169 research outputs found
The transition between stochastic and deterministic behavior in an excitable gene circuit
We explore the connection between a stochastic simulation model and an
ordinary differential equations (ODEs) model of the dynamics of an excitable
gene circuit that exhibits noise-induced oscillations. Near a bifurcation point
in the ODE model, the stochastic simulation model yields behavior dramatically
different from that predicted by the ODE model. We analyze how that behavior
depends on the gene copy number and find very slow convergence to the large
number limit near the bifurcation point. The implications for understanding the
dynamics of gene circuits and other birth-death dynamical systems with small
numbers of constituents are discussed.Comment: PLoS ONE: Research Article, published 11 Apr 201
Nonidentifiability of the Source of Intrinsic Noise in Gene Expression from Single-Burst Data
Over the last few years, experimental data on the fluctuations in gene activity
between individual cells and within the same cell over time have confirmed that
gene expression is a “noisy” process. This variation is in
part due to the small number of molecules taking part in some of the key
reactions that are involved in gene expression. One of the consequences of this
is that protein production often occurs in bursts, each due to a single promoter
or transcription factor binding event. Recently, the distribution of the number
of proteins produced in such bursts has been experimentally measured, offering a
unique opportunity to study the relative importance of different sources of
noise in gene expression. Here, we provide a derivation of the theoretical
probability distribution of these bursts for a wide variety of different models
of gene expression. We show that there is a good fit between our theoretical
distribution and that obtained from two different published experimental
datasets. We then prove that, irrespective of the details of the model, the
burst size distribution is always geometric and hence determined by a single
parameter. Many different combinations of the biochemical rates for the
constituent reactions of both transcription and translation will therefore lead
to the same experimentally observed burst size distribution. It is thus
impossible to identify different sources of fluctuations purely from protein
burst size data or to use such data to estimate all of the model parameters. We
explore methods of inferring these values when additional types of experimental
data are available
Bayesian inference of biochemical kinetic parameters using the linear noise approximation
Background
Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data.
Results
We use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo.
Conclusion
The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods
Regulatory control and the costs and benefits of biochemical noise
Experiments in recent years have vividly demonstrated that gene expression
can be highly stochastic. How protein concentration fluctuations affect the
growth rate of a population of cells, is, however, a wide open question. We
present a mathematical model that makes it possible to quantify the effect of
protein concentration fluctuations on the growth rate of a population of
genetically identical cells. The model predicts that the population's growth
rate depends on how the growth rate of a single cell varies with protein
concentration, the variance of the protein concentration fluctuations, and the
correlation time of these fluctuations. The model also predicts that when the
average concentration of a protein is close to the value that maximizes the
growth rate, fluctuations in its concentration always reduce the growth rate.
However, when the average protein concentration deviates sufficiently from the
optimal level, fluctuations can enhance the growth rate of the population, even
when the growth rate of a cell depends linearly on the protein concentration.
The model also shows that the ensemble or population average of a quantity,
such as the average protein expression level or its variance, is in general not
equal to its time average as obtained from tracing a single cell and its
descendants. We apply our model to perform a cost-benefit analysis of gene
regulatory control. Our analysis predicts that the optimal expression level of
a gene regulatory protein is determined by the trade-off between the cost of
synthesizing the regulatory protein and the benefit of minimizing the
fluctuations in the expression of its target gene. We discuss possible
experiments that could test our predictions.Comment: Revised manuscript;35 pages, 4 figures, REVTeX4; to appear in PLoS
Computational Biolog
Interplay between pleiotropy and secondary selection determines rise and fall of mutators in stress response
Dramatic rise of mutators has been found to accompany adaptation of bacteria
in response to many kinds of stress. Two views on the evolutionary origin of
this phenomenon emerged: the pleiotropic hypothesis positing that it is a
byproduct of environmental stress or other specific stress response mechanisms
and the second order selection which states that mutators hitchhike to fixation
with unrelated beneficial alleles. Conventional population genetics models
could not fully resolve this controversy because they are based on certain
assumptions about fitness landscape. Here we address this problem using a
microscopic multiscale model, which couples physically realistic molecular
descriptions of proteins and their interactions with population genetics of
carrier organisms without assuming any a priori fitness landscape. We found
that both pleiotropy and second order selection play a crucial role at
different stages of adaptation: the supply of mutators is provided through
destabilization of error correction complexes or fluctuations of production
levels of prototypic mismatch repair proteins (pleiotropic effects), while rise
and fixation of mutators occur when there is a sufficient supply of beneficial
mutations in replication-controlling genes. This general mechanism assures a
robust and reliable adaptation of organisms to unforeseen challenges. This
study highlights physical principles underlying physical biological mechanisms
of stress response and adaptation
Transport mode choice and body mass index: Cross-sectional and longitudinal evidence from a European-wide study.
BACKGROUND: In the fight against rising overweight and obesity levels, and unhealthy urban environments, the renaissance of active mobility (cycling and walking as a transport mode) is encouraging. Transport mode has been shown to be associated to body mass index (BMI), yet there is limited longitudinal evidence demonstrating causality. We aimed to associate transport mode and BMI cross-sectionally, but also prospectively in the first ever European-wide longitudinal study on transport and health. METHODS: Data were from the PASTA project that recruited adults in seven European cities (Antwerp, Barcelona, London, Oerebro, Rome, Vienna, Zurich) to complete a series of questionnaires on travel behavior, physical activity levels, and BMI. To assess the association between transport mode and BMI as well as change in BMI we performed crude and adjusted linear mixed-effects modeling for cross-sectional (n = 7380) and longitudinal (n = 2316) data, respectively. RESULTS: Cross-sectionally, BMI was 0.027 kg/m2 (95%CI 0.015 to 0.040) higher per additional day of car use per month. Inversely, BMI was -0.010 kg/m2 (95%CI -0.020 to -0.0002) lower per additional day of cycling per month. Changes in BMI were smaller in the longitudinal within-person assessment, however still statistically significant. BMI decreased in occasional (less than once per week) and non-cyclists who increased cycling (-0.303 kg/m2, 95%CI -0.530 to -0.077), while frequent (at least once per week) cyclists who stopped cycling increased their BMI (0.417 kg/m2, 95%CI 0.033 to 0.802). CONCLUSIONS: Our analyses showed that people lower their BMI when starting or increasing cycling, demonstrating the health benefits of active mobility
Stochastic E2F Activation and Reconciliation of Phenomenological Cell-Cycle Models
A new, stochastic model of entry into the mammalian cell cycle provides a mechanistic understanding of the temporal variability observed across populations of cells and reconciles previously proposed phenomenological cell-cycle models
Effect of promoter architecture on the cell-to-cell variability in gene expression
According to recent experimental evidence, the architecture of a promoter,
defined as the number, strength and regulatory role of the operators that
control the promoter, plays a major role in determining the level of
cell-to-cell variability in gene expression. These quantitative experiments
call for a corresponding modeling effort that addresses the question of how
changes in promoter architecture affect noise in gene expression in a
systematic rather than case-by-case fashion. In this article, we make such a
systematic investigation, based on a simple microscopic model of gene
regulation that incorporates stochastic effects. In particular, we show how
operator strength and operator multiplicity affect this variability. We examine
different modes of transcription factor binding to complex promoters
(cooperative, independent, simultaneous) and how each of these affects the
level of variability in transcription product from cell-to-cell. We propose
that direct comparison between in vivo single-cell experiments and theoretical
predictions for the moments of the probability distribution of mRNA number per
cell can discriminate between different kinetic models of gene regulation.Comment: 35 pages, 6 figures, Submitte
Evaluating Gene Expression Dynamics Using Pairwise RNA FISH Data
Recently, a novel approach has been developed to study gene expression in single cells with high time resolution using RNA Fluorescent In Situ Hybridization (FISH). The technique allows individual mRNAs to be counted with high accuracy in wild-type cells, but requires cells to be fixed; thus, each cell provides only a “snapshot” of gene expression. Here we show how and when RNA FISH data on pairs of genes can be used to reconstruct real-time dynamics from a collection of such snapshots. Using maximum-likelihood parameter estimation on synthetically generated, noisy FISH data, we show that dynamical programs of gene expression, such as cycles (e.g., the cell cycle) or switches between discrete states, can be accurately reconstructed. In the limit that mRNAs are produced in short-lived bursts, binary thresholding of the FISH data provides a robust way of reconstructing dynamics. In this regime, prior knowledge of the type of dynamics – cycle versus switch – is generally required and additional constraints, e.g., from triplet FISH measurements, may also be needed to fully constrain all parameters. As a demonstration, we apply the thresholding method to RNA FISH data obtained from single, unsynchronized cells of Saccharomyces cerevisiae. Our results support the existence of metabolic cycles and provide an estimate of global gene-expression noise. The approach to FISH data presented here can be applied in general to reconstruct dynamics from snapshots of pairs of correlated quantities including, for example, protein concentrations obtained from immunofluorescence assays
Noise Reduction by Diffusional Dissipation in a Minimal Quorum Sensing Motif
Cellular interactions are subject to random fluctuations (noise) in quantities of interacting molecules. Noise presents a major challenge for the robust function of natural and engineered cellular networks. Past studies have analyzed how noise is regulated at the intracellular level. Cell–cell communication, however, may provide a complementary strategy to achieve robust gene expression by enabling the coupling of a cell with its environment and other cells. To gain insight into this issue, we have examined noise regulation by quorum sensing (QS), a mechanism by which many bacteria communicate through production and sensing of small diffusible signals. Using a stochastic model, we analyze a minimal QS motif in Gram-negative bacteria. Our analysis shows that diffusion of the QS signal, together with fast turnover of its transcriptional regulator, attenuates low-frequency components of extrinsic noise. We term this unique mechanism “diffusional dissipation” to emphasize the importance of fast signal turnover (or dissipation) by diffusion. We further show that this noise attenuation is a property of a more generic regulatory motif, of which QS is an implementation. Our results suggest that, in a QS system, an unstable transcriptional regulator may be favored for regulating expression of costly proteins that generate public goods
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