153 research outputs found
Statistical mechanics of transcription-factor binding site discovery using Hidden Markov Models
Hidden Markov Models (HMMs) are a commonly used tool for inference of
transcription factor (TF) binding sites from DNA sequence data. We exploit the
mathematical equivalence between HMMs for TF binding and the "inverse"
statistical mechanics of hard rods in a one-dimensional disordered potential to
investigate learning in HMMs. We derive analytic expressions for the Fisher
information, a commonly employed measure of confidence in learned parameters,
in the biologically relevant limit where the density of binding sites is low.
We then use techniques from statistical mechanics to derive a scaling principle
relating the specificity (binding energy) of a TF to the minimum amount of
training data necessary to learn it.Comment: 25 pages, 2 figures, 1 table V2 - typos fixed and new references
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Deterministic and stochastic descriptions of gene expression dynamics
A key goal of systems biology is the predictive mathematical description of
gene regulatory circuits. Different approaches are used such as deterministic
and stochastic models, models that describe cell growth and division explicitly
or implicitly etc. Here we consider simple systems of unregulated
(constitutive) gene expression and compare different mathematical descriptions
systematically to obtain insight into the errors that are introduced by various
common approximations such as describing cell growth and division by an
effective protein degradation term. In particular, we show that the population
average of protein content of a cell exhibits a subtle dependence on the
dynamics of growth and division, the specific model for volume growth and the
age structure of the population. Nevertheless, the error made by models with
implicit cell growth and division is quite small. Furthermore, we compare
various models that are partially stochastic to investigate the impact of
different sources of (intrinsic) noise. This comparison indicates that
different sources of noise (protein synthesis, partitioning in cell division)
contribute comparable amounts of noise if protein synthesis is not or only
weakly bursty. If protein synthesis is very bursty, the burstiness is the
dominant noise source, independent of other details of the model. Finally, we
discuss two sources of extrinsic noise: cell-to-cell variations in protein
content due to cells being at different stages in the division cycles, which we
show to be small (for the protein concentration and, surprisingly, also for the
protein copy number per cell) and fluctuations in the growth rate, which can
have a significant impact.Comment: 23 pages, 5 figures; Journal of Statistical physics (2012
A line-of-sight electron cyclotron emission receiver for electron cyclotron resonance heating feedback control of tearing modes
An electron cyclotron emission (ECE) receiver inside the electron cyclotron resonance heating (ECRH) transmission line has been brought into operation. The ECE is extracted by placing a quartz plate acting as a FabryÂżPerot interferometer under an angle inside the electron cyclotron wave (ECW) beam. ECE measurements are obtained during high power ECRH operation. Thisdemonstrates the successful operation of the diagnostic and, in particular, a sufficient suppression of the gyrotron component preventing it from interfering with ECE measurements. When integratedinto a feedback system for the control of plasma instabilities this line-of-sight ECE diagnosticremoves the need to localize the instabilities in absolute coordinates
Mean first-passage time of surface-mediated diffusion in spherical domains
We present an exact calculation of the mean first-passage time to a target on
the surface of a 2D or 3D spherical domain, for a molecule alternating phases
of surface diffusion on the domain boundary and phases of bulk diffusion. The
presented approach is based on an integral equation which can be solved
analytically. Numerically validated approximation schemes, which provide more
tractable expressions of the mean first-passage time are also proposed. In the
framework of this minimal model of surface-mediated reactions, we show
analytically that the mean reaction time can be minimized as a function of the
desorption rate from the surface.Comment: to appear in J. Stat. Phy
Kinetics of active surface-mediated diffusion in spherically symmetric domains
We present an exact calculation of the mean first-passage time to a target on
the surface of a 2D or 3D spherical domain, for a molecule alternating phases
of surface diffusion on the domain boundary and phases of bulk diffusion. We
generalize the results of [J. Stat. Phys. {\bf 142}, 657 (2011)] and consider a
biased diffusion in a general annulus with an arbitrary number of regularly
spaced targets on a partially reflecting surface. The presented approach is
based on an integral equation which can be solved analytically. Numerically
validated approximation schemes, which provide more tractable expressions of
the mean first-passage time are also proposed. In the framework of this minimal
model of surface-mediated reactions, we show analytically that the mean
reaction time can be minimized as a function of the desorption rate from the
surface.Comment: Published online in J. Stat. Phy
Salerno's model of DNA reanalysed: could solitons have biological significance?
We investigate the sequence-dependent behaviour of localised excitations in a
toy, nonlinear model of DNA base-pair opening originally proposed by Salerno.
Specifically we ask whether ``breather'' solitons could play a role in the
facilitated location of promoters by RNA polymerase. In an effective potential
formalism, we find excellent correlation between potential minima and {\em
Escherichia coli} promoter recognition sites in the T7 bacteriophage genome.
Evidence for a similar relationship between phage promoters and downstream
coding regions is found and alternative reasons for links between AT richness
and transcriptionally-significant sites are discussed. Consideration of the
soliton energy of translocation provides a novel dynamical picture of sliding:
steep potential gradients correspond to deterministic motion, while ``flat''
regions, corresponding to homogeneous AT or GC content, are governed by random,
thermal motion. Finally we demonstrate an interesting equivalence between
planar, breather solitons and the helical motion of a sliding protein
``particle'' about a bent DNA axis.Comment: Latex file 20 pages, 5 figures. Manuscript of paper to appear in J.
Biol. Phys., accepted 02/09/0
Gene Regulation in the Pi Calculus: Simulating Cooperativity at the Lambda Switch
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4230).Also part of the Lecture Notes in Bioinformatics book sub series (volume 4230).International audienceWe propose to model the dynamics of gene regulatory networks as concurrent processes in the stochastic pi calculus. As a first case study, we show how to express the control of transcription initiation at the lambda switch, a prototypical example where cooperative enhancement is crucial. This requires concurrent programming techniques that are new to systems biology, and necessitates stochastic parameters that we derive from the literature. We test all components of our model by exhaustive stochastic simulations. A comparison with previous results reported in the literature, experimental and simulation based, confirms the appropriateness of our modeling approach
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