18,962 research outputs found
Computation of biochemical pathway fluctuations beyond the linear noise approximation using iNA
The linear noise approximation is commonly used to obtain intrinsic noise
statistics for biochemical networks. These estimates are accurate for networks
with large numbers of molecules. However it is well known that many biochemical
networks are characterized by at least one species with a small number of
molecules. We here describe version 0.3 of the software intrinsic Noise
Analyzer (iNA) which allows for accurate computation of noise statistics over
wide ranges of molecule numbers. This is achieved by calculating the next order
corrections to the linear noise approximation's estimates of variance and
covariance of concentration fluctuations. The efficiency of the methods is
significantly improved by automated just-in-time compilation using the LLVM
framework leading to a fluctuation analysis which typically outperforms that
obtained by means of exact stochastic simulations. iNA is hence particularly
well suited for the needs of the computational biology community.Comment: 5 pages, 2 figures, conference proceeding IEEE International
Conference on Bioinformatics and Biomedicine (BIBM) 201
Efficient Reactive Brownian Dynamics
We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle
simulations of reaction-diffusion systems based on the Doi or volume reactivity
model, in which pairs of particles react with a specified Poisson rate if they
are closer than a chosen reactive distance. In our Doi model, we ensure that
the microscopic reaction rules for various association and disassociation
reactions are consistent with detailed balance (time reversibility) at
thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to
separate reaction and diffusion, and solves both the diffusion-only and
reaction-only subproblems exactly, even at high packing densities. To
efficiently process reactions without uncontrolled approximations, SRBD employs
an event-driven algorithm that processes reactions in a time-ordered sequence
over the duration of the time step. A grid of cells with size larger than all
of the reactive distances is used to schedule and process the reactions, but
unlike traditional grid-based methods such as Reaction-Diffusion Master
Equation (RDME) algorithms, the results of SRBD are statistically independent
of the size of the grid used to accelerate the processing of reactions. We use
the SRBD algorithm to compute the effective macroscopic reaction rate for both
reaction- and diffusion-limited irreversible association in three dimensions.
We also study long-time tails in the time correlation functions for reversible
association at thermodynamic equilibrium. Finally, we compare different
particle and continuum methods on a model exhibiting a Turing-like instability
and pattern formation. We find that for models in which particles diffuse off
lattice, such as the Doi model, reactions lead to a spurious enhancement of the
effective diffusion coefficients.Comment: To appear in J. Chem. Phy
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
Effective simulation techniques for biological systems
In this paper we give an overview of some very recent work on the stochastic simulation of systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge-Kutta methods and the Balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and discuss how novel computing implementations can enhance the performance of these simulations
Mathematics at the eve of a historic transition in biology
A century ago physicists and mathematicians worked in tandem and established
quantum mechanism. Indeed, algebras, partial differential equations, group
theory, and functional analysis underpin the foundation of quantum mechanism.
Currently, biology is undergoing a historic transition from qualitative,
phenomenological and descriptive to quantitative, analytical and predictive.
Mathematics, again, becomes a driving force behind this new transition in
biology.Comment: 5 pages, 2 figure
Coarse Stability and Bifurcation Analysis Using Stochastic Simulators: Kinetic Monte Carlo Examples
We implement a computer-assisted approach that, under appropriate conditions,
allows the bifurcation analysis of the coarse dynamic behavior of microscopic
simulators without requiring the explicit derivation of closed macroscopic
equations for this behavior. The approach is inspired by the so-called
time-step per based numerical bifurcation theory. We illustrate the approach
through the computation of both stable and unstable coarsely invariant states
for Kinetic Monte Carlo models of three simple surface reaction schemes. We
quantify the linearized stability of these coarsely invariant states, perform
pseudo-arclength continuation, detect coarse limit point and coarse Hopf
bifurcations and construct two-parameter bifurcation diagrams.Comment: 26 pages, 5 figure
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