a stationary environment, species modeled by the diffusive logistic equation evolves towards smaller diffusion rate. A particular consequence is that in the competition model of N species differing only by the diffusion rate, an equilibrium is locally stable if and only if it is the one dominated by the slowest moving species, assuming other factors are equal. It is conjectured that such an equilibrium is also globally attractive, namely, the slowest moving species always competitively exclude all other species. In the first part of the talk, we survey some recent progress on the conjecture. In the second part of the talk, we describe a recent competition experiment with nematode worm population performed by B. Zhang, in which fast dispersal can be advantageous even though there is little temporal fluctuation in the environment. Motivated by the experimental observation, we introduce a single population model where the organism switches between two alternative physiological states (high vs low food storage), and demonstrate that for such a population model, fast diffusion can be selected in stationary environments.
3. Yijun Lou The Hong Kong Polytechnic University
   "Dynamics of a Reaction-diffusion System with Time-periodic and Spatially Dependent Delay: A Quotient Space Approach"
Understanding the impact of temporal and spatial heterogeneity on population dynamics has significantly advanced mathematical theories in reaction-diffusion systems. This talk reports the global dynamics of a reaction-diffusion system with time delay, where all model parameters are spatially and temporally dependent. The main focus lie in threefold: (i) formulating a stage-structured model that incorporates diffusion and temporally and spatially inhomogeneous development delay; (ii) proposing a dynamical systems framework that employs a quotient phase space to establish strong monotonicity of the periodic semiflow; (iii) establishing a threshold-type result under minimal assumptions, for both increasing and unimodal birth functions. This synthesized approach is expected to motivate further studies when strong monotonicity of the solution semiflow fails in conventional phase spaces.
4. Chunyi Gai University of Northern British Columbia
   "Resource-mediated Competition between Two Plant Species with Different Rates of Water Intake"
We propose an extension of the well-known Klausmeier model of vegetation to two plant species that consume water at different rates. Rather than competing directly, the plants compete through their intake of water, which is a shared resource between them. In semi-arid regions, the Klausmeier model produces vegetation spot patterns. We are interested in how the competition for water affects the co-existence and stability of patches of different plant species. We consider two plant types: a “thirsty” species and a “frugal” species, that only differ by the amount of water they consume per unit growth, while being identical in other aspects. We find that there is a finite range of precipitation rate for which two species can co-exist. Outside of that range (when the rate is either sufficiently low or high), the frugal species outcompetes the thirsty species. As the precipitation rate is decreased, there is a sequence of stability thresholds such that thirsty plant patches are the first to die off, while the frugal spots remain resilient for longer. The pattern consisting of only frugal spots is the most resilient. The next-most-resilient pattern consists of all-thirsty patches, with the mixed pattern being less resilient than either of the homogeneous patterns. We also examine numerically what happens for very large precipitation rates. We find that for a sufficiently high rate, the frugal plant takes over the entire range, outcompeting the thirsty plant.

Organized by: Joshua S. Weitz (University of Maryland, Department of Biology & Physics and U of Maryland Institute for Health Computing), Asher Leeks, University of British Columbia, Department of Zoology

1. Antoni Luque University of Miami
   "Impact and prediction of phage decay in natural microbial communities"
Phage decay is a key factor in the ecology and evolution of phages and their bacterial hosts. However, estimating the phage decay of different viruses in a community remains challenging. In this talk, I will share the approach that my lab is developing to address this problem. It relies on three complementary strategies. First, I will introduce a new transient dynamic method that facilitates identifying when phage decay and other processes are relevant in the community and under what circumstances a tipping point is expected to occur and significantly impact the community’s dynamics. Second, I will share the multiscale methods we are integrating to obtain phage decay rates for different phages from genomic data. This step relies strongly on the ability to identify structural proteins in metagenomes and the combination of several biophysical models. Third, I will show our initial attempts to relate our modeling approaches to phage decay experiments from aquatic environmental communities. I will conclude by emphasizing how the strategies discussed here could be valuable for other viruses and for optimizing phage biotechnological applications.
2. Asher Leeks University of British Columbia
   "Modelling the dynamics of cheating in natural populations of filamentous phages"
Diverse species of filamentous phages are found across natural environments, often encoding bacterial virulence traits, antimicrobial resistance, and novel metabolic capacity. In the laboratory, filamentous phages are vulnerable to cheating: mutants spontaneously emerge which have deleted shared gene products, and as a result can out-replicate full-length cooperative phages in coinfection. If these cheat mutants also emerge and spread in natural filamentous phage populations, this would have profound consequences for our understanding of phage population dynamics, and the dependent ecological and pathogenic consequences. However, it is difficult to detect cheating in natural populations for two key reasons: we lack longitudinal data, and so cannot directly measure the fitness of putative cheats; and most filamentous phage species are known only from sequence data, hence we cannot predict a priori which genes might have been deleted by cheats. Here, we use a quantitative approach to overcome these limitations, in order to measure cheating in natural filamentous phage populations. We construct a birth-death model that incorporates mutation, demographic noise, and a frequency-dependent selective advantage to cheating. We explicitly model the distribution of genome lengths expected under different dynamical regimes possible in the model, showing that the selective advantage to cheating can be quantified without requiring longitudinal data, analogous to signatures of selection commonly used in population genetics. This approach allows us to identify which environments allow cheats to spread, which genes are cheated across uncharacterised filamentous species, and to explore the demographic consequences of cheating for natural filamentous phage populations.
3. Jaye Sudweeks University of British Columbia
   "Environmental feedback can maintain cooperation in phages"
The evolution and maintenance of cooperation is a fundamental problem in evolutionary biology. Because cooperative behaviors impose a cost, cooperators are vulnerable to exploitation by defectors that do not pay the cost to cooperate but still benefit from the cooperation of others. Bacteriophages exhibit cooperative and defective phenotypes in infection: during replication, phages produce essential gene products in the host cell environment. Coinfection between multiple phages is possible, so if a phage cannot guarantee exclusive access to its own gene products, the products act as a public good; cooperators contribute to the common pool while defectors contribute less and instead appropriate goods from cooperators. Defective phage phenotypes experience negative frequency dependence in coinfection. For some phages, negative frequency dependence is strong enough to maintain the cooperative phenotype. For other phages, negative frequency dependence alone is not sufficient to maintain the cooperative phenotype, in which case the fate of cooperation is unclear. Here we propose that if coinfection is not enforced, and host and viral densities can vary, environmental feedback can maintain cooperation in such phage populations by modulating the rate of co-infection and shifting the advantages of cooperation versus defection. We build and analyze an ODE model and find that for a wide range of parameter values, environmental feedback maintains cooperation.
4. Nanami Kubota University of Pittsburgh
   "Cheater phages drive bacterial and phage populations to lower fitness"
How can a less reproductively fit antagonist invade a seemingly fitter population? In this study, we can partially explain such a paradox in the context of Pseudomonas phages and game theory. Most Pseudomonas aeruginosa strains carry filamentous phages called Pf that establish chronic infections and do not require host lysis to spread. However, spontaneous mutations in the Pf repressor gene (pf5r) can facilitate extreme phage production, slowing bacterial growth and increasing cell death, violating an apparent détente between bacterium and phage. Furthermore, high intracellular phage replication enables another evolutionary conflict: “cheater miniphages” lacking capsid genes invade populations of full-length phages within cells. Despite the lower absolute fitness of the pf5r bacteria, bacteria carrying both hyperactive full-length phages and miniphages outcompete the wildtype bacteria in direct competition. Surprisingly, infection by both full-length phages and miniphages can shift games between infected bacteria and naïve, uninfected cells to prisoner’s dilemma, undermining coexistence. Finally, although bacteria containing full-length phages and miniphages are most immune to superinfection by limiting the Pf receptor, this hybrid is extremely unstable, as a classic Tragedy of the Commons scenario results in complete prophage loss. The entire cycle–from phage hyperactivation to miniphage invasion to prophage loss–can occur within 24 hours, showcasing rapid coevolution between bacteria and their filamentous phages. This study demonstrates that P. aeruginosa, and potentially many other bacterial species that carry filamentous prophages, risk being exploited by Pf phages in a runaway process that reduces the fitness of both host and virus.

Organized by: Frank M. Hilker (Osnabrück University), Rebecca C. Tyson (University of British Columbia Okanagan)

1. Brian Beckage University of Vermont
   "Why We Do What We Do: A Mathematical Framework for Modeling Human Behavior in Coupled Human-Environmental Systems"
Many 'wicked' problems superficially appear to be problems in management of environmental systems but are actually problems in the interactions of human social and behavioral systems (HSBs) with biophysical systems. Prominent examples include climate change, loss of biodiversity, emerging diseases, or any number of the planetary boundaries that the Earth system is being pushed beyond. The models used to address these wicked problems have traditionally paid minimal attention to the social and behavioral system using static scenarios or low dimensional representations of the human system while expending great effort to represent the biophysical system in great detail. The focus on the biophysical system stems in part from the fundamental limitation in how to represent the human behavioral and social system in mathematical and computational models. There are a large number of diverse theories proposed to understand various aspects of human behavior but few of these have been translated into mathematical or algorithmic representations. We present a framework that represents a minimal set of processes for constructing computational models of human behavioral systems. This framework, based on key processes of contagion and cognition within a cultural context, enables more realistic modeling of human-environment interactions and could improve our ability to address critical environmental challenges.
2. Jonas Wahl Osnabrück University, Germany
   "Evolutionary dynamics of constant and proportional harvest strategies in a coupled human-environment system with dynamic resources"
Two of the classical harvesting strategies considered in ecological modelling are constant and proportional harvesting. They show different characteristics in their impact on a harvested resource or population. While these strategies and their consequences are well-documented on their own and fully analyzed in isolation, this talk will put the strategies in a competition within one joint model: each of the two strategies is represented by the fraction of harvesters applying it to an underlying logistically growing resource, and the fractions dynamically change according to the replicator equation from evolutionary game theory, which is set up based on the economic payoff of the strategies. This is done for a model with a fixed number of harvesters and a model with a dynamic number of harvesters. The talk will present an analysis of the models' equilibria and their stability leading to a bifurcation analysis, which is then used to derive the economical and ecological implications of the models as well as to interpret the results of the competition of the harvesting strategies with an additional focus on the management of such a system, especially regarding the regulation of access to the resource.
3. Amrita Punnavajhala University of Waterloo
   "Region-level mitigation in a coupled social-climate model"
Mathematical models of climate change have traditionally described anthropogenic carbon emissions as functions of evolving socio-economic scenarios. A drawback of this approach is that the underlying dynamics of human behaviour that are, ultimately, responsible for the carbon emissions causing contemporary climate change, are ignored. So far, there exist a handful of `social-climate’ models that address this shortcoming, results from which make a compelling case for the inclusion of social and behavioural processes in models of climate change. We have constructed and analyzed a coupled social-climate model with region-level structure, parameterized by data on costs of renewables, vulnerability to climate change and the strength of social norms, combined with socio-economic data. Our results show that social learning rates have an outsized effect on mitigation across all regions, mitigation progresses spreads faster in regions more vulnerable to climate change impacts and that interventions to increase mitigation are more effective when introduced early and universally. While increasing the social learning rate always reduces the magnitude of the peak temperature, the time at which this peak occurs can be move forward or backward, depending on which region the increase is implemented in.
4. Christina A. Cobbold University of Glasgow
   "Mathematics for Rewilding: opportunities and challenges"
Achieving a sustainable coexistence of humans with well-functioning ecological systems providing key essential ecosystem services is now vitally important under global change. Rewilding is an increasingly popular approach which provides a paradigm shift to return degraded ecosystems to a state regulated by natural processes, by using and recovering ecological processes, interactions and conditions. Crucially, rewilding occurs in complex systems over large spatio-temporal scales, under high uncertainty. Predicting such ecological changes also requires integration with socio-economic dimensions and thinking. We evaluate the current state of the quantitative treatment of rewilding, highlighting significant deficiencies and opportunities for harnessing mathematics for rewilding. We present an emerging quantitative framework, encompassing four key areas across the entire cycle of rewilding projects - design and planning, metrics for assessment, ecological modelling, and coupled human-ecological systems, informed by recent progress in multiple areas of mathematics and ecological modelling.

Organized by: Zhisheng Shuai (University of Central Florida), Junping Shi, College of William & Mary; Yixiang Wu, Middle Tennessee State University

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, and Part-3.

1. Tingting Tang San Diego State University
   "Exploring the impact of household size on COVID-19 with coupled SEAIR mode"
During the COVID pandemic, studies have found increasing evidence indicating indoor transmission is very significant and secondary infection rate from household transmission is high. Heterogeneity of transmission among different household has shown higher contact frequency contribute to higher transmission. In this talk, we study the role of household size in the spreading of the virus by developing a coupled SEAIR model. The reproduction number is calculated analytically under simplified condition. Global sensitivity study shows that the contact frequency among family members has high impact on the basic reproduction number, peak infection time and volume. In comparison, quarantined effectiveness from large or small household has little implications.
2. Collin Kilmer University of Tennessee at Chattanooga
   "Modeling Zoonotic Disease Transmission Under the Impact of Land Use Change"
Land conversion is occurring worldwide due to a growing population and expanding economy. This process increases the likelihood of pathogen spillover, posing significant economic and public health risks. The objective of this presentation is to investigate pathogen spillover from three distinct reservoir species to humans under the impact of land use change. Our models introduce a land conversion index to capture the dependence of the carrying capacity and death rate of wildlife on the proportion of converted land. This index is then used to examine how different levels of land conversion influence pathogen spillover. This is a joint work with Prof. Xiunan Wang at the University of Tennessee at Chattanooga.
3. Han Lu University of Alberta
   "Analysis of a diffusive host-pathogen epidemic model with two-stage mechanism in a spatially heterogeneous environment"
Due to the spatial heterogeneity present in many aspects of disease transmission, the rate of transmission of infectious diseases, human birth/mortality rate, and the mobility ability of infected humans should be different in different geographical locations. On the other hand, infected humans may exhibit distinct differences in symptoms during the different stages of the disease transmission. This paper aims to study threshold dynamics of a reaction-diffusion host-pathogen model governed by two-stage mechanism and no flux boundary condition. By carrying out strict analysis, the paper establishes the threshold-type results with the basic reproduction number. Specifically, in a homogeneous case that all parameters are constants, we establish the global attractivity of the endemic equilibrium. Our numerical results validate the theoretical results and indicate the importance of the infected humans in the second stage and pathogens in the environment in disease transmission, which greatly contribute to disease spread in a bounded domain and should not be ignored.
4. Sameras Pal University of Kalyani, India
   "The impact of microbial diseases of corals under macroalgal toxicity, overfishing and rising sea surface temperature (SST)"
Competition between macroalgae and corals for occupying the available space in sea bed is an important ecological process underlying coral-reef dynamic. We investigate coral-macroalgal phase shift in presence of macroalgal allelopathy and microbial infection on corals by means of an eco-epidemiological model under the assumption that the transmission of infection occurs through both contagious and non-contagious pathways. We also investigate coral-macroalgal phase shift in presence of elevated SST and macroalgal toxicity. We found that the system is capable of exhibiting the existence of two stable configurations by saddle-node bifurcations.

Organized by: Hye-Won Kang (University of Maryland Baltimore County), Arnab Ganguly, Louisiana State University, aganguly@lsu.edu

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, and Part-3.

1. Joshua McGinnis University of Pennsylvania
   "Homogenization of a Spatially Extended, Stochastic Ion Channel Model"
Simulations of stochastic neuron potential models, which describe the voltage potential along the length of a neuron’s axon and incorporate ion channel noise as Gaussian fluctuations, have shown that channel noise can induce complex phenomena such as jitters and splitting of action potentials [1] and place constraints on the miniaturization of axons [2]. To develop a robust analytic framework for understanding stochastic effects of channel noise on action potential propagation in a neuron, we need to begin by investigating how many independent, spatially distributed ion channels can collectively yield deterministic behavior. We start with an electrophysiological derivation of a simple discrete model and contrast this with a common, yet less physically accurate approach where the law of large numbers and the central limit theorem are more easily applied. Our model couples a spatially discretized diffusive PDE for the voltage with continuous-time Markov processes that govern the behavior of the ion channels. We will then outline an argument using homogenization theory to estimate the rate of strong convergence to the typical deterministic PDE as the spacing between ion channels approaches zero. Finally, we present a numerical technique for simulating our model and discuss the challenges involved in increasing computational efficiency of simulations. [1] Faisal AA, Laughlin SB. Stochastic simulations on the reliability of action potential propagation in thin axons. PLoS Comput Biol. 2007 May;3(5):e79. doi: 10.1371/journal.pcbi.0030079. PMID: 17480115; PMCID: PMC1864994. [2] Faisal AA, White JA, Laughlin SB. Ion-channel noise places limits on the miniaturization of the brain's wiring. Curr Biol. 2005 Jun 21;15(12):1143-9. doi: 10.1016/j.cub.2005.05.056. PMID: 15964281.
2. Radek Erban University of Oxford
   "Chemical Reaction Networks: Systematic Design, Limit Cycles and Spatio-Temporal Modelling"
I will discuss mathematical methods for describing biochemical reaction networks, with applications to modelling of intracellular processes. Several types of mathematical models of chemical reaction systems will be considered, including (i) deterministic models which are written in terms of reaction rate equations (i.e. ordinary differential equations (ODEs) for concentrations of chemical species involved); (ii) stochastic models of reaction networks, given in terms of the Gillespie stochastic simulation algorithm, which provides more detailed information about the simulated system than ODEs; and (iii) spatio-temporal models described by the reaction-diffusion master equation and Brownian dynamics simulations. I will discuss methods for systematic design of relatively simple reaction systems with prescribed dynamical behaviour, including reaction systems with multiple oscillating solutions (limit cycles). I will also present methods for efficient spatio-temporal modelling of intracellular processes.
3. David Lipshutz Baylor College of Medicine
   "Methods for Comparing Sensitivities of Stochastic Neural Networks"
Biological neural networks (and some artificial neural networks) transform stimuli into stochastic neural responses. Each network induces a Riemannian geometry in stimulus space via the Fisher-Rao metric and it is of interest in various applications to compare the local geometries on stimulus space that are induced by different networks. Such comparisons can be challenging when stimulus space is high-dimensional (e.g., images), so one approach is to identify a few directions in stimulus space along which to compare the induced geometries. We propose a method for optimally selecting directions in stimulus space that maximally differentiate a set of networks in terms of the induced local geometries along these directions. We apply our method to compare a set of simple models of the early visual system and show that our method produces image distortions that allow for immediate visual comparison of these models. This is joint work with Jenelle Feather, Sarah Harvey, Alex Williams and Eero Simoncelli.
4. TBA TBA
   "TBA"
TBA

Organized by: Jinsu Kim (POSTECH), Eric Foxall (The University of British Columbia - Okanagan Campus), and Linh Huynh (Dartmouth College)

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, Part-2, and Part-4.

1. Hwai-Ray Tung University of Utah
   "Extreme first passage times with fast immigration"
Many scientific questions can be framed as asking for a first passage time (FPT), which generically describes the time it takes a random 'searcher' to find a 'target.' The important timescale in a variety of biophysical systems is the time it takes the fastest searcher(s) to find a target out of many searchers. Previous work on such fastest FPTs assumes that all searchers are initially present in the domain, which makes the problem amenable to extreme value theory. In this paper, we consider an alternative model in which searchers progressively enter the domain at some 'immigration' rate, which may be constant, time inhomogeneous, or proportional to the population size. In the fast immigration rate limit, we determine the probability distribution and moments of the k-th fastest FPT. Our rigorous theory applies to many models of stochastic motion, including random walks on discrete networks and diffusion on continuous state spaces. Mathematically, our analysis involves studying the extrema of an infinite sequence of random variables which are both not independent and not identically distributed. Our results constitute a rare instance in which extreme value statistics can be determined exactly for strongly correlated random variables.

Organized by: Tomas Helikar (University of Nebraska - Lincoln), Juilee Thakar (Juilee_Thakar@URMC.Rochester.edu) - University of Rochester Medical Center James Glazier (jaglazier@gmail.com) - Indiana University

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, and Part-2.

1. Juilee Thakar University of Rochester
   "Monocyte digital twin and HIV associated vascular disease"
People living with HIV (PLWH) continue to show a heightened risk for atherosclerosis (AS) even under effective antiretroviral therapy (ART). Monocytes are key drivers of AS pathogenesis. They can directly contribute to lesion formation by differentiating into lipid-laden macrophages (foam cells) in the arterial intima. Indirectly, their persistent immune activation and secretion of inflammatory cytokines support chronic inflammation, a hallmark of HIV-associated vascular disease. Because monocytes continuously replenish the macrophage pool in the vessel wall, they represent an important early predictor of AS progression in HIV. To investigate this, we performed single-cell transcriptomic profiling of 138,487 circulating monocytes from four well-matched participant groups—HIV-AS−, HIV-AS+, HIV+AS−, and HIV+AS+—stratified by age, sex, and Reynolds cardiovascular risk score. We identified eight transcriptionally distinct monocyte subsets, including canonical CD14+ cells and a previously undescribed population characterized by platelet interaction, referred to as platelet-monocyte complexes (PMCs). We used Boolean Omics Network Invariant Time Analysis (BONITA) developed in our group to identify pathway specific stable cellular states and their basin of attraction. Using these cellular states we have defined monocyte digital twins that predict the AS pathogenesis.
2. Esteban Hernandez Vargas University of Idaho
   "Adaptive Observers in Digital Twins for Drug Resistance Mitigation in HIV"
High mutation rates in HIV pose a significant challenge for long-term therapy, as the virus can quickly develop resistance to specific antiretroviral drugs. Despite extensive research, there remains no clear consensus on how to schedule treatments to maintain viral suppression and mitigate resistance optimally. In this talk, I present a digital twin framework for modeling HIV mutation dynamics, employing an adaptive observer to approximate a surrogate of a higher-order nonlinear mutation model. This approach enables us to monitor and anticipate the emergence of drug-resistant strains in silico, providing a foundation for exploring adaptive treatment strategies. Preliminary simulation results indicate that this computational framework can outperform standard clinical scheduling recommendations, offering a more individualized and responsive alternative to conventional therapy. This work represents a step toward leveraging digital twins to support clinical decision-making in the treatment of complex, mutating viral infections. Funding: This research was supported by the National Science Foundation grant DMS -2315862.
3. Heber L. Rocha Indiana University
   "Multiscale Modeling of Immune Surveillance for Cancer Patient Digital Twins"
Tumors are complex ecosystems characterized by heterogeneous cellular behaviors, intercellular interactions, and stochastic processes, which collectively challenge the development of personalized cancer therapies due to unpredictable therapeutic responses. Digital twins—computational representations of individual patients—offer a transformative approach to simulate and predict treatment outcomes, enabling precision oncology. This presentation describes an multiscale agent-based model, developed using the PhysiCell framework, to investigate immune surveillance in micrometastases, early metastatic clusters critical to cancer progression. Through high-throughput simulations of over 100,000 virtual patient trajectories, our model revealed a spectrum of outcomes, ranging from tumor proliferation to immune-mediated eradication. These analyses identified critical parameters, such as immune cell functionality and tumor immunogenicity, that govern these divergent dynamics. These findings provide a robust foundation for constructing cancer patient digital twins to optimize therapeutic strategies. To enhance model reliability, our ongoing efforts focus on uncertainty quantification, employing sensitivity analysis and parameter calibration to address inherent biological variability and epistemic uncertainties, thereby advancing the development of clinically actionable digital twins.
4. Gary An University of Vermont
   "NASEM-compliant Critical Illness Digital Twins to cure sepsis"
To date there are no pharmacological agents that can substantively and reliably affect the underlying host pathophysiology of sepsis. The effective control of sepsis requires personalized precision medicine, which requires the capabilities provided by digital twins compliant with industrial standards and consistent with the definition put forth in the National Academies of Science, Engineering and Medicine (NASEM) report entitled 'Foundational Research Gaps and Future Directions for Digital Twins' that provides an operational definition for a digital twin and lists specific challenges moving forward for the development of this technology. NASEM defines a digital twin thusly: 'The key elements that comprise a digital twin include (1) modeling and simulation to create a virtual representation of a physical counterpart, and (2) a bidirectional interaction between the virtual and the physical. This bidirectional interaction forms a feedback loop that comprises dynamic data-driven model updating (e.g., sensor fusion, inversion, data assimilation) and optimal decision-making (e.g., control, sensor steering).' Notably, this definition is not met by the vast majority of currently described biomedical “digital twins,” and this insufficiency limits the applicability of non-NASEM compliant digital twins to provide the true personalized precision medicine required to treat complex immune diseases such as sepsis. We present a prototype Critical Illness Digital Twin developed with a workflow that utilizes mechanistic models with machine learning and artificial intelligence for clinically relevant parameter space identification, trajectory personalization, discovery of novel multimodal/adaptive therapeutic control and guidance for sensor/actuator development. The CIDT is based on a previously validated agent-based model of systemic inflammation, and constructed to conform to a mathematical object terms the Model Rule Matrix (MRM). The MRM employs the Maximal Entropy Principle to account for the latent space of 'what is left out' (e.g. Epistemic Uncertainty) in the rule structure of the CIDT. Operating on the CIDT with a workflow that includes genetic algorithms and active learning we identified non-falsifiable configurations of the MRM with respect to two distinct clinical cytokine time-series datasets, one for burns, one for trauma. We further applied deep reinforcement learning to train an artificial intelligence that can cure sepsis arising from a novel pathogen by modulating host cytokines using only currently FDA-approved biologics. Additional future work must include testing with a sufficiently complex large animal model that can recapitulate the heterogeneity seen in clinical sepsis.

Organized by: Raluca EFTIMIE (University of Marie & Louis Pasteur, France), Dumitru TRUCU, University of Dundee, UK

1. 1. Marom Yosef*, Svetlana Bunimovich Ariel University
   "Mathematical Models to Improve Bladder Cancer Therapies"
Bladder cancer (BC) represents a significant clinical challenge, affecting 549,000 new patients annually, with over 200,000 deaths per year. Despite initial surgical intervention, approximately 70%, of patients experience tumor recurrence, necessitating additional treatment. The current gold standard, Bacillus Calmette-Guérin (BCG) immunotherapy, demonstrates limited efficacy: only 50% of patients achieve complete response, while 80% experience adverse effects ranging from mild discomfort to severe complications requiring treatment discontinuation. In the first part of my talk, I show the mathematical models to improve BCG therapy and have explored various protocols, including six-week induction therapy and extended maintenance treatments. However, these modifications have shown limited success in improving patient outcomes. Recent models including combining BCG with interleukin-2 (IL-2) or Interferon (IFN) immunomodulator therapy have demonstrated promising results, potentially enabling reduced BCG dosages while maintaining therapeutic efficacy. However, the unpredictable nature of immune responses to this combined treatment has hindered its widespread clinical adoption. I present a significant advance in translating mathematical modeling into clinical practice, enabling more precise and personalized treatment protocols while minimizing adverse effects. The framework's ability to provide stable, analytical solutions for combined immunotherapy treatments offers immediate applications for BC treatment optimization and broader implications for other immunotherapy-based cancer treatments. In the second part of the talk, I explain the mathematical model for optimizing Mitomycin-C (MMC) treatment for BC. Current drug dosing strategies rely on general guidelines without precise quantitative justification. Our model revolutionizes this approach by introducing analysis for drug-tumor interactions. While existing methods cannot predict required drug doses theoretically, our framework enables precise calculation of MMC concentrations needed for tumor elimination based on specific tumor characteristics. This innovation transforms MMC dosing from an empirical process to a mathematically guided procedure. These innovations enable a shift from standardized protocols to personalized treatment strategies. Unlike current approaches that modify treatments through trial and error, our models provide a theoretical foundation for optimizing treatment protocols based on individual tumor characteristics, potentially improving outcomes while minimizing unnecessary drug exposure. Keywords: bladder cancer, immunotherapy, BCG treatment, Mitomycin-C, mathematical modeling, tumor-immune interactions, treatment optimization, personalized medicine
2. Haralampos Hatzikirou: Khalifa University
   "From cell patterns in biopsies to clinical predictions"
Understanding the dynamic role of immune cells in cancer progression is essential for predicting disease outcomes and developing targeted therapies. This talk delves into the transition from cellular patterns observed in biopsies to clinical predictions, with a particular focus on the role of macrophages in the tumor microenvironment (TME). Drawing on advanced computational models and experimental data, we explore how macrophage phenotypic changes, particularly their transition from pro-inflammatory to pro-tumorigenic (M2) states, influence tumor progression and recurrence. By examining macrophage-fibroblast interactions in kidney transplant biopsies, we uncover key insights into macrophage behavior that can be translated to cancer research, particularly in gliomas and other solid tumors. The talk will discuss how macrophage dynamics, observed through transcriptomic profiling and tissue-specific modeling, can be integrated into predictive models of tumor growth and recurrence. This framework has the potential to improve clinical decision-making by enabling earlier interventions and more accurate predictions of treatment outcomes, highlighting the importance of macrophage-driven processes in cancer biology.
3. Ali Daher University of Marie & Louis Pasteur
   "Integrating High-Throughput Genomic Data with Biologically-Informed Models of Spatiotemporal Dynamics of Skin Lesions: A Computational Parameter Extraction Pipeline"
Skin wound healing typically progresses through three chronologically overlapping stages: inflammation, proliferation, and remodelling [1]. However, in some cases, prolonged or excessive inflammatory and proliferative phases can lead to abnormal wound healing; one such example is keloid scarring. Keloids are benign fibroproliferative tumours characterized by excessive collagen production and extracellular matrix (ECM) deposition by fibroblasts following dermal injury or irritation. Known for their aggressive nature and pathological spread beyond the original wound boundaries, keloids often result in disfiguring scars, have high recurrence rates, and show poor response to current treatment approaches. The rapid advancement of single-cell RNA sequencing (scRNA-seq) techniques has enabled detailed characterization of the cellular landscape, heterogeneity, and intercellular interactions in skin samples from both normal and abnormal wound healing. In the case of keloids, studies have revealed high immune cell infiltration, with a positive correlation between immune cell abundance and keloid recurrence [2]. Additional findings have identified close interactions between immune cells and fibroblasts, whereby immune cells release cytokines and growth factors that drive ECM production and fibroblast proliferation, further fuelling keloid progression [2]. As such, keloids are increasingly regarded as an inflammatory skin disease [2]. Given the limited success of current treatments in resolving or preventing keloid formation and recurrence and the growing evidence of the inflammatory component of keloids, immunotherapy has emerged as a promising novel treatment avenue [3-5], particularly by targeting the communication pathways between immune cells and fibroblasts [2,6]. One prominent communication pathway is mediated by TGF-β, a key effector cytokine secreted by inflammatory cells that promotes fibrotic responses in fibroblasts. Several investigational agents targeting the TGF-β pathway are currently underway in clinical trials for fibrotic and cancer-related diseases [2,7]. However, our current understanding of the immunological underpinnings of keloid pathogenesis remains neither specific nor comprehensive, limiting the effective development of targeted immunotherapies. For instance, persistent inhibition of TGF-β can suppress fibrosis but may also eliminate its anti-inflammatory functions, potentially exacerbating inflammation [8]. The integration of high-throughput genomics technologies, such as scRNA-seq and spatial transcriptomics, has advanced our understanding of the spatial cellular architecture and communication networks in skin wounds, including keloids. Nevertheless, the data generated from these high-resolution technologies alone are insufficient to fully elucidate the inflammatory origins and progression of keloids or to reliably identify optimal immunotherapeutic strategies. In this context, mathematical and computational models, especially spatiotemporal ones, provide powerful complementary tools. They enable the integration and interpretation of experimental data, facilitating in-silico experimentation and hypothesis testing of biological mechanisms underlying normal and abnormal wound healing. These models can simulate the spatiotemporal dynamics of wound healing and keloid progression, offering insights not readily obtainable through conventional experiments. Additionally, they serve as safe and cost-effective testbeds for evaluating immunotherapeutic interventions before clinical application. To this end, we first develop a biologically grounded model capturing the interactions between immune cells (primarily macrophages) and fibroblasts during wound healing. This is achieved through the construction of both particle-based and continuum reaction-diffusion models that describe the production, secretion, diffusion, and uptake of growth factors and ligands mediating these interactions. We then analyse high-throughput genomics data from skin samples of both normal and abnormal wound healing, leveraging matched scRNA-seq and spatial transcriptomics (Visium) data. Through spatial deconvolution, we infer cell type densities across the tissue domain, and we perform intercellular communication analyses to estimate the strength of interactions mediated by specific ligands. Subsequently, we develop a parameter learning framework that combines approximate Bayesian computation with machine learning and backpropagation techniques to infer the parameters of the reaction-diffusion model from the experimental data. By integrating a biologically informed mathematical framework with genomics-derived data, we ensure that our model is both mechanistically and data-driven—an essential requirement for clinical and research relevance. References 1. Liu, Z., et al. “538 Spatiotemporal Single-Cell Roadmap of Human Skin Wound Healing.” Journal of Investigative Dermatology, vol. 144, no. 12, Dec. 2024, p. S321. DOI.org, https://doi.org/10.1016/j.jid.2024.10.551. 2. Zhang, Xiya, et al. “The Communication from Immune Cells to the Fibroblasts in Keloids: Implications for Immunotherapy.” International Journal of Molecular Sciences, vol. 24, no. 20, Oct. 2023, p. 15475. DOI.org, https://doi.org/10.3390/ijms242015475. 3. Zhang, Tao, et al. “Current Potential Therapeutic Strategies Targeting the TGF-β/Smad Signaling Pathway to Attenuate Keloid and Hypertrophic Scar Formation.” Biomedicine & Pharmacotherapy, vol. 129, Sept. 2020, p. 110287. DOI.org, https://doi.org/10.1016/j.biopha.2020.110287. 4. Ekstein, Samuel F., et al. “Keloids: A Review of Therapeutic Management.” International Journal of Dermatology, vol. 60, no. 6, June 2021, pp. 661–71. DOI.org, https://doi.org/10.1111/ijd.15159. 5. Huang, Chenyu, et al. “Managing Keloid Scars: From Radiation Therapy to Actual and Potential Drug Deliveries.” International Wound Journal, vol. 16, no. 3, June 2019, pp. 852–59. DOI.org, https://doi.org/10.1111/iwj.13104. 6. Shan, Mengjie, and Youbin Wang. “Viewing Keloids within the Immune Microenvironment.” American Journal of Translational Research, vol. 14, no. 2, Feb. 2022, pp. 718–27. PubMed Central, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8902558/. 7. Moss, Marcia L., and Dmitry Minond. “Recent Advances in ADAM17 Research: A Promising Target for Cancer and Inflammation.” Mediators of Inflammation, vol. 2017, 2017, pp. 1–21. DOI.org, https://doi.org/10.1155/2017/9673537. 8. Teicher, Beverly A. “TGFβ-Directed Therapeutics: 2020.” Pharmacology & Therapeutics, vol. 217, Jan. 2021, p. 107666. DOI.org, https://doi.org/10.1016/j.pharmthera.2020.107666.
4. Donggu Lee(*,1), Sunju Oh(2), Sean Lawler(3), and Yangjin Kim (1,3) (1) Konkuk University, (2) Konkuk University, (3) Brown University
   "Bistable dynamics of TAN-NK cells in tumor growth and control of radiotherapy-induced neutropenia in lung cancer treatment"
Neutrophils play a crucial role in the innate immune response as a first line of defense in many diseases, including cancer. Tumor-associated neutrophils (TANs) can either promote or inhibit tumor growth in various steps of cancer progression via mutual interactions with cancer cells in a complex tumor microenvironment (TME). In this study, we developed and analyzed mathematical models to investigate the role of natural killer cells (NK cells) and the dynamic transition between N1 and N2 TAN phenotypes in killing cancer cells through key signaling networks and how adjuvant therapy with radiation can be used in combination to increase anti-tumor efficacy. We examined the complex immune-tumor dynamics among N1/N2 TANs, NK cells, and tumor cells, communicating through key extracellular mediators (Transforming growth factor (TGF-beta), Interferon gamma (IFN-gamma)) and intracellular regulation in the apoptosis signaling network. We developed several tumor prevention strategies to eradicate tumors, including combination (IFN-gamma, exogenous NK, TGF-beta inhibitor) therapy and optimally-controlled ionizing radiation in a complex TME. Using this model, we investigated the fundamental mechanism of radiation-induced changes in the TME and the impact of internal and external immune composition on the tumor cell fate and their response to different treatment schedules.

Organized by: Einar Bjarki Gunnarsson (Science Institute, University of Iceland), Maximilian Strobl (Cleveland Clinic, USA, stroblm@ccf.org)

Note: this minisymposia has multiple sessions. The other session is: and Part-1.

1. Jana Gevertz The College of New Jersey
   "Mitigating non-genetic resistance to checkpoint inhibition based on multiple states of exhaustion"
Despite the revolutionary impact of immune checkpoint inhibition (ICI) on cancer therapy, for most indications the majority of patients do not sustain a durable clinical benefit. In this work, we explore the theoretical consequences of the existence of multiple states of immune cell exhaustion on response to ICI therapy. In particular, we consider the emerging understanding that T cells can exist in various states: fully functioning cytotoxic cells, reversibly exhausted cells that are minimally cytotoxic but targetable by ICIs, and terminally exhausted cells that are cytotoxic yet not targetable by ICIs. Under the assumption that tumor-induced inflammation triggers the transition between these T cell phenotypes, we developed a conceptual mathematical model of tumor progression subject to treatment with an ICI that accounts for multi-stage immune cell exhaustion. Simulations of a ‘baseline patient’ without intrinsic resistance to ICI reveal that treatment response (complete responder versus non-responder with non-genetic resistance) sensitively depends on both the dose and frequency of drug administration. A virtual population analysis uncovered that while the standard high-dose, low-frequency protocol is indeed an effective strategy for our baseline patient, it fails a significant fraction of the population. Conversely, a metronomic-like strategy that distributes a fixed amount of drug over many doses given close together is predicted to be effective across the largest proportion of the virtual population. Taken together, our theoretical analyses demonstrate the potential of mitigating resistance to checkpoint inhibitors via dose modulation, and also suggest avenues for selecting combination drug partners.
2. Raymond Ng University of Pennsylvania
   "The role of tumor gene expression variability in evading CD8+ T cells"
Melanoma cells escape CD8+ T cell killing during tumor progression and development of immunotherapy resistance. While genetic alterations affecting antigen presentation and interferon response pathways are well-established mechanisms of immune escape, melanoma cells display substantial gene expression heterogeneity even prior to acquiring these genetic changes, potentially enabling some cells to survive T cell attack. Here, we investigate how this pre-existing gene expression heterogeneity facilitates melanoma cell evasion of T cell recognition and destruction. Using a model system of ovalbumin-expressing melanoma cells cocultured with OT-I CD8+ T cells, we demonstrate that a subset of melanoma cells consistently survives both acute and prolonged T cell selection. By integrating DNA barcoding and single-cell RNA sequencing with computational approaches, we developed a robust framework to identify survivor versus non-survivor cell lineages. Our bootstrap simulation framework generated empirical null distributions of lineage selection frequencies, enabling robust statistical inference to distinguish “survivor” from “non-survivor” lineages with defined confidence levels. These 'survivor' lineages exhibited elevated expression of oxidative stress response and ferroptosis protection pathways, coupled with reduced expression of epithelial-to-mesenchymal transition (EMT) markers. Through long-term coculture experiments, we generated and characterized T cell-resistant melanoma populations, revealing consistent upregulation of interferon-gamma response pathways while maintaining suppressed EMT-like signatures. Our findings uncover previously unrecognized gene expression programs that enable melanoma immune evasion and suggest potential therapeutic vulnerabilities in pathways controlling oxidative stress responses and cellular plasticity.
3. Chenyu Wu University of Minnesota
   "A statistical framework for detecting therapy-induced resistance from drug screens"
Resistance to therapy remains a significant challenge in cancer treatment, often due to the presence of a stem-like cell population that drives tumor recurrence post-treatment. Moreover, many anticancer therapies induce plasticity, converting initially drug-sensitive cells to a more resistant state, e.g. through epigenetic processes and de-differentiation programs. Understanding the balance between therapeutic anti-tumor effects and induced resistance is critical for identifying treatment strategies. In this study, we introduce a robust statistical framework, based on multi-type branching process models of the evolutionary dynamics of tumor cell populations, to detect and quantify therapy-induced resistance phenomena from high throughput drug screening data. Through comprehensive in silico experiments, we show the efficacy of our framework in estimating parameters governing population dynamics and drug responses in a heterogeneous tumor population where cell state transitions are influenced by the drug. Finally, using recent in vitro data from multiple sources, we demonstrate that our framework is effective for analyzing real-world data and generating meaningful predictions.
4. Michael Cotner The University of Texas at Austin
   "Tracking Resistance to Targeted Therapy in TNBC with Cell Barcodes"
Triple negative breast cancer (TBNC) is marked by fewer standard-of-care treatment options and poorer treatment outcomes than other breast cancer subtypes, with approximately 40% of TNBC patients developing treatment resistance. High intratumoral heterogeneity, a characteristic of TNBC, leads to its difficulty in treatment and rapid acquisition of resistance. To investigate how this heterogeneity influences treatment response and resistance in TNBC, we employ ClonMapper, our DNA barcoding technology that utilizes integrated and heritable unique DNA barcodes, to track clonal cell populations across treatment. ClonMapper barcodes are identifiable in scRNA-seq, which enables tracking of clonal subpopulations and their transcriptomic diversity before and after treatment. We use ClonMapper to follow barcoded heterogenous tumor cell populations through their response to treatment with three clinically-relevant targeted inhibitor chemotherapies, revealing the diverse transcriptomic trajectories taken by different cell subpopulations and how these diverse responses arise from a heterogenous transcriptomic landscape prior to treatment.

Organized by: Tyler Simmons (Therapy Modeling and Design Center, University of Minnesota), John Metzcar and Sarah Anderson: Therapy Modeling and Design Center, University of Minnesota

1. Gabriel Côté Sainte-Justine University Hospital Azrieli Research Centre / Université de Montréal
   "The role of chronobiology on immunotherapies to prevent neutrophil infiltration into the tumour microenvironment in lung cancer"
BACKGROUND: Oscillations, particularly circadian rhythms, are ubiquitous in physiology. A sound understanding of these phenomena may have important implications for the administration of treatments targeting oscillatory behavior. For example, neutrophils, the most abundant immune cells, display circadian oscillating properties under the control of CXCR2 and CXCR4 receptors. In lung cancer, neutrophil infiltration in the tumour promotes metastases. CXCR2 inhibitors were suggested to reduce such events. However, experiments in mice showed that their administration must align with circadian rhythms; when timed improperly these inhibitors were found to have little to no effect. Even worse, improper timing could result in the dangerous depletion of neutrophils, leading to worst outcomes. Thus, there is a need for rationalizing CXCR2 inhibitor treatment schedules. METHODS: We developed a mathematical model of neutrophil dynamics, incorporating CXCR2 regulation, and added a PK/PD model of AZD5069, a CXCR2 inhibitor. We adjusted our parameters to murine data and performed global sensitivity analyses to determine main regulation mechanisms. We then simulated therapeutic responses in virtual cohorts to optimize treatment regimens. RESULTS: Our results highlight key circadian mechanisms regulating circulating neutrophil counts. Further, our virtual clinical trial predicted that neutrophil oscillations are determinant for establishing effective yet non-toxic CXCR2 inhibitor treatment schedules. IMPACT: This study underlines the importance of chronobiology to drug and immune responses. Our work may be extended to investigate immunity in shift workers, jet-lagged travelers, and individuals with circadian rhythm sleep disorders.
2. Jason T. George, MD, PhD Texas A&M University
   "Stochastic modeling of immunomodulation in the tumor-immune microenvironment"
The advent of T cell-based immunotherapy has ushered in a new age of cancer treatment. Cancer immunotherapy – despite durable efficacy in several disease contexts – is still limited in many disease subtypes, often resulting from unfavorable microenvironmental features and subsequent cancer immune-specific adaptation and ultimate evasion. Recent modeling and empirical directions have thus focused on enhancing immunotherapy’s existing anti-tumor effects and activating the immune system in cases that currently lack any therapeutic response. This talk will discuss our recent efforts at understanding cancer immune evasion and our model’s predicted role of the microenvironment on escape dynamics. I will first discuss our group’s development of a stochastic model of ‘variable evasion’ with implications for antigen targeting. Lastly, I will describe how immunomodulation of tumor-specific T cells can impact cancer escape dynamics, which we then use to study clinically observed cancer recurrence times in breast and bladder cancer.
3. Riley Manning University of Minnesota
   "Agent-based modeling of glioblastoma immunotherapy strategies"
Glioblastoma is an aggressive, highly infiltrative malignant brain tumor with minimal treatment options for patients. Integrated genomic analysis of patient tumors enabled the classification of three molecular subtypes of glioblastoma: proneural, classical, and mesenchymal. Despite distinct alterations in the expression of migration and immune activation-related genes these subtypes are all treated with the same standard of care clinically. Clinical trials investigating T cell based-immunotherapies have had limited success, with many patients quickly developing resistance to treatment. In this work, we use a three-dimensional agent based model of glioblastoma to model the progression of two subtypes: proneural and mesenchymal. Mesenchymal tumors have faster single cell migration speeds and increased infiltration of several immune cell types, including cytotoxic T cells. In contrast, proneural tumors have slower cell migration speeds and are immunologically cold. We model migration, proliferation, and T cell-cancer cell interactions at the single cell level. Cytotoxic T cells deliver sublethal hits to cancer cells, ultimately leading to cancer cell death as damage accumulates. We simulated anti-migratory and T cell-based immunotherapies to identify subtype-specific treatment strategies. We observed differential efficacy between the two tumor subtypes, highlighting the need to account for patient subtype in glioblastoma therapy development. Cytotoxic T cells struggled to eliminate diffuse tumors and escaping tumor cells at the periphery, even at high effector to target ratios. Simulated treatment efficacy was improved with the addition of cancer cell-targeting anti-migratory therapy. This research enhances our understanding of the mechanisms driving therapy failure in glioblastoma and provides a strategy for predicting effective future treatments.
4. Katherine Owens Fred Hutchinson Cancer Center, Seattle, WA
   "Spatiotemporal dynamics of tumor - CAR T-cell interaction following local administration in solid cancers"
The success of chimeric antigen receptor (CAR) T-cell therapy in treating hematologic malignancies has generated widespread interest in translating this technology to solid cancers. However, issues like tumor infiltration, the immunosuppressive tumor microenvironment, and tumor heterogeneity limit its efficacy in the solid tumor setting. Recent experimental and clinical studies propose local administration directly into the tumor or at the tumor site to increase CAR T-cell infiltration and improve treatment outcomes. Characteristics of the types of solid tumors that may be the most receptive to this treatment approach remain unclear. In this work, we develop a simplified spatiotemporal model for CAR T-cell treatment of solid tumors, and use numerical simulations to compare the effect of introducing CAR T cells via intratumoral injection versus intracavitary administration in diverse cancer types. We demonstrate that the model can reproduce tumor and CAR T-cell data from small imaging studies of local administration of CAR T cells in mouse models. Our results suggest that locally administered CAR T cells will be most successful against slowly proliferating, highly diffusive tumors. In our simulations, assuming equal detectable tumor diameters at the time of treatment, low average tumor cell density is a better predictor of treatment success than total tumor burden or volume doubling time. These findings affirm the clinical observation that CAR T cells will not perform equally across different types of solid tumors, and suggest that measuring tumor density may be helpful when considering the feasibility of CAR T-cell therapy and planning dosages for a particular patient. We additionally find that local delivery of CAR T cells can result in deep tumor responses, provided that the initial CAR T-cell dose does not contain a significant fraction of exhausted cells.

Organized by: Stacey Smith? (The University of Ottawa)

Note: this minisymposia has multiple sessions. The other session is: and Part-2.

1. Kathleen Hoffman University of Maryland, Baltimore County
   "Improvement of Quantitative Reasoning Skills in Transfer and Direct Entry Students Exposed to Cell Biology Modules"
Calls for transforming biological curricula have emphasized a need for interdisciplinary STEM education. To address this, we designed six modules to develop quantitative reasoning competencies for a sophomore-level Cell Biology course. We analyzed validated, pre-post measurements of specific quantitative competencies to determine the effects of the modules on student proficiencies. Students showed significant total growth in quantitative goals for all modules and had significant positive correlations between final course grades, post-assessment performance, and overall gain across the modules with some differences between direct-entry and transfers students. Attitude assessments showed that students had an overall positive experience with the modules. Our data suggest that adding quantitative modules to core biology courses can promote student understanding of quantitative concepts for both direct entry and transfer students and can promote transfer student success in particular.
2. Stacey Smith? The University of Ottawa
   "To pre-record or not to pre-record? Lessons learned from video instruction in a flipped classroom"
Educational theory suggests that students benefit when students become responsible for their own learning outside the classroom while utilising the teacher's expert knowledge for in-class help. However, flipping a large classroom without additional resources requires scaling up strategies from smaller classrooms. A calculus class was flipped twice in successive years, once requiring the students to read the course notes in advance, the second time requiring them to watch pre-recorded videos. Metrics of learning included Bloom's taxonomy, grades, teaching evaluations and anecdotal feedback. Class participation was high and phone use was low, but students largely did not read the material in advance. However, they did watch the videos before and during class. Exam marks were not noticably different without videos, but improved markedly with them. Metacognition was significantly improved in both semesters, with students gaining a deeper insight, more peer connection and less classroom fear than had previously been available. Flipping a large classroom requires significant investment outside of the classroom. Students learn best from visual aides, so pre-recorded videos are a vital tool in managing such an educational delivery option.
3. Angela Peace Texas Tech University
   "Teaching Mathematical Ecology across the disciplines"
Effective collaboration between mathematics and biology is essential for tackling today’s complex ecological challenges—but it starts in the classroom. Here, I explore strategies for teaching Mathematical Ecology in a cross-disciplinary setting, with a focus on fostering communication and collaboration between mathematics and biology graduate students. I’ll share approaches for designing integrative courses and team-based projects where students learn not only ecological modeling and quantitative analysis, but also how to bridge disciplinary languages, assumptions, and problem-solving styles. I will highlight lessons I learned in designing and delivering curricula that bring students together and discuss common challenges: like mismatched expectations, uneven preparation, and differing views on modelling approaches.
4. Rebecca Everett Haverford College
   "Building an Applied Track at a Small Liberal Arts College: A Work in Progress"
As a new hire at Haverford College seven years ago, one of the goals of the department was to incorporate applied math into the math major. We have now completed our second year with three focuses/tracks through our major: pure, applied, and statistics. In this talk, I will reflect on various aspects of incorporating applied mathematics into our program. We will discuss our applied track courses and adjustments we are making along the way, applied projects in the intro and upper-level courses, and the department’s learning goals of mastery; communication; breadth of knowledge; and independence, resilience, and persistence.

Organized by: Marissa Renardy (Quantitative Systems Pharmacology, GSK), Kathryn G. Link, Quantitative Systems Pharmacology, Pfizer Inc.

Note: this minisymposia has multiple sessions. The other session is: and Part-2.

1. Christian T. Michael University of Michigan - Michigan Medicine
   "Regimen-ranking methodology influences outcomes in a multi-scale systems pharmacology model of tuberculosis treatment."
Pulmonary tuberculosis, caused by lung infection with Mycobacterium tuberculosis (Mtb), is a potentially-fatal disease affecting one quarter of the world's population. Treatment of pulmonary TB requires antibiotic regimens that are expensive, intensive, and extensive, requiring 6 months of consistent treatment with multiple antibiotics. To explore optimal treatments, we created a multi-scale quantitative systems pharmacology model that we calibrated using multimodal pharmacokinetics and pharmacodynamics datasets from humans, rabbits, non-human primates, and in vitro studies. We have integrated this model with our previously-published whole-host model of pulmonary Mtb infection, HostSim. Using this platform, we studied the efficacy of dozens of front-line multi-drug antibiotic regimens in the form of virtual pre-clinical trials. By computing virtual analogues of efficacy measurements from clinical trials and experiments, we validated our model by recapitulating the relative efficacy several well-studied and frequently-prescribe antibiotic regimens. However, we found several cases in which regimen efficacy rankings differed substantially if calculated using seemingly-similar measurements. This highlights the problems that arise with in silico or in vivo studies when we use one single heuristic for drug efficacy as an intuitive proxy for another, which may cause us to infer seemingly- contradictory conclusions. Conversely, examining differences between seemingly-similar ranking schemes may provide insights into subtle behaviors of the underlying biological system.
2. Olivia Walch Arcascope
   "Better drug discovery through circadian science: theoretical considerations for chronomedicine."
Time-specifically biological, circadian time—is an underexploited dimension in drug development. This presentation will discuss the dose-dependent nature of optimal timing: how the best time to administer a drug varies with the dose, the drug’s half-life, and the temporal dynamics of the biological target. Shorter-acting drugs may require precise timing, while longer-acting ones may shift the window of efficacy. Moreover, variations in circadian amplitude can alter optimal strategies for both dosing and trial design. Finally, a case study will illustrate how neglecting time-of-day effects in a clinical trial could lead to the erroneous conclusion that a truly effective drug lacks efficacy.
3. Kathryn G. Link Pfizer Inc.
   "Virtual Clinical Trial Simulations Using a Quantitative Systems Pharmacology (QSP) Model of Antibody Drug Conjugate (ADC) Therapy in Patients with HER2- positive and HER2-low metastatic breast cancer."
Antibody-drug conjugates (ADCs) are typically composed of a monoclonal antibody (mAbs) backbone covalently attached to a cytotoxic drug, known as payload, via chemical linker. They combine both the advantages of highly specific targeting ability of the antibody with the highly potent killing mechanism of the payload to eliminate cancer cells. Given the increased success of approved vedotin ADCs (ADCENTRIS, PADCEV, AIDIX, and TIDCEV) and continued interest in vedotin-based therapeutics, a quantitative systems pharmacology (QSP) model of vedotin-based ADC disposition and efficacy could streamline the development of innovative medicines by assessing dose regimens and combination therapy strategies. In this talk, we discuss the development of a mechanistic ADC model capturing ADC disposition, target-specific binding, tumor growth inhibition, and efficacy. In vitro potency and in vivo TGI data inform initial model calibrations and validation. Additionally, the model was calibrated with published clinical PK and target expression data. Next, we implemented an integrated quantitative systems pharmacology virtual population approach to incorporate oncology efficacy endpoints. A HER2-positive and HER2-low virtual population were matched to the progression free survival (PFS) and best percentage change in sum of diameters from baseline to published RC48 C001 C003 CANCER studies. Here we present a virtual population pipeline utilizing a mechanistic QSP model of tumor growth, target expression, ADC disposition, preclinical potency and TGI data, as well as clinical PK/efficacy data. Our ADC QSP model captures key PK, PD, and target expression dynamics observed from clinical studies of vedotin-based therapeutic interventions. The model can further support future drug development by informing questions such as the selection of optimal dosing regimens for pivotal clinical trials.
4. Morgan Craig Universite de Montreal
   "Targeting tumour-associated macrophages and microglia in glioblastoma"
Glioblastoma is a deadly brain cancer for which standard-of-care (SOC) provides only moderate survival benefits, with 100% of patients experiencing recurrence. Despite high expression of PD-L1 in glioblastoma, with or without SOC, all immune checkpoint inhibitor (ICI) clinical trials have failed to efficacy in mixed patient populations. Using mathematical and computational models combined with spatial data, we have shown that the peculiarities of the tumour microenvironment and the immune response in the brain limit ICI success in glioblastoma. To study potential immunotherapeutic treatment options for glioblastoma, we developed a comprehensive, mechanistic mathematical model of SOC and nivolumab that describes tumour-immune interactions within the tumour microenvironment. Our results suggest that tumour-associated macrophages/microglia (TAMs) are compelling targets to improve treatment outcomes and lay the framework for continued experimental work developing TAM-targeting therapies for glioblastoma.