18,468 research outputs found
Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation
We present computer-assisted methods for analyzing stochastic models of gene
regulatory networks. The main idea that underlies this equation-free analysis
is the design and execution of appropriately-initialized short bursts of
stochastic simulations; the results of these are processed to estimate
coarse-grained quantities of interest, such as mesoscopic transport
coefficients. In particular, using a simple model of a genetic toggle switch,
we illustrate the computation of an effective free energy and of a
state-dependent effective diffusion coefficient that characterize an
unavailable effective Fokker-Planck equation. Additionally we illustrate the
linking of equation-free techniques with continuation methods for performing a
form of stochastic "bifurcation analysis"; estimation of mean switching times
in the case of a bistable switch is also implemented in this equation-free
context. The accuracy of our methods is tested by direct comparison with
long-time stochastic simulations. This type of equation-free analysis appears
to be a promising approach to computing features of the long-time,
coarse-grained behavior of certain classes of complex stochastic models of gene
regulatory networks, circumventing the need for long Monte Carlo simulations.Comment: 33 pages, submitted to The Journal of Chemical Physic
Experimental Biological Protocols with Formal Semantics
Both experimental and computational biology is becoming increasingly
automated. Laboratory experiments are now performed automatically on
high-throughput machinery, while computational models are synthesized or
inferred automatically from data. However, integration between automated tasks
in the process of biological discovery is still lacking, largely due to
incompatible or missing formal representations. While theories are expressed
formally as computational models, existing languages for encoding and
automating experimental protocols often lack formal semantics. This makes it
challenging to extract novel understanding by identifying when theory and
experimental evidence disagree due to errors in the models or the protocols
used to validate them. To address this, we formalize the syntax of a core
protocol language, which provides a unified description for the models of
biochemical systems being experimented on, together with the discrete events
representing the liquid-handling steps of biological protocols. We present both
a deterministic and a stochastic semantics to this language, both defined in
terms of hybrid processes. In particular, the stochastic semantics captures
uncertainties in equipment tolerances, making it a suitable tool for both
experimental and computational biologists. We illustrate how the proposed
protocol language can be used for automated verification and synthesis of
laboratory experiments on case studies from the fields of chemistry and
molecular programming
Global parameter identification of stochastic reaction networks from single trajectories
We consider the problem of inferring the unknown parameters of a stochastic
biochemical network model from a single measured time-course of the
concentration of some of the involved species. Such measurements are available,
e.g., from live-cell fluorescence microscopy in image-based systems biology. In
addition, fluctuation time-courses from, e.g., fluorescence correlation
spectroscopy provide additional information about the system dynamics that can
be used to more robustly infer parameters than when considering only mean
concentrations. Estimating model parameters from a single experimental
trajectory enables single-cell measurements and quantification of cell--cell
variability. We propose a novel combination of an adaptive Monte Carlo sampler,
called Gaussian Adaptation, and efficient exact stochastic simulation
algorithms that allows parameter identification from single stochastic
trajectories. We benchmark the proposed method on a linear and a non-linear
reaction network at steady state and during transient phases. In addition, we
demonstrate that the present method also provides an ellipsoidal volume
estimate of the viable part of parameter space and is able to estimate the
physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems
Biology
The validity of quasi steady-state approximations in discrete stochastic simulations
In biochemical networks, reactions often occur on disparate timescales and
can be characterized as either "fast" or "slow." The quasi-steady state
approximation (QSSA) utilizes timescale separation to project models of
biochemical networks onto lower-dimensional slow manifolds. As a result, fast
elementary reactions are not modeled explicitly, and their effect is captured
by non-elementary reaction rate functions (e.g. Hill functions). The accuracy
of the QSSA applied to deterministic systems depends on how well timescales are
separated. Recently, it has been proposed to use the non-elementary rate
functions obtained via the deterministic QSSA to define propensity functions in
stochastic simulations of biochemical networks. In this approach, termed the
stochastic QSSA, fast reactions that are part of non-elementary reactions are
not simulated, greatly reducing computation time. However, it is unclear when
the stochastic QSSA provides an accurate approximation of the original
stochastic simulation. We show that, unlike the deterministic QSSA, the
validity of the stochastic QSSA does not follow from timescale separation
alone, but also depends on the sensitivity of the non-elementary reaction rate
functions to changes in the slow species. The stochastic QSSA becomes more
accurate when this sensitivity is small. Different types of QSSAs result in
non-elementary functions with different sensitivities, and the total QSSA
results in less sensitive functions than the standard or the pre-factor QSSA.
We prove that, as a result, the stochastic QSSA becomes more accurate when
non-elementary reaction functions are obtained using the total QSSA. Our work
provides a novel condition for the validity of the QSSA in stochastic
simulations of biochemical reaction networks with disparate timescales.Comment: 21 pages, 4 figure
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