Bayesian parameter estimation for the Wnt pathway: an infinite mixture models approach.

MOTIVATION: Likelihood-free methods, like Approximate Bayesian Computation (ABC), have been extensively used in model-based statistical inference with intractable likelihood functions. When combined with Sequential Monte Carlo (SMC) algorithms they constitute a powerful approach for parameter estimation and model selection of mathematical models of complex biological systems. A crucial step in the ABC-SMC algorithms, significantly affecting their performance, is the propagation of a set of parameter vectors through a sequence of intermediate distributions using Markov kernels. RESULTS: In this article, we employ Dirichlet process mixtures (DPMs) to design optimal transition kernels and we present an ABC-SMC algorithm with DPM kernels. We illustrate the use of the proposed methodology using real data for the canonical Wnt signaling pathway. A multi-compartment model of the pathway is developed and it is compared to an existing model. The results indicate that DPMs are more efficient in the exploration of the parameter space and can significantly improve ABC-SMC performance. In comparison to alternative sampling schemes that are commonly used, the proposed approach can bring potential benefits in the estimation of complex multimodal distributions. The method is used to estimate the parameters and the initial state of two models of the Wnt pathway and it is shown that the multi-compartment model fits better the experimental data. AVAILABILITY AND IMPLEMENTATION: Python scripts for the Dirichlet Process Gaussian Mixture model and the Gibbs sampler are available at https://sites.google.com/site/kkoutroumpas/software CONTACT: konstantinos.koutroumpas@ecp.fr.

Taming the complexity of biological pathways through parallel computing.

Biological systems are characterised by a large number of interacting entities whose dynamics is described by a number of reaction equations. Mathematical methods for modelling biological systems are mostly based on a centralised solution approach: the modelled system is described as a whole and the solution technique, normally the integration of a system of ordinary differential equations (ODEs) or the simulation of a stochastic model, is commonly computed in a centralised fashion. In recent times, research efforts moved towards the definition of parallel/distributed algorithms as a means to tackle the complexity of biological models analysis. In this article, we present a survey on the progresses of such parallelisation efforts describing the most promising results so far obtained.

The Relevance of Topology in Parallel Simulation of Biological Networks.

Important achievements in traditional biology has deepened the knowledge about living systems leading to an extensive identification of parts-list of the cell as well as of the interactions among biochemical species responsible for cell's regulation. Such an expanding knowledge also introduces new issues. For example the increasing comprehension of the inter- dependencies between pathways (pathways cross-talk) has resulted, on one hand, in the growth of informational complexity, on the other, in a strong lack of information coherence. The overall grand challenge remains unchanged: to be able to assemble the knowledge of every 'piece' of a system in order to figure out the behavior of the whole (integrative approach). In light of these considerations high performance computing plays a fundamental role in the context of in-silico biology. Stochastic simulation is a renowned analysis tool, which, although widely used, is subject to stringent computational requirements, in particular when dealing with heterogeneous and high dimensional systems. Here we introduce and discuss a methodology aimed at alleviating the burden of simulating complex biological networks. Such a method, which springs from graph theory, is based on the principle of fragmenting the computational space of a simulation trace and delegating the computation of fragments to a number of parallel processes.