16,526 research outputs found
Reduction of dynamical biochemical reaction networks in computational biology
Biochemical networks are used in computational biology, to model the static
and dynamical details of systems involved in cell signaling, metabolism, and
regulation of gene expression. Parametric and structural uncertainty, as well
as combinatorial explosion are strong obstacles against analyzing the dynamics
of large models of this type. Multi-scaleness is another property of these
networks, that can be used to get past some of these obstacles. Networks with
many well separated time scales, can be reduced to simpler networks, in a way
that depends only on the orders of magnitude and not on the exact values of the
kinetic parameters. The main idea used for such robust simplifications of
networks is the concept of dominance among model elements, allowing
hierarchical organization of these elements according to their effects on the
network dynamics. This concept finds a natural formulation in tropical
geometry. We revisit, in the light of these new ideas, the main approaches to
model reduction of reaction networks, such as quasi-steady state and
quasi-equilibrium approximations, and provide practical recipes for model
reduction of linear and nonlinear networks. We also discuss the application of
model reduction to backward pruning machine learning techniques
Uniformisation techniques for stochastic simulation of chemical reaction networks
This work considers the method of uniformisation for continuous-time Markov
chains in the context of chemical reaction networks. Previous work in the
literature has shown that uniformisation can be beneficial in the context of
time-inhomogeneous models, such as chemical reaction networks incorporating
extrinsic noise. This paper lays focus on the understanding of uniformisation
from the viewpoint of sample paths of chemical reaction networks. In
particular, an efficient pathwise stochastic simulation algorithm for
time-homogeneous models is presented which is complexity-wise equal to
Gillespie's direct method. This new approach therefore enlarges the class of
problems for which the uniformisation approach forms a computationally
attractive choice. Furthermore, as a new application of the uniformisation
method, we provide a novel variance reduction method for (raw) moment
estimators of chemical reaction networks based upon the combination of
stratification and uniformisation
Markov chain aggregation and its application to rule-based modelling
Rule-based modelling allows to represent molecular interactions in a compact
and natural way. The underlying molecular dynamics, by the laws of stochastic
chemical kinetics, behaves as a continuous-time Markov chain. However, this
Markov chain enumerates all possible reaction mixtures, rendering the analysis
of the chain computationally demanding and often prohibitive in practice. We
here describe how it is possible to efficiently find a smaller, aggregate
chain, which preserves certain properties of the original one. Formal methods
and lumpability notions are used to define algorithms for automated and
efficient construction of such smaller chains (without ever constructing the
original ones). We here illustrate the method on an example and we discuss the
applicability of the method in the context of modelling large signalling
pathways
On Projection-Based Model Reduction of Biochemical Networks-- Part II: The Stochastic Case
In this paper, we consider the problem of model order reduction of stochastic
biochemical networks. In particular, we reduce the order of (the number of
equations in) the Linear Noise Approximation of the Chemical Master Equation,
which is often used to describe biochemical networks. In contrast to other
biochemical network reduction methods, the presented one is projection-based.
Projection-based methods are powerful tools, but the cost of their use is the
loss of physical interpretation of the nodes in the network. In order alleviate
this drawback, we employ structured projectors, which means that some nodes in
the network will keep their physical interpretation. For many models in
engineering, finding structured projectors is not always feasible; however, in
the context of biochemical networks it is much more likely as the networks are
often (almost) monotonic. To summarise, the method can serve as a trade-off
between approximation quality and physical interpretation, which is illustrated
on numerical examples.Comment: Submitted to the 53rd CD
Accurate reduction of a model of circadian rhythms by delayed quasi steady state assumptions
Quasi steady state assumptions are often used to simplify complex systems of
ordinary differential equations in modelling of biochemical processes. The
simplified system is designed to have the same qualitative properties as the
original system and to have a small number of variables. This enables to use
the stability and bifurcation analysis to reveal a deeper structure in the
dynamics of the original system. This contribution shows that introducing
delays to quasi steady state assumptions yields a simplified system that
accurately agrees with the original system not only qualitatively but also
quantitatively. We derive the proper size of the delays for a particular model
of circadian rhythms and present numerical results showing the accuracy of this
approach.Comment: Presented at Equadiff 2013 conference in Prague. Accepted for
publication in Mathematica Bohemic
Fast stochastic simulation of biochemical reaction systems by\ud alternative formulations of the Chemical Langevin Equation
The Chemical Langevin Equation (CLE), which is a stochastic differential equation (SDE) driven by a multidimensional Wiener process, acts as a bridge between the discrete Stochastic Simulation Algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finite-dimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation. On the practical side, we show that in the case where there are m1 pairs of reversible reactions and m2 irreversible reactions only m1+m2 Wiener processes are required in the formulation of the CLE, whereas the standard approach uses 2m1 + m2. We illustrate our findings by considering alternative formulations of the CLE for a\ud
HERG ion channel model and the Goldbeter–Koshland switch. We show that there are considerable computational savings when using our insights
- …