786 research outputs found
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
Jump-Diffusion Approximation of Stochastic Reaction Dynamics: Error bounds and Algorithms
Biochemical reactions can happen on different time scales and also the
abundance of species in these reactions can be very different from each other.
Classical approaches, such as deterministic or stochastic approach, fail to
account for or to exploit this multi-scale nature, respectively. In this paper,
we propose a jump-diffusion approximation for multi-scale Markov jump processes
that couples the two modeling approaches. An error bound of the proposed
approximation is derived and used to partition the reactions into fast and slow
sets, where the fast set is simulated by a stochastic differential equation and
the slow set is modeled by a discrete chain. The error bound leads to a very
efficient dynamic partitioning algorithm which has been implemented for several
multi-scale reaction systems. The gain in computational efficiency is
illustrated by a realistically sized model of a signal transduction cascade
coupled to a gene expression dynamics.Comment: 32 pages, 7 figure
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
Model reduction for stochastic CaMKII reaction kinetics in synapses by graph-constrained correlation dynamics.
A stochastic reaction network model of Ca(2+) dynamics in synapses (Pepke et al PLoS Comput. Biol. 6 e1000675) is expressed and simulated using rule-based reaction modeling notation in dynamical grammars and in MCell. The model tracks the response of calmodulin and CaMKII to calcium influx in synapses. Data from numerically intensive simulations is used to train a reduced model that, out of sample, correctly predicts the evolution of interaction parameters characterizing the instantaneous probability distribution over molecular states in the much larger fine-scale models. The novel model reduction method, 'graph-constrained correlation dynamics', requires a graph of plausible state variables and interactions as input. It parametrically optimizes a set of constant coefficients appearing in differential equations governing the time-varying interaction parameters that determine all correlations between variables in the reduced model at any time slice
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
Approximation and inference methods for stochastic biochemical kinetics-a tutorial review
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics
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