RESUMEN
Parameter estimation in discrete or continuous deterministic cell cycle models is challenging for several reasons, including the nature of what can be observed, and the accuracy and quantity of those observations. The challenge is even greater for stochastic models, where the number of simulations and amount of empirical data must be even larger to obtain statistically valid parameter estimates. The two main contributions of this work are (1) stochastic model parameter estimation based on directly matching multivariate probability distributions, and (2) a new quasi-Newton algorithm class QNSTOP for stochastic optimization problems. QNSTOP directly uses the random objective function value samples rather than creating ensemble statistics. QNSTOP is used here to directly match empirical and simulated joint probability distributions rather than matching summary statistics. Results are given for a current state-of-the-art stochastic cell cycle model of budding yeast, whose predictions match well some summary statistics and one-dimensional distributions from empirical data, but do not match well the empirical joint distributions. The nature of the mismatch provides insight into the weakness in the stochastic model.
Asunto(s)
Ciclo Celular/fisiología , Saccharomycetales , Biología de Sistemas/métodos , Algoritmos , Simulación por Computador , Modelos Biológicos , Saccharomycetales/citología , Saccharomycetales/genética , Saccharomycetales/fisiología , Procesos EstocásticosRESUMEN
BACKGROUND: Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. RESULTS: In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. CONCLUSION: Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.