We are interested in studying the evolution of large homogeneous populations of cells, where each cell is assumed to be composed of a group of biological players (species) whose dynamics is governed by a complex biological pathway, identical for all cells. Modeling the inherent variability of the species concentrations in different cells is crucial to understand the dynamics of the population. In this work, we focus on handling this variability by modeling each species by a random variable that evolves over time. This appealing approach runs into the curse of dimensionality since exactly representing a joint probability distribution involving a large set of random variables quickly becomes intractable as the number of variables grows. To make this approach amenable to biopathways, we explore different techniques to (i) approximate the exact joint distribution at a given time point, and (ii) to track its evolution as time elapses. We start with the problem of approximating the probability distribution of biological species in a population of cells at some given time point. Data come from different fine-grained models of biological pathways of increasing complexities, such as (perturbed) Ordinary Differential Equations (ODEs). Classical approximations rely on the strong and unrealistic assumption that variables/species are independent, or that they can be grouped into small independent clusters. We propose instead to use the Chow-Liu tree representation, based on overlapping clusters of two variables, which better captures correlations between variables. Our experiments show that the proposed approximation scheme is more accurate than existing ones to model probability distributions deriving from biopathways. Then we address the problem of tracking the dynamics of a population of cells, that is computing from an initial distribution the evolution of the (approximate) joint distribution of species over time, called the inference problem. We evaluate several approximate inference algorithms (e.g., [14] , [17] ) for coarse-grained abstractions [12], [16] of biological pathways. Using the Chow-Liu tree approximation, we develop a new inference algorithm which is very accurate according to the experiments we report, for a minimal computation overhead. Our implementation is available at https://codeocean.com/capsule/6491669/tree.

MOTIVATION: Quantitative models are increasingly used in systems biology. Usually, these quantitative models involve many molecular species and their associated reactions. When simulating a tissue with thousands of cells, using these large models becomes computationally and time limiting. RESULTS: In this paper, we propose to construct abstractions using information theory notions. Entropy is used to discretize the state space and mutual information is used to select a subset of all original variables and their mutual dependencies. We apply our method to an hybrid model of TRAIL-induced apoptosis in HeLa cell. Our abstraction, represented as a Dynamic Bayesian Network (DBN), reduces the number of variables from 92 to 10, and accelerates numerical simulation by an order of magnitude, yet preserving essential features of cell death time distributions. AVAILABILITY AND IMPLEMENTATION: This approach is implemented in the tool DBNizer, freely available at http://perso.crans.org/genest/DBNizer . CONTACT: [email protected] or [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.