127 research outputs found
Modelling the burden caused by gene expression: an in silico investigation into the interactions between synthetic gene circuits and their chassis cell
In this paper we motivate and develop a model of gene expression for the
purpose of studying the interaction between synthetic gene circuits and the
chassis cell within which they are in- serted. This model focuses on the
translational aspect of gene expression as this is where the literature
suggests the crucial interaction between gene expression and shared resources
lies
Distributed Reconstruction of Nonlinear Networks: An ADMM Approach
In this paper, we present a distributed algorithm for the reconstruction of
large-scale nonlinear networks. In particular, we focus on the identification
from time-series data of the nonlinear functional forms and associated
parameters of large-scale nonlinear networks. Recently, a nonlinear network
reconstruction problem was formulated as a nonconvex optimisation problem based
on the combination of a marginal likelihood maximisation procedure with
sparsity inducing priors. Using a convex-concave procedure (CCCP), an iterative
reweighted lasso algorithm was derived to solve the initial nonconvex
optimisation problem. By exploiting the structure of the objective function of
this reweighted lasso algorithm, a distributed algorithm can be designed. To
this end, we apply the alternating direction method of multipliers (ADMM) to
decompose the original problem into several subproblems. To illustrate the
effectiveness of the proposed methods, we use our approach to identify a
network of interconnected Kuramoto oscillators with different network sizes
(500~100,000 nodes).Comment: To appear in the Preprints of 19th IFAC World Congress 201
Bounding stationary averages of polynomial diffusions via semidefinite programming
We introduce an algorithm based on semidefinite programming that yields
increasing (resp. decreasing) sequences of lower (resp. upper) bounds on
polynomial stationary averages of diffusions with polynomial drift vector and
diffusion coefficients. The bounds are obtained by optimising an objective,
determined by the stationary average of interest, over the set of real vectors
defined by certain linear equalities and semidefinite inequalities which are
satisfied by the moments of any stationary measure of the diffusion. We
exemplify the use of the approach through several applications: a Bayesian
inference problem; the computation of Lyapunov exponents of linear ordinary
differential equations perturbed by multiplicative white noise; and a
reliability problem from structural mechanics. Additionally, we prove that the
bounds converge to the infimum and supremum of the set of stationary averages
for certain SDEs associated with the computation of the Lyapunov exponents, and
we provide numerical evidence of convergence in more general settings
Shaping Pulses to Control Bistable Biological Systems
In this paper we study how to shape temporal pulses to switch a bistable
system between its stable steady states. Our motivation for pulse-based control
comes from applications in synthetic biology, where it is generally difficult
to implement real-time feedback control systems due to technical limitations in
sensors and actuators. We show that for monotone bistable systems, the
estimation of the set of all pulses that switch the system reduces to the
computation of one non-increasing curve. We provide an efficient algorithm to
compute this curve and illustrate the results with a genetic bistable system
commonly used in synthetic biology. We also extend these results to models with
parametric uncertainty and provide a number of examples and counterexamples
that demonstrate the power and limitations of the current theory. In order to
show the full potential of the framework, we consider the problem of inducing
oscillations in a monotone biochemical system using a combination of temporal
pulses and event-based control. Our results provide an insight into the
dynamics of bistable systems under external inputs and open up numerous
directions for future investigation.Comment: 14 pages, contains material from the paper in Proc Amer Control Conf
2015, (pp. 3138-3143) and "Shaping pulses to control bistable systems
analysis, computation and counterexamples", which is due to appear in
Automatic
Approximations of countably-infinite linear programs over bounded measure spaces
We study a class of countably-infinite-dimensional linear programs (CILPs)
whose feasible sets are bounded subsets of appropriately defined weighted
spaces of measures. We show how to approximate the optimal value, optimal
points, and minimal points of these CILPs by solving finite-dimensional linear
programs. The errors of our approximations converge to zero as the size of the
finite-dimensional program approaches that of the original problem and are easy
to bound in practice. We discuss the use of our methods in the computation of
the stationary distributions, occupation measures, and exit distributions of
Markov~chains
Global Network Prediction from Local Node Dynamics
The study of dynamical systems on networks, describing complex interactive
processes, provides insight into how network structure affects global
behaviour. Yet many methods for network dynamics fail to cope with large or
partially-known networks, a ubiquitous situation in real-world applications.
Here we propose a localised method, applicable to a broad class of dynamical
models on networks, whereby individual nodes monitor and store the evolution of
their own state and use these values to approximate, via a simple computation,
their own steady state solution. Hence the nodes predict their own final state
without actually reaching it. Furthermore, the localised formulation enables
nodes to compute global network metrics without knowledge of the full network
structure. The method can be used to compute global rankings in the network
from local information; to detect community detection from fast, local
transient dynamics; and to identify key nodes that compute global network
metrics ahead of others. We illustrate some of the applications of the
algorithm by efficiently performing web-page ranking for a large internet
network and identifying the dynamic roles of inter-neurons in the C. Elegans
neural network. The mathematical formulation is simple, widely applicable and
easily scalable to real-world datasets suggesting how local computation can
provide an approach to the study of large-scale network dynamics
A coarse-grained bacterial cell model for resource-aware analysis and design of synthetic gene circuits
Within a cell, synthetic and native genes compete for expression machinery, influencing cellular process dynamics through resource couplings. Models that simplify competitive resource binding kinetics can guide the design of strategies for countering these couplings. However, in bacteria resource availability and cell growth rate are interlinked, which complicates resource-aware biocircuit design. Capturing this interdependence requires coarse-grained bacterial cell models that balance accurate representation of metabolic regulation against simplicity and interpretability. We propose a coarse-grained E. coli cell model that combines the ease of simplified resource coupling analysis with appreciation of bacterial growth regulation mechanisms and the processes relevant for biocircuit design. Reliably capturing known growth phenomena, it provides a unifying explanation to disparate empirical relations between growth and synthetic gene expression. Considering a biomolecular controller that makes cell-wide ribosome availability robust to perturbations, we showcase our model's usefulness in numerically prototyping biocircuits and deriving analytical relations for design guidance
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