7,385 research outputs found
Compositionality, stochasticity and cooperativity in dynamic models of gene regulation
We present an approach for constructing dynamic models for the simulation of
gene regulatory networks from simple computational elements. Each element is
called a ``gene gate'' and defines an input/output-relationship corresponding
to the binding and production of transcription factors. The proposed reaction
kinetics of the gene gates can be mapped onto stochastic processes and the
standard ode-description. While the ode-approach requires fixing the system's
topology before its correct implementation, expressing them in stochastic
pi-calculus leads to a fully compositional scheme: network elements become
autonomous and only the input/output relationships fix their wiring. The
modularity of our approach allows to pass easily from a basic first-level
description to refined models which capture more details of the biological
system. As an illustrative application we present the stochastic repressilator,
an artificial cellular clock, which oscillates readily without any cooperative
effects.Comment: 15 pages, 8 figures. Accepted by the HFSP journal (13/09/07
Stochastic timing in gene expression for simple regulatory strategies
Timing is essential for many cellular processes, from cellular responses to
external stimuli to the cell cycle and circadian clocks. Many of these
processes are based on gene expression. For example, an activated gene may be
required to reach in a precise time a threshold level of expression that
triggers a specific downstream process. However, gene expression is subject to
stochastic fluctuations, naturally inducing an uncertainty in this
threshold-crossing time with potential consequences on biological functions and
phenotypes. Here, we consider such "timing fluctuations", and we ask how they
can be controlled. Our analytical estimates and simulations show that, for an
induced gene, timing variability is minimal if the threshold level of
expression is approximately half of the steady-state level. Timing fuctuations
can be reduced by increasing the transcription rate, while they are insensitive
to the translation rate. In presence of self-regulatory strategies, we show
that self-repression reduces timing noise for threshold levels that have to be
reached quickly, while selfactivation is optimal at long times. These results
lay a framework for understanding stochasticity of endogenous systems such as
the cell cycle, as well as for the design of synthetic trigger circuits.Comment: 10 pages, 5 figure
The stochastic behavior of a molecular switching circuit with feedback
Background: Using a statistical physics approach, we study the stochastic
switching behavior of a model circuit of multisite phosphorylation and
dephosphorylation with feedback. The circuit consists of a kinase and
phosphatase acting on multiple sites of a substrate that, contingent on its
modification state, catalyzes its own phosphorylation and, in a symmetric
scenario, dephosphorylation. The symmetric case is viewed as a cartoon of
conflicting feedback that could result from antagonistic pathways impinging on
the state of a shared component.
Results: Multisite phosphorylation is sufficient for bistable behavior under
feedback even when catalysis is linear in substrate concentration, which is the
case we consider. We compute the phase diagram, fluctuation spectrum and
large-deviation properties related to switch memory within a statistical
mechanics framework. Bistability occurs as either a first-order or second-order
non-equilibrium phase transition, depending on the network symmetries and the
ratio of phosphatase to kinase numbers. In the second-order case, the circuit
never leaves the bistable regime upon increasing the number of substrate
molecules at constant kinase to phosphatase ratio.
Conclusions: The number of substrate molecules is a key parameter controlling
both the onset of the bistable regime, fluctuation intensity, and the residence
time in a switched state. The relevance of the concept of memory depends on the
degree of switch symmetry, as memory presupposes information to be remembered,
which is highest for equal residence times in the switched states.
Reviewers: This article was reviewed by Artem Novozhilov (nominated by Eugene
Koonin), Sergei Maslov, and Ned Wingreen.Comment: Version published in Biology Direct including reviewer comments and
author responses, 28 pages, 7 figure
Identification of Piecewise Linear Models of Complex Dynamical Systems
The paper addresses the realization and identification problem or a subclass
of piecewise-affine hybrid systems. The paper provides necessary and sufficient
conditions for existence of a realization, a characterization of minimality,
and an identification algorithm for this subclass of hybrid systems. The
considered system class and the identification problem are motivated by
applications in systems biology
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