Stochastic gene expression as a many body problem

Abstract

Gene expression has a stochastic component owing to the single molecule nature of the gene and the small number of copies of individual DNA binding proteins in the cell. We show how the statistics of such systems can be mapped on to quantum many body problems. The dynamics of a single gene switch resembles the spin boson model of a two site polaron or an electron transfer reaction. Networks of switches can be approximately described as quantum spin systems by using an appropriate variational principle. In this way the concept of frustration for magnetic systems can be taken over into gene networks. The landscape of stable attractors depends on the degree and style of frustration, much as for neural networks. We show the number of attractors, which may represent cell types, is much smaller for appropriately designed, weakly frustrated stochastic networks than for randomly connected networks.

to appear in Proc. Natl. Acad. Sci. USA

Cited by in corpus (66)

• The Yeast Cell-Cycle Network Is Robustly Designed
• Nonequilibrium Physics in Biology
• Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. II: construction of SDS with nonlinear force and multiplicative noise
• Structure of Stochastic Dynamics near Fixed Points
• Stochastic fluctuations in metabolic pathways
• Absolute Rate Theories of Epigenetic Stability
• Master equations and the theory of stochastic path integrals
• Calculating Biological Behaviors of Epigenetic States in Phage lambda Life Cycle
• Self consistent proteomic field theory of stochastic gene switches
• Inferring gene regulatory networks from single-cell data: a mechanistic approach
• Graded and Binary Responses in Stochastic Gene Expression
• A stochastic spectral analysis of transcriptional regulatory cascades
• Stochastic Simulations of the Repressilator Circuit
• Single-cell stochastic gene expression kinetics with coupled positive-plus-negative feedback
• Probing Quantum Frustrated Systems via Factorization of the Ground State
• Brownian motion: a paradigm of soft matter and biological physics
• A framework towards understanding mesoscopic phenomena: Emergent unpredictability, symmetry breaking and dynamics across scales
• A stochastic and dynamical view of pluripotency in mouse embryonic stem cells
• Reducing Frustration in Spin Systems: Social Balance as an XOR-SAT problem
• Emergence of cooperative bistability and robustness of gene regulatory networks
• A variational approach to the stochastic aspects of cellular signal transduction
• Rare-Event Sampling of Epigenetic Landscapes and Phenotype Transitions
• Non-equilibrium dynamics of gene expression and the Jarzynski equality
• The stochastic pump current and the non-adiabatic geometrical phase
• The interplay between discrete noise and nonlinear chemical kinetics in a signal amplification cascade
• The effect of phenotypic selection on stochastic gene expression
• Stable stochastic dynamics in yeast cell cycle
• Dichotomous noise models of gene switches
• Regulation by small RNAs via coupled degradation: mean-field and variational approaches
• Effects of the DNA state fluctuation on single-cell dynamics of self-regulating gene
• Funneled Potential and Flux Landscapes Dictate the Stabilities of both the States and the Flow: Fission Yeast Cell Cycle
• Stochastic epigenetic dynamics of gene switching
• Statistical physics approaches to subnetwork dynamics in biochemical systems
• Evolution models with base substitutions, insertions, deletions and selection
• Testing the transition state theory in stochastic dynamics of a genetic switch
• A stochastic model for gene transcription on Drosophila melanogaster embryos
• EPR-Net: Constructing non-equilibrium potential landscape via a variational force projection formulation
• Construction of stochastic hybrid path integrals using "quantum-mechanical'' operators
• Approximation scheme for master equations: variational approach to multivariate case
• Non-equilibrium phase transitions in biomolecular signal transduction
• Ergodic and Nonergodic Anomalous Diffusion in Coupled Stochastic Processes
• A Model of Gene Expression Based on Random Dynamical Systems Reveals Modularity Properties of Gene Regulatory Networks
• Gene-gene cooperativity in small networks
• Molecular Systems with Infinite and Finite Degrees of Freedom. Part II: Deterministic Dynamics and Examples
• Field theories and quantum methods for stochastic reaction-diffusion systems
• Approximation scheme based on effective interactions for stochastic gene regulation
• Spin coherent states and stochastic hybrid path integrals
• Molecular Systems with Infinite and Finite Degrees of Freedom. Part I: Multi-Scale Analysis
• Landscape and flux for quantifying global stability and dynamics of game theory
• Coagulation kinetics beyond mean field theory using an optimised Poisson representation
• A field theoretic approach to master equations and a variational method beyond the Poisson ansatz
• Cell biology: Networks, regulation, pathways
• Duality-based calculations for transition probabilities in stochastic chemical reactions
• Chemical master equation parameter exploration using DMRG
• Redundant basis interpretation of Doi-Peliti method and an application
• Coarse-graining stochastic biochemical networks: quasi-stationary approximation and fast simulations using a stochastic path integral technique
• Intermediate time scale in the first product formation time distribution of Michaelis-Menten kinetics with inhibitors
• Path integrals for stochastic hybrid reaction-diffusion processes
• On the bursting of gene products
• Exploring the underlying mechanisms of Xenopus laevis embryonic cell cycle
• Reconstructing an epigenetic landscape using a genetic `pulling' approach
• A Model for the Dynamics of Gene Networks
• The stochastic behavior of a molecular switching circuit with feedback
• Topology of the simplest gene switch
• Counting statistics for genetic switches based on effective interaction approximation
• Noise reduction by coupling of stochastic processes and canalization in biology