A biophysical model of supercoiling dependent transcription predicts a structural aspect to gene regulation

Abstract

Background: Transcription in Escherichia coli generates positive supercoiling in the DNA, which is relieved by the enzymatic activity of gyrase. Recently published experimental evidence suggests that transcription initiation and elongation are inhibited by the buildup of positive supercoiling. It has therefore been proposed that intermittent binding of gyrase plays a role in transcriptional bursting. Considering that transcription is one of the most fundamental cellular processes, it is desirable to be able to account for the buildup and release of positive supercoiling in models of transcription.

Results: Here we present a detailed biophysical model of gene expression that incorporates the effects of supercoiling due to transcription. By directly linking the amount of positive supercoiling to the rate of transcription, the model predicts that highly transcribed genes' mRNA distributions should substantially deviate from Poisson distributions, with enhanced density at low mRNA copy numbers. Additionally, the model predicts a high degree of correlation between expression levels of genes inside the same supercoiling domain.

Conclusions: Our model, incorporating the supercoiling state of the gene, makes specific predictions that differ from previous models of gene expression. Genes in the same supercoiling domain influence the expression level of neighboring genes. Such structurally dependent regulation predicts correlations between genes in the same supercoiling domain. The topology of the chromosome therefore creates a higher level of gene regulation, which has broad implications for understanding the evolution and organization of bacterial genomes.

Keywords: Bursting; Gene expression; Gyrase; RNA polymerase; Supercoiling; Transcription.

Fig. 1

Positive Supercoiling (Pcoil) is produced when mRNA is transcribed. Pcoil inhibits the production of mRNA by reducing the initiation rate. In order to relieve Pcoil gyrase must bind (Gyrase’), which converts Pcoil into the “regular” state (Rcoil)

Fig. 2

a Experimental data from [20] for T7 RNAP where the fluorescence intensity corresponds to the rate of transcript initiation in the absence of gyrase and the presence of Topo I. b The cumulative sum (red line) of the data in a corresponding to the total number of mRNA transcripts produced through time. Also shown are the times of average transcription events (green triangles) determined from the original data, see text. c The time between average transcription events. d The initiation rate by transcription event number (green triangles) and a linear fit (dashed line)

Fig. 3

a The theoretical change in free energy needed to melt the base pairs of the promoter sequence by supercoiling density σ, from Eq. 2. b The change in the rate, K, by supercoiling density (dots) and a single exponential fit (line). c Transcription initiation rate vs the number of transcription events (green triangles) from experiment [20], the full theory Eq. 3 (red line) and the linear theory Eq. 4 (black line). The full theory had a fit R-square = 0.97 and the linear theory R-square = 0.96

Fig. 4

a Experimental data from [20] compared to the results from the model. Fluorescence intensity directly corresponds to transcription initiation rate. b The cumulative sum of the data in a compared to results from the model. c Comparison of the time between average transcription events between theory and experiment. d The initiation rate by transcription event number for the experimental data and for the model

Fig. 5

a The distribution of mRNA for a gene with a strong promoter (blue bars), a fit of the simulated data to a Poisson distribution (red line) and a fit to the zero-spike model (cyan line). b The same as in a for a gene with a weak promoter

Fig. 6

The Fano factor, variance/mean, of mRNA of a single gene inside a supercoiling domain with varying initiation rate a _j and gyrase binding affinity K1

Fig. 7

a The bursting model of gene expression. b The protein distribution generated from our model fit to a Gamma distribution. (Where the probability distribution above is for K1=10). c+d The percent error in the a and b values [ 100·(fit−actual)/actual] determined by fitting a gamma distribution to the data from the simulations

Fig. 8

a The mean mRNA and b protein levels (blue bars) for genes from the simulations. Genes 1–5 share a supercoiling domain, while genes 6–10 share a supercoiling domain. A red bar shows the expression level of a gene if it was in its own supercoiling domain. c The correlation in the mRNA and d protein between the genes

Fig. 9

The mean mRNA level of the genes in a supercoiling domain with all genes expressed (blue) and when gene 1 is inhibited (red)