| 1. |
- Jiang, Richard M., et al.
(författare)
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Accelerated regression-based summary statistics for discrete stochastic systems via approximate simulators
- 2021
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Ingår i: BMC Bioinformatics. - : BioMed Central (BMC). - 1471-2105. ; 22
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Tidskriftsartikel (refereegranskat)abstract
- Background: Approximate Bayesian Computation (ABC) has become a key tool for calibrating the parameters of discrete stochastic biochemical models. For higher dimensional models and data, its performance is strongly dependent on having a representative set of summary statistics. While regression-based methods have been demonstrated to allow for the automatic construction of effective summary statistics, their reliance on first simulating a large training set creates a significant overhead when applying these methods to discrete stochastic models for which simulation is relatively expensive. In this tau work, we present a method to reduce this computational burden by leveraging approximate simulators of these systems, such as ordinary differential equations and tau-Leaping approximations.Results: We have developed an algorithm to accelerate the construction of regression-based summary statistics for Approximate Bayesian Computation by selectively using the faster approximate algorithms for simulations. By posing the problem as one of ratio estimation, we use state-of-the-art methods in machine learning to show that, in many cases, our algorithm can significantly reduce the number of simulations from the full resolution model at a minimal cost to accuracy and little additional tuning from the user. We demonstrate the usefulness and robustness of our method with four different experiments.Conclusions: We provide a novel algorithm for accelerating the construction of summary statistics for stochastic biochemical systems. Compared to the standard practice of exclusively training from exact simulator samples, our method is able to dramatically reduce the number of required calls to the stochastic simulator at a minimal loss in accuracy. This can immediately be implemented to increase the overall speed of the ABC workflow for estimating parameters in complex systems.
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| 2. |
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| 3. |
- Coulier, Adrien, 1992-
(författare)
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Multiscale Modeling in Systems Biology : Methods and Perspectives
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In the last decades, mathematical and computational models have become ubiquitous to the field of systems biology. Specifically, the multiscale nature of biological processes makes the design and simulation of such models challenging. In this thesis we offer a perspective on available methods to study and simulate such models and how they can be combined to handle biological processes evolving at different scales.The contribution of this thesis is threefold. First, we introduce Orchestral, a multiscale modular framework to simulate multicellular models. By decoupling intracellular chemical kinetics, cell-cell signaling, and cellular mechanics by means of operator-splitting, it is able to combine existing software into one massively parallel simulation. Its modular structure makes it easy to replace its components, e.g. to adjust the level of modeling details. We demonstrate the scalability of our framework on both high performance clusters and in a cloud environment.We then explore how center-based models can be used to study cellular mechanics in biological tissues. We show how modeling and numerical choices can affect the results of the simulation and mislead modelers into incorrect biological conclusions if these errors are not monitored properly. We then propose CBMOS, a Python framework specifically designed for the numerical study of such models.Finally, we study how spatial details in intracellular chemical kinetics can be efficiently approximated in a multiscale compartment-based model. We evaluate how this model compares to two other alternatives in terms of accuracy and computational cost. We then propose a computational pipeline to study and compare such models in the context of Bayesian parameter inference and illustrate its usage in three case studies.
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| 4. |
- Coulier, Adrien, et al.
(författare)
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Systematic comparison of modeling fidelity levels and parameter inference settings applied to negative feedback gene regulation
- 2022
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Ingår i: PloS Computational Biology. - : Public Library of Science (PLoS). - 1553-734X .- 1553-7358. ; 18:12
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Tidskriftsartikel (refereegranskat)abstract
- Quantitative stochastic models of gene regulatory networks are important tools for studying cellular regulation. Such models can be formulated at many different levels of fidelity. A practical challenge is to determine what model fidelity to use in order to get accurate and representative results. The choice is important, because models of successively higher fidelity come at a rapidly increasing computational cost. In some situations, the level of detail is clearly motivated by the question under study. In many situations however, many model options could qualitatively agree with available data, depending on the amount of data and the nature of the observations. Here, an important distinction is whether we are interested in inferring the true (but unknown) physical parameters of the model or if it is sufficient to be able to capture and explain available data. The situation becomes complicated from a computational perspective because inference needs to be approximate. Most often it is based on likelihood-free Approximate Bayesian Computation (ABC) and here determining which summary statistics to use, as well as how much data is needed to reach the desired level of accuracy, are difficult tasks. Ultimately, all of these aspects—the model fidelity, the available data, and the numerical choices for inference—interplay in a complex manner. In this paper we develop a computational pipeline designed to systematically evaluate inference accuracy for a wide range of true known parameters. We then use it to explore inference settings for negative feedback gene regulation. In particular, we compare a detailed spatial stochastic model, a coarse-grained compartment-based multiscale model, and the standard well-mixed model, across several data-scenarios and for multiple numerical options for parameter inference. Practically speaking, this pipeline can be used as a preliminary step to guide modelers prior to gathering experimental data. By training Gaussian processes to approximate the distance function values, we are able to substantially reduce the computational cost of running the pipeline.
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| 6. |
- Engblom, Stefan, et al.
(författare)
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Simulation of stochastic reaction-diffusion processes on unstructured meshes
- 2008
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic level, the master equation for a well stirred chemical system is combined with Brownian motion in space to obtain the reaction-diffusion master equation. The space is covered by an unstructured mesh and the diffusion coefficients on the mesoscale are obtained from a finite element discretization of the Laplace operator on the macroscale. The resulting method is a flexible hybrid algorithm in that the diffusion can be handled either on the meso- or on the macroscale level. The accuracy and the efficiency of the method are illustrated in three numerical examples inspired by molecular biology.
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| 8. |
- Ferm, Lars, et al.
(författare)
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A hierarchy of approximations of the master equation scaled by a size parameter
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Solutions of the master equation are approximated using a hierarchy of models based on the solution of ordinary differential equations: the macroscopic equations, the linear noise approximation and the moment equations. The advantage with the approximations is that the computational work with deterministic algorithms grows as a polynomial in the number of species instead of an exponential growth with conventional methods for the master equation. The relation between the approximations is investigated theoretically and in numerical examples. The solutions converge to the macroscopic equations when a parameter measuring the size of the system grows. A computational criterion is suggested for estimating the accuracy of the approximations. The numerical examples are models for the migration of people, in population dynamics and in molecular biology.
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| 9. |
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| 10. |
- Ferm, Lars, et al.
(författare)
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An adaptive algorithm for simulation of stochastic reaction-diffusion processes
- 2009
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction-diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie's stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the time steps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.
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