The interplay of intrinsic and extrinsic bounded noises in genetic networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: $(i)$ the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, $(ii)$ a model of enzymatic futile cycle and $(iii)$ a genetic toggle switch. In $(ii)$ and $(iii)$ we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possibile functional role of bounded noises

PMAC:Probabilistic Multimodality Adaptive Control

This paper develops a probabilistic multimodal adaptive control approach for systems that are characterised by temporal multimodality where the system dynamics are subject to abrupt mode switching at arbitrary times. In this framework, the control objective is redefined such that it utilises the complete probability distribution of the system dynamics. The derived probabilistic control law is thus of a dual type that incorporates the functional uncertainty of the controlled system. A multi-modal density model with prediction error-dependent mixing coefficients is introduced to effect the mode switching. This approach can deal with arbitrary noise distributions, nonlinear plant dynamics and arbitrary mode switching. For the affine systems focussed upon for illustration in this paper the approach has global stability. The theoretical architecture constructs are verified by validation on a simulation example

A stochastic and dynamical view of pluripotency in mouse embryonic stem cells

Pluripotent embryonic stem cells are of paramount importance for biomedical research thanks to their innate ability for self-renewal and differentiation into all major cell lines. The fateful decision to exit or remain in the pluripotent state is regulated by complex genetic regulatory network. Latest advances in transcriptomics have made it possible to infer basic topologies of pluripotency governing networks. The inferred network topologies, however, only encode boolean information while remaining silent about the roles of dynamics and molecular noise in gene expression. These features are widely considered essential for functional decision making. Herein we developed a framework for extending the boolean level networks into models accounting for individual genetic switches and promoter architecture which allows mechanistic interrogation of the roles of molecular noise, external signaling, and network topology. We demonstrate the pluripotent state of the network to be a broad attractor which is robust to variations of gene expression. Dynamics of exiting the pluripotent state, on the other hand, is significantly influenced by the molecular noise originating from genetic switching events which makes cells more responsive to extracellular signals. Lastly we show that steady state probability landscape can be significantly remodeled by global gene switching rates alone which can be taken as a proxy for how global epigenetic modifications exert control over stability of pluripotent states.Comment: 11 pages, 7 figure