RESUMO
In this paper, a finite volume discretization scheme for partial integro-differential equations (PIDEs) describing the temporal evolution of protein distribution in gene regulatory networks is proposed. It is shown that the obtained set of ODEs can be formally represented as a compartmental kinetic system with a strongly connected reaction graph. This allows the application of the theory of nonnegative and compartmental systems for the qualitative analysis of the approximating dynamics. In this framework, it is straightforward to show the existence, uniqueness and stability of equilibria. Moreover, the computation of the stationary probability distribution can be traced back to the solution of linear equations. The discretization scheme is presented for one and multiple dimensional models separately. Illustrative computational examples show the precision of the approach, and good agreement with previous results in the literature.
Assuntos
Redes Reguladoras de Genes , Conceitos Matemáticos , Modelos Biológicos , Cinética , ProbabilidadeRESUMO
Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called CausalKinetiX, that identifies structure from discrete time, noisy observations, generated from heterogeneous experiments. The algorithm assumes the existence of an underlying, invariant kinetic model, a key criterion for reproducible research. Results on both simulated and real-world examples suggest that learning the structure of kinetic systems benefits from a causal perspective. The identified variables and models allow for a concise description of the dynamics across multiple experimental settings and can be used for prediction in unseen experiments. We observe significant improvements compared to well-established approaches focusing solely on predictive performance, especially for out-of-sample generalization.