Grant Lythe

Quorum-Sensing in CD4(+) T Cell Homeostasis: A Hypothesis and a Model.

Homeostasis of lymphocyte numbers is believed to be due to competition between cellular populations for a common niche of restricted size, defined by the combination of interactions and trophic factors required for cell survival. Here we propose a new mechanism: homeostasis of lymphocyte numbers could also be achieved by the ability of lymphocytes to perceive the density of their own populations. Such a mechanism would be reminiscent of the primordial quorum-sensing systems used by bacteria, in which some bacteria sense the accumulation of bacterial metabolites secreted by other elements of the population, allowing them to “count” the number of cells present and adapt their growth accordingly. We propose that homeostasis of CD4+ T cell numbers may occur via a quorum-sensing-like mechanism, where IL-2 is produced by activated CD4+ T cells and sensed by a population of CD4+ Treg cells that expresses the high-affinity IL-2Rα-chain and can regulate the number of activated IL-2-producing CD4+ T cells and the total CD4+ T cell population. In other words, CD4+ T cell populations can restrain their growth by monitoring the number of activated cells, thus preventing uncontrolled lymphocyte proliferation during immune responses. We hypothesize that malfunction of this quorum-sensing mechanism may lead to uncontrolled T cell activation and autoimmunity. Finally, we present a mathematical model that describes the key role of IL-2 and quorum-sensing mechanisms in CD4+ T cell homeostasis during an immune response.

How many dendritic cells are required to initiate a T cell response

T-cell activation in lymph nodes relies on encounters with antigen (Ag)-bearing dendritic cells (DCs) but the number of DCs required to initiate an immune response is unknown. Here we have used a combination of flow cytometry, 2-photon imaging, and computational modeling to quantify the probability of T cell-DC encounters. We calculated that the chance for a T cell residing 24 hours in a murine popliteal lymph nodes to interact with a DC was 8%, 58%, and 99% in the presence of 10, 100, and 1000 Ag-bearing DCs, respectively. Our results reveal the existence of a threshold in DC numbers below which T-cell responses fail to be elicited for probabilistic reasons. In mice and probably humans, we estimate that a minimum of 85 DCs are required to initiate a T-cell response when starting from precursor frequency of 10(-6). Our results have implications for the rational design of DC-based vaccines.

Numerical Methods for Second-Order Stochastic Differential Equations

We seek numerical methods for second-order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second-order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous-time and discrete-time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge-Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

Coexisting periodic attractors in injection-locked diode lasers

We present experimental evidence of coexisting periodic attractors in a semiconductor laser subject to external optical injection. The coexisting attractors appear after the semiconductor laser has undergone a Hopf bifurcation from the locked steady state. We consider the single-mode rate equations and derive a third-order differential equation for the phase of the laser field. We then analyse the bifurcation diagram of the time-periodic states in terms of the frequency detuning and the injection rate and show the existence of multiple periodic attractors.

Exponential Timestepping with Boundary Test for Stochastic Differential Equations

We present new numerical methods for scalar stochastic differential equations. Successive time increments are independent random variables with an exponential distribution. We perform numerical experiments using a double-well potential. Exponential timestepping algorithms are efficient for escape-time problems because a simple boundary test can be performed at the end of each step.

Efficient Numerical Solution of Stochastic Differential Equations Using Exponential Timestepping

We present an exact timestepping method for Brownian motion that does not require Gaussian random variables to be generated. Time is incremented in steps that are exponentially-distributed random variables; boundaries can be explicitly accounted for at each timestep. The method is illustrated by numerical solution of a system of diffusing particles.

How many TCR clonotypes does a body maintain

We consider the lifetime of a T cell clonotype, the set of T cells with the same T cell receptor, from its thymic origin to its extinction in a multiclonal repertoire. Using published estimates of total cell numbers and thymic production rates, we calculate the mean number of cells per TCR clonotype, and the total number of clonotypes, in mice and humans. When there is little peripheral division, as in a mouse, the number of cells per clonotype is small and governed by the number of cells with identical TCR that exit the thymus. In humans, peripheral division is important and a clonotype may survive for decades, during which it expands to comprise many cells. We therefore devise and analyse a computational model of homeostasis of a multiclonal population. Each T cell in the model competes for self pMHC stimuli, cells of any one clonotype only recognising a small fraction of the many subsets of stimuli. A constant mean total number of cells is maintained by a balance between cell division and death, and a stable number of clonotypes by a balance between thymic production of new clonotypes and extinction of existing ones. The number of distinct clonotypes in a human body may be smaller than the total number of naive T cells by only one order of magnitude.

Continuous Effector CD8+ T Cell Production in a Controlled Persistent Infection Is Sustained by a Proliferative Intermediate Population

Highly functional CD8(+) effector T (Teff) cells can persist in large numbers during controlled persistent infections, as exemplified by rare HIV-infected individuals who control the virus. Here we examined the cellular mechanisms that maintain ongoing T effector responses using a mouse model for persistent Toxoplasma gondii infection. In mice expressing the protective MHC-I molecule, H-2L(d), a dominant T effector response against a single parasite antigen was maintained without a contraction phase, correlating with ongoing presentation of the dominant antigen. Large numbers of short-lived Teff cells were continuously produced via a proliferative, antigen-dependent intermediate (Tint) population with a memory-effector hybrid phenotype. During an acute, resolved infection, decreasing antigen load correlated with a sharp drop in the Tint cell population and subsequent loss of the ongoing effector response. Vaccination approaches aimed at the development of Tint populations might prove effective against pathogens that lead to chronic infection.

Mathematical Models and Immune Cell Biology

Preface.- Thymocyte development.- A review of mathematical models for T cell receptor triggering and antigen discrimination.- Dynamic tuning of T cell receptor specificity by co-receptors and costimulation.- T cell activation and function: role of signal strength.- The cyton model for lymphocyte proliferation and differentiation.- Modeling itravital two-photon data of lymphocyte migration and interaction.- Modeling lymphocyte dynamics in vivo.- Continuous-time birth and death processes: diversity maintenance of naive T cells in the periphery.- Multivariate competition processes: a model for two competing T cell clonotypes.- Stochastic modeling of T Cell homeostasis for two competing clonotypes via the master equation.- Dendritic cell migration in the intestinal tract.- Reassessing germinal center reaction concepts.- B cell strategies of Ag recognition in a stratified immune system.- Dynamics of Peripheral regulatory and effector T cells competing for antigen presenting cells.- Mathematical models of the role of IL-2 in the interactions between helper and regulstory CD4+ T cells.- A Physicists approach to immunology.- Timescales of the adaptive immune response.- Using mathematical models to explore the role of cytoxic T lymphocytes in HIV infection.- Viral immunity and persistence.- Index.

From pre-DP, post-DP, SP4, and SP8 Thymocyte Cell Counts to a Dynamical Model of Cortical and Medullary Selection.

Cells of the mature αβ T cell repertoire arise from the development in the thymus of bone marrow precursors (thymocytes). αβ T cell maturation is characterized by the expression of thousands of copies of identical αβ T cell receptors and the CD4 and/or CD8 co-receptors on the surface of thymocytes. The maturation stages of a thymocyte are: (1) double negative (DN) (TCR−, CD4− and CD8−), (2) double positive (DP) (TCR+, CD4+ and CD8+), and (3) single positive (SP) (TCR+, CD4+ or CD8+). Thymic antigen presenting cells provide the appropriate micro-architecture for the maturation of thymocytes, which “sense” the signaling environment via their randomly generated TCRs. Thymic development is characterized by (i) an extremely low success rate, and (ii) the selection of a functional and self-tolerant T cell repertoire. In this paper, we combine recent experimental data and mathematical modeling to study the selection events that take place in the thymus after the DN stage. The stable steady state of the model for the pre-DP, post-DP, and SP populations is identified with the experimentally measured cell counts from 5.5- to 17-week-old mice. We make use of residence times in the cortex and the medulla for the different populations, as well as recently reported asymmetric death rates for CD4 and CD8 SP thymocytes. We estimate that 65.8% of pre-DP thymocytes undergo death by neglect. In the post-DP compartment, 91.7% undergo death by negative selection, 4.7% become CD4 SP, and 3.6% become CD8 SP. Death by negative selection in the medulla removes 8.6% of CD4 SP and 32.1% of CD8 SP thymocytes. Approximately 46.3% of CD4 SP and 27% of CD8 SP thymocytes divide before dying or exiting the thymus.