Prediction of temporal gene expression

Abstract

A computational approach is used to analyse temporal gene expression in the context of metabolic regulation. It is based on the assumption that cells developed optimal adaptation strategies to changing environmental conditions. Timedependent enzyme profiles are calculated which optimize the function of a metabolic pathway under the constraint of limited total enzyme amount. For linear model pathways it is shown that wave-like enzyme profiles are optimal for a rapid substrate turnover. For the central metabolism of yeast cells enzyme profiles are calculated which ensure long-term homeostasis of key metabolites under conditions of a diauxic shift. These enzyme profiles are in close correlation with observed gene expression data. Our results demonstrate that optimality principles help to rationalize observed gene expression profiles.Keywords: evolutionary optimization; mathematical modelling; metabolic regulation; gene expression.Microarray technologies provide the means to measure simultaneously the expression patterns of thousands of genes [1,2]. These expression data and the availability of more than 80 fully sequenced genomes represent an enormous quantity of experimental data. The conversion of this genomic information into knowledge on phenotype characteristics such as metabolic pathways or signal transduction networks is a challenging task that cannot be effectively tackled without broad application of theoretical and computational methods.Time resolved tracing of expression levels for large sets of genes has provided evidence that mRNA levels of metabolic enzymes often change within the same time scale as variations of external conditions [1][2][3][4]. Quantitative simulation of these time dependent gene expression patterns meets with difficulties due to incomplete knowledge of the underlying regulatory mechanisms. However, statistical methods have been successfully applied, such as cluster analysis of time-dependent gene expression patterns for identifying functionally related proteins [5][6][7][8][9][10].It has been stressed that even without detailed knowledge of gene regulatory mechanisms phenotype properties can be rationalized by evolutionary optimization principles [11]. The basis of this approach is the hypothesis that a permanent change of phenotype properties due to mutation and selection leads to an optimal adaptation of an organism to given environmental conditions. Most optimization studies in the field of metabolic regulation are aimed at prediction of time independent characteristics of enzymes ensuring optimal performance of metabolic pathways [11][12][13][14][15]. The microarray data suggests applying optimization concepts to also explain time courses of enzyme concentrations.The basic idea of our paper is that time dependent gene expression enables cells to adapt their metabolic capabilities in an optimal way to varying external conditions. Our approach consists in (a) establishing a mathematical model of the metabolic pathways under consideration, (b) defining a performance function to ev...

Dynamic optimization of biological networks under parametric uncertainty

“…This is acceptable, as long as cell viability is not compromised. Comparing this with experimental results for amino-acid biosynthetic pathways in Escherichia coli [38, 40, 41] a sequential activation of the enzymes can be observed in the enzyme concentration profiles.…”

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“…For example, pathways appear to have evolved to maximize flux for a minimum amount of protein, because the enzyme concentration may be limited by both the protein synthesizing capacity and the solvent capacity of a cell [43]. In fact, theoretical studies suggest that adaptive responses of yeast to environmental changes trigger a gene expression profile that is optimal under the constraint of minimal total enzyme production [2],[44],[45].…”

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