arXiv subjects

F. Hayot

Publications and source records attributed to F. Hayot.

5 recordsLinked to original sources

arXiv2007

Transcriptional pulsing and consequent stochasticity in gene expression

Transcriptional pulsing has been observed in both prokaryotes and eukaryotes and plays a crucial role in cell to cell variability of protein and mRNA numbers. The issue is how the time constants associated with episodes of transcriptional bursting impact cellular mRNA and protein distributions and reciprocally, to what extent experimentally observed distributions can be attributed to transcriptional pulsing. We address these questions by investigating the exact time-dependent solution of the Master equation for a transcriptional pulsing model of mRNA distributions. We find a plethora of results: we show that, among others, bimodal and long-tailed (power law) distributions occur in the steady state as the rate constants are varied over biologically significant time scales. Since steady state distributions may not be reached experimentally we present results for the time evolution of the distributions. Because cellular behavior is essentially determined by proteins, we investigate the effect of the different mRNA distributions on the corresponding protein distributions. We delineate the regimes of rate constants for which the protein distribution mimics the mRNA distribution and those for which the protein distribution deviates significantly from the mRNA distribution.

q-bio.QM↗

arXiv2005

NF-kappa B oscillations and cell-to-cell variability

Oscillations of the transcription factor NF-kappa B have been observed experimentally both for cell populations by Hoffmann et al. (2002) and for single cells by Nelson et al. (2004). The latter experiments show significant cell-to-cell variability. We use the (stochastic) Gillespie algorithm to study the set of reactions proposed by Hoffmann et al. and variants thereof. The amounts of cellular NF-kappa B and activated kinase IKK are treated as external parameters. We show that intrinsic fluctuations are small in a model with strong transcription, while they are large for weak transcription. Extrinsic noise can be significant: fluctuations in NF-kappa B affect mainly the amplitude of oscillations, whereas fluctuations in activated IKK affect both their amplitude and period. The latter results are in qualitative agreement with the observations of Nelson et al.

q-bio.QM↗

arXiv2002

An exact derivation of the dissipation rate correlation exponent μin fully-developed turbulence

We derive for the Navier-Stokes equation an exact equation satisfied by the dissipation rate correlation function. In the equal time limit, in the inertial range, for the homogeneous, isotropic state of fully-developed turbulence, we show that the correlation is characterized by two exponents, one of which depends on the sixth-order static structure function exponent and the other involves the behavior of the fourth-order dynamical structure function. This provides a direct derivation of the intermittency exponent of the dissipation-rate correlation.

nlin.CD↗

arXiv2000

Aspects of the stochastic Burgers equation and their connection with turbulence

We present results for the 1 dimensional stochastically forced Burgers equation when the spatial range of the forcing varies. As the range of forcing moves from small scales to large scales, the system goes from a chaotic, structureless state to a structured state dominated by shocks. This transition takes place through an intermediate region where the system exhibits rich multifractal behavior. This is mainly the region of interest to us. We only mention in passing the hydrodynamic limit of forcing confined to large scales, where much work has taken place since that of Polyakov. In order to make the general framework clear, we give an introduction to aspects of isotropic, homogeneous turbulence, a description of Kolmogorov scaling, and, with the help of a simple model, an introduction to the language of multifractality which is used to discuss intermittency corrections to scaling. We continue with a general discussion of the Burgers equation and forcing, and some aspects of three dimensional turbulence where - because of the mathematical analogy between equations derived from the Navier-Stokes and Burgers equations - one can gain insight from the study of the simpler stochastic Burgers equation. These aspects concern the connection of dissipation rate intermittency exponents with those characterizing the structure functions of the velocity field, and the dynamical behavior, characterized by different time constants, of velocity structure functions. We also show how the exponents characterizing the multifractal behavior of velocity structure functions in the above mentioned transition region can effectively be calculated in the case of the stochastic Burgers equation.

nlin.CD↗

arXiv1999

Intermittency in Turbulence

We derive from the Navier-Stokes equation an exact equation satisfied by the dissipation rate correlation function. We exploit its mathematical similarity to the corresponding equation derived from the 1-dimensional stochastic Burgers equation to determine the intermittency exponents in terms of the exponents characterizing the behavior of the dynamical velocity structure functions. We discuss the role of sweeping and Galilean invariance in determining the intermittency exponents

chao-dyn↗