Dynamic Models of Hormesis and Ageing in Gene Expression Networks

BMC Research Notes, 2009

Most transcriptional activity is a result of environmental variability. This cause (environment) and effect (gene expression) relationship is essential to survival in any changing environment. The specific relationship between environmental perturbation and gene expression -and stability of the response -has yet to be measured in detail. We describe a method to quantitatively relate perturbation magnitude to response at the level of gene expression. We test our method using Saccharomyces cerevisiae as a model organism and osmotic stress as an environmental stress.

The Journal of Chemical Physics, 2018

The transient response to a stimulus and subsequent recovery to a steady state are the fundamental characteristics of a living organism. Here we study the relaxation kinetics of autoregulatory gene networks based on the chemical master equation model of single-cell stochastic gene expression with nonlinear feedback regulation. We report a novel relation between the rate of relaxation, characterized by the spectral gap of the Markov model, and the feedback sign of the underlying gene circuit. When a network has no feedback, the relaxation rate is exactly the decaying rate of the protein. We further show that positive feedback always slows down the relaxation kinetics while negative feedback always speeds it up. Numerical simulations demonstrate that this relation provides a possible method to infer the feedback topology of autoregulatory gene networks by using time-series data of gene expression.

2005

Gene expression is the process by which a gene makes its effect on a cell or organism. Linear differential equations have been explored as a model for gene expression. We discuss the shortcomings of this model, and we propose a system of nonlinear differential equations to mathematically model gene expression in prokaryotes, specifically bacteria. We investigate this biological system using explicit functions that describe the processes of protein synthesis which includes transcription, translation, degradation, and feedback in hope of shedding light on their associated rates. We analyze the transient and steady state solutions of the model and give a biological interpretation of these results.

Scientific Reports, 2015

Several animal species are considered to exhibit what is called negligible senescence, i.e. they do not show signs of functional decline or any increase of mortality with age, and do not have measurable reductions in reproductive capacity with age. Recent studies in Naked Mole Rat (NMR) and longlived sea urchin showed that the level of gene expression changes with age is lower than in other organisms. These phenotypic observations correlate well with exceptional endurance of NMR tissues to various genotoxic stresses. Therefore, the lifelong transcriptional stability of an organism may be a key determinant of longevity. However, the exact relation between genetic network stability, stress-resistance and aging has not been defined. We analyze the stability of a simple geneticnetwork model of a living organism under the influence of external and endogenous factors. We demonstrate that under most common circumstances a gene network is inherently unstable and suffers from exponential accumulation of gene-regulation deviations leading to death. However, should the repair systems be sufficiently effective, the gene network can stabilize so that gene damage remains constrained along with mortality of the organism, which may then enjoy a remarkable degree of stability over very long times. We clarify the relation between stress-resistance and aging and suggest that stabilization of the genetic network may provide a mathematical explanation of the Gompertz equation describing the relationship between age and mortality in many species, and of the apparently negligible senescence observed in exceptionally long-lived animals. The model may support a range of applications, such as systematic searches for therapeutics to extend lifespan and healthspan.

2009

of a thesis submitted in partial fulfilment of the requirements for the Degree of Doctor of Philosophy Abstract Living cells are made up of networks of interacting genes, proteins and other bio-molecules. Simple interactions between network components in forms of feedback regulations can lead to complex collective dynamics. A key task in cell biology is to gain a thorough understanding of the dynamics of intracellular systems and processes. In this thesis, a combined approach of mathematical modelling, computational simulation and analytical techniques, has been used to obtain a deeper insight into the dynamical aspects of a variety of feedback systems commonly encountered in cells. These systems range from model system with detailed available molecular knowledge to general regulatory motifs with varying network structures. Deterministic as well as stochastic modelling techniques have been employed, depending primarily on the specific questions asked.

Functional & Integrative Genomics, 2001

Powerful new methods, like expression profiles using cDNA arrays, have been used to monitor changes in gene expression levels as a result of a variety of metabolic, xenobiotic or pathogenic challenges. This potentially vast quantity of data enables, in principle, the dissection of the complex genetic networks that control the patterns and rhythms of gene expression in the cell. Here we present a general approach to developing dynamic models for analyzing time series of whole genome expression. In this approach, a self-consistent calculation is performed that involves both linear and non-linear response terms for interrelating gene expression levels. This calculation uses singular value decomposition (SVD) not as a statistical tool but as a means of inverting noisy and near-singular matrices. The linear transition matrix that is determined from this calculation can be used to calculate the underlying network reflected in the data. This suggests a direct method of classifying genes according to their place in the resulting network. In addition to providing a means to model such a large multivariate system this approach can be used to reduce the dimensionality of the problem in a rational and consistent way, and suppress the strong noise amplification effects often encountered with expression profile data. Non-linear and higher-order Markov behavior of the network are also determined in this self-consistent method. In data sets from yeast, we calculate the Markov matrix and the gene classes based on the linear-Markov network. These results compare favorably with previously used methods like cluster analysis. Our dynamic method appears to give a broad and general framework for data analysis and modeling of gene expression arrays.

BMC Bioinformatics, 2007

Background: This work explores the quantitative characteristics of the local transcriptional regulatory network based on the availability of time dependent gene expression data sets. The dynamics of the gene expression level are fitted via a stochastic differential equation model, yielding a set of specific regulators and their contribution. Results: We show that a beta sigmoid function that keeps track of temporal parameters is a novel prototype of a regulatory function, with the effect of improving the performance of the profile prediction. The stochastic differential equation model follows well the dynamic of the gene expression levels. Conclusion: When adapted to biological hypotheses and combined with a promoter analysis, the method proposed here leads to improved models of the transcriptional regulatory networks.

Metabolic Engineering, 1999

One of the important goals of biology is to understand the relationship between DNA sequence information and nonlinear cellular responses. This relationship is central to the ability to effectively engineer cellular phenotypes, pathways, and characteristics. Expression arrays for monitoring total gene expression based on mRNA can provide quantitative insight into which gene or genes are on or off; but this information is insufficient to fully predict dynamic biological phenomena. Using nonlinear stability analysis we show that a combination of gene expression information at the message level and at the protein level is required to describe even simple models of gene networks. To help illustrate the need for such information we consider a mechanistic model for circadian rhythmicity which shows agreement with experimental observations when protein and mRNA information are included and we propose a framework for acquiring and analyzing experimental and mathematically derived information about gene networks.

2011

Background: This work explores the quantitative characteristics of the local transcriptional regulatory network based on the availability of time dependent gene expression data sets. The dynamics of the gene expression level are fitted via a stochastic differential equation model, yielding a set of specific regulators and their contribution. Results: We show that a beta sigmoid function that keeps track of temporal parameters is a novel prototype of a regulatory function, with the effect of improving the performance of the profile prediction. The stochastic differential equation model follows well the dynamic of the gene expression levels. Conclusion: When adapted to biological hypotheses and combined with a promoter analysis, the method proposed here leads to improved models of the transcriptional regulatory networks.

BMC Bioinformatics, 2007

Time course gene expression experiments are a popular means to infer co-expression. Many methods have been proposed to cluster genes or to build networks based on similarity measures of their expression dynamics. In this paper we apply a correlation based approach to network reconstruction to three datasets of time series gene expression following system perturbation: 1) Conditional, Tamoxifen dependent, activation of the cMyc proto-oncogene in rat fibroblast; 2) Genomic response to nutrition changes in D. melanogaster; 3) Patterns of gene activity as a consequence of ageing occurring over a life-span time series (25y-90y) sampled from T-cells of human donors.