Stochastic modelling for quantitative description of heterogeneous biological systems

Abstract

Two related developments are currently changing traditional approaches to computational systems biology modelling. First, stochastic models are being used increasingly in preference to deterministic models to describe biochemical network dynamics at the single-cell level. Second, sophisticated statistical methods and algorithms are being used to fit both deterministic and stochastic models to time course and other experimental data. Both frameworks are needed to adequately describe observed noise, variability and heterogeneity of biological systems over a range of scales of biological organization.

Mathematical modeling of GATA-switching for regulating the differentiation of hematopoietic stem cell

“…Recently a minimal model has been designed by combining cell-extrinsic and cell-intrinsic elements of regulation to understand how both instructive and stochastic events could inform cell commitment decision in hematopoiesis [34]. However, compared with the advances in developing various stochastic models to investigate the key functions of noise in genetic and cellular processes [35-37], the critical role of noise in determining the stem cell differentiation has not been well established. This work is aimed at developing the first stochastic model to explore the critical function of GATA switch and noise in determining the differentiation pathways of HSCs.…”

Quantum probes for fractional Gaussian processes

“…a real function of the measurements outcomes {x k } to the parameters space. Classically, the variance Var(γ) of any unbiased estimator satisfies the Cramer-Rao bound Var(γ) ≥ 1/MF(γ), which establishes a lower bound on variance in terms of the number of independent measurements M and the Fisher Information 2 , p(x|γ) being the conditional probability of obtaining the value x when the parameter has the value γ. When quantum systems are involved, we have p(x|γ) = Tr γ P x , {P x } being the probability operator-valued measure (POVM) describing the measurement.…”

“…situations where the goal is to estimate the unknown values of the parameter γ ∈ [1,2], and cases where we know in advance that only two possible values γ 1 and γ 2 are admissible and want to discriminate between them [12].…”

“…Stochastic modelling is often the most effective tool available in order to describe complex systems in physical, biological and social networks [1,2,3,4]. In particular, since natural noise sources are mostly Gaussian, stationary and nonstationary Gaussian processes are often used to model the response of a system exposed to environmental noise.…”

Modeling Three-Dimensional Spatial Regulation of Bacterial Cell Division (Dissertation)

“…Intracellular spatial features that can influence polymer assembly and function include the 3D position of subunits and polymer nucleation sites (Lutkenhaus, 2007), volume exclusion by polymer filaments (Haviv et al, 2006), molecular crowding (Popp et al, 2007;Wieczorek and Zielenkiewicz, 2008), intercompartmental interaction and subcellular localization of reacting molecules (Lutkenhaus, 2007), and diffusion-influenced reactions of molecules that are either small numbered or heterogeneously distributed (Shih et al, 2002;Lutkenhaus, 2007). Diffusion and small numbers of reacting molecules may also induce stochasticity (Rao et al, 2002;Bhalla, 2004;Wilkinson, 2009) in polymer assembly (VanBuren et al, 2002).…”