Protozoan colonies undergo stimulus driven motion for purposes such as and nutrient acquisition. Colonial response to a stimulus is mediated through a mechanical aggregation of the response properties of members of the colony. We develop and apply asymptotic analysis to stochastic models for two separate classes of stimulus driven response of the constituent cells - taxis and kinesis. We investigate in particular the maintenance of effectiveness of taxis and kinesis in the transition from unicellular to multicellular organisms, using experimental observations of chemotaxis and aerotaxis of protozoa as a reference. Our taxis model based on a steering response of individual cells actually leads to a counterproductive drift of the colony down the stimulus gradient, together with a constructive drift up the gradient which is proportional to a measure of asymmetry of the flagellar placement. The strength of taxis drift up the stimulus gradient decreases with colony size while the counterproductive term does not, indicating a failure for colonial taxis based on a steering response of individual cells. Under a kinesis response of the cellular flagellar motion, enhancing the noise as the cell is facing away from the stimulus gradient, the colony does drift up the gradient with a speed independent of colony size, even under a completely symmetric placement of flagella.

Smooth muscle cells (SMCs) play a fundamental role in the development of atherosclerotic plaques. They ingest lipids in a similar way to monocyte-derived macrophages (MDMs) in the plaque. This can stimulate SMCs to undergo a phenotypic switch to a macrophage-like phenotype. We formulate an ordinary differential equation (ODE) model for the populations of SMCs, MDMs and smooth muscle cell-derived macrophages (SDMs) and the internalised lipid load in each population. We use this model to explore the effect on plaque fate of SMC phenotype switching. We find that when SMCs switch to a macrophage-like phenotype, there is an increase in the lipid quantity in the model plaque that is internalised inside cells. Additionally, removal of SMCs from the model plaque via phenotype switching reduces the number of SMCs in the fibrous cap, increases the lipid in the necrotic core, and increases plaque inflammation. These features are hallmarks of vulnerable plaques, whose rupture can cause heart attacks or strokes. When SDMs are highly proliferative or resistant to cell death, the model plaque becomes increasingly pathological. The model suggests that the switch of SMCs to a macrophage-like phenotype may drive the development of unstable and pathological plaques.

In a 1952 paper, Alan Turing showed that spatially distributed chemical reactions evolving in time by local kinetic rate laws and in space by unbiased molecular diffusion can develop a stable, time-independent, spatial pattern from a spatially homogeneous, steady state solution subjected to small, spatially periodic perturbations over a critical range of wavelengths. He proposed this mechanism as a potential chemical basis for biological morphogenesis. Although his proposal was initially ignored and remains controversial, Turing's idea still plays a major role in any discussion of spontaneous pattern formation in biological and chemical systems. Nevertheless, it is safe to say that few people have carefully studied his 1952 paper, which is notoriously difficult to read. For this reason, I am 'revisiting' Turing's paper to help new investigators to understand and appreciate his remarkable contribution to mathematical biology. Along the way, we shall resolve several 'peculiarities' of Turing's reaction mechanisms and numerical simulations, and place his work in context with later textbook examples. The relation of stationary Turing patterns to time-dependent traveling waves of chemical activity is also described.

Chimeric antigen receptor (CAR) T cell therapy has shown remarkable success in hematological malignancies, yet patient responses remain highly variable and the roles of CD4+ and CD8+ subsets are not fully understood. We present an extended mathematical framework of CAR-T cell dynamics that explicitly models CD4+ helper and CD8+ cytotoxic lineages and their interactions with tumor antigen burden. Building on a recent model of antigen-regulated memory-effector-exhaustion transitions in CAR-T cells, our system of differential equations incorporates CD4+-mediated modulation of CD8+ proliferation, cytotoxicity, and memory regeneration through biologically grounded, saturating interactions. Sensitivity analyses identify effector proliferation, antigen turnover, and CD8+ expansion rates as dominant drivers of treatment outcome. Virtual patient simulations recover reported qualitative trends in CAR-T composition, including enhanced expansion and tumor clearance for defined CD4:CD8 products relative to CD8-only formulations, while also revealing inter-patient variability and time-dependent effects. To assess the practical limits of patient-level prediction under parameter uncertainty, we introduce controlled noise into key parameters and show that direct mechanistic classification rapidly degrades. We then demonstrate that a simple feed-forward neural network can partially recover predictive signal from noisy inputs, outperforming a naïve baseline while remaining consistent with mechanistic sensitivities. This work positions the extended model as a hypothesis generator, and illustrates how data-driven methods can complement mechanistic modeling when parameter uncertainty constrains predictive confidence.

We extend the formulation of a non-local PDE model of collective cell migration involving attracting or repelling cellular interactions to the case of time-dependent spatial domains as present, for instance, in modelling developmental processes from embryology. We restrict to a spatially one-dimensional setting, as is appropriate for the modelling of neural crest cell invasion, and focus on the case of spatially homogeneous domain change as this already highlights many of the modelling and numerical challenges. The approach is illustrated and numerical simulations are presented and discussed for a model of an aggregating cellular population and for a simple model of neural crest cell invasion accounting for contact inhibition of locomotion.

It is often debated whether group selection can explain altruistic behaviors that lower the fitness of individual organisms for the benefit of their group. Several models of group selection are simulated here with more details and fewer simplifying assumptions than previous quantitative studies. The simulated models include island models with selective extinction, selective dispersal, selective migration, outsider exclusion, conformity, altruistic punishment, haystack model, and a new model with floating group territories. The simulations are repeated with different parameter sets in order to map the parameter areas that lead to either fixation of altruism, fixation of egoism, or stable polymorphism. This can help decide whether a particular behavior can be explained by genetic group selection. The conditions for group selection to override counteracting individual selection are found to be very restrictive. These conditions are met for eusocial insects, some parasites, and a few other species. The necessary conditions are unlikely to have been met in the evolutionary history of humans and most other group-living animals. Altruistic behaviors in humans could not have evolved without involving cultural mechanisms, including norms, rewards and punishments, reputation, and leadership. A comprehensive open-source simulation program is provided to facilitate further research.

Platelet adhesion and aggregation at sites of vascular injury play a critical role in both physiological hemostasis and pathological thrombosis. Platelets rely on their surface receptors to form bonds with von Willebrand factor (VWF) and exposed subendothelial collagen to initiate the clotting process. Clot formation is a complex, multistep phenomenon involving mechanical and biochemical signaling that activates key surface receptors and drives morphological changes to form aggregates. Here, we perform dissipative particle dynamics (DPD) simulations in combination with experiments using collagen- and VWF-coated microfluidic channels perfused with human blood to investigate platelet adhesion and aggregation mechanisms under physiological flow conditions. We use a viscoelastic spring-dashpot system to model platelet-platelet and platelet-coated surface interactions and introduce a probabilistic approach to capture platelet attachment or detachment on collagen- and VWF-coated surfaces. We quantitatively compare our numerical simulation with experimental results and explain the observed dynamics. Our simulation results show scattered multilayer clots over collagen-coated surfaces, and single-layer, isolated platelet adhesion on VWF-coated surfaces, corroborating experimental observations. The platelet-covered area over collagen-coated surfaces monotonically increases over time, whereas it reaches a plateau after a period of perfusion on VWF-coated surfaces.Supplementary InformationThe online version contains supplementary material available at 10.1007/s11538-026-01615-5.

Thermal reaction norms, or thermal performance curves (TPCs), describe how ectothermic organisms respond to temperature variation. Here, we investigate how stochastic environmental noise, by modulating competitive interactions among individuals with differing TPC shapes, can drive long-term evolutionary changes in thermal performance. We develop a Ricker competition model within the framework of adaptive dynamics to examine how environmental variability, corresponding to the joint effect of both periodic and stochastic temperature fluctuations, influences the evolution of competition TPCs. Growth, carrying capacity and competitive interactions are all temperature-dependent, with competition coefficients defined by the ratio of individuals’ thermal performance curve at the prevailing temperature. Competition TPCs are modelled using a beta probability density function. Previous results from periodically (i.e., deterministically) fluctuating environments established that the thermal optimum converges to the mean environmental temperature, while performance breadth collapses under constant conditions. In contrast, we show that under stochastic environments, increasing thermal noise broadens competition TPCs and shifts the thermal optimum leftward, away from the environmental mean. This results in right-skewed competition TPCs and suggests an evolutionary bias towards cooler temperature optima for competition under moderate to high environmental noise. Alongside the broadening of competition TPCs to buffer against thermal fluctuations, the shift towards cooler optima reflects a more conservative thermal strategy for competition performance in the face of environmental uncertainty.Supplementary InformationThe online version contains supplementary material available at 10.1007/s11538-026-01614-6.

Advances in multiregion sequencing have revealed extensive intratumor heterogeneity (ITH) - the presence of genetically distinct subclones within a single tumor. ITH profoundly influences tumor behavior, including well-accepted hallmarks of cancer such as sustained proliferation, resistance to apoptosis, and immune evasion, and the emergence of therapeutic resistance. In this work, we introduce a hallmark-integrated branching evolution process agent-based model (BEP-HI) to study the emergence of intratumor heterogeneity (ITH) in melanoma under coupled genetic, immune, and spatial selection pressures. Using this model, we identify three distinct evolutionary ITH modes and demonstrate a mechanistic decoupling between tumor growth kinetics and heterogeneity. We further show that immune recruitment exerts the strongest influence on ITH through nonlinear immune-editing feedback, while motility of melanoma cells shapes complex morphologies in different ITH modes as observed in clinical SSM tumors. This work provides a biologically grounded and adaptable computational framework for exploring how hallmark interactions shape ITH evolution and for generating virtual tumor cohorts that link genetic diversity with tumor behavior, morphology, and treatment resistance.

Kinetic modeling of microbial growth is essential for the design, optimization, and scale-up of industrial bioprocesses. Classical empirical models often lack biologically interpretable parameters or fail to capture complex multiphasic (polyauxic) behaviors, while fully mechanistic models are impractical for systems involving complex substrates and mixed cultures. This study proposes a unified mathematical framework that reformulates the canonical Boltzmann and Gompertz equations into semi-mechanistic forms, explicitly defining the maximum specific reaction rate and lag phase duration. Polyauxic growth is represented as a weighted sum of sigmoidal phases, subject to stringent constraints that ensure parameter identifiability, temporal consistency, and biological plausibility. The methodology integrates a workflow to address nonlinear regression in high-dimensional parameter spaces. A two-stage optimization strategy using Differential Evolution for global search followed by L-BFGS-B for local refinement avoid bias and heuristic parameter initialization. A Charbonnier loss function and the Robust Regression and Outlier Removal procedure are employed to identify and mitigate experimental outliers. Model parsimony is enforced using Akaike (AIC, AICc) and Bayesian (BIC) information criteria to select the optimal number of growth phases and avoid overparameterization. The framework was evaluated using experimental anaerobic digestion datasets, demonstrating that conventional single-phase models can obscure relevant metabolic transitions in co-digestion systems.