Chimeric Antigen Receptor T (CAR-T) cell therapy has been proven to be successful against different leukaemias and lymphomas. This paper makes an analytical and numerical study of a mathematical model describing the competition of CAR-T, leukaemias tumor and B cells. Considering its significance in sustaining anti-CD19 CAR T-cell stimulation, we integrate a B-cell source term into the model. Through stability and bifurcation analyses, we reveal the potential for tumor eradication contingent on the continuous influx of B-cells, uncovering a transcritical bifurcation at a critical B-cell input. Additionally, we identify an almost heteroclinic cycle between equilibrium points, providing a theoretical basis for understanding disease relapse. Analyzing the oscillatory behavior of the system, we approximate the time-dependent dynamics of CAR T-cells and leukemic cells, shedding light on the impact of initial tumor burden on therapeutic outcomes. In conclusion, our study provides insights into CAR T-cell therapy dynamics for acute lymphoblastic leukemias, offering a theoretical foundation for clinical observations and suggesting avenues for future immunotherapy modeling research.
As an adoptive cellular therapy, Chimeric Antigen Receptor T-cell (CAR T-cell) therapy has shown remarkable success in hematological malignancies, but only limited efficacy against solid tumors. Compared with blood cancers, solid tumors present a unique set of challenges that ultimately neutralize the function of CAR T-cells. One such barrier is antigen heterogeneity - variability in the expression of the antigen on tumor cells. Success of CAR T-cell therapy in solid tumors is unlikely unless almost all the tumor cells express the specific antigen that CAR T-cells target. A critical question for solving the heterogeneity problem is whether CAR T therapy induces bystander effects, such as antigen spreading. Antigen spreading occurs when CAR T-cells activate other endogenous antitumor CD8 T cells against antigens that were not originally targeted. In this work, we develop a mathematical model of CAR T-cell therapy for solid tumors that takes into consideration both antigen heterogeneity and bystander effects. Our model is based on in vivo treatment data that includes a mixture of target antigen-positive and target antigen-negative tumor cells. We use our model to simulate large cohor
Adaptive therapy (AT) is designed to postpone the emergence of drug resistance by exploiting evolutionary competition among tumor subclones. Most mathematical models of AT assume a binary population structure of drug-sensitive and drug-resistant cells, which neglects the continuous nature of phenotypic plasticity. In this study, we propose a mathematical model that integrates a continuous drug susceptibility index with a probabilistic inheritance function to describe clonal dynamics under therapy. The resulting integro-differential system generalizes traditional two-type competition models and captures both heterogeneity and plasticity of tumor cells. Analytical and numerical studies show that (i) continuous therapy drives rapid expansion of resistant clones, (ii) adaptive therapy maintains long-term tumor control by dynamically regulating sensitive populations, and (iii) high phenotypic plasticity accelerates phenotype switching, leading to earlier tumor relapse following continuous therapy. These results identify critical parameter regimes where adaptive therapy outperforms fixed regimens and highlight the essential role of plasticity in shaping treatment outcomes. The proposed f
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.
We study the dynamics and interactions between combined chemotherapy and chimeric antigen receptor (CAR-T) cells therapy and malignant gliomas (MG). MG is one of the most common primary brain tumor, with high resistance to therapy and unfavorable prognosis. Here, we develop a mathematical model that describes the application of chemo- and CAR-T cell therapies and the dynamics of sensitive and resistant populations of tumor cells. This model is a five-dimensional dynamical system with impulsive inputs corresponding to clinical administration of chemo- and immunotherapy. We provide a proof of non-negativeness of solutions of the proposed model for non-negative initial data. We demonstrate that if we apply both therapies only once, the trajectories will be attracted to an invariant surface that corresponds to the tumor carrying capacity. On the other hand, if we apply both treatments constantly, we find regions of the parameter where the tumor is eradicated. Moreover, we study applications of different combinations of the above treatments in order to find an optimal combination at the population level. To this aim, we generate a population of $10^{4}$ virtual patients with the model p
We generated a computational approach to analyze the biomechanics of epithelial cell aggregates, either island or stripes or entire monolayers, that combines both vertex and contact-inhibition-of-locomotion models to include both cell-cell and cell-substrate adhesion. Examination of the distribution of cell protrusions (adhesion to the substrate) in the model predicted high order profiles of cell organization that agree with those previously seen experimentally. Cells acquired an asymmetric distribution of basal protrusions, traction forces and apical aspect ratios that decreased when moving from the edge to the island center. Our in silico analysis also showed that tension on cell-cell junctions and apical stress is not homogeneous across the island. Instead, these parameters are higher at the island center and scales up with island size, which we confirmed experimentally using laser ablation assays and immunofluorescence. Without formally being a 3-dimensional model, our approach has the minimal elements necessary to reproduce the distribution of cellular forces and mechanical crosstalk as well as distribution of principal stress in cells within epithelial cell aggregates. By mak
The entropy production rate of cancer cell is always higher than healthy cell under the case of no external field applied. Different entropy production between two kinds of cells determines the direction of entropy flow among cells. The entropy flow is the carrier of information flow. The entropy flow from cancer to healthy cell takes along the harmful information of cancerous cell, propagating its toxic action to healthy tissues. We demonstrate that a low-frequency and low-intensity electromagnetic field or ultrasound irradiation may increase the entropy production rate of a cell in normal tissue than that in cancer, consequently reverse the direction of entropy current between two kinds of cells. The modification of PH value of cells may also cause the reversal of the direction of entropy flow between healthy and cancerous cells. So, the biological tissue under the irradiation of electromagnetic field or ultrasound or under the appropriate change of cell acidity can avoid the propagation of harmful information from cancer cells. We suggest that this entropy mechanism possibly provides a basis for a novel approach to anticancer therapy.
Cancer stem cells are controlled by developmental networks that are often topologically indistinguishable from normal, healthy stem cells. The question is why cancer stem cells can be both phenotypically distinct and have morphological effects so different from normal stem cells. The difference between cancer stem cells and normal stem cells lies not in differences their network architecture, but rather in the spatial-temporal locality of their activation in the genome and the resulting expression in the body. The metastatic potential cancer stem cells is not based primarily on their network divergence from normal stem cells, but on non-network based genetic changes that enable the evolution of gene-based phenotypic properties of the cell that permit its escape and travel to other parts of the body. Stem cell network theory allows the precise prediction of stem cell behavioral dynamics and a mathematical description of stem cell proliferation for both normal and cancer stem cells. It indicates that the best therapeutic approach is to tackle the highest order stem cells first, otherwise spontaneous remission of so called cured cancers will always be a danger. Stem cell networks poin
We introduce Transfusion, a recipe for training a multi-modal model over discrete and continuous data. Transfusion combines the language modeling loss function (next token prediction) with diffusion to train a single transformer over mixed-modality sequences. We pretrain multiple Transfusion models up to 7B parameters from scratch on a mixture of text and image data, establishing scaling laws with respect to a variety of uni- and cross-modal benchmarks. Our experiments show that Transfusion scales significantly better than quantizing images and training a language model over discrete image tokens. By introducing modality-specific encoding and decoding layers, we can further improve the performance of Transfusion models, and even compress each image to just 16 patches. We further demonstrate that scaling our Transfusion recipe to 7B parameters and 2T multi-modal tokens produces a model that can generate images and text on a par with similar scale diffusion models and language models, reaping the benefits of both worlds.
Cell-cell communication is essential for tissue development, regeneration and function, and its disruption can lead to diseases and developmental abnormalities. The revolution of single-cell genomics technologies offers unprecedented insights into cellular identities, opening new avenues to resolve the intricate cellular interactions present in tissue niches. CellPhoneDB is a bioinformatics toolkit designed to infer cell-cell communication by combining a curated repository of bona fide ligand-receptor interactions with a set of computational and statistical methods to integrate them with single-cell genomics data. Importantly, CellPhoneDB captures the multimeric nature of molecular complexes, thus representing cell-cell communication biology faithfully. Here we present CellPhoneDB v5, an updated version of the tool, which offers several new features. Firstly, the repository has been expanded by one-third with the addition of new interactions. These encompass interactions mediated by non-protein ligands such as endocrine hormones and GPCR ligands. Secondly, it includes a differentially expression-based methodology for more tailored interaction queries. Thirdly, it incorporates novel
Chimeric Antigen Receptor (CAR) T-cell therapy is an immunotherapy that has recently become highly instrumental in the fight against life-threatening diseases. A variety of modeling and computational simulation efforts have addressed different aspects of CAR T therapy, including T-cell activation, T- and malignant cell population dynamics, therapeutic cost-effectiveness strategies, and patient survival analyses. In this article, we present a systematic review of those efforts, including mathematical, statistical, and stochastic models employing a wide range of algorithms, from differential equations to machine learning. To the best of our knowledge, this is the first review of all such models studying CAR T therapy. In this review, we provide a detailed summary of the strengths, limitations, methodology, data used, and data lacking in current published models. This information may help in designing and building better models for enhanced prediction and assessment of the benefit-risk balance associated with novel CAR T therapies, as well as with the data collection essential for building such models.
Organisms across all domains of life regulate the size of their cells. However, the means by which this is done is poorly understood. We study two abstracted "molecular" models for size regulation: inhibitor dilution and initiator accumulation. We apply the models to two settings: bacteria like Escherichia coli, that grow fully before they set a division plane and divide into two equally sized cells, and cells that form a bud early in the cell division cycle, confine new growth to that bud, and divide at the connection between that bud and the mother cell, like the budding yeast Saccharomyces cerevisiae. In budding cells, delaying cell division until buds reach the same size as their mother leads to very weak size control, with average cell size and standard deviation of cell size increasing over time and saturating up to 100-fold higher than those values for cells that divide when the bud is still substantially smaller than its mother. In budding yeast, both inhibitor dilution or initiator accumulation models are consistent with the observation that the daughters of diploid cells add a constant volume before they divide. This adder behavior has also been observed in bacteria. We f
Chimeric antigen receptor T-cell (CAR-T) therapy is considered a promising cancer treatment. The dynamic response to this therapy can be broadly divided into a short-term phase, ranging from weeks to months, and a long-term phase, ranging from months to years. While the short-term response, encompassing the multiphasic kinetics of CAR-T cells, is better understood, the mechanisms underlying the outcomes of the long-term response, characterized by sustained remission, relapse, or disease progression, remain less understood due to limited clinical data. Here, we analyze the long-term dynamics of a previously validated mathematical model of CAR-T cell therapy. We perform a comprehensive stability and bifurcation analysis, examining model equilibria and their dynamics over the entire parameter space. Our results show that therapy failure results from a combination of insufficient CAR-T cell proliferation and increased tumor immunosuppression. By combining different techniques of nonlinear dynamics, we identify Hopf and Bogdanov-Takens bifurcations, which allow to elucidate the mechanisms behind oscillatory remissions and transitions to tumor escape. In particular, rapid expansion of CA
In this study, we present a stochastic simulation model designed to explicitly incorporate cell cycle length, overcoming limitations associated with classical compartmental models. Our approach employs a delay mechanism to represent the cell cycle, allowing the use of arbitrary distributions for cell cycle lengths. We demonstrate the feasibility of our model by fitting it to experimental data from melanoma cell lines previously studied by Vittadello et al. Notably, our model successfully replicates experimentally observed synchronization phenomena that multi-stage models could not adequately explain. By using a gamma distribution to model cell cycle lengths, we achieved excellent agreement between our simulations and empirical data, while significantly reducing computational complexity and parameter estimation challenges inherent in multi-stage approaches. Our results highlight the importance of explicitly incorporating cell cycle lengths in modeling cell populations, with potential implications for optimizing cell cycle-dependent tumor therapies.
A virus infection can be initiated with very few or even a single infectious virion, and as such can become extinct, i.e. stochastically fail to take hold or spread significantly. There are many ways that a fully competent infectious virion, having successfully entered a cell, can fail to cause a productive infection, i.e. one that yields infectious virus progeny. Though many discrete, stochastic mathematical models (DSMs) have been developed and used to estimate a virus infection's extinction probability, these typically neglect infection failure post viral entry. The DSM presented herein introduces parameter $γ\in(0,1]$ which corresponds to the probability that a virion's entry into a cell will result in a productive cell infection. We derive an expression for the likelihood of infection extinction in this new DSM, and find that prophylactic therapy with an antiviral acting to reduce $γ$ is best at increasing an infection's extinction probability, compared to antivirals acting on the rates of virus production or virus entry into cells. Using the DSM, we investigate the difference in the fraction of cells consumed by so-called extinct versus established virus infections, and find
The discovery of general principles underlying the complexity and diversity of cellular and developmental systems is a central and long-standing aim of biology. Whilst new technologies collect data at an ever-accelerating rate, there is growing concern that conceptual progress is not keeping pace. We contend that this is due to a paucity of appropriate conceptual frameworks to serve as a basis for general theories of mesoscale biological phenomena. In exploring this issue, we have developed a foundation for one such framework, termed the Core and Periphery (C&P) hypothesis, which reveals hidden generality across the diverse and complex behaviors exhibited by cells and tissues. Here, we present the C&P concept, provide examples of its applicability across multiple scales, argue its consistency with evolution, and discuss key implications and open questions. We propose that the C&P hypothesis could unlock new avenues of conceptual progress in cell and developmental biology.
Regulation of cell proliferation is a crucial aspect of tissue development and homeostasis and plays a major role in morphogenesis, wound healing, and tumor invasion. A phenomenon of such regulation is contact inhibition, which describes the dramatic slowing of proliferation, cell migration and individual cell growth when multiple cells are in contact with each other. While many physiological, molecular and genetic factors are known, the mechanism of contact inhibition is still not fully understood. In particular, the relevance of cellular signaling due to interfacial contact for contact inhibition is still debated. Cellular automata (CA) have been employed in the past as numerically efficient mathematical models to study the dynamics of cell ensembles, but they are not suitable to explore the origins of contact inhibition as such agent-based models assume fixed cell sizes. We develop a minimal, data-driven model to simulate the dynamics of planar cell cultures by extending a probabilistic CA to incorporate size changes of individual cells during growth and cell division. We successfully apply this model to previous in-vitro experiments on contact inhibition in epithelial tissue: A
Clinical transfusion-outcomes research faces unique methodological challenges compared with other areas of clinical research. These challenges arise because patients frequently receive multiple transfusions, each unit originates from a different donor, and the probability of receiving specific blood product characteristics is influenced by external, often uncontrollable, factors. These complexities complicate causal inference in observational studies of transfusion effectiveness and safety. This guide addresses key challenges in observational transfusion research, with a focus on time-varying exposure, time-varying confounding, and treatment-confounder feedback. Using the example of donor sex and pregnancy history in relation to recipient mortality, we illustrate the strengths and limitations of commonly used analytical approaches. We compare restriction-based analyses, time-varying Cox regression, and inverse probability weighted marginal structural models using a large observational dataset of male transfusion recipients. In the applied example, restriction and conventional time-varying approaches suggested an increased mortality risk associated with transfusion of red blood cell
The functionality and viability of stored human red blood cells (RBCs) is an important clinical issue in transfusion. To systematically investigate changes in stored whole blood, the hematological properties of individual RBCs were quantified in blood samples stored for various periods with and without a preservation solution called CPDA-1. With 3-D quantitative phase imaging techniques, the optical measurements of the 3-D refractive index (RI) distributions and membrane fluctuations were done at the individual cell level. From the optical measurements, the morphological (volume, surface area and sphericity), biochemical (hemoglobin content and concentration), and mechanical parameters (dynamic membrane fluctuation) were simultaneously quantified to investigate the functionalities and their progressive alterations in stored RBCs. Our results show that the stored RBCs without CPDA-1 had a dramatic morphological transformation from discocytes to spherocytes within 2 weeks which was accompanied with significant decreases in cell deformability and cell surface area, and increases in sphericity. However, the stored RBCs with CPDA-1 maintained their morphology and deformability for up to
Bacteria are able to maintain a narrow distribution of cell sizes by regulating the timing of cell divisions. In rich nutrient conditions, cells divide much faster than their chromosomes replicate. This implies that cells maintain multiple rounds of chromosome replication per cell division by regulating the timing of chromosome replications. Here, we show that both cell size and chromosome replication may be simultaneously regulated by the long-standing initiator accumulation strategy. The strategy proposes that initiators are produced in proportion to the volume increase and is accumulated at each origin of replication, and chromosome replication is initiated when a critical amount per origin has accumulated. We show that this model maps to the incremental model of size control, which was previously shown to reproduce experimentally observed correlations between various events in the cell cycle and explains the exponential dependence of cell size on the growth rate of the cell. Furthermore, we show that this model also leads to the efficient regulation of the timing of initiation and the number of origins consistent with existing experimental results.