Random timing in signaling cascades

Molecular mechanisms of precise timing in cell lysis

Many biological systems exhibit precise timing of events, and one of the most known examples is cell lysis, which is a process of breaking bacterial host cells in the virus infection cycle. However, the underlying microscopic picture of precise timing remains not well understood. We present a novel theoretical approach to explain the molecular mechanisms of effectively deterministic dynamics in biological systems. Our hypothesis is based on the idea of stochastic coupling between relevant underlying biophysical and biochemical processes that lead to noise cancellation. To test this hypothesis, we introduced a minimal discrete-state stochastic model to investigate how holin proteins produced by bacteriophages break the inner membranes of gram-negative bacteria. By explicitly solving this model, the dynamic properties of cell lysis are fully evaluated, and theoretical predictions quantitatively agree with available experimental data for both wild-type and holin mutants. It is found that the observed threshold-like behavior is a result of the balance between holin proteins entering the membrane and leaving the membrane during the lysis. Theoretical analysis suggests that the cell lysis achieves precise timing for wild-type species by maximizing the number of holins in the membrane and narrowing their spatial distribution. In contrast, for mutated species, these conditions are not satisfied. Our theoretical approach presents a possible molecular picture of precise dynamic regulation in intrinsically random biological processes.

Avoiding the All-or-None Response in Gene Expression During E. coli Continuous Cultivation Based on the On-Line Monitoring of Cell Phenotypic Switching Dynamics

Different expression vectors are available for the effective production of recombinant proteins by bacterial populations. However, the productivity of such systems is limited by the inherent noise of the gene circuits used for the synthesis of recombinant products. An extreme case of cell-to-cell heterogeneity that has been previously reported for the ara- and lac-based expression systems in E. coli is the all-or-none response. According to this mode of response, two subpopulations of cells are generated, i.e., a "low-" subpopulation exhibiting a shallow expression level and a "high-" subpopulation exhibiting a high-expression level. The "low-" subpopulation can be considered as a cluster of non-producing cells contributing to the loss of productivity. Here we describe the setup, design, and operation of a continuous culture where inducer addition is operated based on microbial population dynamics. The determination of population dynamics is done based on an automated flow cytometry (FC) procedure previously denoted as segregostat. We illustrate how this setup can be used to control the activation of an ara-based expression system and avoid phenotypic diversification leading to an all-or-none response. Upon the determination of the natural frequency of the gene circuit used as an expression system, our current protocol can be set up without the requirement of a feedback controller.

First passage time properties of miRNA-mediated protein translation

An important function of microRNAs in gene regulation is to repress the protein synthesis in a multi-step process with implications in timing efficiency of the regulatory network. We propose a stochastic description of translation-initiation mechanism and solve for the steady state distribution of protein number in the linear regime. The time-dependent moments have been approximately calculated and the role of miRNAs in determining the First Passage Time (FPT) properties of protein dynamics has been established. We analytically show that the modulation of slow rates of the translation process will result in efficient and robust timing mechanism. For a general nonlinear model our numerical simulation results are in qualitative agreement with the linear model.

Maximization of information transmission influences selection of native phosphorelay architectures

Phosphorelays are signal transduction circuits that sense environmental changes and adjust cellular metabolism. Five different circuit architectures account for 99% of all phosphorelay operons annotated in over 9,000 fully sequenced genomes. Here we asked what biological design principles, if any, could explain selection among those architectures in nature. We began by studying kinetically well characterized phosphorelays (Spo0 of Bacillus subtilis and Sln1 of Saccharomyces cerevisiae). We find that natural circuit architecture maximizes information transmission in both cases. We use mathematical models to compare information transmission among the architectures for a realistic range of concentration and parameter values. Mapping experimentally determined phosphorelay protein concentrations onto that range reveals that the native architecture maximizes information transmission in sixteen out of seventeen analyzed phosphorelays. These results suggest that maximization of information transmission is important in the selection of native phosphorelay architectures, parameter values and protein concentrations.

First passage time in post-transcriptional regulation by multiple small RNAs

The post-transcriptional regulation of a protein by multiple small RNA molecules has been formulated as a stochastic process. An approximate solution of the master equation shows that the protein statistics can exhibit a generic form applicable for many regulatory scenarios. The first passage time (FPT) statistics has been obtained for regulation by single sRNA, with negative and positive regulations as limiting cases, as well as regulation by multiple sRNAs. The multiple sRNAs are able to independently control protein mean and variance, and we show that this is an advantageous mechanism to control FPT fluctuations in order to improve timing efficiency in post-transcriptional regulation.

Timing effciency in small-RNA-regulated post-transcriptional processes

Gene regulation in a cellular environment is a stochastic phenomenon leading to a large variability in mRNAs and protein numbers that are often produced in bursts. The regulation leading to varied protein dynamics can be ascribed to transcriptional or post-transcriptional mechanisms. In transcriptional regulation, the gene dynamically switches between an active and an inactive state, while in the post-transcriptional regulation small RNAs tune the activity of mRNAs. In either scenario, it is possible to calculate the time-dependent probability distribution of proteins and address the interesting question pertaining to their first passage time statistics. The coefficient of variation of first passage time can be considered to be an indicator of efficiency in controlling regulatory pathways and we show that post-transcriptional regulation performs better than simple transcriptional regulation for comparable protein yields.

Added value of autoregulation and multi-step kinetics of transcription initiation

Bacterial gene expression regulation occurs mostly during transcription, which has two main rate-limiting steps: the close complex formation, when the RNA polymerase binds to an active promoter, and the subsequent open complex formation, after which it follows elongation. Tuning these steps' kinetics by the action of e.g. transcription factors, allows for a wide diversity of dynamics. For example, adding autoregulation generates single-gene circuits able to perform more complex tasks. Using stochastic models of transcription kinetics with empirically validated parameter values, we investigate how autoregulation and the multi-step transcription initiation kinetics of single-gene autoregulated circuits can be combined to fine-tune steady state mean and cell-to-cell variability in protein expression levels, as well as response times. Next, we investigate how they can be jointly tuned to control complex behaviours, namely, time counting, switching dynamics and memory storage. Overall, our finding suggests that, in bacteria, jointly regulating a single-gene circuit's topology and the transcription initiation multi-step dynamics allows enhancing complex task performance.

The Timing of Transcriptional Regulation in Synthetic Gene Circuits

Transcription factors and their target promoters are central to synthetic biology. By arranging these components into novel gene regulatory circuits, synthetic biologists have been able to create a wide variety of phenotypes, including bistable switches, oscillators, and logic gates. However, transcription factors (TFs) do not instantaneously regulate downstream targets. After the gene encoding a TF is turned on, the gene must first be transcribed, the transcripts must be translated, and sufficient TF must accumulate in order to bind operator sites of the target promoter. The time to complete this process, here called the "signaling time," is a critical aspect in the design of dynamic regulatory networks, yet it remains poorly characterized. In this work, we measured the signaling time of two TFs in Escherichia coli commonly used in synthetic biology: the activator AraC and the repressor LacI. We found that signaling times can range from a few to tens of minutes, and are affected by the expression rate of the TF. Our single-cell data also show that the variability of the signaling time increases with its mean. To validate these signaling time measurements, we constructed a two-step genetic cascade, and showed that the signaling time of the full cascade can be predicted from those of its constituent steps. These results provide concrete estimates for the time scales of transcriptional regulation in living cells, which are important for understanding the dynamics of synthetic transcriptional gene circuits.

Stochastic timing in gene expression for simple regulatory strategies

Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to reach in a precise time a threshold level of expression that triggers a specific downstream process. However, gene expression is subject to stochastic fluctuations, naturally inducing an uncertainty in this threshold-crossing time with potential consequences on biological functions and phenotypes. Here, we consider such ‘timing fluctuations’ and we ask how they can be controlled. Our analytical estimates and simulations show that, for an induced gene, timing variability is minimal if the threshold level of expression is approximately half of the steady-state level. Timing fluctuations can be reduced by increasing the transcription rate, while they are insensitive to the translation rate. In presence of self-regulatory strategies, we show that self-repression reduces timing noise for threshold levels that have to be reached quickly, while self-activation is optimal at long times. These results lay a framework for understanding stochasticity of endogenous systems such as the cell cycle, as well as for the design of synthetic trigger circuits.

First-passage time approach to controlling noise in the timing of intracellular events

In the noisy cellular environment, gene products are subject to inherent random fluctuations in copy numbers over time. How cells ensure precision in the timing of key intracellular events despite such stochasticity is an intriguing fundamental problem. We formulate event timing as a first-passage time problem, where an event is triggered when the level of a protein crosses a critical threshold for the first time. Analytical calculations are performed for the first-passage time distribution in stochastic models of gene expression. Derivation of these formulas motivates an interesting question: Is there an optimal feedback strategy to regulate the synthesis of a protein to ensure that an event will occur at a precise time, while minimizing deviations or noise about the mean? Counterintuitively, results show that for a stable long-lived protein, the optimal strategy is to express the protein at a constant rate without any feedback regulation, and any form of feedback (positive, negative, or any combination of them) will always amplify noise in event timing. In contrast, a positive feedback mechanism provides the highest precision in timing for an unstable protein. These theoretical results explain recent experimental observations of single-cell lysis times in bacteriophage [Formula: see text] Here, lysis of an infected bacterial cell is orchestrated by the expression and accumulation of a stable [Formula: see text] protein up to a threshold, and precision in timing is achieved via feedforward rather than feedback control. Our results have broad implications for diverse cellular processes that rely on precise temporal triggering of events.

The Low Noise Limit in Gene Expression

Protein noise measurements are increasingly used to elucidate biophysical parameters. Unfortunately noise analyses are often at odds with directly measured parameters. Here we show that these inconsistencies arise from two problematic analytical choices: (i) the assumption that protein translation rate is invariant for different proteins of different abundances, which has inadvertently led to (ii) the assumption that a large constitutive extrinsic noise sets the low noise limit in gene expression. While growing evidence suggests that transcriptional bursting may set the low noise limit, variability in translational bursting has been largely ignored. We show that genome-wide systematic variation in translational efficiency can–and in the case of E. coli does–control the low noise limit in gene expression. Therefore constitutive extrinsic noise is small and only plays a role in the absence of a systematic variation in translational efficiency. These results show the existence of two distinct expression noise patterns: (1) a global noise floor uniformly imposed on all genes by expression bursting; and (2) high noise distributed to only a select group of genes.

Noisy localized structures induced by large noise

We investigate the influence of large noise on the formation of localized patterns in the framework of the cubic-quintic complex Ginzburg-Landau equation. The interaction of localization and noise can lead to filling in or noisy localized structures for fixed noise strength. To focus on the interaction between noise and localization we cover a region in parameter space, in particular, subcriticality, for which stationary stable deterministic pulses do not exist. Possible experimental tests of the work presented for autocatalytic chemical reactions and bioinspired systems are outlined.

Event timing at the single-cell level

The timing of a cellular event often hides critical information on the process leading to the event. Our ability to measure event times in single cells along with other quantities allow us to learn about the drivers of the timed process and its downstream effects. In this review, we cover different types of events that have been timed in single cells, methods to time such events and types of analysis that have been applied to event timings. We show how different timing distributions suggest different natures for the process. The statistical relations between the timing of different events may reveal how their respective processes are related biologically: Do they occur in sequence or in parallel? Are they independent or inter-dependent? Finally, quantifying morphological and molecular variables may help assess their contribution to the timing of an event and its related process.