5,345 research outputs found
Global parameter identification of stochastic reaction networks from single trajectories
We consider the problem of inferring the unknown parameters of a stochastic
biochemical network model from a single measured time-course of the
concentration of some of the involved species. Such measurements are available,
e.g., from live-cell fluorescence microscopy in image-based systems biology. In
addition, fluctuation time-courses from, e.g., fluorescence correlation
spectroscopy provide additional information about the system dynamics that can
be used to more robustly infer parameters than when considering only mean
concentrations. Estimating model parameters from a single experimental
trajectory enables single-cell measurements and quantification of cell--cell
variability. We propose a novel combination of an adaptive Monte Carlo sampler,
called Gaussian Adaptation, and efficient exact stochastic simulation
algorithms that allows parameter identification from single stochastic
trajectories. We benchmark the proposed method on a linear and a non-linear
reaction network at steady state and during transient phases. In addition, we
demonstrate that the present method also provides an ellipsoidal volume
estimate of the viable part of parameter space and is able to estimate the
physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems
Biology
Hybrid Pathwise Sensitivity Methods for Discrete Stochastic Models of Chemical Reaction Systems
Stochastic models are often used to help understand the behavior of
intracellular biochemical processes. The most common such models are continuous
time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of
expectations of model output quantities with respect to model parameters, are
useful in this setting for a variety of applications. In this paper, we
introduce a class of hybrid pathwise differentiation methods for the numerical
estimation of parametric sensitivities. The new hybrid methods combine elements
from the three main classes of procedures for sensitivity estimation, and have
a number of desirable qualities. First, the new methods are unbiased for a
broad class of problems. Second, the methods are applicable to nearly any
physically relevant biochemical CTMC model. Third, and as we demonstrate on
several numerical examples, the new methods are quite efficient, particularly
if one wishes to estimate the full gradient of parametric sensitivities. The
methods are rather intuitive and utilize the multilevel Monte Carlo philosophy
of splitting an expectation into separate parts and handling each in an
efficient manner.Comment: 30 pages. The numerical example section has been extensively
rewritte
The Nondeterministic Waiting Time Algorithm: A Review
We present briefly the Nondeterministic Waiting Time algorithm. Our technique
for the simulation of biochemical reaction networks has the ability to mimic
the Gillespie Algorithm for some networks and solutions to ordinary
differential equations for other networks, depending on the rules of the
system, the kinetic rates and numbers of molecules. We provide a full
description of the algorithm as well as specifics on its implementation. Some
results for two well-known models are reported. We have used the algorithm to
explore Fas-mediated apoptosis models in cancerous and HIV-1 infected T cells
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
- …