Palestrante
Descrição
A chemical reaction network (CRN) is a framework for mathematical modeling of the dynamical behavior of reaction systems with a wide range of applications. (1) The theory aims at modeling concentration of species subject to a set of reactions altering the state space, concerning with the dynamics resulting from the network topology. For many systems, especially in a biochemical context, low count numbers of species result on higher importance of stochasticity, with deterministic models failing to describe the system. Stochastic analysis of CRNs is performed with continuous time Markov process models, giving a forward Kolmogorov equation, or a chemical master equation (CME), for the time evolution of densities. In a nonlinear context, CMEs can always be simulated by stochastic simulation algorithms but usually are analytically intractable. To understand structural behavior and systems' motifs, we can then make approximations. The linear noise approximation is a first order systematic expansion on the system’s size that gives a Gaussian, linearized, evolution of systems' densities and is similar to Langevin approximations of the CME. (2) This framework gives a complete and tractable model for the system, where we can obtain approximate dynamical behavior, moments and steady-states, but lacks a rigorous connection to measurements (often incomplete and obscured by undetermined noise). We can address this by using a measurement model and applying inference and filtering theory to extract estimates for parameters and hidden states from observation, using densities conditioned on measurements. (3) Our work is especially concerned with methodology development and application of this framework of analysis and inference to oscillating networks, in particular to the context of genetic and circadian systems. Usually, approximation and inference methods need to be adapted or extended to grant more accuracy or robustness of analysis for specific behaviors and network structures. As a practical example and application system, we consider the stochastic form of the Goodwin oscillator, a model for biochemical oscillations that can be considered as the simplest topology of feedback loop capable of undergoing sustained oscillations via limit cycles (past a Hopf bifurcation point).
Referências
1 SCHNOERR, D.; SANGUINETTI, G.; GRIMA, R. Approximation and inference methods for stochastic biochemical kinetics: a tutorial review. Journal of Physics A, v. 50, n. 9, p. 093001-1-093001-60, 2017.
2 van KAMPEN, N. G. Stochastic processes in physics and chemistry. Amsterdam: Elsevier. 1992. v. 1.
3 SÄRKKÄ, S. Bayesian filtering and smoothing. Cambridge: Cambridge University Press, 2013. (Institute of Mathematical Statistics Textbooks, 3).
| Subárea | Sistemas Complexos |
|---|---|
| Apresentação do trabalho acadêmico para o público geral | Não |
