16 research outputs found
Fitness in time-dependent environments includes a geometric contribution
Phenotypic evolution implies sequential fixations of new genomic sequences.
The speed at which these mutations fixate depends, in part, on the relative
fitness (selection coefficient) of the mutant vs. the ancestor. Using a simple
population dynamics model we show that the relative fitness in dynamical
environments is not equal to the fitness averaged over individual environments.
Instead it includes a term that explicitly depends on the sequence of the
environments. This term is geometric in nature and depends only on the oriented
area enclosed by the trajectory taken by the system in the environment state
space. It is related to the well-studied geometric phases in classical and
quantum physical systems. We discuss possible biological implications of these
observations, focusing on evolution of novel metabolic or stress-resistant
functions
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
Investigating Rare Events by Transition Interface Sampling
We briefly review simulation schemes for the investigation of rare
transitions and we resume the recently introduced Transition Interface
Sampling, a method in which the computation of rate constants is recast into
the computation of fluxes through interfaces dividing the reactant and product
state.Comment: 12 pages, 1 figure, contributed paper to the proceedings of NEXT
2003, Second Sardinian International Conference on News and Expectations in
Thermostatistics, 21-28 Sep 2003, Cagliari (Italy
The fidelity of dynamic signaling by noisy biomolecular networks
This is the final version of the article. Available from Public Library of Science via the DOI in this record.Cells live in changing, dynamic environments. To understand cellular decision-making, we must therefore understand how fluctuating inputs are processed by noisy biomolecular networks. Here we present a general methodology for analyzing the fidelity with which different statistics of a fluctuating input are represented, or encoded, in the output of a signaling system over time. We identify two orthogonal sources of error that corrupt perfect representation of the signal: dynamical error, which occurs when the network responds on average to other features of the input trajectory as well as to the signal of interest, and mechanistic error, which occurs because biochemical reactions comprising the signaling mechanism are stochastic. Trade-offs between these two errors can determine the system's fidelity. By developing mathematical approaches to derive dynamics conditional on input trajectories we can show, for example, that increased biochemical noise (mechanistic error) can improve fidelity and that both negative and positive feedback degrade fidelity, for standard models of genetic autoregulation. For a group of cells, the fidelity of the collective output exceeds that of an individual cell and negative feedback then typically becomes beneficial. We can also predict the dynamic signal for which a given system has highest fidelity and, conversely, how to modify the network design to maximize fidelity for a given dynamic signal. Our approach is general, has applications to both systems and synthetic biology, and will help underpin studies of cellular behavior in natural, dynamic environments.We acknowledge support from a Medical Research Council and Engineering and Physical Sciences Council funded Fellowship in Biomedical Informatics (CGB) and a Scottish Universities Life Sciences Alliance chair in Systems Biology (PSS). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript
Thermodynamic formalism for systems with Markov dynamics
The thermodynamic formalism allows one to access the chaotic properties of
equilibrium and out-of-equilibrium systems, by deriving those from a dynamical
partition function. The definition that has been given for this partition
function within the framework of discrete time Markov chains was not suitable
for continuous time Markov dynamics. Here we propose another interpretation of
the definition that allows us to apply the thermodynamic formalism to
continuous time.
We also generalize the formalism --a dynamical Gibbs ensemble construction--
to a whole family of observables and their associated large deviation
functions. This allows us to make the connection between the thermodynamic
formalism and the observable involved in the much-studied fluctuation theorem.
We illustrate our approach on various physical systems: random walks,
exclusion processes, an Ising model and the contact process. In the latter
cases, we identify a signature of the occurrence of dynamical phase
transitions. We show that this signature can already be unravelled using the
simplest dynamical ensemble one could define, based on the number of
configuration changes a system has undergone over an asymptotically large time
window.Comment: 64 pages, LaTeX; version accepted for publication in Journal of
Statistical Physic
Adjusting Phenotypes by Noise Control
Genetically identical cells can show phenotypic variability. This is often caused by stochastic events that originate from randomness in biochemical processes involving in gene expression and other extrinsic cellular processes. From an engineering perspective, there have been efforts focused on theory and experiments to control noise levels by perturbing and replacing gene network components. However, systematic methods for noise control are lacking mainly due to the intractable mathematical structure of noise propagation through reaction networks. Here, we provide a numerical analysis method by quantifying the parametric sensitivity of noise characteristics at the level of the linear noise approximation. Our analysis is readily applicable to various types of noise control and to different types of system; for example, we can orthogonally control the mean and noise levels and can control system dynamics such as noisy oscillations. As an illustration we applied our method to HIV and yeast gene expression systems and metabolic networks. The oscillatory signal control was applied to p53 oscillations from DNA damage. Furthermore, we showed that the efficiency of orthogonal control can be enhanced by applying extrinsic noise and feedback. Our noise control analysis can be applied to any stochastic model belonging to continuous time Markovian systems such as biological and chemical reaction systems, and even computer and social networks. We anticipate the proposed analysis to be a useful tool for designing and controlling synthetic gene networks
Fuselage, Wing, Elevator Entstehung, Wahl und Entwicklung zentraler englischer Termini der Luftfahrt ''schwerer als Luft''
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