Related papers: Mathematical Models of Gene Expression
Stochastic Process Model has many applications in analysis of longitudinal biodemographic data. Such data contain various physiological variables (sometimes known as covariates). It also can potentially contain genetic information available…
In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…
In this paper physical multi-scale processes governed by their own principles for evolution or equilibrium on each scale are coupled by matching the stored and dissipated energy, in line with the Hill-Mandel principle. In our view the…
Multiple phenotypic states often arise in a single cell with different gene-expression states that undergo transcription regulation with positive feedback. Recent experiments have shown that at least in E. coli, the gene state switching can…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
A probabilistic discrete model for 2D protein crystal growth is presented. This model takes into account the available space and can describe growing processes of different nature due to the versatility of its parameters which gives the…
We consider a stochastic model of gene expression in which transcription depends on a multistate promoter, including the famous two-state model and refractory promoters as special cases, and focus on deriving the exact stationary…
Translation is a crucial step in gene expression. During translation, macromolecules called ribosomes "read" the mRNA strand in a sequential manner and produce a corresponding protein. Translation is known to consume most of the cell's…
The time evolution of complex systems usually can be described through stochastic processes. These processes are measured at finite resolution, what necessarily reduces them to finite sequences of real numbers. In order to relate these data…
This work demonstrates how a complete statistical model quantifying the evolution of pairs of aligned proteins can be constructed from a time-parameterised substitution matrix and a time-parameterised 3-state alignment machine. All…
We argue that the stochastic dynamics of interacting agents which replicate, mutate and die constitutes a non-equilibrium physical process akin to aging in complex materials. Specifically, our study uses extensive computer simulations of…
Growth-fragmentation processes describe the evolution of systems of cells which grow continuously and fragment suddenly; they are used in models of cell division and protein polymerisation. Typically, we may expect that in the long run, the…
Markovian population models are suitable abstractions to describe well-mixed interacting particle systems in situation where stochastic fluctuations are significant due to the involvement of low copy particles. In molecular biology,…
Stochastic oscillations in individual cells are usually characterized by a non-monotonic power spectrum with an oscillatory autocorrelation function. Here we develop an analytical approach of stochastic oscillations in a minimal hybrid…
Simplified stochastic models are widely used in the study of frequency-resolved noise propagation in biochemical reaction networks, a common measure being the coherence between random fluctuations in molecule number trajectories. Such…
Gene regulation is an important fundamental biological process. The regulation of gene expression is managed through a variety of methods including epigenetic processes (e.g., DNA methylation). Understanding the role of epigenetic changes…
A modeling framework for the internal conformational dynamics and external mechanical movement of single biological macromolecules in aqueous solution at constant temperature is developed. Both the internal dynamics and external movement…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have…
Gene expression is a stochastic process governed by the presence of specific transcription factors. Here we study the dynamics of gene expression in the presence of feedback, where a gene regulates its own expression. The nonlinear coupling…