Assigning numbers to the arrows: parameterizing a gene regulation network by using accurate expression kinetics

Abstract

A basic challenge in systems biology is to understand the dynamical behavior of gene regulation networks. Current approaches aim at determining the network structure based on genomic-scale data. However, the network connectivity alone is not sufficient to define its dynamics; one needs to also specify the kinetic parameters for the regulation reactions. Here, we ask whether effective kinetic parameters can be assigned to a transcriptional network based on expression data. We present a combined experimental and theoretical approach based on accurate high temporal-resolution measurement of promoter activities from living cells by using green fluorescent protein (GFP) reporter plasmids. We present algorithms that use these data to assign effective kinetic parameters within a mathematical model of the network. To demonstrate this, we employ a well defined network, the SOS DNA repair system of Escherichia coli. We find a strikingly detailed temporal program of expression that correlates with the functional role of the SOS genes and is driven by a hierarchy of effective kinetic parameter strengths for the various promoters. The calculated parameters can be used to determine the kinetics of all SOS genes given the expression profile of just one representative, allowing a significant reduction in complexity. The concentration profile of the master SOS transcriptional repressor can be calculated, demonstrating that relative protein levels may be determined from purely transcriptional data. This finding opens the possibility of assigning kinetic parameters to transcriptional networks on a genomic scale.

Fig 1.

Present approach for assigning effective kinetic parameters to E. coli transcription regulation networks. Transcriptional regulation networks are usually represented by arrow diagrams, where the arrows represent interactions between transcription factors and DNA regulatory sites. The present approach aims to assign kinetic parameters (numbers on the arrows) that capture the dynamics of the network within a quantitative mathematical model, as well as the transcription factor activity profile A(t).

Fig 2.

The bacterial SOS DNA repair system (35). DNA damage is sensed by RecA, which induces autocleavage of the repressor LexA. LexA binds to the promoters of the SOS operons, including its own promoter and that of RecA. This study attempts to assign effective parameters (β_i and k_i) to the arrows representing transcriptional regulation of the various operons. ssDNA, single-stranded DNA.

Fig 3.

(a) Fluorescence of SOS reporter strains as a function of time after UV irradiation. (b) SOS Promoter activity, rate of GFP production per OD unit. E. coli strain AB1157 with SOS reporter plasmids was grown in 96-well plates at 37°C in a multiwell fluorimeter; a UV dose of 5 Jm⁻² was given at midexponential growth (t = 0). (c) Unsmoothed GFP fluorescence (background subtracted) for repeat experiments performed on different days. Each point represents one time point, for a total of 99 time points per operon for eight operons. A perfect repeat would be on the x = y diagonal; also shown are parallel diagonal lines representing 10% errors. The mean error is 10.4%. UV = 5 Jm⁻².

Fig 4.

Promoter activity (solid line) and promoter activity predicted from the kinetics of a single promoter (uvrA) by using the β_i and k_i values and Eq. 3 (dashed line) at UV = 5 Jm⁻². The promoter activity of recA and lexA is multiplied by 0.25.

Fig 5.

The effective relative repressor concentration A(t) at UV = 5 Jm⁻² (solid line) and UV = 20 Jm⁻² (dotted line). The cell cycle time is 45 min. Relative uncleaved LexA protein levels measured by using immunoblots by Sassanfar and Roberts (24), at UV = 5 Jm⁻² (*) and UV = 20 Jm⁻² (○) in the same strain and conditions.