Network-level dynamics of diffusively coupled cells

We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular perturbation, which extend the classical asymptotic stability results for singularly perturbed systems. Based on these results, we show that with common models of intracellular dynamics, the cell population is coordinated in the sense that all cells converge close to a common equilibrium point. We then study a more specific example of coupled cells which behave as bistable switches, where the intracellular dynamics are such that cells may be in one of two equilibrium points. Here, we find that the whole population is bistable in the sense that it converges to a population state where either all cells are close to the one equilibrium point, or all cells are close to the other equilibrium point. Finally, we discuss applications of these results for the robustness of cellular decision making in coupled populations

Cooperative H-infinity Estimation for Large-Scale Interconnected Linear Systems

In this paper, a synthesis method for distributed estimation is presented, which is suitable for dealing with large-scale interconnected linear systems with disturbance. The main feature of the proposed method is that local estimators only estimate a reduced set of state variables and their complexity does not increase with the size of the system. Nevertheless, the local estimators are able to deal with lack of local detectability. Moreover, the estimators guarantee H-infinity-performance of the estimates with respect to model and measurement disturbances.Comment: Short version published in Proc. American Control Conference (ACC), pp.2119-2124. Chicago, IL, 201

Estimation of biochemical network parameter distributions in cell populations

Populations of heterogeneous cells play an important role in many biological systems. In this paper we consider systems where each cell can be modelled by an ordinary differential equation. To account for heterogeneity, parameter values are different among individual cells, subject to a distribution function which is part of the model specification. Experimental data for heterogeneous cell populations can be obtained from flow cytometric fluorescence microscopy. We present a heuristic approach to use such data for estimation of the parameter distribution in the population. The approach is based on generating simulation data for samples in parameter space. By convex optimisation, a suitable probability density function for these samples is computed. To evaluate the proposed approach, we consider artificial data from a simple model of the tumor necrosis factor (TNF) signalling pathway. Its main characteristic is a bimodality in the TNF response: a certain percentage of cells undergoes apoptosis upon stimulation, while the remaining part stays alive. We show how our modelling approach allows to identify the reasons that underly the differential response.Comment: 14 pages, 5 figure