Negative feedback and oscillations in a model for mRNA translation
The ribosome flow model (RFM) is a phenomenological model for the unidirectional flow of particles along a 1D chain of $n$ sites. The RFM has been extensively used to study the dynamics of ribosome flow along a single mRNA molecule during translation. In this case, the particles model ribosomes and each site corresponds to a consecutive group of codons. Networks of interconnected RFMs have been used to model and analyze large-scale translation in the cell and, in particular, the effects of competition for shared resources. Here, we analyze the RFM with a negative feedback connection from the protein production rate to the initiation rate. This models, for example, the production of proteins that inhibit the translation of their own mRNA. Using tools from the theory of 2-cooperative dynamical systems, we provide a simple condition guaranteeing that the closed-loop system admits at least one non-trivial periodic solution. When this condition holds, we also explicitly characterize a large set of initial conditions such that any solution emanating from this set converges to a non-trivial periodic solution. Such a solution corresponds to a periodic pattern of ribosome densities along the mRNA, and to a periodic pattern of protein production.
Code (0)
등록된 구현이 없습니다.
Tasks
TranslationMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Tunability of the Dual Feedback Genetic Oscillator Modeled by the Asymmetry in Transcription and Translation
Oscillatory gene circuits are ubiquitous to biology and are involved in fundamental processes of cell cycle, circadian rhythms and developmental systems. The synthesis of small, non-natural oscillatory genetic circuits h…
TranslationEffect of transcription reinitiation in stochastic gene expression
Gene expression (GE) is an inherently random or stochastic or noisy process. The randomness in different steps of GE, e.g., transcription, translation, degradation, etc., leading to cell-to-cell variations in mRNA and pr…
Degradation rate uniformity determines success of oscillations in repressive feedback regulatory networks
Ring oscillators are biochemical circuits consisting of a ring of interactions capable of sustained oscillations. The non-linear interactions between genes hinder the analytical insight into their function, usually requi…
Exact power spectrum in a minimal hybrid model of stochastic gene expression oscillations
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…
Gene length as a regulator for ribosome recruitment and protein synthesis: theoretical insights
Protein synthesis rates are determined, at the translational level, by properties of the transcript's sequence. The efficiency of an mRNA can be tuned by varying the ribosome binding sites controlling the recruitment of …
Translation