Estimation of the proliferation and maturation functions in a physiologically structured model of thymocyte development

Model discrimination in dynamic molecular systems: application to parotid de-differentiation network

In modern systems biology the modeling of longitudinal data, such as changes in mRNA concentrations, is often of interest. Fully parametric, ordinary differential equations (ODE)-based models are typically developed for the purpose, but their lack of fit in some examples indicates that more flexible Bayesian models may be beneficial, particularly when there are relatively few data points available. However, under such sparse data scenarios it is often difficult to identify the most suitable model. The process of falsifying inappropriate candidate models is called model discrimination. We propose here a formal method of discrimination between competing Bayesian mixture-type longitudinal models that is both sensitive and sufficiently flexible to account for the complex variability of the longitudinal molecular data. The ideas from the field of Bayesian analysis of computer model validation are applied, along with modern Markov Chain Monte Carlo (MCMC) algorithms, in order to derive an appropriate Bayes discriminant rule. We restrict attention to the two-model comparison problem and present the application of the proposed rule to the mRNA data in the de-differentiation network of three mRNA concentrations in mammalian salivary glands as well as to a large synthetic dataset derived from the model used in the recent DREAM6 competition.

Multi-scale Modelling for Threshold Dependent Differentiation

The maintenance of a stable stem cell population in the epidermis is important for robust regeneration of the stratified epithelium. The population size is usually regulated by cell secreted extracellular signalling molecules as well as intracellular molecules. In this paper, a simple model incorporating both levels of regulation is developed to examine the balance between growth and differentiation for the stem cell population. In particular, the dynamics of a known differentiation regulator c-Myc, its threshold dependent differentiation, and feedback regulation on maintaining a stable stem cell population are investigated.

Distributed parameter identification for a label-structured cell population dynamics model using CFSE histogram time-series data

In this work we address the problem of the robust identification of unknown parameters of a cell population dynamics model from experimental data on the kinetics of cells labelled with a fluorescence marker defining the division age of the cell. The model is formulated by a first order hyperbolic PDE for the distribution of cells with respect to the structure variable x (or z) being the intensity level (or the log(10)-transformed intensity level) of the marker. The parameters of the model are the rate functions of cell division, death, label decay and the label dilution factor. We develop a computational approach to the identification of the model parameters with a particular focus on the cell birth rate alpha(z) as a function of the marker intensity, assuming the other model parameters are scalars to be estimated. To solve the inverse problem numerically, we parameterize alpha(z) and apply a maximum likelihood approach. The parametrization is based on cubic Hermite splines defined on a coarse mesh with either equally spaced a priori fixed nodes or nodes to be determined in the parameter estimation procedure. Ill-posedness of the inverse problem is indicated by multiple minima. To treat the ill-posed problem, we apply Tikhonov regularization with the regularization parameter determined by the discrepancy principle. We show that the solution of the regularized parameter estimation problem is consistent with the data set with an accuracy within the noise level in the measurements.

T cell development in the thymus: From periodic seeding to constant output

T cell development occurs in the thymus throughout life. Recent experimental findings show that the seeding of the thymus by multi-potent stem cells from the bone marrow is periodic rather than continuous, as previously assumed. However it is well known that the output rate of cells from the thymus is relatively constant. A quantitative model is used to verify the current hypotheses regarding T cell development in the steady state mouse thymus. The results show that the thymus could be at a periodic steady state with out-of-phase thymocyte populations. Experiments to examine possible periodic fluctuations in the thymus are proposed and methods for further analysis are outlined.