27,490 research outputs found
Parameter estimation and inference for stochastic reaction-diffusion systems: application to morphogenesis in D. melanogaster
Background: Reaction-diffusion systems are frequently used in systems biology to model developmental and signalling processes. In many applications, count numbers of the diffusing molecular species are very low, leading to the need to explicitly model the inherent variability using stochastic methods. Despite their importance and frequent use, parameter estimation for both deterministic and stochastic reaction-diffusion systems is still a challenging problem.
Results: We present a Bayesian inference approach to solve both the parameter and state estimation problem for stochastic reaction-diffusion systems. This allows a determination of the full posterior distribution of the parameters (expected values and uncertainty). We benchmark the method by illustrating it on a simple synthetic experiment. We then test the method on real data about the diffusion of the morphogen Bicoid in Drosophila melanogaster. The results show how the precision with which parameters can be inferred varies dramatically, indicating that the ability to infer full posterior distributions on the parameters can have important experimental design consequences.
Conclusions: The results obtained demonstrate the feasibility and potential advantages of applying a Bayesian approach to parameter estimation in stochastic reaction-diffusion systems. In particular, the ability to estimate credibility intervals associated with parameter estimates can be precious for experimental design. Further work, however, will be needed to ensure the method can scale up to larger problems
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
A Constrained Approach to Multiscale Stochastic Simulation of\ud Chemically Reacting Systems
Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper we introduce a multiscale methodology suitable to address this problem. It is based on the Conditional Stochastic Simulation Algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the Constrained Multiscale Algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Stochastic Differential Equation (SDE) approximation, we can in turn approximate average switching times in stochastic chemical systems
Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation
We present computer-assisted methods for analyzing stochastic models of gene
regulatory networks. The main idea that underlies this equation-free analysis
is the design and execution of appropriately-initialized short bursts of
stochastic simulations; the results of these are processed to estimate
coarse-grained quantities of interest, such as mesoscopic transport
coefficients. In particular, using a simple model of a genetic toggle switch,
we illustrate the computation of an effective free energy and of a
state-dependent effective diffusion coefficient that characterize an
unavailable effective Fokker-Planck equation. Additionally we illustrate the
linking of equation-free techniques with continuation methods for performing a
form of stochastic "bifurcation analysis"; estimation of mean switching times
in the case of a bistable switch is also implemented in this equation-free
context. The accuracy of our methods is tested by direct comparison with
long-time stochastic simulations. This type of equation-free analysis appears
to be a promising approach to computing features of the long-time,
coarse-grained behavior of certain classes of complex stochastic models of gene
regulatory networks, circumventing the need for long Monte Carlo simulations.Comment: 33 pages, submitted to The Journal of Chemical Physic
The stochastic quasi-steady-state assumption: Reducing the model but not the noise
Highly reactive species at small copy numbers play an important role in many biological reaction networks. We have described previously how these species can be removed from reaction networks using stochastic quasi-steady-state singular perturbation analysis (sQSPA). In this paper we apply sQSPA to three published biological models: the pap operon regulation, a biochemical oscillator, and an intracellular viral infection. These examples demonstrate three different potential benefits of sQSPA. First, rare state probabilities can be accurately estimated from simulation. Second, the method typically results in fewer and better scaled parameters that can be more readily estimated from experiments. Finally, the simulation time can be significantly reduced without sacrificing the accuracy of the solution
- …