Approximating solutions of the chemical master equation using neural networks

The Chemical Master Equation (CME) provides an accurate description of stochastic biochemical reaction networks in well-mixed conditions, but it cannot be solved analytically for most systems of practical interest. Although Monte Carlo methods provide a principled means to probe system dynamics, the large number of simulations typically required can render the estimation of molecule number distributions and other quantities infeasible. In this article, we aim to leverage the representational power of neural networks to approximate the solutions of the CME and propose a framework for the Neural Estimation of Stochastic Simulations for Inference and Exploration (Nessie). Our approach is based on training neural networks to learn the distributions predicted by the CME from relatively few stochastic simulations. We show on biologically relevant examples that simple neural networks with one hidden layer can capture highly complex distributions across parameter space, thereby accelerating computationally intensive tasks such as parameter exploration and inference

Parameter estimation for biochemical reaction networks using Wasserstein distances

We present a method for estimating parameters in stochastic models of biochemical reaction networks by fitting steady-state distributions using Wasserstein distances. We simulate a reaction network at different parameter settings and train a Gaussian process to learn the Wasserstein distance between observations and the simulator output for all parameters. We then use Bayesian optimization to find parameters minimizing this distance based on the trained Gaussian process. The effectiveness of our method is demonstrated on the three-stage model of gene expression and a genetic feedback loop for which moment-based methods are known to perform poorly. Our method is applicable to any simulator model of stochastic reaction networks, including Brownian Dynamics.Comment: 22 pages, 8 figures. Slight modifications/additions to the text; added new section (Section 4.4) and Appendi

Training deep neural density estimators to identify mechanistic models of neural dynamics

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators—trained using model simulations—to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin–Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics

Inference and Uncertainty Quantification of Stochastic Gene Expression via Synthetic Models

Estimating uncertainty in model predictions is a central task in quantitative biology. Biological models at the single-cell level are intrinsically stochastic and nonlinear, creating formidable challenges for their statistical estimation which inevitably has to rely on approximations that trade accuracy for tractability. Despite intensive interest, a sweet spot in this trade-off has not been found yet. We propose a flexible procedure for uncertainty quantification in a wide class of reaction networks describing stochastic gene expression including those with feedback. The method is based on creating a tractable coarse-graining of the model that is learned from simulations, a synthetic model, to approximate the likelihood function. We demonstrate that synthetic models can substantially outperform state-of-the-art approaches on a number of non-trivial systems and datasets, yielding an accurate and computationally viable solution to uncertainty quantification in stochastic models of gene expression

JuliaGaussianProcesses/KernelFunctions.jl: v0.10.58

<h2>KernelFunctions v0.10.58</h2> <p><a href="https://github.com/JuliaGaussianProcesses/KernelFunctions.jl/compare/v0.10.57...v0.10.58">Diff since v0.10.57</a></p> <p><strong>Merged pull requests:</strong></p> <ul> <li>Fix Matern AD failures (#528) (@simsurace)</li> <li>Stop using deprecated signatures from Distances.jl (#529) (@simsurace)</li> </ul&gt