Algebraic structure of hierarchic first-order reaction networks applicable to models of clone size distribution and stochastic gene expression
In biology, stochastic branching processes with a two-stage, hierarchical structure arise in the study of population dynamics, gene expression, and phylogenetic inference. These models have been commonly analyzed using generating functions, the method of characteristics and various perturbative approximations. Here we describe a general method for analyzing hierarchic first-order reaction networks using Lie theory. Crucially, we identify the fact that the Lie group associated to hierarchic reaction networks decomposes as a wreath product of the groups associated to the subnetworks of the independent and dependent types. After explaining the general method, we illustrate it on a model of population dynamics and the so-called two-state or telegraph model of single-gene transcription. Solutions to such processes provide essential input to downstream methods designed to attempt to infer parameters of these and related models.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Semigroup models for biochemical reaction networks
The catalytic reaction system (CRS) formalism by Hordijk and Steel is a versatile method to model autocatalytic biochemical reaction networks. It is particularly suited, and has been widely used, to study self-sustainmen…
Information geometry of chemical reaction networks: Cramer-Rao bound and absolute sensitivity revisited
Information geometry is based on classical Legendre duality but allows to incorporate additional structure such as algebraic constraints and Bregman divergence functions. It is naturally suited, and has been successfully…
SensitivityAn Inductive Formalization of Self Reproduction in Dynamical Hierarchies
Formalizing self reproduction in dynamical hierarchies is one of the important problems in Artificial Life (AL) studies. We study, in this paper, an inductively defined algebraic framework for self reproduction on macros…
Artificial LifeSensitivity of metabolic networks: perturbing metabolite concentrations
Sensitivity studies the network response to perturbations. We consider local perturbations of the concentrations of metabolites at an equilibrium. We investigate the responses in the network, both of the metabolite conce…
SensitivityAn algebraic characterization of self-generating chemical reaction networks using semigroup models
The ability of a chemical reaction network to generate itself by catalyzed reactions from constantly present environmental food sources is considered a fundamental property in origin-of-life research. Based on Kaufmann's…