1,185 research outputs found
Ratiometric control for differentiation of cell populations endowed with synthetic toggle switches
We consider the problem of regulating by means of external control inputs the
ratio of two cell populations. Specifically, we assume that these two cellular
populations are composed of cells belonging to the same strain which embeds
some bistable memory mechanism, e.g. a genetic toggle switch, allowing them to
switch role from one population to another in response to some inputs. We
present three control strategies to regulate the populations' ratio to
arbitrary desired values which take also into account realistic physical and
technological constraints occurring in experimental microfluidic platforms. The
designed controllers are then validated in-silico using stochastic agent-based
simulations.Comment: Accepted to CDC'201
Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations
We construct a new framework for accelerating Markov chain Monte Carlo in
posterior sampling problems where standard methods are limited by the
computational cost of the likelihood, or of numerical models embedded therein.
Our approach introduces local approximations of these models into the
Metropolis-Hastings kernel, borrowing ideas from deterministic approximation
theory, optimization, and experimental design. Previous efforts at integrating
approximate models into inference typically sacrifice either the sampler's
exactness or efficiency; our work seeks to address these limitations by
exploiting useful convergence characteristics of local approximations. We prove
the ergodicity of our approximate Markov chain, showing that it samples
asymptotically from the \emph{exact} posterior distribution of interest. We
describe variations of the algorithm that employ either local polynomial
approximations or local Gaussian process regressors. Our theoretical results
reinforce the key observation underlying this paper: when the likelihood has
some \emph{local} regularity, the number of model evaluations per MCMC step can
be greatly reduced without biasing the Monte Carlo average. Numerical
experiments demonstrate multiple order-of-magnitude reductions in the number of
forward model evaluations used in representative ODE and PDE inference
problems, with both synthetic and real data.Comment: A major update of the theory and example
Genetic noise control via protein oligomerization
Gene expression in a cell entails random reaction events occurring over
disparate time scales. Thus, molecular noise that often results in phenotypic
and population-dynamic consequences sets a fundamental limit to biochemical
signaling. While there have been numerous studies correlating the architecture
of cellular reaction networks with noise tolerance, only a limited effort has
been made to understand the dynamic role of protein-protein interactions. Here
we have developed a fully stochastic model for the positive feedback control of
a single gene, as well as a pair of genes (toggle switch), integrating
quantitative results from previous in vivo and in vitro studies. We find that
the overall noise-level is reduced and the frequency content of the noise is
dramatically shifted to the physiologically irrelevant high-frequency regime in
the presence of protein dimerization. This is independent of the choice of
monomer or dimer as transcription factor and persists throughout the multiple
model topologies considered. For the toggle switch, we additionally find that
the presence of a protein dimer, either homodimer or heterodimer, may
significantly reduce its random switching rate. Hence, the dimer promotes the
robust function of bistable switches by preventing the uninduced (induced)
state from randomly being induced (uninduced). The specific binding between
regulatory proteins provides a buffer that may prevent the propagation of
fluctuations in genetic activity. The capacity of the buffer is a non-monotonic
function of association-dissociation rates. Since the protein oligomerization
per se does not require extra protein components to be expressed, it provides a
basis for the rapid control of intrinsic or extrinsic noise
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
Monostability and multistability of genetic regulatory networks with different types of regulation functions
The official published version of the article can be found at the link below.Monostability and multistability are proven to be two important topics in synthesis biology and system biology. In this paper, both monostability and multistability are analyzed in a unified framework by applying control theory and mathematical tools. The genetic regulatory networks (GRNs) with multiple time-varying delays and different types of regulation functions are considered. By putting forward a general sector-like regulation function and utilizing up-to-date techniques, a novel Lyapunov–Krasovskii functional is introduced for achieving delay dependence to ensure less conservatism. A new condition is then proposed for the general stability of a GRN in the form of linear matrix inequalities (LMIs) that are dependent on the upper and lower bounds of the delays. Our general stability conditions are applicable to several frequently used regulation functions. It is shown that the existing results for monostability of GRNs are special cases of our main results. Five examples are employed to illustrate the applicability and usefulness of the developed theoretical results.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the U.K. under Grant BB/C506264/1, the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 60504008 and 60804028, the Program for New Century Excellent Talents in Universities of China, and the Alexander von Humboldt Foundation of Germany
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