Andre S. Ribeiro

A General Modeling Strategy for Gene Regulatory Networks with Stochastic Dynamics

A stochastic genetic toggle switch model that consists of two identical, mutually repressive genes is built using the Gillespie algorithm with time delays as an example of a simple stochastic gene regulatory network. The stochastic kinetics of this model is investigated, and it is found that the delays for the protein productions can highly weaken the global fluctuations for the expressions of the two genes, making the two mutually repressive genes coexist for a long time. Starting from this model, we propose a practical modeling strategy for more complex gene regulatory networks. Unlike previous applications of the Gillespie algorithm to simulate specific genetic networks dynamics, this modeling strategy is proposed for an ensemble approach to study the dynamical properties of these networks. The model allows any combination of gene expression products, forming complex multimers, and each one of the multimers is assigned to a randomly chosen gene promoter site as an activator or inhibitor. In addition, each gene, although it has only one promoter site, can have multiple regulatory sites and distinct rates of translation and transcription. Also, different genes have different time delays for transcription and translation and all reaction constant rates are initially randomly chosen from a range of values. Therefore, the general strategy here proposed may be used to simulate real genetic networks.

Stochastic and delayed stochastic models of gene expression and regulation

Gene expression and gene regulatory networks dynamics are stochastic. The noise in the temporal amounts of proteins and RNA molecules in cells arises from the stochasticity of transcription initiation and elongation (e.g., due to RNA polymerase pausing), translation, and post-transcriptional regulation mechanisms, such as reversible phosphorylation and splicing. This is further enhanced by the fact that most RNA molecules and proteins exist in cells in very small amounts. Recently, the time needed for transcription and translation to be completed once initiated were shown to affect the stochasticity in gene networks. This observation stressed the need of either introducing explicit delays in models of transcription and translation or to model processes such as elongation at the single nucleotide level. Here we review stochastic and delayed stochastic models of gene expression and gene regulatory networks. We first present stochastic non-delayed and delayed models of transcription, followed by models at the single nucleotide level. Next, we present models of gene regulatory networks, describe the dynamics of specific stochastic gene networks and available simulators to implement these models.

SGN Sim, a Stochastic Genetic Networks Simulator

UNLABELLEDnWe present SGNSim, Stochastic Gene Networks Simulator, a tool to model gene regulatory networks (GRN) where transcription and translation are modeled as multiple time delayed events and its dynamics is driven by a stochastic simulation algorithm (SSA) able to deal with multiple time delayed events. The delays can be drawn from several distributions and the reaction rates from complex functions or from physical parameters. SGNSim can generate ensembles of GRNs, within a set of user-defined parameters, such as topology. It can also be used to model specific GRNs and systems of chemical reactions. Perturbations, e.g. gene deletion, over-expression, copy and mutation, can be modeled as well. As examples, we present a model of a toggle switch without cooperative binding subject to perturbations, a system of reactions within a compartmentalized environment where membrane crossing is controlled by a negative feedback mechanism and a simulation based on the yeast transcriptional network.nnnAVAILABILITYnSGNSim program, instructions and examples available at www.ucalgary.ca/~aribeiro/SGNtheSim/SGNtheSim.html.

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.

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

MOTIVATIONnCell 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.nnnRESULTSnWe 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.nnnAVAILABILITYnSGNS2, instructions and examples available at www.cs.tut.fi/~lloydpri/sgns2/ (open source under New BSD license).nnnCONTACTnjason.lloyd-price@tut.fi.nnnSUPPLEMENTARY INFORMATIONnSupplementary data are available at Bioinformatics online.

Reversible disruption of neuronal mitochondria by ischemic and traumatic injury revealed by quantitative two-photon imaging in the neocortex of anesthetized mice.

Mitochondria play a variety of functional roles in cortical neurons, from metabolic support and neuroprotection to the release of cytokines that trigger apoptosis. In dendrites, mitochondrial structure is closely linked to their function, and fragmentation (fission) of the normally elongated mitochondria indicates loss of their function under pathological conditions, such as stroke and brain trauma. Using in vivo two-photon microscopy in mouse brain, we quantified mitochondrial fragmentation in a full spectrum of cortical injuries, ranging from severe to mild. Severe global ischemic injury was induced by bilateral common carotid artery occlusion, whereas severe focal stroke injury was induced by Rose Bengal photosensitization. The moderate and mild traumatic injury was inflicted by focal laser lesion and by mild photo-damage, respectively. Dendritic and mitochondrial structural changes were tracked longitudinally using transgenic mice expressing fluorescent proteins localized either in cytosol or in mitochondrial matrix. In response to severe injury, mitochondrial fragmentation developed in parallel with dendritic damage signified by dendritic beading. Reconstruction from serial section electron microscopy confirmed mitochondrial fragmentation. Unlike dendritic beading, fragmentation spread beyond the injury core in focal stroke and focal laser lesion models. In moderate and mild injury, mitochondrial fragmentation was reversible with full recovery of structural integrity after 1–2 weeks. The transient fragmentation observed in the mild photo-damage model was associated with changes in dendritic spine density without any signs of dendritic damage. Our findings indicate that alterations in neuronal mitochondria structure are very sensitive to the tissue damage and can be reversible in ischemic and traumatic injuries. SIGNIFICANCE STATEMENT During ischemic stroke or brain trauma, mitochondria can either protect neurons by supplying ATP and adsorbing excessive Ca2+, or kill neurons by releasing proapoptotic factors. Mitochondrial function is tightly linked to their morphology: healthy mitochondria are thin and long; dysfunctional mitochondria are thick (swollen) and short (fragmented). To date, fragmentation of mitochondria was studied either in dissociated cultured neurons or in brain slices, but not in the intact living brain. Using real-time in vivo two-photon microscopy, we quantified mitochondrial fragmentation during acute pathological conditions that mimic severe, moderate, and mild brain injury. We demonstrated that alterations in neuronal mitochondria structural integrity can be reversible in traumatic and ischemic injuries, highlighting mitochondria as a potential target for therapeutic interventions.

Dissecting the stochastic transcription initiation process in live Escherichia coli

We investigate the hypothesis that, in Escherichia coli, while the concentration of RNA polymerases differs in different growth conditions, the fraction of RNA polymerases free for transcription remains approximately constant within a certain range of these conditions. After establishing this, we apply a standard model-fitting procedure to fully characterize the in vivo kinetics of the rate-limiting steps in transcription initiation of the Plac/ara-1 promoter from distributions of intervals between transcription events in cells with different RNA polymerase concentrations. We find that, under full induction, the closed complex lasts ∼788 s while subsequent steps last ∼193 s, on average. We then establish that the closed complex formation usually occurs multiple times prior to each successful initiation event. Furthermore, the promoter intermittently switches to an inactive state that, on average, lasts ∼87 s. This is shown to arise from the intermittent repression of the promoter by LacI. The methods employed here should be of use to resolve the rate-limiting steps governing the in vivo dynamics of initiation of prokaryotic promoters, similar to established steady-state assays to resolve the in vitro dynamics.

Polar Localization of the Serine Chemoreceptor of Escherichia coli Is Nucleoid Exclusion-Dependent

We studied whether nucleoid exclusion contributes to the segregation and retention of Tsr chemoreceptor clusters at the cell poles. Using live time-lapse, single-cell microscopy measurements, we show that the single-cell spatial distributions of Tsr clusters have heterogeneities and asymmetries that are consistent with nucleoid exclusion and cannot be explained by the diffusion-and-capture mechanism supported by Tol-Pal complexes at the poles. Also, in cells subjected to ampicillin, which enhances relative nucleoid lengths, Tsr clusters locate relatively closer to the cell extremities, whereas in anucleated cells (deletion mutants for mukB), the Tsr clusters are closer to midcell. In addition, we find that the fraction of Tsr clusters at the poles is smaller in deletion mutants for Tol-Pal than in wild-type cells, although it is still larger than would be expected by chance. Also in deletion mutants, the distribution of Tsr clusters differs widely between cells with relatively small and large nucleoids, in a manner consistent with nucleoid exclusion from midcell. This comparison further showed that diffusion-and-capture by Tol-Pal complexes and nucleoid exclusion from the midcell have complementary effects. Subsequently, we subjected deletion mutants to suboptimal temperatures that are known to enhance cytoplasm viscosity, which hampers nucleoid exclusion effects. As the temperature was lowered, the fraction of clusters at the poles decreased linearly. Finally, a stochastic model including nucleoid exclusion at midcell and diffusion-and-capture due to Tol-Pal at the poles is shown to exhibit a cluster dynamics that is consistent with the empirical data. We conclude that nucleoid exclusion also contributes to the preference of Tsr clusters for polar localization.

Effects of σ factor competition are promoter initiation kinetics dependent

In Escherichia coli, the expression of a σ factor is expected to indirectly down-regulate the expression of genes recognized by another σ factor, due to σ factor competition for a limited pool of RNA polymerase core enzymes. Evidence suggests that the sensitivity of genes to indirect down-regulation differs widely. We studied the variability in this sensitivity in promoters primarily recognized by RNAP holoenzymes carrying σ(70). From qPCR and live single-cell, single-RNA measurements of the transcription kinetics of several σ(70)-dependent promoters in various conditions and from the analysis of σ factors population-dependent models of transcription initiation, we find that, the smaller is the time-scale of the closed complex formation relative to the open complex formation, the weaker is a promoters responsiveness to changes in σ(38) numbers. We conclude that, in E. coli, a promoters responsiveness to indirect regulation by σ factor competition is determined by the sequence-dependent kinetics of the rate limiting steps of transcription initiation.