Jason Lloyd-Price

Mutual information in random Boolean models of regulatory networks

The amount of mutual information contained in the time series of two elements gives a measure of how well their activities are coordinated. In a large, complex network of interacting elements, such as a genetic regulatory network within a cell, the average of the mutual information over all pairs, , is a global measure of how well the system can coordinate its internal dynamics. We study this average pairwise mutual information in random Boolean networks (RBNs) as a function of the distribution of Boolean rules implemented at each element, assuming that the links in the network are randomly placed. Efficient numerical methods for calculating show that as the number of network nodes, N, approaches infinity, the quantity N exhibits a discontinuity at parameter values corresponding to critical RBNs. For finite systems it peaks near the critical value, but slightly in the disordered regime for typical parameter variations. The source of high values of N is the indirect correlations between pairs of elements from different long chains with a common starting point. The contribution from pairs that are directly linked approaches zero for critical networks and peaks deep in the disordered regime.

In vivo kinetics of transcription initiation of the lar promoter in Escherichia coli. Evidence for a sequential mechanism with two rate-limiting steps

BackgroundIn Escherichia coli the mean and cell-to-cell diversity in RNA numbers of different genes vary widely. This is likely due to different kinetics of transcription initiation, a complex process with multiple rate-limiting steps that affect RNA production.ResultsWe measured the in vivo kinetics of production of individual RNA molecules under the control of the lar promoter in E. coli. From the analysis of the distributions of intervals between transcription events in the regimes of weak and medium induction, we find that the process of transcription initiation of this promoter involves a sequential mechanism with two main rate-limiting steps, each lasting hundreds of seconds. Both steps become faster with increasing induction by IPTG and Arabinose.ConclusionsThe two rate-limiting steps in initiation are found to be important regulators of the dynamics of RNA production under the control of the lar promoter in the regimes of weak and medium induction. Variability in the intervals between consecutive RNA productions is much lower than if there was only one rate-limiting step with a duration following an exponential distribution. The methodology proposed here to analyze the in vivo dynamics of transcription may be applicable at a genome-wide scale and provide valuable insight into the dynamics of prokaryotic genetic networks.

In vivo single-molecule kinetics of activation and subsequent activity of the arabinose promoter

Using a single-RNA detection technique in live Escherichia coli cells, we measure, for each cell, the waiting time for the production of the first RNA under the control of PBAD promoter after induction by arabinose, and subsequent intervals between transcription events. We find that the kinetics of the arabinose intake system affect mean and diversity in RNA numbers, long after induction. We observed the same effect on Plac/ara-1 promoter, which is inducible by arabinose or by IPTG. Importantly, the distribution of waiting times of Plac/ara-1 is indistinguishable from that of PBAD, if and only if induced by arabinose alone. Finally, RNA production under the control of PBAD is found to be a sub-Poissonian process. We conclude that inducer-dependent waiting times affect mean and cell-to-cell diversity in RNA numbers long after induction, suggesting that intake mechanisms have non-negligible effects on the phenotypic diversity of cell populations in natural, fluctuating environments.

Asymmetric disposal of individual protein aggregates in Escherichia coli, one aggregate at a time

Escherichia coli cells employ an asymmetric strategy at division, segregating unwanted substances to older poles, which has been associated with aging in these organisms. The kinetics of this process is still poorly understood. Using the MS2 coat protein fused to green fluorescent protein (GFP) and a reporter construct with multiple MS2 binding sites, we tracked individual RNA-MS2-GFP complexes in E. coli cells from the time when they were produced. Analyses of the kinetics and brightness of the spots showed that these spots appear in the midcell region, are composed of a single RNA-MS2-GFP complex, and reach a pole before another target RNA is formed, typically remaining there thereafter. The choice of pole is probabilistic and heavily biased toward one pole, similar to what was observed by previous studies regarding protein aggregates. Additionally, this mechanism was found to act independently on each disposed molecule. Finally, while the RNA-MS2-GFP complexes were disposed of, the MS2-GFP tagging molecules alone were not. We conclude that this asymmetric mechanism to segregate damage at the expense of aging individuals acts probabilistically on individual molecules and is capable of the accurate classification of molecules for disposal.

Stochastic sequence-level model of coupled transcription and translation in prokaryotes

BackgroundIn prokaryotes, transcription and translation are dynamically coupled, as the latter starts before the former is complete. Also, from one transcript, several translation events occur in parallel. To study how events in transcription elongation affect translation elongation and fluctuations in protein levels, we propose a delayed stochastic model of prokaryotic transcription and translation at the nucleotide and codon level that includes the promoter open complex formation and alternative pathways to elongation, namely pausing, arrests, editing, pyrophosphorolysis, RNA polymerase traffic, and premature termination. Stepwise translation can start after the ribosome binding site is formed and accounts for variable codon translation rates, ribosome traffic, back-translocation, drop-off, and trans-translation.ResultsFirst, we show that the model accurately matches measurements of sequence-dependent translation elongation dynamics. Next, we characterize the degree of coupling between fluctuations in RNA and protein levels, and its dependence on the rates of transcription and translation initiation. Finally, modeling sequence-specific transcriptional pauses, we find that these affect protein noise levels.ConclusionsFor parameter values within realistic intervals, transcription and translation are found to be tightly coupled in Escherichia coli, as the noise in protein levels is mostly determined by the underlying noise in RNA levels. Sequence-dependent events in transcription elongation, e.g. pauses, are found to cause tangible effects in the degree of fluctuations in protein levels.

Regulation of mean and noise of the in vivo kinetics of transcription under the control of the lac/ara-1 promoter

The kinetics of transcription initiation in Escherichia coli depend on the duration of two rate‐limiting steps, the closed and the open complex formation. In a lac promoter variant, P lac/ara‐1 , the kinetics of these steps is controlled by IPTG and arabinose. From in vivo single‐RNA measurements, we find that induction affects the mean and normalized variance of the intervals between consecutive RNA productions. Transcript production is sub‐Poissonian in all conditions tested. The kinetics of each step is independently controlled by a different inducer. We conclude that the regulatory mechanism of P lac/ara‐1 allows the stochasticity of gene expression to be environment‐dependent.

In Vivo Kinetics of Segregation and Polar Retention of MS2-GFP-RNA Complexes in Escherichia coli

The cytoplasm of Escherichia coli is a crowded, heterogeneous environment. From single cell live imaging, we investigated the spatial kinetics and heterogeneities of synthetic RNA-protein complexes. First, although their known tendency to accumulate at the cell poles does not appear to introduce asymmetries between older and newer cell poles within a cell lifetime, these emerge with cell divisions. This suggests strong polar retention of the complexes, which we verified in their history of positions and mean escape time from the poles. Next, we show that the polar retention relies on anisotropies in the displacement distribution in the region between midcell and poles, whereas the speed is homogeneous along the major cell axis. Afterward, we establish that these regions are at the border of the nucleoid and shift outward with cell growth, due to the nucleoids replication. Overall, the spatiotemporal kinetics of the complexes, which is robust to suboptimal temperatures, suggests that nucleoid occlusion is a source of dynamic heterogeneities of macromolecules in E. coli that ultimately generate phenotypic differences between sister cells.

SGNS2: a compartmentalized stochastic chemical kinetics simulator for dynamic cell populations

MOTIVATION Cell growth and division affect the kinetics of internal cellular processes and the phenotype diversity of cell populations. Since the effects are complex, e.g. different cellular components are partitioned differently in cell division, to account for them in silico, one needs to simulate these processes in great detail. RESULTS We present SGNS2, a simulator of chemical reaction systems according to the Stochastic Simulation Algorithm with multi-delayed reactions within hierarchical, interlinked compartments which can be created, destroyed and divided at runtime. In division, molecules are randomly segregated into the daughter cells following a specified distribution corresponding to one of several partitioning schemes, applicable on a per-molecule-type basis. We exemplify its use with six models including a stochastic model of the disposal mechanism of unwanted protein aggregates in Escherichia coli, a model of phenotypic diversity in populations with different levels of synchrony, a model of a bacteriophages infection of a cell population and a model of prokaryotic gene expression at the nucleotide and codon levels. AVAILABILITY SGNS2, instructions and examples available at www.cs.tut.fi/~lloydpri/sgns2/ (open source under New BSD license). CONTACT jason.lloyd-price@tut.fi. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

Information propagation within the Genetic Network of Saccharomyces cerevisiae.

BackgroundA gene networks capacity to process information, so as to bind past events to future actions, depends on its structure and logic. From previous and new microarray measurements in Saccharomyces cerevisiae following gene deletions and overexpressions, we identify a core gene regulatory network (GRN) of functional interactions between 328 genes and the transfer functions of each gene. Inferred connections are verified by gene enrichment.ResultsWe find that this core network has a generalized clustering coefficient that is much higher than chance. The inferred Boolean transfer functions have a mean p-bias of 0.41, and thus similar amounts of activation and repression interactions. However, the distribution of p-biases differs significantly from what is expected by chance that, along with the high mean connectivity, is found to cause the core GRN of S. cerevisiaes to have an overall sensitivity similar to critical Boolean networks. In agreement, we find that the amount of information propagated between nodes in finite time series is much higher in the inferred core GRN of S. cerevisiae than what is expected by chance.ConclusionsWe suggest that S. cerevisiae is likely to have evolved a core GRN with enhanced information propagation among its genes.

Dynamics of small genetic circuits subject to stochastic partitioning in cell division.

In prokaryotes, partitioning errors during cell division are expected to be a non-negligible source of cell-to-cell diversity in protein numbers. Here, we make use of stochastic simulations to investigate how different degrees of partitioning errors in division affect the cell-to-cell diversity of the dynamics of two genetic circuits, a bistable switch and a clock. First, we find that on average, the stability of the switch decreases with increasing partitioning errors. Despite this, anti-correlations between sister cells, introduced by the partitioning errors, enhance the chances that one of them will remain in the mother cells state in the next generation, even if the switch is unstable. This reduces the variance of the proportion of phenotypes across generations. In the genetic clock, we find that the robustness of the period decreases with increasing partitioning errors. Nevertheless, the population synchrony is remarkably robust to most errors, only significantly decreasing for the most extreme degree of errors. We conclude that errors in partitioning affect the dynamics of genetic circuits, but the effects are network-dependent and qualitatively different from noise in gene expression.