Organized by: Ioana Bouros (University of Oxford), Alexander Browning, University of Melbourne

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

1. Yurij Salmaniw University of Oxford
   "Structural identifiability of linear-in-parameter parabolic PDEs through auxiliary elliptic operators"
In this talk, I will discuss results appearing in a recent manuscript (collaboration with Dr. Alexander P. Browning, Melbourne) under the same title (arXiv: 2411.17553). In it, we develop a relatively elementary approach to establishing parameter identifiability in parabolic partial differential equations and systems under an assumption of 'perfect' data observation. Key to this approach is an assumption of linearity in the parameters, which allows one to reduce the problem of parameter identifiability to a problem of identification of the kernel of a related elliptic operator. We will discuss our notion of parameter distinguishability, and how this connects to the more commonly used notion of parameter identifiability. We will appeal to several common examples from ecological modelling literature to clearly illustrate our results. These insights highlight the intimate connection between idenfiability, the influence of boundary conditions, and the role played by certain eigenfunctions and the linear dependence between low and higher order terms. Despite an ideal assumption of perfect data observation, these insights have consequences for parameter identifiability in practice, which we will also discuss. We will conclude briefly with some future directions, challenges, and open problems.
2. Dasuni Salpadoru Queensland University of Technology
   "Parameter estimation and identifiability analysis of bistable ecosystems"
Bistable ecosystems, such as lacustrine ecosystems, exhibit two stable equilibria: one representing a healthy equilibrium (oligotrophic) and the other representing an unhealthy equilibrium (eutrophic). Environmental perturbations can push a bistable ecosystem beyond a critical threshold, triggering a shift between these equilibria. Understanding bistable dynamics for ecosystem management requires these thresholds to be identified, as these sudden behavioural changes can potentially lead to irreversible damage. However, a key challenge in studying bistable ecosystems is determining if typical phosphorus monitoring data are sufficient for an ecological model parameter to be identifiable. Although parameter identifiability is important, it has been largely overlooked in bistable ecosystem studies. In this work, we use a profile likelihood approach, which is well-suited for assessing parameter identifiability by quantifying uncertainty and detecting potential non-identifiability issues. This method is applied to estimate parameters and analyse the practical identifiability of key parameters and critical thresholds for the Carpenter Lake eutrophication model in a range of different monitoring scenarios. Understanding the effects of different monitoring strategies on parameter identifiability can inform risk assessment and management plans to maintain water quality in a lake and prevent irreversible degradation. Beyond lake ecosystems, our analysis is generalisable to other bistable ecosystems that may be targets of conservation management. Keywords: Bistable ecosystems, Parameter estimation, Identifiability analysis, Profile likelihood, Lake eutrophication
3. Liam O'Brien Ohio State University
   "Structural causes of pattern formation and its breakdown - through model independent bifurcation analysis"
During development, precise cellular patterning is essential for the formation of functional tissues and organs. These patterns arise from conserved signaling networks that regulate communication both within and between cells. Here, we develop and present a model-independent ordinary differential equation (ODE) framework for analyzing pattern formation in a homogeneous cell array. In contrast to traditional approaches that focus on specific equations, our method relies solely on general assumptions about global intercellular communication (between cells) and qualitative properties of local intracellular biochemical signaling (within cells). Prior work has shown that global intercellular communication networks alone determine the possible emergent patterns in a generic system. We build on these results by demonstrating that additional constraints on the local intracellular signaling network lead to a single stable pattern which depends on the qualitative features of the network. Our framework enables the prediction of cell fate patterns with minimal modeling assumptions, and provides a powerful tool for inferring unknown interactions within signaling networks by analyzing tissue-level patterns.
4. Ioana Bouros University of Oxford
   "A retrospective analysis of the robustness of existing compartmental models for modelling future pandemics"
Background & aims of study For the duration of the Covid pandemic, the UK government consulted a number of mathematical models of transmission dynamics to help to guide policy response. Several of these epidemiological models use compartments to sort the population into, and ODEs to describe the infection dynamics. However, these models rely on a number of modelling assumptions about the disease, which sacrifice accuracy for model tractability. These differences in turn impact the forecasts of the epidemic trajectory and may lead to incongruent recommendations to policy makers. In this talk, we conduct a retrospective analysis of the performance of three models used for modelling the rapid progression of the Covid pandemic in the UK to test the robustness of the results and whether they can be used interchangeably to inform policy response: the “Cambridge-PHE”, the 'Warwick Household model”, and the “Roche model”. Methods & Results For each model, we produce forecasts for cases, deaths and inferred instantaneous reproduction number trajectories both in the actual and in the unmitigated epidemic scenario, by fitting to the same early 2020 UK epidemic death dataset. We identified that each of the three considered models produced very different death and case trajectories in the counterpart scenario, i.e. when no non-pharmaceutical interventions are put in place and contacts are maintained at the same rates throughout the simulation - which suggests that we cannot substitute the conclusions of on of these models for the other. Additionally, we analysed how the time of application of NPIs impacts the model outcomes. Finally, we include a sensitivity analysis to assess robustness to parameter changes of the three models. Implications This work highlights the pitfalls of relying on individual models to inform policy responses for future epidemics and pandemics, as well as the need for a more in-depth study of the impact of modelling assumptions on the quality of model outputs.

Organized by: Fanze Kong (University of Washington), Michael Jeffrey Ward and University of British Columbia

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

1. Jack Hughes University of British Columbia
   " Pulses, Waves, and Mesas in Mass Conserved Reaction-Diffusion Media: From Theory to Actin Polymerization"
The transition from random walk to directional propagation (and back) is one of the intriguing phenomena observed in motile eukaryotic cells. However, typically, theoretical studies distinguish between the two phenomena and focus either on dissipative models or models obeying gradient flows, respectively. Using a three-variable dissipative reaction-diffusion system with mass conservation modelling patterns in the cortex of cells, we show how pulses, waves, fronts, and (stationary) mesas generically organize about high codimension bifurcations. Specifically, we demonstrate the novelty of mass conservation, which enters via a long-wavenumber bifurcation of a large-scale mode. Lastly, following the biological interest, we will address the bistability between travelling wave and wave-pinning solution branches, which emerge from a codimension-2 bifurcation to a finite wavenumber Hopf and a conserved large-scale mode.
2. Thomas Hillen University of Alberta
   "Mean First Passage Times for Transport Equations"
Many transport processes in ecology, physics and biochemistry can be described by the average time to first find a site or exit a region, starting from an initial position. Here, we develop a general theory for the mean first passage time (MFPT) for velocity jump processes. We focus on two scenarios that are relevant to biological modelling; the diffusive case and the anisotropic case. For the anisotropic case we also perform a parabolic scaling, leading to a well known anisotropic MFPT equation. To illustrate the results we consider a two-dimensional circular domain under radial symmetry, where the MFPT equations can be solved explicitly. Furthermore, we consider the MFPT of a random walker in an ecological habitat that is perturbed by linear features, such as wolf movement in a forest habitat that is crossed by seismic lines. (Joint work with M. D'Orsogna, JC. Mantooth, AE. Lindsay)
3. Chunyi Gai The University of Northern British Columbia
   "An Asymptotic Analysis of Spike Self-Replication and Spike Nucleation of Reaction-Diffusion Patterns on Growing 1-D Domains"
Pattern formation on growing domains is one of the key issues in developmental biology, where domain growth has been shown to generate robust patterns under Turing instability. In this work, we investigate the mechanisms responsible for generating new spikes on a growing domain within the semi-strong interaction regime, focusing on three classical reaction-diffusion models: the Schnakenberg, Brusselator, and Gierer-Meinhardt (GM) systems. Our analysis identifies two distinct mechanisms of spike generation as the domain length increases. The first mechanism is spike self-replication, in which individual spikes split into two, effectively doubling the number of spikes. The second mechanism is spike nucleation, where new spikes emerge from a quiescent background via a saddle-node bifurcation of spike equilibria. Critical stability thresholds for these processes are derived, and global bifurcation diagrams are computed using the bifurcation software pde2path. These results yield a phase diagram in parameter space, outlining the distinct dynamical behaviors that can occur.
4. Alan Lindsay University of Notre Dame
   "Asymptotic and numerical methods for cellular signaling and directional sensing"
Diffusive arrivals to membrane surfaces provide cues for cellular decision making, for example when and where to move. In this talk we will describe the advancement of both asymptotic and numerical methodologies to describe and interpret these signals. A particular focus of these new methods are to describe the full time dependent fluxes over the cell surface during signaling processes. We will show several examples how early arrivals to the cell surface, combined with cellular geometry, can increase the strength and quality of directional signaling.

Organized by: Sungrim Seirin-Lee (Kyoto University/Graduate School of Medicine), Jaekyoung Kim (KAIST), So Miyoshi (Pfizer)

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

1. Sungrim Seirin-Lee Kyoto University
   "Pathological State Inference System based on Skin Eruption Morphology for Personalized Treatments in Dermatology"
Skin diseases typically appear as visible information-skin eruptions distributed across the body. However, the biological mechanisms underlying these manifestations are often inferred from fragmented, time-point-specific data such as skin biopsies. The challenge is further compounded for human-specific conditions like urticaria, where animal models are ineffective, leaving researchers to rely heavily on in vitro experiments and sparse clinical observations. In this presentation, I propose a novel mathematical modeling framework that bridges the gap between the visible geometry of skin eruptions and the invisible molecular and cellular dynamics driving them. This interdisciplinary approach integrates mathematical science, data-driven analysis, and clinical dermatology to overcome current limitations in understanding disease pathophysiology. Furthermore, I will introduce an innovative methodology that combines mathematical modeling with topological data analysis, allowing for the estimation of patient-specific parameters directly from morphological patterns of skin eruptions. This framework offers a new pathway for personalized analysis and mechanistic insight into complex skin disorders.
2. Alexander Anderson Moffitt Cancer Center
   "Adaptive Therapy from Board to Bench to Bedside and Back Again"
Our current approach to cancer treatment has been largely driven by finding molecular targets, those patients fortunate enough to have a targetable mutation will receive a fixed treatment schedule designed to deliver the maximum tolerated dose (MTD). Cancers are complex evolving systems that adapt to therapeutic intervention through a suite of resistance mechanisms, therefore whilst MTD therapies generally achieve impressive short-term responses, they unfortunately give way to treatment resistance and tumor relapse. The importance of evolution during both tumor progression, metastasis and treatment response is becoming more widely accepted. However, MTD treatment strategies continue to dominate the precision oncology landscape. Evolutionary therapy is a new evolution inspired treatment paradigm that seeks to exploit how a cancer evolves under treatment through smart drug dosing and sequencing often informed by mathematical modelling. Adaptive therapy is an evolutionary therapy that aims to slow down the emergence of drug resistance by controlling tumor burden through competition between drug sensitive and resistant cell populations. Adaptive therapy specifically alters the treatment schedule (timing and dose) in response to a patient’s disease dynamics, often stopping therapy or deescalating dose when burden is low and starting therapy or increasing dose when burden is high. This approach was inspired by pest management and developed through mathematical model driven insights and has been shown to work in preclinical animal models (prostate, ovarian, melanoma, breast) and in pilot clinical trials (NCT02415621; NCT05189457; NCT03543969). Recently, phase 2 adaptive therapy trials in prostate (NCT05393791) and ovarian cancer (NCT05080556) are testing the treatment break and treatment deescalation approaches respectively. In this talk we will discuss different aspects of adaptive therapy including (i) How to pick patients who will benefit from it; (ii) How best to optimize the treatment switch threshold; (iii) The importance of appointment frequency; (iv) Robustness when patients miss appointments. We will utilize differential equation and cellular automata models as well as deep reinforcement learning.
3. Adrien Hallou University of Oxford
   "Spatial mechano-transcriptomics: mapping at single-cell resolution mechanical forces and gene expression in tissues"
Advances in spatial profiling technologies are providing insights into how molecular programs are influenced by local signalling and environmental cues. However, cell fate specification and tissue patterning involve the interplay of biochemical and mechanical feedback. Here, we propose a new computational framework that enables the joint statistical analysis of transcriptional and mechanical signals in the context of spatial transcriptomics. To illustrate the application and utility of the approach, we use spatial transcriptomics data from the developing mouse embryo to infer the forces acting on individual cells, and use these results to identify mechanical, morphometric, and gene expression signatures that are predictive of tissue compartment boundaries. In addition, we use geoadditive structural equation modelling to identify gene modules that predict the mechanical behaviour of cells in an unbiased manner. This computational framework is easily generalized to other spatial profiling contexts, providing a generic scheme for exploring the interplay of biomolecular and mechanical cues in tissues.
4. Jae Kyoung Kim KAIST
   "Improving Biological Predictions: Rethinking Markovian and Diffusion Assumptions"
Mathematical modeling plays a critical role in understanding complex biological systems and making accurate predictions. However, incorrect probabilistic assumptions embedded in mathematical models can lead to significant errors. In this talk, I will highlight two such cases. First, I will discuss how the unrealistic assumption of Markovian dynamics in modeling the latent period of infectious diseases can produce misleading predictions about the spread of COVID-19, and present methods to overcome this issue. Second, I will address the limitations of the widely-used Fick’s law in describing molecular diffusion within cells. Contrary to experimental observations, Fick’s law cannot accurately reproduce the tracked movement of molecules. Instead, Chapman’s law, which accounts for physical interactions with cellular structures such as the endoplasmic reticulum, provides a more accurate depiction of intracellular protein diffusion.

Organized by: Veronica Ciocanel (Duke University), Hye-Won Kang, University of Maryland Baltimore County

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

1. Scott McKinley Tulane University
   "Robust inference and model selection for particle tracking in live cells"
There is now an expansive collection of mathematical work on building models for the transport of intracellular cargo by molecular motors. Commonly studied cargo undergo “saltatory” motion (bidirectional ballistic motion, intermixed with periods of stationarity) along often unobserved microtubules. Traditionally microparticle transport is quantified in terms of mean-squared displacement, but this ubiquitous statistic averages over periods of motion and pauses, eliminating important biophysical information. In this talk, I will discuss our group’s approach to segmentation analysis: an in-house changepoint detection algorithm coupled with a focus on summary statistics that are robust with respect to the inevitable mistakes that changepoint detection algorithms make.
2. Peter Kramer Rensselaer Polytechnic Institute
   "Molecular Mechanisms in Actively Driven Passively Crosslinked Microtubule Pairs"
We apply stochastic modeling to interpret in vitro experiments involving microtubules interacting with the passive crosslinker PRC1 while being crowdsurfed by kinesin in a gliding assay configuration. When an antiparallel pair of microtubules is crosslinked by PRC1, the kinesin slides the microtubules apart while the PRC1 resists this separation. We examine molecular-scale mechanisms for the two distinct modes of resistance which are observed in experiments. We further describe a supporting model for how the microtubules being slid by kinesin respond to the load from the PRC1 crosslinkers.
3. Yangyang Wang Brandeis University
   "A conceptual framework for modeling a latching mechanism for cell cycle regulation"
Two identical van der Pol oscillators with mutual inhibition are considered as a conceptual framework for modeling a latching mechanism for cell cycle regulation. In particular, the oscillators are biased to a latched state in which there is a globally attracting steady-state equilibrium without coupling. The inhibitory coupling induces stable alternating large-amplitude oscillations that model the normal cell cycle. A homoclinic bifurcation within the model is found to be responsible for the transition from normal cell cycling to endocycles in which only one of the two oscillators undergoes large-amplitude oscillations.
4. Kasia Rejniak Moffitt Cancer Center
   "Data-driven models for guiding adoptive cell therapies in bladder cancer"
Adoptive cell therapy with tumor infiltrating lymphocytes (ACT-TIL) is a personalized immunotherapy approach that consists of three phases: tumor infiltration by the autologous T cells, ex vivo expansion of the T cells collected after tumor resection, and reinfusion of the expanded T cells into the cancer patient. The specificity of bladder cancer allows for intravesical delivery of drugs and T cells directly to the tumor. Thus, each of the three ACT-TIL phases gives us opportunity to improve and optimize these procedures by combining mathematical modeling with (pre)clinical data. I will discuss mathematical models: agent-based, continuous, and machine learning, that were driven by demographic, histology, and longitudinal ultrasound data, and used to address patient stratification for the ACT-TIL, the role of tumor immune and metabolic landscapes in treatment efficacy, and optimization of multi-treatment scheduling with the goal to maximize bladder tumor response to ACT-TIL.

Organized by: Veronica Ciocanel (Duke University), Hye-Won Kang, University of Maryland Baltimore County

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

1. Grzegorz Rempala The Ohio State University
   "Modeling Epidemics on Networks"
This talk presents an overview of recent advances in modeling epidemic dynamics on networks, with a focus on pairwise and edge-based formulations of SIR-type processes on random graphs. I will outline a systematic framework for deriving and analyzing models across multiple levels of complexity, emphasizing the role of closure and approximation techniques. Particular attention will be given to conditions under which models become exact or analytically tractable, and to clarifying how commonly used heuristic models relate to their rigorous mathematical foundations.
2. Paul Hurtado University of Nevada, Reno
   "SIER-type ODE models with phase-type latent and infectious period distributions"
SEIR-type ODE models can be viewed as a mean-field model corresponding to (often unspecified) individual-based stochastic model. These typically assume that the latent and infectious periods follow exponential distributions, or Erlang (gamma) distributions, if formulated using the linear chain trick (LCT). SEIR models based on the generalized linear chain trick (GLCT) expand these assumptions to possibly include the much broader class of 'phase-type' distributions, which can be thought of as the absorption time distributions for finite-state Continuous Time Markov Chains. These include Coxian distributions, hypoexponential (generalized Erlang) distributions, and mixtures of these distributions. In this talk, I will present some preliminary explorations of how SEIR-type model behaviors change when we replace those traditional (exponential or Erlang) distribution assumptions for the latent and infectious period distributions with these more flexible alternatives. I'll also discuss implications for the empirical estimation of these distributions in applications.
3. Deena Schmidt University of Nevada, Reno
   "Modeling network formation in ecological systems"
Understanding how networks form and evolve is an important question in many fields such as ecology, epidemiology, economics, and sociology. Studying the mechanisms of network formation can yield insights into which factors are involved in edge formation and network growth. In this talk, I will give an overview of network formation models and then focus on such modeling in ecological systems, specifically thinking about caterpillar-plant interaction networks using data collected from Ecuador. I will discuss two modeling frameworks, the repeated choice model (RCM) and the stochastic actor-oriented model (SAOM). The RCM models network formation as a series of choices, where caterpillars select plants based on observable features such as leaf count. The SAOM focuses on the stochastic choices individuals make and how their choices are influenced by the network structure as well as their own attributes. I will present some preliminary results for the Ecuador interaction networks. This is work in progress with graduate student Andrew Chavez.
4. Wenrui Hao Pennsylvania State University
   "A Systematic Computational Framework for Practical Identifiability Analysis"
Practical identifiability is a fundamental challenge in data-driven modeling of mathematical systems. In this talk, I will present our recent work on a novel framework for practical identifiability analysis, designed to assess parameter identifiability in mathematical models of biological systems. I will begin with a rigorous mathematical definition of practical identifiability and establish its equivalence to the invertibility of the Fisher Information Matrix. Our framework connects practical identifiability with coordinate identifiability, introducing a novel metric that simplifies and accelerates parameter identifiability evaluation compared to the profile likelihood method. Additionally, we incorporate new regularization terms to address non-identifiable parameters, enhancing uncertainty quantification and improving model reliability. To support experimental design, we propose an optimal data collection algorithm that ensures all model parameters are practically identifiable. Applications to Hill functions, neural networks, and dynamic biological models illustrate the framework’s effectiveness in uncovering critical biological processes and identifying key observable variables.

Organized by: Andrew Eckford (Department of Electrical Engineering and Computer Science, York University, Toronto)

1. Massimiliano Pierobon University of Nebraska-Lincoln
   "On the Usefulness and Subjectivity of Life-supporting Information"
In recent years, the exploration of information flow within biological systems has become a groundbreaking approach for delving into the complex mechanisms at play in the life sciences. This approach serves a dual purpose: it not only provides a quantitative grasp of how biological systems store, transmit, sense, receive, and process information across various scales and contexts, but it also paves the way for designing and engineering systems that either mimic or are integrated with biochemical environments. At this interdisciplinary juncture, bridging the gap between diverse fields of expertise presents numerous challenges. These range from developing a shared vocabulary to addressing the limitations of applying theories and concepts across different contexts and assumptions. In our talk, we will share insights and lessons from organizing the Workshop on Information, Communication, and Coding Theory in Biology sponsored by the US National Science Foundation. We'll highlight cutting-edge interdisciplinary research areas and the major challenges that lie ahead. Our discussion will then delve into our research contributions, focusing on how communication theory can accurately describe biological processes and introducing the concept of subjective information as a new metric for biological information. We will also present practical applications derived from our research, offering recommendations for best practices and sharing personal anecdotes from our journey. This talk aims to illuminate the path forward for interdisciplinary collaboration in understanding and harnessing the principles of information flow in biological systems.
2. Alexander Moffett Northeastern University
   "Evolution of Environmental Sensing"
Organisms sense and respond to environmental cues, allowing for within-lifetime adaptation to an ever-changing world. A growing body of work has sought to connect the accuracy of environmental sensing with fitness, with the fitness value of information emerging as a key concept. Despite the progress made in this direction, we still lack a good understanding of how environmental sensing evolves in necessarily finite populations with metabolically costly sensory machinery. We attempt to construct a model capable of addressing these gaps in understanding, using concepts from rate-distortion theory and population genetics.
3. Andrew Eckford York University
   "Kelly Bets and Single-Letter Codes: Optimal Information Processing in Natural Systems"
In an information-processing investment game, such as the growth of a population of organisms in a changing environment, Kelly betting maximizes the expected log rate of growth. In this talk, we show that Kelly bets are closely related to optimal single-letter codes (i.e., they can achieve the rate-distortion bound with equality). Thus, natural information processing systems with limited computational resources can achieve information-theoretically optimal performance. We show that the rate-distortion tradeoff for an investment game has a simple linear bound, and that the bound is achievable at the point where the corresponding single-letter code is optimal. Moreover, since evolution is expected to optimize an organism's information processing capabilities, this bound allows prediction of biological behaviour. Examples illustrating the results in simplified biological scenarios are presented.
4. Peter Thomas Case Western Reserve University
   "Tradeoffs in the energetic value of neuromodulation in a closed-loop neuromechanical system"
Rhythmic motor behaviors controlled by neuromechanical systems, consisting of central neural circuitry, biomechanics, and sensory feedback, show efficiency in energy expenditure. The biomechanical elements (e.g., muscles) are modulated by peripheral neuromodulation which may improve their strength and speed properties. However, there are relatively few studies on neuromodulatory control of muscle function and metabolic mechanical efficiency in neuromechanical systems. To investigate the role of neuromodulation on the system’s mechanical efficiency, we consider a neuromuscular model of motor patterns for feeding in the marine mollusk Aplysia californica. By incorporating muscle energetics and neuromodulatory effects into the model, we demonstrate tradeoffs in the energy efficiency of Aplysia’s rhythmic swallowing behavior as a function of the level of neuromodulation. A robust efficiency optimum arises from an intermediate level of neuromodulation, and excessive neuromodulation may be inefficient and disadvantageous to an animal’s metabolism. This optimum emerges from physiological constraints imposed upon serotonergic modulation trajectories on the energy efficiency landscape. Our results may lead to experimentally testable hypotheses of the role of neuromodulation in rhythmic motor control.

Organized by: Fanze Kong (University of Washington), Michael Jeffrey Ward and University of British Columbia

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

1. Fanze Kong University of Washington
   "Spike Dynamics in Several Keller-Segel Models with Logistic Growth"
The Keller–Segel models, a class of strongly coupled PDEs, were introduced by E. Keller and L. Segel in the 1970s to describe cell motility driven by chemical signals. Due to their relatively simple structures yet rich dynamical behaviors, Keller–Segel systems have attracted extensive attention, with numerous studies devoted to the qualitative properties of the solutions, including global well-posedness, singularity formation, etc. This talk focuses on the localized pattern formation in several Keller-Segel models with logistic growth, where two singular limit regimes are considered: large chemotactic movement and small chemical diffusivity. We will show the results concerning the existence and stability of multi-spikes. Furthermore, some complex but intriguing spike dynamics including oscillation, slow motion and nucleation will be discussed. In particular, we highlight the connection between logistic Keller–Segel and Gierer–Meinhardt models, and discuss the application of logistic Keller-Segel models to explaining economic agglomeration.
2. Mohammad El Smaily University of Northern British Columbia
   "A Wol­bachia infec­tion mod­el with free bound­ary"
We develop a reaction-diffusion model, with free-boundary, to describe how Wolbachia can be used to eliminate mosquitoes that spread human disease. The mosquito population infected with Wolbachia invades the environment with a spreading front governed by a free boundary satisfying the well-known one-phase Stefan condition. We establish criteria under which spreading and vanishing occur. Our results provide useful insights on designing a feasible mosquito releasing strategy that infects the whole mosquito population with Wolbachia and eradicates the mosquito-borne diseases eventually.
3. Michael Ward University of British Columbia
   "Diffusion-Induced Synchrony for a Cell-Bulk Compartmental Reaction-Diffusion System in 3-D"
We investigate diffusion induced oscillations and synchrony for a 3-D PDE-ODE bulk-cell model, where a scalar bulk diffusing species is coupled to nonlinear intracellular reactions that are confined within a disjoint collection of small spheres. The bulk species is coupled to the spatially segregated intracellular reactions through Robin conditions across the boundaries of the small spheres. For this system, we derive a new memory-dependent ODE integro-differential system that characterizes how intracellular oscillations occur 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 is examined for various spatial arrangements of cells. This theoretical modeling framework, relevant to applications such as quorum sensing when spatially localized nonlinear oscillators are coupled through a PDE diffusion field, is distinct from the traditional Kuramoto paradigm for studying oscillator synchronization through ODEs coupled on networks or graphs. (Joint work with Merlin Pelz, UBC and UMinnesota).
4. Shuangquan Xie Hunan University
   "Spiky patterns and their dynamics in a three-component food chain system"
We study a three-component reaction-diffusion system modeling interactions among water (resource), vegetation (primary consumer), and a predator (secondary consumer). The water-vegetation dynamics follow Klausmeier-type kinetics, while the vegetation-predator interaction incorporates logistic growth with nonlinear predation. This framework captures scenarios like arid ecosystems (water-limited vegetation) with predator-driven vegetation suppression. We asymptotically construct spiky spatial solutions in certain parameter regimes and demonstrate that these solutions undergo Hopf bifurcations due to translational instability.

Organized by: Joanna Wares (University of Richmond), Luis Melara, Shippensburg University

1. Luis Melara Shippensburg University
   "Optimal Bandwith Selection in Bio-FET Measurements"
The use of stochastic regression to separate signal from noise produced by Bio-FETs will be discussed in this talk. The noise realized by BioFETs interferes with quantitative and qualitative analysis, thus determining optimal bandwidth associated with experimental Bio-FET data measurements is an important task. Presented results suggest consistent across aspect rations and a choice of stochastic regression kernel function and yield what appear to be good results.
2. Joanna R. Wares University of Richmond
   "Comparison of Virtual Clinical Trial Techniques"
Virtual clinical trials (VCTs) are growing in popularity as a tool for quantitatively predicting heterogeneous treatment responses across a population. In the context of a VCT, a plausible patient is an instance of a mathematical model with parameter (or attribute) values chosen to reflect features of the disease and response to treatment for that particular patient. In a previous work, we rigorously quantified the impact that VCT design choices have on VCT prediction. We found that the prior distribution, rather than the inclusion/exclusion criteria, has a larger impact on the heterogeneity of the plausible population. Yet, the percent of treatment responders in the plausible population was more sensitive to the inclusion/exclusion criteria utilized. Here I discuss past results and preview a new study that seeks to understand how the underlying complexity of the chosen mathematical model affects the results of virtual clinical trials.

Organized by: Ioana Bouros (University of Oxford), Alexander Browning, University of Melbourne

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

1. Hyukpyo Hong University of Wisconsin–Madison
   "Inferring delays in partially observed gene regulation processes"
Cell function is regulated by gene regulatory networks (GRNs) defined by protein-mediated interaction between constituent genes. Despite advances in experimental techniques, we can still measure only a fraction of the processes that govern GRN dynamics. To infer the properties of GRNs using partial observation, unobserved sequential processes can be replaced with distributed time delays, yielding non-Markovian models. Inference methods based on the resulting model suffer from the curse of dimensionality. We develop a simulation-based Bayesian MCMC method for the efficient and accurate inference of GRN parameters when only some of their products are observed. We illustrate our approach using a two-step activation model: An activation signal leads to the accumulation of an unobserved regulatory protein, which triggers the expression of observed fluorescent proteins. Our method is scalable and can be used to analyze other non-Markovian models with hidden components. References [1] Hyukpyo Hong, Mark Jayson Cortez, Yu-Yu Cheng, Hang Joon Kim, Boseung Choi, Krešimir Josić, Jae Kyoung Kim, Inferring delays in partially observed gene regulation processes, Bioinformatics, 39 (11): btad670, 2023.
2. Hui Jia Farm University of Oxford
   "Ensuring parameter identifiability in cardiac cell models is an essential prerequisite for reliable prediction"
Computational modelling of heart cells, especially the binding of drugs to the ion channel, is now an essential part of the drug development process, aiming to predict a drug’s risk to the heart from channel-level reactions. The ion channel controls the flow of ions across the cell membrane and the beating of the heart. The ion channel is susceptible to drug inhibition which can disrupt the heart’s beating cycle and can be fatal. Some drugs can get “trapped” within the channel, meaning they are unable to unbind from the channel while it is closed, and this is believed to increase the risk they pose. The trapping component introduced in a popular model of the drug-binding mechanism (the ORd-CiPAv1 model) has a limited effect on the beating cycle of heart cells, running counter to the claim that a drug’s risk depends on its trapping behaviour. We show that this limited effect of the trapping component is due to the non-identifiability of its parameters which stems from the insignificant contribution of the trapping component to the current. We propose two alternative drug-binding models which do not suffer from the problem of non-identifiability of the trapping component. With fewer parameters and/or constraints, the alternative models are more interpretable and/or more identifiable. Despite not having an explicit drug-trapping component, our proposed models can capture the drug-trapping phenotype observed in the experimentally-measured current. Even though all drug-binding models have limitations, one of our alternative models can replicate the risk categorisation of drugs predicted by the ORd-CiPAv1 model. We conclude that the trapping component defined in the ORd-CiPAv1 model is not necessary for the risk categorisation of drugs. Moreover, a model with identifiable and interpretable components each of which has an impact on model predictions would be preferable over complex models that contain more components but where those additional components have little to no effect.
3. Marisa Eisenberg University of Michigan
   "Identifiability, uncertainty, and model reduction in mathematical biology"
The interactions between parameters, model structure, and outputs can determine what inferences, predictions are possible for a given system and whether it is possible to select intervention strategies for a given situation. Identifiability, estimability, and parameter reduction methods can help to determine what inferences and predictions are possible from a given model and data set, and help guide control strategies and new data collection. In this talk, we will explore how identifiability can be used in practice to help inform epidemiological decision-making, and when intervention strategies are or are not robust to uncertainty in the model parameters and structure.
4. Tyler Cassidy University of Leeds
   "Parameter estimation and identifiability from clinical data in viral dynamics models"
Mathematical models have been instrumental in our understanding of viral kinetics. These models have identified important portions of the viral life cycle in many infections, like HIV and HBV, and are increasingly used to understand data from clinical trials of new treatments for these infections. I'll discuss some recent work focused on understanding how we can leverage analytical approximations and hierarchical parameter estimation techniques to identify model parameters from participants in early-stage clinical trials.

Organized by: David Sabin-Miller (University of Michigan)

1. Heather Zinn Brooks Harvey Mudd College
   "An opinion reproduction number for infodemics in a bounded-confidence content-spreading process on networks"
We study the spreading dynamics of content on networks. Our content-spreading model, which one can also interpret as an independent-cascade model, introduces a twist into bounded-confidence models of opinion dynamics by using bounded confidence for the content spread itself. We define an analog of the basic reproduction number from disease dynamics that we call an opinion reproduction number. A critical value of the opinion reproduction number indicates whether or not there is an “infodemic” (i.e., a large content-spreading cascade) of content that reflects a particular opinion. By determining this critical value, one can determine whether or not an opinion dies off or propagates widely as a cascade in a population of agents. Using configuration-model networks, we quantify the size and shape of content dissemination by calculating a variety of summary statistics, and we illustrate how network structure and spreading-model parameters affect these statistics.
2. Olivia Chu Bryn Mawr College
   "Adaptive network models and the dynamics of political polarization and social activism"
The formation of activist groups can spark social movements, coalitions, and revolutions. The creation of such groups can be influenced by social ties, network structure, ideology and culture, and the institutional environment. Still, the relative importance of these factors, the mechanisms through which individuals develop or lose their commitment to various causes, and the channels through which like-minded individuals find each other and establish social connections are not thoroughly understood. In this work, we develop a theory that begins to explain two phenomena: 1) how a potential activist's conviction co-evolves with their social network, and 2) how 'socially-mobilizable activist networks' tend to arise or disappear based on the distribution of potential activists and overall environment. We illustrate this theory by modifying the adaptive voter model (AVM) with a conviction variable, which represents the strength with which an individual holds on to their beliefs and the comfort of holding on to them in their surroundings, encapsulating the co-evolutionary dynamics of networks and attitudes. As is expected from empirical evidence, we find that activists are systematically discouraged by exposure to disengaged individuals. However, some situations with increased interaction payoffs and strong homophily preferences favor the formation and persistence of activist networks.
3. Alexandria Volkening Purdue University
   " Forecasting U.S. elections with compartmental models of infection"
Election dynamics are a rich complex system, and forecasting U.S. elections is a high-stakes problem with many sources of subjectivity and uncertainty. In this talk, I take a dynamical-systems perspective on election forecasting, with the goal of helping to shed light on choices in this process and raising questions for future work. By adapting a Susceptible-Infected-Susceptible model to account for interactions between voters in different states, I will show how to combine a compartmental approach with polling data to produce forecasts of senatorial, gubernatorial, and presidential elections at the state level. Our results for the last two decades of U.S. elections are largely in agreement with those of popular analysts, and we correctly called all of the state-level outcomes of the 2024 U.S. presidential race. We use our modeling framework to determine how weighting polling data by polling organization affects our forecasts, and explore how our forecast accuracy changes in time in the months leading up to each election.
4. David Sabin-Miller University of Michigan
   "Data-driven modeling of US information-ideological dynamics"
We may view the ideological ecosystem as an interplay between individuals’ acceptance and rejection of political ideas, and the algorithmically-mediated information environment which supplies those ideas according to each individual’s preference. This framework may help us make sense of the frustrating coexistence of seemingly contradictory worldviews in today’s polarized ideological climate; each may seem totally nonsensical or irrational to the opposing side, leaving little room for productive discourse or compromise. However, with fresh eyes and an interdisciplinary mindset, it is possible to make useful progress on this classically social-science domain by seeking an underlying dynamical model supported by data. This talk will present recent empirical results from a purpose-built ideological survey which find robust and seemingly universal patterns in individual-level political reasoning, a quantitative estimate of the political information landscape, and the implications of dynamically connecting the two. These efforts point to further illuminative data-gathering possibilities, laying the groundwork for a theory-experiment loop towards accurately understanding this powerful aspect of modern society.

Organized by: Sungrim Seirin-Lee (Kyoto University/Graduate School of Medicine), Jaekyoung Kim (KAIST), So Miyoshi (Pfizer)

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

1. So Miyoshi Pfizer
   "Transforming Drug Research and Development: The Paradigm Shift Driven by Mathematical Models"
Mathematical modeling and simulation technologies are playing a critical role in revolutionizing pharmaceutical research and development. Model-Informed Drug Development (MIDD), built upon the foundations of pharmacometrics and quantitative systems pharmacology (QSP), has emerged as a powerful approach to streamline the drug development process. It enables quantitative decision-making for optimizing clinical trial designs, improving dosing strategies, and ultimately accelerating the delivery of new therapies to patients. In particular, the integration of mechanistic modeling through QSP has demonstrated its value in recent real-world applications. As the pharmaceutical industry embraces MIDD, the roles of pharmacometricians, clinical pharmacologists, and systems modelers are becoming increasingly prominent across academia, regulatory agencies, and industry. This evolution calls for deeper interdisciplinary collaboration, especially with the mathematical biology community, to address the complexity of human disease and treatment responses. In this presentation, I will provide an overview of the current landscape and future directions of MIDD, illustrating its impact with practical examples from pharmaceutical development. We can shape a future in which mathematical models serve as a bridge from data to decision, accelerating the creation of innovative therapies across various disease areas.
2. Nessy Tania Pfizer
   "Advancing Quantitative Systems Pharmacology Model for Inflammatory Bowel Disease for Clinical Efficacy Predictions in Ulcerative Colitis"
Inflammatory Bowel Disease (IBD) is a chronic autoimmune disease associated with gastrointestinal inflammation. While therapeutic options for the disease have expanded, patient response to these treatments can be highly variable. In this presentation, I will present a mechanistic Quantitative Systems Pharmacology Model for IBD that can be connected to clinical endpoint, specifically Mayo endoscopic score for Ulcerative Colitis. As a specific case study, the application of the model and virtual population simulations to predict the effect of a novel target combination (p40 and TL1A) will be discussed. In the future, the model can be further developed to account for additional mechanisms and utilized to predict biomarker response and efficacy for novel IBD therapies.
3. Eamonn Gaffney University of Oxford
   "Modelling immunological systems, as exemplified by Short Peptide Vaccinations Simulations for Immuno-oncology"
A prospective immunologically-based cancer treatment is multi-peptide vaccination, targeting multiple tumour-associated peptides. However, a recent multiple short-peptide vaccination trial for renal cell carcinoma failed to show benefit, with many patients responding to only one of the administered peptides. An in-silico model is considered to enable an exploration of the determinants of the initial immunological response following multiple short peptide vaccination, suggesting mechanisms for the observed lack of benefit in the recent clinical trial. These insights may also used to suggest possible improvements to the trial design and more generally illustrate one means by which in silico studies can be used to test and improve the design of clinical trials. Further recent work investigating the modelling of immunological systems will also be surveyed.
4. Brian Corrigan Metrum
   "Superconvergence: Charting the Course from Lab to Global Health Outcomes in Translational Clinical Sciences for the Next Decade"
The presentation will highlight the important roles that various disciplines in Translational Clinical Sciences will play in bringing new medicines to patients over the next decade. It will examine the convergence of advances in genetics, biotechnologies, and AI on medicines development, and how these changes will impact our roles throughout the research spectrum, from non-clinical to human, from patients to practice, and from practice to our impact on population health. It will highlight the impact of new data sources, analytic and decision-making techniques, and explore patient centric approaches to Medicine development that increase trial accessibility and broaden representation in our clinical trials.

Organized by: Veronica Ciocanel (Duke University), Hye-Won Kang, University of Maryland Baltimore County

1. Jae Kyoung Kim Korea Advanced Institute of Science & Technology
   "Advancing Static and Time-series data: Random Matrix Theory, Causal Inference and Mathematical Modeling"
In this talk, I will discuss methods for extracting meaningful information from static and time-series data. For static data, Principal Component Analysis (PCA) is widely used to detect signals in noisy datasets. However, determining the appropriate number of signals often relies on subjective judgment. I will introduce an approach based on random matrix theory to objectively select the optimal number of signals. For time-series data, causal inference techniques such as Granger causality are commonly employed. Unfortunately, these methods often yield high false-positive rates. I will present a novel mathematical model-based approach to causal inference.
2. Janet Best The Ohio State University
   "Energy Allocation and Sleep Homeostasis"
The upregulation of diverse functions, including memory consolidation and restorative processes, suggests sleep is a time for specialized energy use. While sleep was long considered an energy conservation strategy, the modest calculated savings led to skepticism that energy conservation is the function of sleep, particularly given sleep’s inherent costs in vulnerability. This talk will present a mathematical model based in an evolutionary perspective on the function and timing of sleep.
3. Punit Gandhi Virginia Commonwealth University
   "Using transformation information to characterize symmetry transitions"
Transformation information (TI) provides a versatile, entropy-based method for identifying approximate symmetries by quantifying deviations from exact symmetry with respect to a parametrized family of transformations. We define notions of approximate symmetry and maximal asymmetry in terms of critical points in TI as a function of a transformation parameter. This framework allows us to characterize transitions in symmetry by tracking qualitative changes with respect to these critical points. We apply TI to mathematical models inspired by developmental biology and actual biological images. Our analysis of the qualitative changes in symmetry properties indicates a potential pathway toward a general mathematical framework for characterizing symmetry transitions akin to bifurcation theory for dynamical systems.
4. Anastasios Matzavinos Pontifical Catholic University of Chile
   "Chemotaxis and Stochastic Gradient Ascent: Fractional Brownian Motion in Optimization and Biological Models"
Chemotaxis, the directed movement of cells and microorganisms in response to chemical signals, is a fundamental biological process. Modern modeling approaches often combine Brownian motion with gradient-driven motility, drawing parallels to stochastic gradient ascent algorithms used in optimization. At its core, chemotaxis can be viewed as a natural optimization process that steers cells toward regions of higher chemoattractant concentration. However, recent experimental findings challenge this classical view. In the absence of chemotactic cues, many cell types exhibit motility patterns that resemble fractional Brownian motion, with correlated increments that differ fundamentally from those of Brownian motion. This shift in perspective has important implications for how we understand and model cell migration. In this talk, we present computational evidence showing that cells with positively correlated movement patterns explore their environment more effectively and are better equipped to handle fluctuations in the chemotactic landscape. We also discuss the broader relevance of these findings in contexts such as tumor-induced angiogenesis and developmental processes. This work was supported in part by ANID FONDECYT Regular grant No. 1221220.

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.

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-1.

1. Farrah Sadre-Marandi qPharmetra
   "Navigating pediatric dose selection: Insights from nifurtimox for Chagas disease"
Pediatric dose selection presents unique mathematical and pharmacological challenges due to developmental changes in drug absorption, distribution, metabolism, and excretion (ADME). In the context of Chagas disease—a neglected tropical disease affecting children across Latin America—this talk presents a quantitative framework used to support the regulatory approval of nifurtimox in pediatric populations. This talk will focus on the mathematical modeling strategies that informed dose selection, highlighting the integration of population pharmacokinetics, allometric scaling, and exposure-response analysis. We explore the nonlinear mixed effects modeling approach applied to sparse clinical data across a wide pediatric age and weight range, and we demonstrate how simulation-based techniques were used to evaluate dose-exposure relationships and optimize weight-band dosing strategies.
2. Sarah Minucci Certara
   "A Quantitative Systems Pharmacology Platform Model of Alzheimer's Disease for Reducing Amyloid Plaque and Tau"
Alzheimer's Disease (AD) is a neurogenerative disease that progressively impacts cognitive function, characterized by the buildup of amyloid-beta (Aβ) and tau into plaques and neurofibrillary tangles (NFTs), respectively.  AD is currently ranked as the seventh leading cause of death in the United States. It has been shown that the removal of Aβ plaques as well as the reduction in tau biomarkers can reduce cognitive decline in AD patients. Furthermore, anti-Aβ treatments have shown effects on tau pathology, indicating a complex interplay between these two proteins and their role in the development of AD. Quantitative systems pharmacology (QSP) models have been developed in the field of AD to understand the impact of plaques and NFTs in disease progression and their responses to therapeutic modulation. We developed a platform QSP model of Aβ and tau pathology in AD and the effects of anti-Aβ and anti-tau therapies on various biomarkers in order to better understand the interplay of Aβ and tau and test potential strategies for mono- and combination anti-Aβ and anti-tau therapies. Current hypotheses regarding tau pathology spreading, NFT formation, and amyloid re-accumulation after depletion were tested throughout model development. The model was calibrated/benchmarked to >70 clinical biomarker datasets to capture disease progression as well as PK and Aβ/tau biomarker changes in response to anti-Aβ mAbs lecanemab, gantenerumab, donanemab, and aducanumab as well as tau-targeting ASO BIIB080. Model simulations were in good agreement to Aβ, tau, and PK data, including plaque reaccumulation after treatment and the effects of anti-Aβ therapy on tau pathology.
3. Sarah Minucci, Olivia Walch, Farrah Sadre-Marandi, Marissa Renardy Certara, Arcascope, qPharmetra, GSK
   "Industry Panel Discussion"
Quantitative systems pharmacology (QSP) combines mathematical and computational modeling tools with mechanistic understanding of biology and pharmacology to guide drug discovery and development. QSP is used in the pharmaceutical industry to accelerate and de-risk drug discovery and development across multiple stages, from target discovery/validation to clinical trial design to lifecycle management. In recent years, QSP has been increasingly used in regulatory submissions for clinical trials across many therapeutic areas (PMID: 34734497). In this session, speakers will present recent advances and perspectives in the field of QSP. The second session will be composed of two technical talks and an industry panel discussion with prepared and audience-driven questions.

Organized by: Kishore Hari and Pradyumna Harlapur (Postdoctoral Research Fellow, Center for Theoretical Biological Physics), Pradyumna Harlapur, PhD Candidate, Dept. of BioEngineering, Indian Institute of Science

1. Claus Kadelka Iowa State University
   "Biological networks operate closer to the edge of chaos than recently proposed"
Since Kauffman introduced Boolean networks to study gene regulatory networks, they have been successfully used to model various biological networks such as cancer signaling pathways and T-cell differentiation. Due to their finite size, Boolean networks eventually exhibit periodic behavior, and the attracting states in a biological Boolean network correspond to phenotypes or cell types. Traditional stability measures, such as the Derrida value or network and basin coherence, quantify the resilience of network dynamics to perturbations of any random state in the network, yet real-world systems typically rest at an attracting state. To address this, we introduce attractor coherence, a metric that quantifies how likely the perturbation of a network attractor causes the system to transition to another attractor. A comparison of attractor coherence and conventional basin coherence in expert-curated Boolean biological network models reveals substantial and systematic differences. Through extensive simulations of random network ensembles, we demonstrate that increased canalization not only boosts the number of fixed‐point attractors but also magnifies the gap between basin and attractor‐focused stability. Similarly, networks with higher fractions of frozen nodes exhibit larger discrepancies between the coherence measures. These findings highlight the importance of attractor‐centric metrics for accurately assessing the phenotype robustness in biological networks.
2. Chandrakala Meena Indian Institute of Science Education and Research Pune
   "Emergent stability in complex biological systems"
First, I will discuss briefly the general dynamical framework to analyze the macroscopic behaviour of biological systems using their microscopic components—network topology and dynamics and then the identification of emergent dynamical states using the dynamical framework. Then, I will present analytical approaches to predict the stability of emergent steady states in complex biological systems, ranging from ecological, and cellular to brain networks. Complex systems are often described by interaction graphs, where the dynamical state is captured by the activities of all nodes, for example, the excitation of neurons in brain networks or the expression levels of genes in subcellular interactions. To capture the system’s stability, we perturb its dynamical states from their fixed-point steady states and analyze its response to the perturbation, such as a local spike in neuronal activity or a sudden increase in the expression of one or several genes. A system is considered stable if the perturbation decays; otherwise, it loses stability and may transition to an entirely new state. The system’s response to perturbations is encoded within its stability matrix - the Jacobian, but retrieving this information is challenging due to the scale and diversity of these systems, their broad parameter space, and their nonlinear interaction dynamics. To address this complexity, we develop the dynamic Jacobian ensemble, which provides a systematic framework for investigating the fixed-point dynamics of a wide range of graph-based nonlinear interaction models, including social, biological, chemical, and technological systems. These Jacobians reveal universal scaling patterns, where structure and dynamics are intricately connected. Further, to predict system stability, we develop some stability classifiers that are based on Jacobian ensembles and the Gershgorin Disk Theorem. These stability classifiers capture the influence of both network topology and dynamics, enabling the prediction and classification of large complex systems into stable, unstable, or sensitively stable categories.
3. Jordan C Rozum Pacific Northwest National Lab
   "Redundant structures and robust dynamics in biomolecular networks"
Cells must cope with noisy, dynamic, and spatially heterogeneous environments. They must balance robustness with adaptability in the biomolecular networks that govern their behavior. For instance, cyanobacteria adapt their metabolism to changing nutrient and light conditions, while phages that infect these organisms carry auxiliary metabolic genes (AMGs) that hijack adaptive responses, ostensibly to promote viral replication. Using a flux network model, we showed how AMGs in a particular host-pathogen system come in two types: those that limit host growth by reconfiguring metabolic fluxes to favor phage production, and those for which the host metabolism can robustly compensate without affecting host-phage biomass trade-offs. More broadly, we and others have observed a high level of redundancy in metabolic networks. For instance, we have shown that key pathways and subsystems can be extracted even after removing over 90% of the connections between metabolic reactions. Indeed, many metabolic genes and reactions, across organisms, are not essential for survival and growth. This robustness is present directly in the metabolism, even before accounting for the substantial redundancy in regulatory and signaling networks that modulate it. In a wide variety of cell process models, it is exceedingly difficult to alter long-term behavior via large transient perturbations. Using novel mathematical and computational techniques, we ascribe this phenomenon to canalization, or buffering of environmental fluctuations, in both the local regulatory logic and the global regulatory topology.
4. Pradyumna Harlapur Indian Institute of Science
   "Characterizing Regulatory Interactions and Dimensionality in Gene Networks Driving Cell-Fate Choices"
Cell-fate decisions involve coordinated genome-wide expression changes, typically leading to a limited number of phenotypes. Although often modeled as simple toggle switches, these rather simplistic representations often disregard the complexity of regulatory networks governing these changes. Here, we unravel design principles underlying complex cell decision-making networks in multiple contexts. We show that the emergent dynamics of these networks are consistently low-dimensional, as quantified by the variance explained by principal component 1 (PC1). This low dimensionality in phenotypic space arises from extensive feedback loops in these networks arranged to effectively enable the formation of two teams of mutually inhibiting nodes (Hari*, Harlapur* et al. iScience 2025). We use team strength as a metric to quantify these feedback interactions and show its strong correlation with PC1 variance. We then examined how biological networks are organized with specific topologies that allow them to remain sparse while effectively coordinating decision-making under various levels of coherent interactions (i.e., structural balance). We found that networks with low coherence needed higher densities to show coordinated expression profiles. The balance between sparsity and coordinated control highlights the role of network architecture in ensuring stable and robust phenotypic outcomes, providing new insights into how GRNs guide cellular behavior precisely yet adaptable. These results shed light on how, despite being very sparse, the networks that govern various cellular decisions follow certain basic design principles to ensure the expression between the nodes involved is well coordinated.

1. Richard Foster Virginia Commonwealth University
   "Practical parameter identifiability of respiratory mechanics in the extremely preterm infant"
The complexity of mathematical models describing respiratory mechanics has grown in recent years, however, parameter identifiability of such models has only been studied in the last decade in the context of observable data. This study investigates parameter identifiability of a nonlinear respiratory mechanics model tuned to the physiology of an extremely preterm infant, using global Morris screening, local deterministic sensitivity analysis, and singular value decomposition-based subset selection. The model predicts airflow and dynamic pulmonary volumes and pressures under varying levels of continuous positive airway pressure, and a range of parameters characterizing both surfactant-treated and surfactant-deficient lung. The model was adapted to data from a spontaneously breathing 1 kg infant using gradient-based optimization to estimate the parameter subset characterizing the patient's state of health.
2. Caleb Mayer Stanford University
   "Mathematical Modeling of Circadian Rhythms: Applications to Phase Prediction and Fatigue Reduction"
As consumer-grade wearable technology has become more prevalent in recent years, large-scale collections of data have been made available for researchers. We analyze significant amounts of wearable data to determine the circadian features that differ across groups and time frames. Using wearable activity, steps, and heart rate data, we adapt mathematical models to accurately estimate circadian phase across populations. This has a number of applications, including chronotherapeutic drug delivery, reducing fatigue, and shift work scheduling. We demonstrate applications to estimating circadian phase (dim light melatonin onset, or DLMO) in a home-based cohort of later-life adults, showing that activity-based models perform similarly or better than light-based models in DLMO estimation. We further use these models to provide wearable-based lighting interventions for reducing cancer-related fatigue. In particular, we test whether these lighting interventions, delivered via a mobile app, reduce cancer-related fatigue in a randomized controlled trial with 138 breast cancer, prostate cancer, and hematopoietic stem cell transplant patients. These interventions, based on real-time assessment of circadian rhythm through wearable devices, improve certain measures of fatigue (e.g., daily measurements of fatigue) in cancer patients. Further studies are needed to tune these models and assess the effect of lighting interventions in broader and more diverse cancer care settings.
3. Vasilis Tsilidis Department of Mathematics, University of Patras
   "Unveiling the Drivers of Fetal Weight Estimation: Which Ultrasound Measurements Matter Most?"
Fetal weight estimation via ultrasound is performed by measuring biometric parameters such as the biparietal diameter (BPD), head circumference (HC), abdominal circumference (AC), and femur length (FL), which are then used in various mathematical formulas to calculate the estimated weight. But do all parameters matter equally? To assess their contribution on fetal weight estimation, we analyzed 29 published formulas across 26 diverse global datasets. Results show that AC is consistently the parameter of greatest importance, while head measurements (BPD, HC) often add little value, particularly in the later stages of pregnancy. Additionally, nearly half of the formulas include redundant parameters, and two-thirds exhibit a crossover in parameter importance—some transition from low to high significance, while others decline from high to low—over the course of gestation. These findings highlight opportunities to simplify fetal weight estimation for clinicians, prioritizing AC reliability and trimming unnecessary inputs. Our work bridges mathematics and prenatal care, offering clearer guidelines to improve ultrasound-based predictions and support healthier pregnancy outcomes.

1. Michael Pan The University of Melbourne
   "Mathematical modelling of subchondral bone adaptation, microdamage, and repair in Thoroughbred racehorses"
Musculoskeletal injuries can significantly impact the careers of racehorses, and are a common cause of lost training days and fatality. Most bone injuries arise from the gradual accumulation of microcracks through repeated training rather than spontaneous events. If severe enough, cracks may propagate through the bone and lead to fractures, often necessitating euthanasia. While training promotes bone adaptation to higher mechanical loads, overtraining can cause excessive damage. To better understand the biological processes underlying bone injury, we developed a lumped parameter model that combines the processes of bone adaptation, microdamage accumulation and bone repair. The model parameters were calibrated to experimental observations of bone volume fraction and time to fracture in racehorses. A sensitivity analysis identified joint loads (arising from training speed) and strides per day (arising from training distance) as key factors contributing to bone damage. Simulations of a typical training program showed that the majority of damage is incurred from training at racing speeds. While some microdamage is repaired during training, our model estimates that this process is insufficient to offset the damage accumulated. These findings emphasise the critical role of regular rest in preventing bone injury.

1. Ashlee Ford Versypt University at Buffalo, The State University of New York
   "A Multi-Cellular Network Model Predicts Changes in Glomerular Endothelial Structure in Diabetic Kidney Disease"
Diabetic kidney disease (DKD) progression is often marked by early glomerular endothelial cell (GEC) dysfunction, including alterations in the fenestration size and number linked to impaired glomerular filtration. However, the cellular mechanisms regulating GEC fenestrations remain poorly understood due to limitations in existing in vitro models, challenges in imaging small fenestrations in vivo, and inconsistencies between in vitro and in vivo findings. This study used a logic-based protein-protein interaction network model with normalized Hill functions for dynamics to explore how glucose-mediated signaling dysregulation impacts fenestration dynamics in GECs. We identified key drivers of fenestration loss and size changes by incorporating signaling pathways related to actin remodeling, myosin light chain kinase, Rho-associated kinase, calcium, and VEGF and its receptor. The model predicted how hyperglycemia in diabetic mice leads to significant fenestration loss and increased size of fenestrations. We found that glycemic control in the pre-DKD stage mitigated signaling dysregulation but was less effective as DKD developed and progressed. The model suggested alternative disease intervention strategies to maintain fenestration structure integrity, such as targeting Rho-associated kinase, VEGF-A, NFκB, and actin stress fibers.
2. Mojgan Ezadian Lindi Wahl, Western University
   "A Continuous-Time Stochastic Model for Mutation Effects in Microbial Population"
Mutation accumulation (MA) experiments are crucial for understanding evolution. In microbial populations, these experiments typically involve periods of population growth, where a single individual forms a visible colony, followed by severe bottlenecks. Studies on the effects of positive and negative selection in MA experiments have shown that, for example, with 20 generations of growth between bottlenecks, beneficial mutations will be substantially over-represented cite{}; this effect is known as ``selection bias''. In previous work, we developed a fully stochastic discrete-time model that includes realistic offspring distributions, accounting for genetic drift and allowing for the loss of rare lineages. We demonstrated that when drift is included, selection bias is even stronger than previously predicted cite{}. Since bacterial division is unlikely to remain synchronized over 20 or more generations, this study extends the discrete-time model to a continuous-time framework. Since lineages that start reproducing early accrue a compounded advantage, a continuous-time model offers an even more accurate correction for selection in MA experiments.