Biology subjects

Abhyudai Singh

Publications and source records attributed to Abhyudai Singh.

9 recordsLinked to original sources

bioRxiv2016

Analysis of noise mechanisms in cell size control

At the single-cell level, noise features in multiple ways through the inherent stochasticity of biomolecular processes, random partitioning of resources at division, and fluctuations in cellular growth rates. How these diverse noise mechanisms combine to drive variations in cell size within an isoclonal population is not well understood. To address this problem, we systematically investigate the contributions of different noise sources in well-known paradigms of cell-size control, such as the adder (division occurs after adding a fixed size from birth) and the sizer (division occurs upon reaching a size threshold). Analysis reveals that variance in cell size is most sensitive to errors in partitioning of volume among daughter cells, and not surprisingly, this process is well regulated among microbes. Moreover, depending on the dominant noise mechanism, different size control strategies (or a combination of them) provide efficient buffering of intercellular size variations. We further explore mixer models of size control, where a timer phase precedes/follows an adder, as has been proposed in Caulobacter crescentus. While mixing a timer with an adder can sometimes attenuate size variations, it invariably leads to higher-order moments growing unboundedly over time. This results in the cell size following a power-law distribution with an exponent that is inversely dependent on the noise in the timer phase. Consistent with theory, we find evidence of power-law statistics in the tail of C. crescentus cell-size distribution, but there is a huge discrepancy in the power-law exponent as estimated from data and theory. However, the discrepancy is removed after data reveals that the size added by individual newborns from birth to division itself exhibits power-law statistics. Taken together, this study provides key insights into the role of noise mechanisms in size homeostasis, and suggests an inextricable link between timer-based models of size control and heavy-tailed cell size distributions.

Systems Biology↗

bioRxiv2016

Controlling noise in the timing of intracellular events: A first-passage time approach

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, in spite of 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. Novel analytical calculations are preformed for the first-passage time distribution in stochastic models of gene expression, including models with feedback regulation. 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. Counter-intuitively, 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{lambda} . Here, lysis of an infected bacterial cell is orchestrated by the expression and accumulation of a stable{lambda} 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.

Biophysics↗

bioRxiv2016

Cell-cycle coupled expression minimizes random fluctuations in gene product levels

Expression of many genes varies as a cell transitions through different cell-cycle stages. How coupling between stochastic expression and cell cycle impacts cell-to-cell variability (noise) in the level of protein is not well understood. We analyze a model, where a stable protein is synthesized in random bursts, and the frequency with which bursts occur varies within the cell cycle. Formulas quantifying the extent of fluctuations in the protein copy number are derived and decomposed into components arising from the cell cycle and stochastic processes. The latter stochastic component represents contributions from bursty expression and errors incurred during partitioning of molecules between daughter cells. These formulas reveal an interesting trade-off: cell-cycle dependencies that amplify the noise contribution from bursty expression also attenuate the contribution from partitioning errors. We investigate existence of optimum strategies for coupling expression to the cell cycle that minimize the stochastic component. Intriguingly, results show that a zero production rate throughout the cell cycle, with expression only occurring just before cell division minimizes noise from bursty expression for a fixed mean protein level. In contrast, the optimal strategy in the case of partitioning errors is to make the protein just after cell division. We provide examples of regulatory proteins that are expressed only towards the end of cell cycle, and argue that such strategies enhance robustness of cell-cycle decisions to the intrinsic stochasticity of gene expression.

Systems Biology↗

bioRxiv2016

Transcriptional bursting explains the noise-versus-mean relationship in mRNA and protein levels

Recent analysis (Dey et al, 2015), demonstrates that the HIV-1 Long Terminal Repeat (HIV LTR) promoter exhibits a range of possible transcriptional burst sizes and frequencies for any mean-expression level. However, these results have also been interpreted as demonstrating that cell-to-cell expression variability (noise) and mean are uncorrelated, a significant deviation from previous results. Here, we re-examine the available mRNA and protein abundance data for the HIV LTR and find that noise in mRNA and protein expression scales inversely with the mean along analytically predicted transcriptional burst-size manifolds. We then experimentally perturb transcriptional activity to test a prediction of the multiple burst-size model: that increasing burst frequency will cause mRNA noise to decrease along given burst-size lines as mRNA levels increase. The data show that mRNA and protein noise decrease as mean expression increases, supporting the canonical inverse correlation between noise and mean.\n\nConflict of InterestThe authors declare that they have no conflict of interest.

Systems Biology↗

bioRxiv2016

Hybrid systems approach to modeling stochastic dynamics of cell size

A ubiquitous feature of all living cells is their growth over time followed by division into two daughter cells. How a population of genetically identical cells maintains size homeostasis, i.e., a narrow distribution of cell size, is an intriguing fundamental problem. We model size using a stochastic hybrid system, where a cell grows exponentially over time and probabilistic division events are triggered at discrete time intervals. Moreover, whenever these events occur, size is randomly partitioned among daughter cells. We first consider a scenario, where a timer (i.e., cell-cycle clock) that measures the time since the last division event regulates cellular growth and the rate of cell division. Analysis reveals that such a timer-driven system cannot achieve size homeostasis, in the sense that, the cell-to-cell size variation grows unboundedly with time. To explore biologically meaningful mechanisms for controlling size we consider three different classes of models: i) a size-dependent growth rate and timer-dependent division rate; ii) a constant growth rate and size-dependent division rate and iii) a constant growth rate and division rate that depends both on the cell size and timer. We show that each of these strategies can potentially achieve bounded intercellular size variation, and derive closed-form expressions for this variation in terms of underlying model parameters. Finally, we discuss how different organisms have adopted the above strategies for maintaining cell size homeostasis.

Systems Biology↗

bioRxiv2015

A mechanistic first-passage time framework for bacterial cell-division timing

How exponentially growing cells maintain size homeostasis is an important fundamental problem. Recent single-cell studies in prokaryotes have uncovered the adder principle, where cells on average, add a fixed size (volume) from birth to division. Interestingly, this added volume differs considerably among genetically-identical newborn cells with similar sizes suggesting a stochastic component in the timing of cell-division. To mechanistically explain the adder principle, we consider a time-keeper protein that begins to get stochastically expressed after cell birth at a rate proportional to the volume. Cell-division time is formulated as the first-passage time for protein copy numbers to hit a fixed threshold. Consistent with data, the model predicts that while the mean cell-division time decreases with increasing size of newborns, the noise in timing increases with size at birth. Intriguingly, our results show that the distribution of the volume added between successive cell-division events is independent of the newborn cell size. This was dramatically seen in experimental studies, where histograms of the added volume corresponding to different newborn sizes collapsed on top of each other. The model provides further insights consistent with experimental observations: the distributions of the added volume and the cell-division time when scaled by their respective means become invariant of the growth rate. Finally, we discuss various modifications to the proposed model that lead to deviations from the adder principle. In summary, our simple yet elegant model explains key experimental findings and suggests a mechanism for regulating both the mean and fluctuations in cell-division timing for size control.

Systems Biology↗

bioRxiv2015

Stochastic Analysis Of An Incoherent Feedforward Genetic Motif

Gene products (RNAs, proteins) often occur at low molecular counts inside individual cells, and hence are subject to considerable random fluctuations (noise) in copy number over time. Not surprisingly, cells encode diverse regulatory mechanisms to buffer noise. One such mechanism is the incoherent feedforward circuit. We analyze a simplistic version of this circuit, where an upstream regulator X affects both the production and degradation of a protein Y. Thus, any random increase in Xs copy numbers would increase both production and degradation, keeping Y levels unchanged. To study its stochastic dynamics, we formulate this network into a mathematical model using the Chemical Master Equation formulation. We prove that if the functional dependence of Ys production and degradation on X is similar, then the steady-distribution of Ys copy numbers is independent of X. To investigate how fluctuations in Y propagate downstream, a protein Z whose production rate only depend on Y is introduced. Intriguingly, results show that the extent of noise in Z increases with noise in X, in spite of the fact that the magnitude of noise in Y is invariant of X. Such counter intuitive results arise because X enhances the time-scale of fluctuations in Y, which amplifies fluctuations in downstream processes. In summary, while feedforward systems can buffer a protein from noise in its upstream regulators, noise can propagate downstream due to changes in the time-scale of fluctuations.

Molecular Biology↗

bioRxiv2015

Decomposing variability in protein levels from noisy expression, genome duplication and partitioning errors during cell-divisions

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 the mother and daughter cells are significant. We derive analytical formulas for the total noise in protein levels for a general class of cell-division time and partitioning error 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 the gene dosage is increased by two-fold 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 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.

Systems Biology↗

bioRxiv2015

Some remarks on moments for stochastic chemical kinetics

We analyze a class of chemical reaction networks for which all moments can be computed by finite-dimensional linear differential equations. This class allows second and higher order reactions, but only under special assumptions on structure and/or conservation laws.

Systems Biology↗