Accelerated regression-based summary statistics for discrete stochastic systems via approximate simulators

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 τ work, we present a method to reduce this computational burden by leveraging approximate simulators of these systems, such as ordinary differential equations and τ-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.

Quantifying Epigenetic Stability with Minimum Action Paths

Chromatin can adopt multiple stable, heritable states with distinct histone modifications and varying levels of gene expression. Insight on the stability and maintenance of such epigenetic states can be gained by mathematical modeling of stochastic reaction networks for histone modifications. Analytical results for the kinetic networks are particularly valuable. Compared to computationally demanding numerical simulations, they often are more convenient at evaluating the robustness of conclusions with respect to model parameters. In this communication, we developed a second-quantization based approach that can be used to analyze discrete stochastic models with a fixed, finite number of particles using a representation of the SU (2) algebra. We applied the approach to a kinetic model of chromatin states that captures the feedback between nucleosomes and the enzymes conferring histone modifications. Using a path integral expression for the transition probability, we computed the epigenetic landscape that helps to identify the emergence of bistability and the most probable path connecting the two steady states. We anticipate the generalizability of the approach will make it useful for studying more complicated models that couple epigenetic modifications with transcription factors and chromatin structure.

Bayesian estimation for stochastic gene expression using multifidelity models

The finite state projection (FSP) approach to solving the chemical master equation has enabled successful inference of discrete stochastic models to predict single-cell gene regulation dynamics. Unfortunately, the FSP approach is highly computationally intensive for all but the simplest models, an issue that is highly problematic when parameter inference and uncertainty quantification takes enormous numbers of parameter evaluations. To address this issue, we propose two new computational methods for the Bayesian inference of stochastic gene expression parameters given single-cell experiments. We formulate and verify an Adaptive Delayed Acceptance Metropolis-Hastings (ADAMH) algorithm to utilize with reduced Krylov-basis projections of the FSP. We then introduce an extension of the ADAMH into a Hybrid scheme that consists of an initial phase to construct a reduced model and a faster second phase to sample from the approximate posterior distribution determined by the constructed model. We test and compare both algorithms to an adaptive Metropolis algorithm with full FSP-based likelihood evaluations on three example models and simulated data to show that the new ADAMH variants achieve substantial speedup in comparison to the full FSP approach. By reducing the computational costs of parameter estimation, we expect the ADAMH approach to enable efficient data-driven estimation for more complex gene regulation models.

Fuga de demanda en el sector comercial de Popayán, Colombia: una aproximación con modelos Logit

El objetivo de este estudio es determinar los motivos por los cuales las familias de Popayán no compran bienes y servicios en el sector comercial local y lo hacen en otros municipios o ciudades. Para lograrlo se realiza un muestreo incidental y se implementa un análisis con modelos estocásticos de variable discreta logística. Entre otros resultados, el estudio muestra que para la población encuestada son las mujeres quienes compran con más frecuencia que los hombres por fuera de la ciudad artículos como ropa, zapatosy accesorios. Adicionalmente, se encuentra que un factor determinante es la variedad, seguida por los precios, aunque esto depende del estrato al que pertenezcan. Finalmente, se concluye que el comercio payanes debe mejorar en aspectos como la atención al público, horarios de atención, entre otros. ABSTRACTThe aim of this study is to determine the reasons why families of Popayan not buy goods and services in the local business sector and do so in other municipalities or cities. To achieve an incidental sampling and analysis is performed with discrete stochastic models logistic variable is implemented. Among other results, the study shows that the surveyed population is women who buy more frequently than men for out of town items such as clothing, shoes and accessories. Additionally, we find that a factor is the variety, followed by the prices, although this depends on the stratum to which they belong. Finally, it is concluded that the commercial sector must impro ve in areas such as customer service, hours of operation, among others. RESUMOO objetivo deste estudo é determinar as razões pelas quais famílias de Popayan não compram produtos e serviços no sector empresarial local e fazê-lo em outros municípios ou cidades. Para conseguir uma amostragem incidental e análise é realizada com modelos estocásticos discretos variável logística é implementado. Entre outros resultados, o estudo mostra que a população pesquisada são as mulheres que compram mais freqüentemente do que os homens para fora da cidade itens como roupas, sapatos e acessórios. Além disso , descobrimos que um factor é a variedade , seguido pelos preços , embora isto dependa do estrato a que pertencem . Por fim , concluímos que Payanes comércio deve melhorar em áreas como atendimento ao cliente , horário de funcionamento , entre outros.

Accuracy of the Michaelis–Menten approximation when analysing effects of molecular noise

Quantitative biology relies on the construction of accurate mathematical models, yet the effectiveness of these models is often predicated on making simplifying approximations that allow for direct comparisons with available experimental data. The Michaelis–Menten (MM) approximation is widely used in both deterministic and discrete stochastic models of intracellular reaction networks, owing to the ubiquity of enzymatic activity in cellular processes and the clear biochemical interpretation of its parameters. However, it is not well understood how the approximation applies to the discrete stochastic case or how it extends to spatially inhomogeneous systems. We study the behaviour of the discrete stochastic MM approximation as a function of system size and show that significant errors can occur for small volumes, in comparison with a corresponding mass-action system. We then explore some consequences of these results for quantitative modelling. One consequence is that fluctuation-induced sensitivity, or stochastic focusing, can become highly exaggerated in models that make use of MM kinetics even if the approximations are excellent in a deterministic model. Another consequence is that spatial stochastic simulations based on the reaction–diffusion master equation can become highly inaccurate if the model contains MM terms.