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A Mathematical Framework for Understanding Four-Dimensional Heterogeneous Differentiation of CD4+ T Cells.

ABSTRACT: At least four distinct lineages of CD4+ T cells play diverse roles in the immune system. Both in vivo and in vitro, naïve CD4+ T cells often differentiate into a variety of cellular phenotypes. Previously, we developed a mathematical framework to study heterogeneous differentiation of two lineages governed by a mutual-inhibition motif. To understand heterogeneous differentiation of CD4+ T cells involving more than two lineages, we present here a mathematical framework for the analysis of multiple stable steady states in dynamical systems with multiple state variables interacting through multiple mutual-inhibition loops. A mathematical model for CD4+ T cells based on this framework can reproduce known properties of heterogeneous differentiation involving multiple lineages of this cell differentiation system, such as heterogeneous differentiation of TH1-TH2, TH1-TH17 and iTReg-TH17 under single or mixed types of differentiation stimuli. The model shows that high concentrations of differentiation stimuli favor the formation of phenotypes with co-expression of lineage-specific master regulators.

SUBMITTER: Hong T

PROVIDER: S-EPMC4474756 | biostudies-literature | 2015 Jun

REPOSITORIES: biostudies-literature

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A Mathematical Framework for Understanding Four-Dimensional Heterogeneous Differentiation of CD4+ T Cells.

Hong Tian T Oguz Cihan C Tyson John J JJ

Bulletin of mathematical biology 20150317 6

At least four distinct lineages of CD4+ T cells play diverse roles in the immune system. Both in vivo and in vitro, naïve CD4+ T cells often differentiate into a variety of cellular phenotypes. Previously, we developed a mathematical framework to study heterogeneous differentiation of two lineages governed by a mutual-inhibition motif. To understand heterogeneous differentiation of CD4+ T cells involving more than two lineages, we present here a mathematical framework for the analysis of multipl ...[more]

PMID: 25779890

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Project description:BackgroundCD4+ T cells have several subsets of functional phenotypes, which play critical yet diverse roles in the immune system. Pathogen-driven differentiation of these subsets of cells is often heterogeneous in terms of the induced phenotypic diversity. In vitro recapitulation of heterogeneous differentiation under homogeneous experimental conditions indicates some highly regulated mechanisms by which multiple phenotypes of CD4+ T cells can be generated from a single population of naïve CD4+ T cells. Therefore, conceptual understanding of induced heterogeneous differentiation will shed light on the mechanisms controlling the response of populations of CD4+ T cells under physiological conditions.ResultsWe present a simple theoretical framework to show how heterogeneous differentiation in a two-master-regulator paradigm can be governed by a signaling network motif common to all subsets of CD4+ T cells. With this motif, a population of naïve CD4+ T cells can integrate the signals from their environment to generate a functionally diverse population with robust commitment of individual cells. Notably, two positive feedback loops in this network motif govern three bistable switches, which in turn, give rise to three types of heterogeneous differentiated states, depending upon particular combinations of input signals. We provide three prototype models illustrating how to use this framework to explain experimental observations and make specific testable predictions.ConclusionsThe process in which several types of T helper cells are generated simultaneously to mount complex immune responses upon pathogenic challenges can be highly regulated, and a simple signaling network motif can be responsible for generating all possible types of heterogeneous populations with respect to a pair of master regulators controlling CD4+ T cell differentiation. The framework provides a mathematical basis for understanding the decision-making mechanisms of CD4+ T cells, and it can be helpful for interpreting experimental results. Mathematical models based on the framework make specific testable predictions that may improve our understanding of this differentiation system.

Project description:Cell migration is essential in animal development, homeostasis, and disease progression, but many questions remain unanswered about how this process is controlled. While many kinds of individual cell movements have been characterized, less effort has been directed towards understanding how clusters of cells migrate collectively through heterogeneous, cellular environments. To explore this, we have focused on the migration of the border cells during Drosophila egg development. In this case, a cluster of different cell types coalesce and traverse as a group between large cells, called nurse cells, in the center of the egg chamber. We have developed a new model for this collective cell migration based on the forces of adhesion, repulsion, migration and stochastic fluctuation to generate the movement of discrete cells. We implement the model using Identical Math Cells, or IMCs. IMCs can each represent one biological cell of the system, or can be aggregated using increased adhesion forces to model the dynamics of larger biological cells. The domain of interest is filled with IMCs, each assigned specific biophysical properties to mimic a diversity of cell types. Using this system, we have successfully simulated the migration of the border cell cluster through an environment filled with larger cells, which represent nurse cells. Interestingly, our simulations suggest that the forces utilized in this model are sufficient to produce behaviors of the cluster that are observed in vivo, such as rotation. Our framework was developed to capture a heterogeneous cell population, and our implementation strategy allows for diverse, but precise, initial position specification over a three- dimensional domain. Therefore, we believe that this model will be useful for not only examining aspects of Drosophila oogenesis, but also for modeling other two or three-dimensional systems that have multiple cell types and where investigating the forces between cells is of interest.

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Project description:Mathematical modelling has been used to study tumor-immune cell interaction. Some models were proposed to examine the effect of circulating lymphocytes, natural killer cells, and CD8+T cells, but they neglected the role of CD4+T cells. Other models were constructed to study the role of CD4+T cells but did not consider the role of other immune cells. In this study, we propose a mathematical model, in the form of a system of nonlinear ordinary differential equations, that predicts the interaction between tumor cells and natural killer cells, CD4+T cells, CD8+T cells, and circulating lymphocytes with or without immunotherapy and/or chemotherapy. This system is stiff, and the Runge-Kutta method failed to solve it. Consequently, the "Adams predictor-corrector" method is used. The results reveal that the patient's immune system can overcome small tumors; however, if the tumor is large, adoptive therapy with CD4+T cells can be an alternative to both CD8+T cell therapy and cytokines in some cases. Moreover, CD4+T cell therapy could replace chemotherapy depending upon tumor size. Even if a combination of chemotherapy and immunotherapy is necessary, using CD4+T cell therapy can better reduce the dose of the associated chemotherapy compared to using combined CD8+T cells and cytokine therapy. Stability analysis is performed for the studied patients. It has been found that all equilibrium points are unstable, and a condition for preventing tumor recurrence after treatment has been deduced. Finally, a bifurcation analysis is performed to study the effect of varying system parameters on the stability, and bifurcation points are specified. New equilibrium points are created or demolished at some bifurcation points, and stability is changed at some others. Hence, for systems turning to be stable, tumors can be eradicated without the possibility of recurrence. The proposed mathematical model provides a valuable tool for designing patients' treatment intervention strategies.

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A Mathematical Framework for Understanding Four-Dimensional Heterogeneous Differentiation of CD4+ T Cells.

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A Mathematical Framework for Understanding Four-Dimensional Heterogeneous Differentiation of CD4+ T Cells.

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