41 papers
Intracellular Measurement-Informed Multiscale Modeling for Scalable iPSC Manufacturing
Scalable manufacturing of human induced pluripotent stem cells (iPSCs) is essential for industrial-scale production of cell therapies and regenerative medicines. However, the 3D aggregate cultures used in manufacturing exhibit substantial spatial and metabolic heterogeneity compared with the relatively homogeneous monolayer systems used in laboratory studies, complicating mechanistic understanding and predictive metabolic modeling across culture scales. To address this challenge, we developed a modular multiscale mechanistic foundation model that links molecular, cellular, and macroscopic processes while accounting for spatial and metabolic heterogeneity. The framework integrates extracellular culture dynamics, intracellular metabolic fluxes, and cellular redox states by extending a previously established monolayer kinetic network and coupling it with a biological systems-of-systems (Bio-SoS) multiscale model for aggregate cultures, incorporating explicit redox interactions. Systematic monolayer and aggregate experiments (including multiple isotopic tracers, extracellular metabolite profiling, and two-photon optical redox imaging) were used to improve and validate the model. This integrated framework unifies heterogeneous datasets across culture configurations and enables mechanistic interpretation of metabolic and redox responses across heterogeneous culture scales, providing a quantitative foundation for scalable iPSC biomanufacturing.
2603.17090Mar 2026
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Single-cell directional sensing at ultra-low chemoattractant concentrations from extreme first-passage events
We investigate single-cell directional sensing from diffusing chemoattractant signals released by a localized source. We focus on the low-concentration regime in which receptor activity is discrete and cellular decisions are made on timescales far shorter than those required for steady-state concentration profiles or receptor occupancy to emerge. We derive analytic expressions for the joint distribution of receptor binding times and binding locations, conditional on the position of the source. We show that early binding events carry disproportionately more information about source directionality than later arrivals. Motivated by this observation, we propose and analyze several source-localization estimates that exploit early receptor binding statistics. Our results demonstrate that, even with a small number of binding events, cells possess sufficient information to rapidly and accurately infer the directionality of a diffusing chemoattractant source.
2603.10207Mar 2026
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Parameter Identifiability Under Limited Experimental Data in Age-Structured Models of the Cell Cycle
The mitotic cell cycle governs DNA replication and cell division. The effectiveness of radiotherapy and chemotherapy depends on cell-cycle position, with increased resistance during DNA replication and mitosis. Thus, accurate mathematical models of the cell cycle are essential for understanding and predicting treatment response. However, mathematical modellers often face the problem of a lack of publicly available, sufficiently resolved, time-series datasets for parametrising models. In this work, we consider how the ability to collate population summary measurements across the literature, from different cell lines and/or experimental set ups, affects identifiability of parameters for a cell cycle model. Initially synchronised cell populations gradually desynchronise over successive cycles, converging to balanced exponential growth (BEG) which is characterised by exponential population growth and steady, time-independent phase proportions. These proportions can be obtained from fluorescence-activated cell sorting (FACS) data. The increasing use of the Fluorescent Ubiquitination-based Cell Cycle Indicator (FUCCI) provides higher-resolution information on phase dynamics, such as minimum phase durations and variability. We present an age-structured PDE model in which cell-cycle phase progression follows a delayed gamma distribution. We derive analytical expressions for BEG phase proportions and other FUCCI-observable quantities, and use them to assess how data availability influences parameter identifiability. When parameters are not uniquely identifiable, we determine identifiable parameter groupings, thereby determining the minimum amount of data that must be available for successfully fitting structured population models of the cell cycle.
2603.06751Mar 2026
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Towards Data-Driven Modeling of Cell Cycle and Wound Closure Processes
Effective wound repair treatments rely on a clear picture of how cell proliferation and migration are coordinated during tissue restoration. Fibroblasts are key contributors to tissue restoration in the dermis, and modern imaging tools allow their cell-cycle progression to be observed directly, enabling comparison between experiments and computational models. Here we investigate how different stages of the cell cycle influence fibroblast-driven wound closure using the Discrete Laplacian Cell Mechanics (DLCM) framework driven by time-lapse microscopy data. \textit{In vitro} assays provide cell positions, migration behaviour, and cycle-stage information, and we show that incorporating proliferation, migration, and cell cycle arrest allows the computational model to reproduce the essential experimental trends. The results reveal that arrest in the G1 phase notably impacts the cell cycle dynamics and that the initial spatial arrangement of cycle states significantly affects wound closure. By linking single-cell cycle dynamics with emergent tissue behaviour this work establishes a quantitative approach for exploring how intracellular processes shape repair processes. More broadly, it demonstrates the value of integrating high-resolution data with cell-based mechanical models and provides a foundation for systematic \textit{in silico} evaluation of therapeutic interventions.
2603.00834Feb 2026
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A mathematical model for the role of macrophage chemotactic emigration in the early atherosclerotic plaque
Atherosclerotic plaques are fatty, cellular lesions that form in artery walls. The early plaque contains monocyte-derived macrophages, which are recruited to consume locally bound lipid deposits. Plaque progression is characterised by an imbalance in the rates of cell entry and exit from the plaque, which can occur if macrophages die in situ rather than leave by emigration. The mechanisms that regulate macrophage emigration are not well understood, but there is evidence that a chemotactic response can guide macrophages out of the plaque towards the artery wall lymphatics. In this paper, we develop a novel spatial model of the early plaque to study the implications of macrophage chemotactic emigration. Using mathematical analysis and numerical simulations, we investigate how the properties of the chemotactic response contribute to the spatial characteristics and lipid burden of the model plaque. Calculations of macrophage transit times are found to provide a reliable indicator of long-term plaque lipid burden, and also highlight the potential rate-limiting effect of the internal elastic lamina (IEL) on chemotactic emigration. When macrophage emigration is rate-limited by the IEL, we observe non-monotonic cell and lipid profiles that are associated with macrophage accumulation deep in the plaque. The model further predicts that when the chemoattractant penetrates only a short distance into the plaque, the proportion of emigrating macrophages may increase relative to that for a longer-range signal. The theoretical observations in this study can potentially be used to identify evidence of macrophage emigration in data from real atherosclerotic plaques.
2602.19521Feb 2026
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How negative feedback from filamentous actin affects cell shapes and motility
The crawling motility of many eukaryotic cells is driven by filamentous actin (F-actin), and regulated by a network of signaling proteins and lipids (including small GTPases). The tangle of positive and negative feedback loops gives rise to various experimentally observed dynamic patterns (``actin waves''). Here we consider a recent prototypical model for actin waves in which F-actin exerts negative feedback onto a GTPase. Guided by recent numerical PDE bifurcation analysis in Hughes (2025) and Hughes et al (2026), we explore cell shapes and motility associated with polar, oscillatory, and traveling waves solutions of a mass-conserved partial differential equation (PDE) model. We use Morpheus (cellular Potts) simulations to investigate the implications of such regimes of behavior on the shapes and motion of cells, and on transitions between modes of behavior. The model demonstrates various cell states, including resting (spatially uniform GTPase), polar cells (static ``zones'' of GTPase), and traveling waves along the cell edge. In some parameter regimes, such states can coexist, so that cells can transition from one behavior to another in response to noisy stimuli.
2602.08779Feb 2026
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Randomness-aware multiscale models of glioma invasion and treatment
In this work, we develop a stochastic multiscale model for glioma growth and invasion in the brain, incorporating the effects of therapeutic interventions. The model accounts for tumor cell migration influenced by brain tissue heterogeneity and anti-crowding mechanisms, while explicitly addressing treatment-related uncertainties through stochastic processes. Starting from a microscopic description of individual cell dynamics, we derive the corresponding system of macroscopic random reaction-diffusion-taxis equations governing cell density and tissue evolution. Finally, we conduct several numerical experiments to assess the efficacy of different treatment protocols, evaluated with respect to both established and newly proposed clinical criteria and measurable outcomes.
2602.08008Feb 2026
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Effects of multi-phase control mechanism on fibroblast dynamics: A segmented mathematical modeling approach
Cell size is a fundamental determinant of cellular physiology, influencing processes such as growth, division, and function. In this study, we develop a segmented mathematical framework to investigate how different control mechanisms operating across multiple phases of the cell cycle affect fibroblast population dynamics. Building on our previous work modeling sizer, timer, and adder strategies, we extend the analysis by introducing phase-specific control schemes in the S and G2 phases, incorporating nonlinear growth dynamics and cell death. Using agent-based stochastic simulations, we examine how these mechanisms shape steady-state size distributions and respond to parameter variations. Our results reveal that the steady-state cell size distribution is primarily governed by division kernels and phase-specific control strategies, and appears remarkably robust to cell death modalities. We identify a fundamental trade-off between extrinsic and intrinsic growth feedbacks: while population-density-dependent regulation tightly limits total cell numbers, cell-size-dependent regulation acts as a proportional homeostatic mechanism, suppressing relative size variability. Furthermore, we demonstrate that population recovery is accelerated by the retention of proliferation-competent large cells. This study provides biologically relevant insights into the complex interplay between growth, division, and homeostasis, with implications for understanding tissue repair and disease progression.
2601.22613Jan 2026
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Modeling tumor progression in heterogeneous microenvironments: A cellular automata approach
Understanding how microenvironmental heterogeneity influences tumor progression is essential for advancing both cancer biology and therapeutic strategies. In this study, we develop a cellular automata (CA) model to simulate tumor growth under varying microenvironmental conditions and genetic mutation rates, addressing a gap in existing studies that rarely integrate these two factors to explain tumor dynamics. The model explicitly incorporates the cellular heterogeneity of stem and non-stem cells, dynamic cell-cell interactions, and tumor-microenvironment crosstalk. Using computational simulations, we examine the synergistic effects of gene mutation rate, initial tumor burden, and microenvironmental state on tumor progression. Our results demonstrate that lowering the mutation rate significantly mitigates tumor expansion and preserves microenvironmental integrity. Interestingly, the initial tumor burden has a limited impact, whereas the initial condition of the microenvironment critically shapes tumor dynamics. A supportive microenvironment promotes proliferation and spatial invasion, while inhibitory conditions suppress tumor growth. These findings highlight the key role of microenvironmental modulation in tumor evolution and provide computational insights that may inform more effective cancer therapies.
2601.16384Jan 2026
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Stability and robustness of a generalized pump-leak model for epithelial cell and lumen volume regulation
Epithelial cells regulate ion concentrations and volume through coordinated membrane pumps, ion channels, and paracellular pathways which can be modeled by classical single-compartment pump-leak equations (PLEs). Many epithelial functions, however, depend on the interaction between a cell and an enclosed luminal space, a geometry that cannot be captured by classical PLEs. To address this, we develop a two-compartment model consisting of an intracellular compartment coupled to a luminal compartment through the apical membrane, with both compartments interfacing an infinite extracellular bath and connected to it through the basolateral membrane and a paracellular pathway. Building on the five-dimensional single-cell PLEs, we formulate a ten-dimensional PLE system for this geometry and derive analytical equilibria and steady-state formulas for both the passive system and the Na+/K+-ATPase (NKA) driven active system. We characterize how these equilibria depend on physiologically relevant parameters, analyze local stability across wide parameter ranges, and apply global sensitivity and robustness methods to identify the principal determinants of ion and volume homeostasis. The model reveals fundamental differences between basolateral and apical placement of the NKA, including the onset of luminal volume blow-up when apical potassium recycling is insufficient. More broadly, this framework provides a mathematically tractable and physiologically grounded foundation for studying epithelial transport and for predicting conditions under which pump localization and conductance changes lead to stable function or pathological lumen expansion.
2601.08975Jan 2026
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Is E. coli good at chemotaxis?
Bacteria seem masters of chemotaxis, yet recent work suggests otherwise. Hudson Mattingly and colleagues (Nature Physics, 2026) argue that Escherichia coli uses only a small fraction of the sensory information available at its surface, challenging the long-held view that bacterial chemotaxis operates near physical sensing limits. This article offers a brief conceptual discussion of their findings, placing them in the context of classical chemotaxis models, robustness to noise, and broader perspectives drawn from physics, biology, and Greek mythology.
2601.05301Jan 2026
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The spontaneous emergence of leaders and followers in a mathematical model of cranial neural crest cell migration
Many agent-based mathematical models of cranial neural crest cell (CNCC) migration impose a binary phenotypic partition of cells into either leaders or followers. In such models, the movement of leader cells at the front of collectives is guided by local chemoattractant gradients, while follower cells behind leaders move according to local cell-cell guidance cues. Although such model formulations have yielded many insights into the mechanisms underpinning CNCC migration, they rely on fixed phenotypic traits that are difficult to reconcile with evidence of phenotypic plasticity in vivo. A later agent-based model of CNCC migration aimed to address this limitation by allowing cells to adaptively combine chemotactic and cell-cell guidance cues during migration. In this model, cell behaviour adapts instantaneously in response to environmental cues, which precludes the identification of a persistent subset of cells as leader-like over biologically relevant timescales, as observed in vivo. Here, we build on previous leader-follower and adaptive phenotype models to develop a polarity-based agent-based model of CNCC migration, in which all cells evolve according to identical rules, interact via a pairwise interaction potential, and carry polarity vectors that evolve according to a dynamical system driven by time-averaged exposure to chemoattractant gradients. Numerical simulations of this model show that a leader-follower phenotypic partition emerges spontaneously from the underlying collective dynamics of the model. Furthermore, the model reproduces behaviour that is consistent with experimental observations of CNCC migration in the chick embryo. Thus, we provide an experimentally consistent, mechanistically-grounded mathematical model that captures the emergence of leader and follower cell phenotypes without their imposition a priori.
2601.00374Jan 2026
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VCWorld: A Biological World Model for Virtual Cell Simulation
Virtual cell modeling aims to predict cellular responses to perturbations. Existing virtual cell models rely heavily on large-scale single-cell datasets, learning explicit mappings between gene expression and perturbations. Although recent models attempt to incorporate multi-source biological information, their generalization remains constrained by data quality, coverage, and batch effects. More critically, these models often function as black boxes, offering predictions without interpretability or consistency with biological principles, which undermines their credibility in scientific research. To address these challenges, we present VCWorld, a cell-level white-box simulator that integrates structured biological knowledge with the iterative reasoning capabilities of large language models to instantiate a biological world model. VCWorld operates in a data-efficient manner to reproduce perturbation-induced signaling cascades and generates interpretable, stepwise predictions alongside explicit mechanistic hypotheses. In drug perturbation benchmarks, VCWorld achieves state-of-the-art predictive performance, and the inferred mechanistic pathways are consistent with publicly available biological evidence.
2512.00306Nov 2025
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Survival and invasion dynamics in cell populations: an analytical framework for threshold behaviour in nonlinear age-structured models
Cell populations invade through a combination of proliferation and motility. Proliferation depends on the internal timing of cell division: how long cells take to complete the cell cycle. This timing varies substantially within (and across) cell types, creating age structure where cells at different times since their last division have different propensities to divide. Classical mathematical models of cell spreading treat division as memoryless and predict exponential cell-cycle-time distributions. Lineage tracing, by contrast, reveals peaked, gamma-like distributions that indicate a maturation delay leading to a fertility window. This gap motivates a modelling framework that incorporates age-dependent cell division rates while retaining analytical tractability. We address this through a moment-hierarchy framework that tracks time since cell division, with age resetting to zero at division. The framework yields explicit formulae for steady-state age distributions, cell-cycle-time distributions, and invasion speeds. For age-independent rates, we recover classical Fisher--KPP. Three fundamental principles emerge. First, age structure systematically reduces a population's carrying capacity and narrows the viable parameter range for positive steady states. Second, classical linear theory overestimates invasion speeds; the true minimal speed is slower when division is age-dependent. Third, the parameter condition for population survival is identical to the condition for a positive invasion speed.
2511.17279Nov 2025
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Matters of Life and Death in Computational Cell Biology
Nearly all cell models explicitly or implicitly deal with the biophysical constraints that must be respected for life to persist. Despite this, there is almost no systematicity in how these constraints are implemented, and we lack a principled understanding of how cellular dynamics interact with them and how they originate in actual biology. Computational cell biology will only overcome these concerns once it treats the life-death boundary as a central concept, creating a theory of cellular viability. We lay the foundation for such a development by demonstrating how specific geometric structures can separate regions of qualitatively similar survival outcomes in our models, offering new global organizing principles for cell fate. We also argue that idealized models of emergent individuals offer a tractable way to begin understanding life's intrinsically generated limits.
2511.07847Nov 2025
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Diffusion Dynamics in Biofilms with Time-Varying Channels
A biofilm is a self-contained community of bacteria that uses signaling molecules called autoinducers (AIs) to coordinate responses through the process of quorum sensing. Biofilms exhibit a dual role that drives interest in both combating antimicrobial resistance (AMR) and leveraging their potential in bioprocessing, since their products can have commercial potential. Previous work has demonstrated how the distinct anisotropic channel geometry in some biofilms affects AIs propagation therein. In this paper, a 2D anisotropic biofilm channel model is extended to be a time-varying channel (TVC), in order to represent the diffusion dynamics during the maturation phase when water channels develop. Since maturation is associated with the development of anisotropy, the time-varying model captures the shift from isotropic to anisotropic diffusion. Particle-based simulation results illustrate how the TVC is a hybrid scenario incorporating propagation features of both isotropic and anisotropic diffusion. This hybrid behavior aligns with biofilm maturation. Further study of the TVC includes characterization of the mutual information (MI), which reveals that an increased AI count, reduced transmitter -- receiver distance, greater degree of anisotropy, and shorter inter-symbol interference lengths increase the MI. Finally, a brief dimensional analysis demonstrates the scalability of the anisotropic channel results for larger biofilms and timescales.
2511.03856Nov 2025
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Glymphatic Clearance in the Optic Nerve: A Multidomain Electro-osmostic Model
Effective metabolic waste clearance and maintaining ionic homeostasis are essential for the health and normal function of the central nervous system. To understand its mechanism and the role of fluid flow, we develop a multidomain electro-osmotic model of optic-nerve microcirculation that couples hydrostatic and osmotic fluid transport with electro-diffusive solute movement across axons, glia, the extracellular space, and arterial/venous/capillary perivascular spaces. Cerebrospinal fluid enters the optic nerve via the arterial parivascular space, passes both the glial and ECS before exiting through the venous parivascular space. Exchanges across astrocytic endfeet are essential and they occur in two distinct and coupled paths: through AQP4 on glial membranes and gaps between glial endfeet, thus establishing a mechanistic substrate for two modes of glymphatic transport, at rest and during stimulus-evoked perturbations. Parameter sweeps show that lowering AQP4-mediated fluid permeability or PVS permeability elevates pressure, suppresses radial exchange and slows clearance, effects most pronounced for solutes reliant on PVS V export. The model reproduces baseline and stimulus-evoked flow and demonstrates that PVS-mediated export is the primary clearance route for both small and moderate solutes. Small molecules clear faster because rapid ECS diffusion broadens their distribution and enhances ECS PVS exchange, whereas moderate species have low ECS diffusivity, depend on transendfoot transfer, and clear more slowly via PVS V convection. Our framework can also be used to explain the sleep-wake effect mechanistically: enlarging ECS volume or permeability increases transinterface flux and accelerates waste removal.
2510.222711Oct 2025
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Mechanical activity enables patterning and discrimination at the immune synapse
Immune cells recognize and discriminate antigens through immunological synapses - dynamic intercellular junctions exhibiting highly organized receptor-ligand patterns. While much work has focused on molecular kinetics and passive mechanisms of pattern formation, the role of active mechanical control in patterning and discrimination remains underexplored. We develop a minimal continuum model coupling receptor binding kinetics, membrane deformation, and cytoskeletal forces, with elastohydrodynamic flow in the synaptic cleft. Numerical simulations and scaling analysis reveal that contractile cortical flows arrest coarsening and stabilize long-lived multifocal clusters, whereas active pulling accelerates cluster dissolution and elevates background receptor binding. Nonequilibrium mechanical forces enable adaptive control over the speed, sensitivity, and dynamic range of affinity discrimination in a pattern-dependent manner. Our results highlight how immune cells exploit cytoskeletal remodeling to robustly regulate antigen recognition through synaptic patterning.
2510.18771Oct 2025
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Competing forces of polarization and adhesion generate directional migration bias in a minimal model
Left-right axis specification establishes embryonic laterality through asymmetric signaling cascades originating at the cellular scale. We previously reported the presence of a directionality bias in confined pairs of endothelial (and fibroblast) cells exhibiting persistent circular motion, with cytoskeletal contractility modulating the direction. The relative simplicity of the experimental setup makes it a perfect testing ground for the physical forces that could endow this system with a tunable directional migration bias. We model self-propelling biological cells migrating in response to confinement, polarity, and pairwise repulsive forces. Our framework reproduces three key experimental observations: spontaneous coherent circular movement of confined cell pairs, emergence of directional bias when cells have asymmetric properties, and contractility-modulated switching of the rotation direction. Two key assumptions are required: an internal torque arising from cytoskeletal organization (previously observed in other cellular systems), and an asymmetric polarity response between cells, which introduces a difference in how quickly each cell reorients its migration direction. New experiments on daughter cell pairs support this asymmetry requirement in cellular properties. Tuning the polarity response timescale (or strength) relative to centering forces from confinement and cell-cell adhesion can amplify or reverse the directional migration bias.
2510.11642Oct 2025
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A Phase-field Model for Apoptotic Cell Death
The process of programmed cell death, namely apoptosis, is a natural mechanism that regulates healthy tissue, multicellular structures, and homeostasis. An improved understanding of apoptosis can significantly enhance our knowledge of biological processes and systems. For instance, pathogens can manipulate the apoptotic process to either evade immune detection or to facilitate their spread. Furthermore, of particular clinical interest is the ability of cancer cells to evade apoptosis, hence allowing them to survive and proliferate uncontrollably. Thus, in this work, we propose a phase-field framework for simulating intrinsic or extrinsic apoptosis induced by an activation field, including deriving the configurational mechanics underlying such phenomena. Along with exploring varying conditions needed to initiate or reduce apoptosis, this can serve as a starting point for computational therapeutic testing. To showcase model capabilities, we present simulations exhibiting different types of cellular dynamics produced when varying the mechanisms underlying apoptosis. The model is subsequently applied to probe different morphological transitions, such as cell shrinkage, membrane blebbing, cavity formation and fragmentation. Lastly, we compare the characteristics observed in our simulations to electron microscopy images, providing additional support for the model.
2507.09038Jul 2025
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