344 research outputs found
Epigenetic Chromatin Silencing: Bistability and Front Propagation
The role of post-translational modification of histones in eukaryotic gene
regulation is well recognized. Epigenetic silencing of genes via heritable
chromatin modifications plays a major role in cell fate specification in higher
organisms. We formulate a coarse-grained model of chromatin silencing in yeast
and study the conditions under which the system becomes bistable, allowing for
different epigenetic states. We also study the dynamics of the boundary between
the two locally stable states of chromatin: silenced and unsilenced. The model
could be of use in guiding the discussion on chromatin silencing in general. In
the context of silencing in budding yeast, it helps us understand the phenotype
of various mutants, some of which may be non-trivial to see without the help of
a mathematical model. One such example is a mutation that reduces the rate of
background acetylation of particular histone side-chains that competes with the
deacetylation by Sir2p. The resulting negative feedback due to a Sir protein
depletion effect gives rise to interesting counter-intuitive consequences. Our
mathematical analysis brings forth the different dynamical behaviors possible
within the same molecular model and guides the formulation of more refined
hypotheses that could be addressed experimentally.Comment: 19 pages, 5 figure
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
Genetic noise control via protein oligomerization
Gene expression in a cell entails random reaction events occurring over
disparate time scales. Thus, molecular noise that often results in phenotypic
and population-dynamic consequences sets a fundamental limit to biochemical
signaling. While there have been numerous studies correlating the architecture
of cellular reaction networks with noise tolerance, only a limited effort has
been made to understand the dynamic role of protein-protein interactions. Here
we have developed a fully stochastic model for the positive feedback control of
a single gene, as well as a pair of genes (toggle switch), integrating
quantitative results from previous in vivo and in vitro studies. We find that
the overall noise-level is reduced and the frequency content of the noise is
dramatically shifted to the physiologically irrelevant high-frequency regime in
the presence of protein dimerization. This is independent of the choice of
monomer or dimer as transcription factor and persists throughout the multiple
model topologies considered. For the toggle switch, we additionally find that
the presence of a protein dimer, either homodimer or heterodimer, may
significantly reduce its random switching rate. Hence, the dimer promotes the
robust function of bistable switches by preventing the uninduced (induced)
state from randomly being induced (uninduced). The specific binding between
regulatory proteins provides a buffer that may prevent the propagation of
fluctuations in genetic activity. The capacity of the buffer is a non-monotonic
function of association-dissociation rates. Since the protein oligomerization
per se does not require extra protein components to be expressed, it provides a
basis for the rapid control of intrinsic or extrinsic noise
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
A Genome-Wide Analysis of Promoter-Mediated Phenotypic Noise in Escherichia coli
Gene expression is subject to random perturbations that lead to fluctuations in the rate of protein production. As a consequence, for any given protein, genetically identical organisms living in a constant environment will contain different amounts of that particular protein, resulting in different phenotypes. This phenomenon is known as “phenotypic noise.” In bacterial systems, previous studies have shown that, for specific genes, both transcriptional and translational processes affect phenotypic noise. Here, we focus on how the promoter regions of genes affect noise and ask whether levels of promoter-mediated noise are correlated with genes' functional attributes, using data for over 60% of all promoters in Escherichia coli. We find that essential genes and genes with a high degree of evolutionary conservation have promoters that confer low levels of noise. We also find that the level of noise cannot be attributed to the evolutionary time that different genes have spent in the genome of E. coli. In contrast to previous results in eukaryotes, we find no association between promoter-mediated noise and gene expression plasticity. These results are consistent with the hypothesis that, in bacteria, natural selection can act to reduce gene expression noise and that some of this noise is controlled through the sequence of the promoter region alon
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
Connecting Variability in Global Transcription Rate to Mitochondrial Variability
The authors demonstrate a connection between variability in the rate of transcription and differences in cellular mitochondrial content
Complex and unexpected dynamics in simple genetic regulatory networks
Peer reviewedPublisher PD
Safe uses of Hill's model: an exact comparison with the Adair-Klotz model
<p>Abstract</p> <p>Background</p> <p>The Hill function and the related Hill model are used frequently to study processes in the living cell. There are very few studies investigating the situations in which the model can be safely used. For example, it has been shown, at the mean field level, that the dose response curve obtained from a Hill model agrees well with the dose response curves obtained from a more complicated Adair-Klotz model, provided that the parameters of the Adair-Klotz model describe strongly cooperative binding. However, it has not been established whether such findings can be extended to other properties and non-mean field (stochastic) versions of the same, or other, models.</p> <p>Results</p> <p>In this work a rather generic quantitative framework for approaching such a problem is suggested. The main idea is to focus on comparing the particle number distribution functions for Hill's and Adair-Klotz's models instead of investigating a particular property (e.g. the dose response curve). The approach is valid for any model that can be mathematically related to the Hill model. The Adair-Klotz model is used to illustrate the technique. One main and two auxiliary similarity measures were introduced to compare the distributions in a quantitative way. Both time dependent and the equilibrium properties of the similarity measures were studied.</p> <p>Conclusions</p> <p>A strongly cooperative Adair-Klotz model can be replaced by a suitable Hill model in such a way that any property computed from the two models, even the one describing stochastic features, is approximately the same. The quantitative analysis showed that boundaries of the regions in the parameter space where the models behave in the same way exhibit a rather rich structure.</p
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
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