相关论文: A dynamic p53-mdm2 model with delay kernel

We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…

From the response to external stimuli to cell division and death, the dynamics of living cells is based on the expression of specific genes at specific times. The decision when to express a gene is implemented by the binding and unbinding…

We revisit the dynamics of a gene repressed by its own protein in the case where the transcription rate does not adapt instantaneously to protein concentration but is a dynamical variable. We derive analytical criteria for the appearance of…

The traditional Wilson-Cowan model of excitatory and inhibitory mean field interactions in neuronal populations considers a weak Gamma distribution of time delays when processing inputs, and is obtained via a time-coarse graining technique…

Much of the complexity observed in gene regulation originates from cooperative protein-DNA binding. While studies of the target search of proteins for their specific binding sites on the DNA have revealed design principles for the…

Transcription is regulated through interplay between transcription factors, an RNA polymerase(RNAP), and a promoter. Even for a simple repressive transcription factor that disturbs promoter activity at the initial binding of RNAP, its…

We consider the model of interaction between the immune system and tumor cells including a memory function that reflect the influence of the past states, to simulate the time needed by the latter to develop a chemical and cell mediated…

The finite duration of collisions appear as time-nonlocality in the kinetic equation. Analyzing the corresponding quantum kinetic equation for dense interacting Fermi systems a delay differential equation is obtained which combines time…

Eukaryotic transcription generally occurs in bursts of activity lasting minutes to hours; however, state-of-the-art measurements have revealed that many of the molecular processes that underlie bursting, such as transcription factor binding…

A general theoretical framework is put forth to organize and understand various observed phenomena and mathematical relationships in the field of molecular biology. By modeling each cell in eukaryotic organisms as a processor having a…

Gene regulation is a complex process involving the role of several genomic elements which work in concert to drive spatio-temporal expression. The experimental characterization of gene regulatory elements is a very complex and…

We present three examples of delayed bifurcations for spike solutions of reaction-diffusion systems. The delay effect results as the system passes slowly from a stable to an unstable regime, and was previously analysed in the context of…

Objective: The reservoir of human immunodeficiency virus (HIV) latently infected cells is the major obstacle for eradication of acquired immunodeficiency syndrome (AIDS). Due to the noisy environment and multiple influencing factors in the…

Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation in reaction-diffusion systems. In particular, past work has shown that such time delays can…

A four-node network consisting of a negative loop controlling a positive one is studied. It models some of the features of the p53 gene network. Using piecewise linear dynamics with thresholds, the allowed dynamical classes are fully…

Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…

This study analyses the dynamical consequences of heterogeneous temporal delays within a quorum sensing-inspired (QS-inspired) system, specifically addressing the differential response kinetics of two sub-populations to signalling…

We model intracellular regulatory dynamics with threshold-type state-dependent delay and investigate the effect of the state-dependent diffusion time. A general model which is an extension of the classic differential equation models with…

In this paper, we consider a continuous-time model with discrete and dis-tributed delays to describe how two pieces of information interact in online social networks. Sufficient conditions are carried out to illustrate the stability of each…

In this article a generalized mathematical model describing the interactions between malignant tumour and immune system with discrete time delay incorporated into the system is considered. Time delay represents the time required to generate…