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

Specific activator and repressor transcription factors which bind to specific regulator DNA sequences, play an important role in gene activity control. Interactions between genes coding such transcription factors should explain the…

The objective of this paper is to investigate the stability of limit cycles of a mathematical model with a distributed delay which describes the interaction between p53 and mdm2. Choosing the delay as a bifurcation parameter we study the…

In this paper we analyze a simple mathematical model which describes the interaction between the proteins p53 and Mdm2. For the stationary state we discuss the local stability and the existence of the Hopf bifurcation. Choosing the delay as…

A feedback mechanism that involves the proteins p53 and mdm2, induces cell death as a controled response to severe DNA damage. A minimal model for this mechanism demonstrates that the respone may be dynamic and connected with the time…

The aim of this paper is to study the steady states of the mathematical models with delay kernels which describe pathogen-immune dynamics of many kinds of infectious diseases. In the study of mathematical models of infectious diseases it is…

Recent studies suggest that PML (Promyelocytic Leukemia) suppresses p53 protein degradation by inhibiting MDM2 protein in the nucleus [1], and regulates a number of biological functions [2]. We modeled a PML-MDM2-p53 regulatory network by…

Systemic properties of living cells are the result of molecular dynamics governed by so-called genetic regulatory networks (GRN). These networks capture all possible features of cells and are responsible for the immense levels of adaptation…

About half of human cancers show normal TP53 gene and aberrant overexpression of Mdm2 and/or MdmX. This fact promotes a promising cancer therapeutic strategy which targeting the interactions between p53 and Mdm2/MdmX. For developing the…

Building upon our previous work on the Wilson-Cowan equations with distributed delays, we study the dynamic behavior in a system of two coupled Wilson-Cowan pairs. We focus in particular on understanding the mechanisms that govern the…

Genes with similar transcriptional activation kinetics can display very different temporal mRNA profiles due to differences in transcription time, degradation rate and RNA processing kinetics. Recent studies have shown that a…

Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…

Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…

Dynamics of p53 is known to play important roles in the regulation of cell fate decisions in response to various stresses, and PDCD5 functions as a co-activator of p53 to modulate the p53 dynamics. In the present paper, we investigate how…

We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables…

Genes are connected in complex networks of interactions where often the product of one gene is a transcription factor that alters the expression of another. Many of these networks are based on a few fundamental motifs leading to switches…

We investigate state dependent delay differential equations with distributed memory, combining discrete state dependent delays and a convolution type memory operator. Under Lipschitz type assumptions on the delay, kernel, and nonlinear…

The p53 protein is well-known for its tumour suppressor function. The p53-MDM2 negative feedback loop constitutes the core module of a network of regulatory interactions activated under cellular stress. In normal cells, the level of p53…

The transcription factor p53 is an important regulator of cell fate. Mutations in p53 gene are associated with many cancers. In response to signals such as DNA damage, p53 controls the transcription of a series of genes that cause cell…

We propose two dynamical models with delay taking advantage of their complex dynamics for information processing tasks. The first model incorporates coupled delayed dynamics of multiple bits, which is shown to have desirable properties as…

Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper we analyse…