Quantal parameters of synapses are fundamental for the temporal dynamics of neurotransmitter release, which is the basis of interneuronal communication. We formulate a general class of models that capture the stochastic dynamics of quantal content (QC), defined as the number of SV fusion events triggered by a single action potential (AP). Considering the probabilistic and time-varying nature of SV docking, undocking, and AP-triggered fusion, we derive an exact statistical distribution for the QC over time. Analyzing this distribution at steady-state and its associated autocorrelation function, we show that QC fluctuation statistics can be leveraged for inferring key presynaptic parameters, such as the probability of SV fusion (release probability) and SV replenishment at empty docking sites (refilling probability). Our model predictions are tested with electrophysiological data obtained from 50-Hz stimulation of auditory MNTB-LSO synapses in brainstem slices from juvenile mice. Our results show that while synaptic depression can be explained by low and constant refilling/release probabilities, this scenario is inconsistent with the statistics of the electrophysiological data, which show a low QC Fano factor and almost uncorrelated successive QCs. Our systematic analysis yields a model that couples a high release probability to a time-varying refilling probability to explain both the synaptic depression and its associated statistical fluctuations. In summary, we provide a general approach that exploits stochastic signatures in QCs to infer neurotransmission regulating processes that cannot be distinguished from simple analysis of averaged synaptic responses.

Random fluctuations (noise) in gene expression can be studied from two complementary perspectives: following expression in a single cell over time or comparing expression between cells in a proliferating population at a given time. Here, we systematically investigated scenarios where both perspectives can lead to different levels of noise in a given gene product. We first consider a stable protein, whose concentration is diluted by cellular growth. This protein inhibits growth at high concentrations, establishing a positive feedback loop. Using a stochastic model with molecular bursting of gene products, we analytically predict and contrast the steady-state distributions of protein concentration in both frameworks. Although positive feedback amplifies the noise in expression, this amplification is much higher in the population framework compared to following a single cell over time. We also study other processes that lead to different noise levels even in the absence of such dilution-based feedback. When considering randomness in the partitioning of molecules between daughters during mitosis, we find that in the single-cell perspective, the noise in protein concentration is independent of noise in the cell cycle duration. In contrast, partitioning noise is amplified in the population perspective by increasing randomness in cell-cycle time. Overall, our results show that the single-cell framework that does not account for proliferating cells can, in some cases, underestimate the noise in gene product levels. These results have important implications for studying the inter-cellular variation of different stress-related expression programs across cell types that are known to inhibit cellular growth.

BACKGROUND: Stochastic modelling plays a crucial role in comprehending the dynamics of intracellular events in various biochemical systems, including gene-expression models. Cell-to-cell variability arises from the stochasticity or noise in the levels of gene products such as messenger RNA (mRNA) and protein. The sources of noise can stem from different factors, including structural elements. Recent studies have revealed that the mRNA structure can be more intricate than previously assumed. RESULTS: Here, we focus on the formation of stem-loops and present a reinterpretation of previous data, offering new insights. Our analysis demonstrates that stem-loops that restrict translation have the potential to reduce noise. CONCLUSIONS: In conclusion, we investigate a structured/generalised version of a stochastic gene-expression model, wherein mRNA molecules can be found in one of their finite number of different states and transition between them. By characterising and deriving non-trivial analytical expressions for the steady-state protein distribution, we provide two specific examples which can be readily obtained from the structured/generalised model, showcasing the model's practical applicability.

Unlike many single-celled organisms, the growth of fission yeast cells within a cell cycle is not exponential. It is rather characterized by three distinct phases (elongation, septation, and reshaping), each with a different growth rate. Experiments also showed that the distribution of cell size in a lineage can be bimodal, unlike the unimodal distributions measured for the bacterium Escherichia coli. Here we construct a detailed stochastic model of cell size dynamics in fission yeast. The theory leads to analytic expressions for the cell size and the birth size distributions, and explains the origin of bimodality seen in experiments. In particular, our theory shows that the left peak in the bimodal distribution is associated with cells in the elongation phase, while the right peak is due to cells in the septation and reshaping phases. We show that the size control strategy, the variability in the added size during a cell cycle, and the fraction of time spent in each of the three cell growth phases have a strong bearing on the shape of the cell size distribution. Furthermore, we infer all the parameters of our model by matching the theoretical cell size and birth size distributions to those from experimental single-cell time-course data for seven different growth conditions. Our method provides a much more accurate means of determining the size control strategy (timer, adder or sizer) than the standard method based on the slope of the best linear fit between the birth and division sizes. We also show that the variability in added size and the strength of size control in fission yeast depend weakly on the temperature but strongly on the culture medium. More importantly, we find that stronger size homeostasis and larger added size variability are required for fission yeast to adapt to unfavorable environmental conditions.

Intracellular reaction rates depend on concentrations and hence their levels are often regulated. However classical models of stochastic gene expression lack a cell size description and cannot be used to predict noise in concentrations. Here, we construct a model of gene product dynamics that includes a description of cell growth, cell division, size-dependent gene expression, gene dosage compensation, and size control mechanisms that can vary with the cell cycle phase. We obtain expressions for the approximate distributions and power spectra of concentration fluctuations which lead to insight into the emergence of concentration homeostasis. We find that (i) the conditions necessary to suppress cell division-induced concentration oscillations are difficult to achieve; (ii) mRNA concentration and number distributions can have different number of modes; (iii) two-layer size control strategies such as sizer-timer or adder-timer are ideal because they maintain constant mean concentrations whilst minimising concentration noise; (iv) accurate concentration homeostasis requires a fine tuning of dosage compensation, replication timing, and size-dependent gene expression; (v) deviations from perfect concentration homeostasis show up as deviations of the concentration distribution from a gamma distribution. Some of these predictions are confirmed using data for E. coli, fission yeast, and budding yeast.

Inside individual cells, protein population counts are subject to molecular noise due to low copy numbers and the inherent probabilistic nature of biochemical processes. We investigate the effectiveness of proportional, integral and derivative (PID) based feedback controllers to suppress protein count fluctuations originating from two noise sources: bursty expression of the protein, and external disturbance in protein synthesis. Designs of biochemical reactions that function as PID controllers are discussed, with particular focus on individual controllers separately, and the corresponding closed-loop system is analyzed for stochastic controller realizations. Our results show that proportional controllers are effective in buffering protein copy number fluctuations from both noise sources, but this noise suppression comes at the cost of reduced static sensitivity of the output to the input signal. In contrast, integral feedback has no effect on the protein noise level from stochastic expression, but significantly minimizes the impact of external disturbances, particularly when the disturbance comes at low frequencies. Counter-intuitively, integral feedback is found to amplify external disturbances at intermediate frequencies. Next, we discuss the design of a coupled feedforward-feedback biochemical circuit that approximately functions as a derivate controller. Analysis using both analytical methods and Monte Carlo simulations reveals that this derivative controller effectively buffers output fluctuations from bursty stochastic expression, while maintaining the static input-output sensitivity of the open-loop system. In summary, this study provides a systematic stochastic analysis of biochemical controllers, and paves the way for their synthetic design and implementation to minimize deleterious fluctuations in gene product levels.

Intrinsic noise, which arises in gene expression at low copy numbers, can be controlled by diverse regulatory motifs, including feedforward loops. Here, we study an example of a feedforward control system based on the interaction between an mRNA molecule and an antagonistic microRNA molecule encoded by the same gene, aiming to quantify the variability (or noise) in molecular copy numbers. Using linear noise approximation, we show that the mRNA noise is sub-Poissonian in case of non-bursty transcription, and exhibits a nonmonotonic response both to the species natural lifetime ratio and to the strength of the antagonistic interaction. Additionally, we use the Chemical Reaction Network Theory to prove that the mRNA copy number distribution is Poissonian in the absence of spontaneous mRNA decay channel. In case of transcriptional bursts, we show that feedforward control can attenuate the super-Poissonian gene-expression noise that is due to bursting, and that the effect is more considerable at the protein than at the mRNA level. Our results indicate that the strong coupling between mRNA and microRNA in the sense of burst stoichiometry and also of timing of production events renders the microRNA based feedforward motif an effective mechanism for the control of gene expression noise.

One challenge in gene network inference is distinguishing between direct and indirect regulation. Some algorithms, including ARACNE and Phixer, approach this problem by using pruning methods to eliminate redundant edges in an attempt to explain the observed data with the simplest possible network structure. However, we hypothesize that there may be a cost in accuracy to simplifying the predicted networks in this way, especially due to the prevalence of redundant connections, such as feed forward loops, in gene networks. In this paper, we evaluate the pruning methods of ARACNE and Phixer, and score their accuracy using receiver operating characteristic curves and precision-recall curves. Our results suggest that while pruning can be useful in some situations, it may have a negative effect on overall accuracy that has not been previously studied. Researchers should be aware of both the advantages and disadvantages of pruning when inferring networks, in order to choose the best inference strategy for their experimental context.

BACKGROUND: How small, fast-growing bacteria ensure tight cell-size distributions remains elusive. High-throughput measurement techniques have propelled efforts to build modeling tools that help to shed light on the relationships between cell size, growth and cycle progression. Most proposed models describe cell division as a discrete map between size at birth and size at division with stochastic fluctuations assumed. However, such models underestimate the role of cell size transient dynamics by excluding them. RESULTS: We propose an efficient approach for estimation of cell size transient dynamics. Our technique approximates the transient size distribution and statistical moment dynamics of exponential growing cells following an adder strategy with arbitrary precision. CONCLUSIONS: We approximate, up to arbitrary precision, the distribution of division times and size across time for the adder strategy in rod-shaped bacteria cells. Our approach is able to compute statistical moments like mean size and its variance from such distributions efficiently, showing close match with numerical simulations. Additionally, we observed that these distributions have periodic properties. Our approach further might shed light on the mechanisms behind gene product homeostasis.

Inside individual cells, expression of genes is inherently stochastic and manifests as cell-to-cell variability or noise in protein copy numbers. Since proteins half-lives can be comparable to the cell-cycle length, randomness in cell-division times generates additional intercellular variability in protein levels. Moreover, as many mRNA/protein species are expressed at low-copy numbers, errors incurred in partitioning of molecules between two daughter cells are significant. We derive analytical formulas for the total noise in protein levels when the cell-cycle duration follows a general class of probability distributions. Using a novel hybrid approach the total noise is decomposed into components arising from i) stochastic expression; ii) partitioning errors at the time of cell division and iii) random cell-division events. These formulas reveal that random cell-division times not only generate additional extrinsic noise, but also critically affect the mean protein copy numbers and intrinsic noise components. Counter intuitively, in some parameter regimes, noise in protein levels can decrease as cell-division times become more stochastic. Computations are extended to consider genome duplication, where transcription rate is increased at a random point in the cell cycle. We systematically investigate how the timing of genome duplication influences different protein noise components. Intriguingly, results show that noise contribution from stochastic expression is minimized at an optimal genome-duplication time. Our theoretical results motivate new experimental methods for decomposing protein noise levels from synchronized and asynchronized single-cell expression data. Characterizing the contributions of individual noise mechanisms will lead to precise estimates of gene expression parameters and techniques for altering stochasticity to change phenotype of individual cells.

MOTIVATION: Stochastic promoter switching between transcriptionally active (ON) and inactive (OFF) states is a major source of noise in gene expression. It is often implicitly assumed that transitions between promoter states are memoryless, i.e. promoters spend an exponentially distributed time interval in each of the two states. However, increasing evidence suggests that promoter ON/OFF times can be non-exponential, hinting at more complex transcriptional regulatory architectures. Given the essential role of gene expression in all cellular functions, efficient computational techniques for characterizing promoter architectures are critically needed. RESULTS: We have developed a novel model reduction for promoters with arbitrary numbers of ON and OFF states, allowing us to approximate complex promoter switching behavior with Weibull-distributed ON/OFF times. Using this model reduction, we created bursty Monte Carlo expectation-maximization with modified cross-entropy method ('bursty MCEM(2)'), an efficient parameter estimation and model selection technique for inferring the number and configuration of promoter states from single-cell gene expression data. Application of bursty MCEM(2) to data from the endogenous mouse glutaminase promoter reveals nearly deterministic promoter OFF times, consistent with a multi-step activation mechanism consisting of 10 or more inactive states. Our novel approach to modeling promoter fluctuations together with bursty MCEM(2) provides powerful tools for characterizing transcriptional bursting across genes under different environmental conditions. AVAILABILITY AND IMPLEMENTATION: R source code implementing bursty MCEM(2) is available upon request. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Gene expression in individual cells is highly variable and sporadic, often resulting in the synthesis of mRNAs and proteins in bursts. Such bursting has important consequences for cell-fate decisions in diverse processes ranging from HIV-1 viral infections to stem-cell differentiation. It is generally assumed that bursts are geometrically distributed and that they arrive according to a Poisson process. On the other hand, recent single-cell experiments provide evidence for complex burst arrival processes, highlighting the need for analysis of more general stochastic models. To address this issue, we invoke a mapping between general stochastic models of gene expression and systems studied in queueing theory to derive exact analytical expressions for the moments associated with mRNA/protein steady-state distributions. These results are then used to derive noise signatures, i.e. explicit conditions based entirely on experimentally measurable quantities, that determine if the burst distributions deviate from the geometric distribution or if burst arrival deviates from a Poisson process. For non-Poisson arrivals, we develop approaches for accurate estimation of burst parameters. The proposed approaches can lead to new insights into transcriptional bursting based on measurements of steady-state mRNA/protein distributions.