Diffusion, dimensionality and noise in transcriptional regulation

The precision of biochemical signaling is limited by randomness in the diffusive arrival of molecules at their targets. For proteins binding to the specific sites on the DNA and regulating transcription, the ability of the proteins to diffuse in one dimension by sliding along the length of the DNA, in addition to their diffusion in bulk solution, would seem to generate a larger target for DNA binding, consequently reducing the noise in the occupancy of the regulatory site. Here we show that this effect is largely cancelled by the enhanced temporal correlations in one dimensional diffusion. With realistic parameters, sliding along DNA has surprisingly little effect on the physical limits to the precision of transcriptional regulation.Comment: 8 pages, 2 figure

Correlated Phenotypic Transitions to Competence in Bacterial Colonies

Genetic competence is a phenotypic state of a bacterial cell in which it is capable of importing DNA, presumably to hasten its exploration of alternate genes in its quest for survival under stress. Recently, it was proposed that this transition is uncorrelated among different cells in the colony. Motivated by several discovered signaling mechanisms which create colony-level responses, we present a model for the influence of quorum-sensing signals on a colony of B. Subtilis cells during the transition to genetic competence. Coupling to the external signal creates an effective inhibitory mechanism, which results in anti-correlation between the cycles of adjacent cells. We show that this scenario is consistent with the specific experimental measurement, which fails to detect some underlying collective signaling mechanisms. Rather, we suggest other parameters that should be used to verify the role of a quorum-sensing signal. We also study the conditions under which phenotypic spatial patterns may emerge

Regulatory activity revealed by dynamic correlations in gene expression noise

Gene regulatory interactions are context dependent, active in some cellular states but not in others. Stochastic fluctuations, or 'noise', in gene expression propagate through active, but not inactive, regulatory links^(1,2). Thus, correlations in gene expression noise could provide a noninvasive means to probe the activity states of regulatory links. However, global, 'extrinsic', noise sources generate correlations even without direct regulatory links. Here we show that single-cell time-lapse microscopy, by revealing time lags due to regulation, can discriminate between active regulatory connections and extrinsic noise. We demonstrate this principle mathematically, using stochastic modeling, and experimentally, using simple synthetic gene circuits. We then use this approach to analyze dynamic noise correlations in the galactose metabolism genes of Escherichia coli. We find that the CRP-GalS-GalE feed-forward loop is inactive in standard conditions but can become active in a GalR mutant. These results show how noise can help analyze the context dependence of regulatory interactions in endogenous gene circuits

A core genetic module : the Mixed Feedback Loop

The so-called Mixed Feedback Loop (MFL) is a small two-gene network where protein A regulates the transcription of protein B and the two proteins form a heterodimer. It has been found to be statistically over-represented in statistical analyses of gene and protein interaction databases and to lie at the core of several computer-generated genetic networks. Here, we propose and mathematically study a model of the MFL and show that, by itself, it can serve both as a bistable switch and as a clock (an oscillator) depending on kinetic parameters. The MFL phase diagram as well as a detailed description of the nonlinear oscillation regime are presented and some biological examples are discussed. The results emphasize the role of protein interactions in the function of genetic modules and the usefulness of modelling RNA dynamics explicitly.Comment: To be published in Physical Review

Accurate prediction of gene feedback circuit behavior from component properties

A basic assumption underlying synthetic biology is that analysis of genetic circuit elements, such as regulatory proteins and promoters, can be used to understand and predict the behavior of circuits containing those elements. To test this assumption, we used time‐lapse fluorescence microscopy to quantitatively analyze two autoregulatory negative feedback circuits. By measuring the gene regulation functions of the corresponding repressor–promoter interactions, we accurately predicted the expression level of the autoregulatory feedback loops, in molecular units. This demonstration that quantitative characterization of regulatory elements can predict the behavior of genetic circuits supports a fundamental requirement of synthetic biology

An excitable gene regulatory circuit induces transient cellular differentiation

Certain types of cellular differentiation are probabilistic and transient. In such systems individual cells can switch to an alternative state and, after some time, switch back again. In Bacillus subtilis, competence is an example of such a transiently differentiated state associated with the capability for DNA uptake from the environment. Individual genes and proteins underlying differentiation into the competent state have been identified, but it has been unclear how these genes interact dynamically in individual cells to control both spontaneous entry into competence and return to vegetative growth. Here we show that this behaviour can be understood in terms of excitability in the underlying genetic circuit. Using quantitative fluorescence time-lapse microscopy, we directly observed the activities of multiple circuit components simultaneously in individual cells, and analysed the resulting data in terms of a mathematical model. We find that an excitable core module containing positive and negative feedback loops can explain both entry into, and exit from, the competent state. We further tested this model by analysing initiation in sister cells, and by re-engineering the gene circuit to specifically block exit. Excitable dynamics driven by noise naturally generate stochastic and transient responses, thereby providing an ideal mechanism for competence regulation

A stochastic model of Min oscillations in Escherichia coli and Min protein segregation during cell division

The Min system in Escherichia coli directs division to the centre of the cell through pole-to-pole oscillations of the MinCDE proteins. We present a one dimensional stochastic model of these oscillations which incorporates membrane polymerisation of MinD into linear chains. This model reproduces much of the observed phenomenology of the Min system, including pole-to-pole oscillations of the Min proteins. We then apply this model to investigate the Min system during cell division. Oscillations continue initially unaffected by the closing septum, before cutting off rapidly. The fractions of Min proteins in the daughter cells vary widely, from 50%-50% up to 85%-15% of the total from the parent cell, suggesting that there may be another mechanism for regulating these levels in vivo.Comment: 19 pages, 12 figures (25 figure files); published at http://www.iop.org/EJ/journal/physbi

Optimizing information flow in small genetic networks. I

In order to survive, reproduce and (in multicellular organisms) differentiate, cells must control the concentrations of the myriad different proteins that are encoded in the genome. The precision of this control is limited by the inevitable randomness of individual molecular events. Here we explore how cells can maximize their control power in the presence of these physical limits; formally, we solve the theoretical problem of maximizing the information transferred from inputs to outputs when the number of available molecules is held fixed. We start with the simplest version of the problem, in which a single transcription factor protein controls the readout of one or more genes by binding to DNA. We further simplify by assuming that this regulatory network operates in steady state, that the noise is small relative to the available dynamic range, and that the target genes do not interact. Even in this simple limit, we find a surprisingly rich set of optimal solutions. Importantly, for each locally optimal regulatory network, all parameters are determined once the physical constraints on the number of available molecules are specified. Although we are solving an over--simplified version of the problem facing real cells, we see parallels between the structure of these optimal solutions and the behavior of actual genetic regulatory networks. Subsequent papers will discuss more complete versions of the problem

Architecture-Dependent Noise Discriminates Functionally Analogous Differentiation Circuits

Gene regulatory circuits with different architectures (patterns of regulatory interactions) can generate similar dynamics. This raises the question of why a particular circuit architecture is selected to implement a given cellular process. To investigate this problem, we compared the Bacillus subtilis circuit that regulates differentiation into the competence state to an engineered circuit with an alternative architecture (SynEx) in silico and in vivo. Time-lapse microscopy measurements showed that SynEx cells generated competence dynamics similar to native cells and reconstituted the physiology of differentiation. However, architectural differences between the circuits altered the dynamic distribution of stochastic fluctuations (noise) during circuit operation. This distinction in noise causes functional differences between the circuits by selectively controlling the timing of competence episodes and response of the system to various DNA concentrations. These results reveal a tradeoff between temporal precision and physiological response range that is controlled by distinct noise characteristics of alternative circuit architectures