Agent-based model of heterogeneous T cell activation in vitro (supplementary material)

We combine modelling and in vitro measurement of T-cell properties at the level of individual cells. Two types of heterogeneity are explicitly simulated: cell-surface marker expression that is time-dependent and varies from cell to cell, and spatial heterogeneity that arises from local influences such as the proximity of IL-2-producing cells. In vitro, the kinetics of the activation of cohorts of CD4+ T cells from 4-6 week-old BALB/c mice was studied, under stimulus with soluble or plate-bound anti-CD3, or a combination of PMA and ionomycin

Dynamics of defect formation

A dynamic symmetry-breaking transition with noise and inertia is analyzed. Exact solution of the linearized equation that describes the critical region allows precise calculation (exponent and prefactor) of the number of defects produced as a function of the rate of increase of the critical parameter. The procedure is valid in both the overdamped and underdamped limits. In one space dimension, we perform quantitative comparison with numerical simulations of the nonlinear nonautonomous stochastic partial differential equation and report on signatures of underdamped dynamics.Comment: 4 pages, LaTeX, 4 figures. Submitted to Physical Revie

The Islamic cemetery at 33 Bartomeu Vicent Ramon, Ibiza: investigating diet and mobility through light stable isotopes in bone collagen and tooth enamel

The Balearic Islands occupy a central space in the western Mediterranean, at the maritime crossroads between North Africa, the Iberian Peninsula and the rest of southwestern Europe. As such, it is well placed to investigate changes in subsistence practices associated with the major cultural transitions following the arrival of Islamic rule. Stable carbon and nitrogen isotope analysis was carried out on bone collagen from the Islamic cemetery (ca. AD 950–1150) population excavated at 33 Bartomeu Vicent Ramon, Ibiza, including human (n = 42) and faunal remains (n = 3). Stable oxygen and carbon isotope analysis was also undertaken on human tooth enamel carbonate (n = 6), and six humans were directly radiocarbon dated, confirming the presence of two distinct burial phases. The collagen results emphasise a C3-based diet, with variable but generally minor contributions from marine and/or C4 foods. However, the enamel carbonate results indicate a far greater importance of C4 crops than suggested by the collagen results, contributing up to 40% of energy intake. In keeping with previous studies of the region and period, the dietary contribution of marine protein is probably limited. A small number of outliers in both collagen and carbonate isotope results are identified, suggesting the presence of individuals originating elsewhere. The results are compared with those from previous investigations on the Balearics and the Spanish mainland, highlighting the complexity of factors—both cultural and methodological—affecting inter-regional dietary investigation

Fate of a Naive T Cell: A Stochastic Journey

The homeostasis of T cell populations depends on migration, division and death of individual cells (1). T cells migrate between spatial compartments (spleen, lymph nodes, lung, liver, etc.), where they may divide or differentiate, and eventually die (2). The kinetics of recirculation influences the speed at which local infections are detected and controlled (3). New experimental techniques have been developed to measure the lifespan of cells, and their migration dynamics; for example, fluorescence-activated cell sorting (4), in vitro time-lapse microscopy (5), or in vivo stable isotope labeling (e.g., deuterium) (6). When combined with mathematical and computational models, they allow estimation of rates of migration, division, differentiation and death (6, 7). In this work, we develop a stochastic model of a single cell migrating between spatial compartments, dividing and eventually dying. We calculate the number of division events during a T cell's journey, its lifespan, the probability of dying in each compartment and the number of progeny cells. A fast-migration approximation allows us to compute these quantities when migration rates are larger than division and death rates. Making use of published rates: (i) we analyse how perturbations in a given spatial compartment impact the dynamics of a T cell, (ii) we study the accuracy of the fast-migration approximation, and (iii) we quantify the role played by direct migration (not via the blood) between some compartments

Accurate stationary densities with partitioned numerical methods for stochastic partial differential equations

We consider the numerical solution, by finite differences, of second-order-in-time stochastic partial differential equations (SPDEs) in one space dimension. New timestepping methods are introduced by generalising recently-introduced methods for second-order-in-time stochastic differential equations to multidimensional systems. These stochastic methods, based on leapfrog and Runge–Kutta methods, are designed to give good approximations to the stationary variances and the correlations in the position and velocity variables. In particular, we introduce the reverse leapfrog method and stochastic Runge–Kutta Leapfrog methods, analyse their performance applied to linear SPDEs and perform numerical experiments to examine their accuracy applied to a type of nonlinear SPDE

T cell and reticular network co-dependence in HIV infection

Fibroblastic reticular cells (FRC) are arranged on a network in the T cell zone of lymph nodes, forming a scaffold for T cell migration, and providing survival factors, especially interleukin-7 (IL- 7). Conversely, CD4+ T cells are the major producers of lymphotoxin-_ (LT-_), necessary for the construction and maintenance of the FRC network. This interdependence creates the possibility of a vicious cycle, perpetuating loss of both FRC and T cells. Furthermore, evidence that HIV infection is responsible for collagenation of the network suggests that long term loss of network function might be responsible for the attenuated recovery in T cell count seen in HIV patients undergoing antiretroviral therapy (ART). We present computational and mathematical models of this interaction mechanism and subsequent naive CD4+ T-cell depletion in which (1) collagen deposition impedes access of naive T cells to IL-7 on the FRC and loss of IL-7 production by loss of FRC network itself, leading to the depletion of naive T cells through increased apoptosis; and (2) depletion of naive T cells as the source of LT-_ on which the FRC depend for survival, leads to loss of the network, thereby amplifying and perpetuating the cycle of depletion of both naive T cells and stromal cells. Our computational model explicitly includes an FRC network and its cytokine exchange with a heterogeneous T-cell population. We also derive lumped models, in terms of partial differential equations and reduced to ordinary differential equations, that provide additional insight into the mechanisms at work. The central conclusions are that 1) damage to the reticular network, caused by HIV infection, is a plausible mechanism for attenuated recovery post-ART; 2) within this, the production of T cell survival factors by FRCs may be the key rate-limiting step; and 3) the methods of model reduction and analysis presented are useful for both immunological studies and other contexts in which agent-based models are severely limited by computational cost

Comparison of Statistical Population Reconstruction Using Full and Pooled Adult Age-Class Data

BACKGROUND: Age-at-harvest data are among the most commonly collected, yet neglected, demographic data gathered by wildlife agencies. Statistical population construction techniques can use this information to estimate the abundance of wild populations over wide geographic areas and concurrently estimate recruitment, harvest, and natural survival rates. Although current reconstruction techniques use full age-class data (0.5, 1.5, 2.5, 3.5, … years), it is not always possible to determine an animal's age due to inaccuracy of the methods, expense, and logistics of sample collection. The ability to inventory wild populations would be greatly expanded if pooled adult age-class data (e.g., 0.5, 1.5, 2.5+ years) could be successfully used in statistical population reconstruction. METHODOLOGY/PRINCIPAL FINDINGS: We investigated the performance of statistical population reconstruction models developed to analyze full age-class and pooled adult age-class data. We performed Monte Carlo simulations using a stochastic version of a Leslie matrix model, which generated data over a wide range of abundance levels, harvest rates, and natural survival probabilities, representing medium-to-big game species. Results of full age-class and pooled adult age-class population reconstructions were compared for accuracy and precision. No discernible difference in accuracy was detected, but precision was slightly reduced when using the pooled adult age-class reconstruction. On average, the coefficient of variation (i.e., SE(θ)/θ) increased by 0.059 when the adult age-class data were pooled prior to analyses. The analyses and maximum likelihood model for pooled adult age-class reconstruction are illustrated for a black-tailed deer (Odocoileus hemionus) population in Washington State. CONCLUSIONS/SIGNIFICANCE: Inventorying wild populations is one of the greatest challenges of wildlife agencies. These new statistical population reconstruction models should expand the demographic capabilities of wildlife agencies that have already collected pooled adult age-class data or are seeking a cost-effective method for monitoring the status and trends of our wild resources