Neural network aided approximation and parameter inference of non-Markovian models of gene expression.
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ABSTRACT:
SUBMITTER: Jiang Q
PROVIDER: S-EPMC8113478 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:Motivation:The structured coalescent is widely applied to study demography within and migration between sub-populations from genetic sequence data. Current methods are either exact but too computationally inefficient to analyse large datasets with many sub-populations, or make strong approximations leading to severe biases in inference. We recently introduced an approximation based on weaker assumptions to the structured coalescent enabling the analysis of larger datasets with many different states. We showed that our approximation provides unbiased migration rate and population size estimates across a wide parameter range. Results:We extend this approach by providing a new algorithm to calculate the probability of the state of internal nodes that includes the information from the full phylogenetic tree. We show that this algorithm is able to increase the probability attributed to the true sub-population of a node. Furthermore we use improved integration techniques, such that our method is now able to analyse larger datasets, including a H3N2 dataset with 433 sequences sampled from five different locations. Availability and implementation:The presented methods are part of the BEAST2 package MASCOT, the Marginal Approximation of the Structured COalescenT. This package can be downloaded via the BEAUti package manager. The source code is available at https://github.com/nicfel/Mascot.git. Supplementary information:Supplementary data are available at Bioinformatics online.
| S-EPMC6223361 | biostudies-literature
Project description:BACKGROUND: Mathematical models for revealing the dynamics and interactions properties of biological systems play an important role in computational systems biology. The inference of model parameter values from time-course data can be considered as a "reverse engineering" process and is still one of the most challenging tasks. Many parameter estimation methods have been developed but none of these methods is effective for all cases and can overwhelm all other approaches. Instead, various methods have their advantages and disadvantages. It is worth to develop parameter estimation methods which are robust against noise, efficient in computation and flexible enough to meet different constraints. RESULTS: Two parameter estimation methods of combining spline theory with Linear Programming (LP) and Nonlinear Programming (NLP) are developed. These methods remove the need for ODE solvers during the identification process. Our analysis shows that the augmented cost function surfaces used in the two proposed methods are smoother; which can ease the optima searching process and hence enhance the robustness and speed of the search algorithm. Moreover, the cores of our algorithms are LP and NLP based, which are flexible and consequently additional constraints can be embedded/removed easily. Eight system biology models are used for testing the proposed approaches. Our results confirm that the proposed methods are both efficient and robust. CONCLUSIONS: The proposed approaches have general application to identify unknown parameter values of a wide range of systems biology models.
| S-EPMC3750107 | biostudies-literature
Project description:Over the years, there have been claims that evolution proceeds according to systematically different processes over different timescales and that protein evolution behaves in a non-Markovian manner. On the other hand, Markov models are fundamental to many applications in evolutionary studies. Apparent non-Markovian or time-dependent behavior has been attributed to influence of the genetic code at short timescales and dominance of physicochemical properties of the amino acids at long timescales. However, any long time period is simply the accumulation of many short time periods, and it remains unclear why evolution should appear to act systematically differently across the range of timescales studied. We show that the observed time-dependent behavior can be explained qualitatively by modeling protein sequence evolution as an aggregated Markov process (AMP): a time-homogeneous Markovian substitution model observed only at the level of the amino acids encoded by the protein-coding DNA sequence. The study of AMPs sheds new light on the relationship between amino acid-level and codon-level models of sequence evolution, and our results suggest that protein evolution should be modeled at the codon level rather than using amino acid substitution models.
| S-EPMC3157587 | biostudies-literature
Project description:Bayesian modelling enables us to accommodate complex forms of data and make a comprehensive inference, but the effect of partial misspecification of the model is a concern. One approach in this setting is to modularize the model and prevent feedback from suspect modules, using a cut model. After observing data, this leads to the cut distribution which normally does not have a closed form. Previous studies have proposed algorithms to sample from this distribution, but these algorithms have unclear theoretical convergence properties. To address this, we propose a new algorithm called the stochastic approximation cut (SACut) algorithm as an alternative. The algorithm is divided into two parallel chains. The main chain targets an approximation to the cut distribution; the auxiliary chain is used to form an adaptive proposal distribution for the main chain. We prove convergence of the samples drawn by the proposed algorithm and present the exact limit. Although SACut is biased, since the main chain does not target the exact cut distribution, we prove this bias can be reduced geometrically by increasing a user-chosen tuning parameter. In addition, parallel computing can be easily adopted for SACut, which greatly reduces computation time.
| S-EPMC7612314 | biostudies-literature
Project description:We derive an easily computable quantum speed limit (QSL) time bound for open systems whose initial states can be chosen as either pure or mixed states. Moreover, this QSL time is applicable to either Markovian or non-Markovian dynamics. By using of a hierarchy equation method, we numerically study the QSL time bound in a qubit system interacting with a single broadened cavity mode without rotating-wave, Born and Markovian approximation. By comparing with rotating-wave approximation (RWA) results, we show that the counter-rotating terms are helpful to increase evolution speed. The problem of non-Markovianity is also considered. We find that for non-RWA cases, increasing system-bath coupling can not always enhance the non-Markovianity, which is qualitatively different from the results with RWA. When considering the relation between QSL and non-Markovianity, we find that for small broadening widths of the cavity mode, non-Markovianity can increase the evolution speed in either RWA or non-RWA cases, while, for larger broadening widths, it is not true for non-RWA cases.
| S-EPMC4649631 | biostudies-other
Project description:As systems approaches to the development of biological models become more mature, attention is increasingly focusing on the problem of inferring parameter values within those models from experimental data. However, particularly for nonlinear models, it is not obvious, either from inspection of the model or from the experimental data, that the inverse problem of parameter fitting will have a unique solution, or even a non-unique solution that constrains the parameters to lie within a plausible physiological range. Where parameters cannot be constrained they are termed 'unidentifiable'. We focus on gaining insight into the causes of unidentifiability using inference-based methods, and compare a recently developed measure-theoretic approach to inverse sensitivity analysis to the popular Markov chain Monte Carlo and approximate Bayesian computation techniques for Bayesian inference. All three approaches map the uncertainty in quantities of interest in the output space to the probability of sets of parameters in the input space. The geometry of these sets demonstrates how unidentifiability can be caused by parameter compensation and provides an intuitive approach to inference-based experimental design.
| S-EPMC6073654 | biostudies-literature
Project description:Summary:Biological models contain many parameters whose values are difficult to measure directly via experimentation and therefore require calibration against experimental data. Markov chain Monte Carlo (MCMC) methods are suitable to estimate multivariate posterior model parameter distributions, but these methods may exhibit slow or premature convergence in high-dimensional search spaces. Here, we present PyDREAM, a Python implementation of the (Multiple-Try) Differential Evolution Adaptive Metropolis [DREAM(ZS)] algorithm developed by Vrugt and ter Braak (2008) and Laloy and Vrugt (2012). PyDREAM achieves excellent performance for complex, parameter-rich models and takes full advantage of distributed computing resources, facilitating parameter inference and uncertainty estimation of CPU-intensive biological models. Availability and implementation:PyDREAM is freely available under the GNU GPLv3 license from the Lopez lab GitHub repository at http://github.com/LoLab-VU/PyDREAM. Contact:c.lopez@vanderbilt.edu. Supplementary information:Supplementary data are available at Bioinformatics online.
| S-EPMC5860607 | biostudies-literature
Project description:BackgroundThe inference of a genetic network is a problem in which mutual interactions among genes are deduced using time-series of gene expression patterns. While a number of models have been proposed to describe genetic regulatory networks, this study focuses on a set of differential equations since it has the ability to model dynamic behavior of gene expression. When we use a set of differential equations to describe genetic networks, the inference problem can be defined as a function approximation problem. On the basis of this problem definition, we propose in this study a new method to infer reduced NGnet models of genetic networks.ResultsThrough numerical experiments on artificial genetic network inference problems, we demonstrated that our method has the ability to infer genetic networks correctly and it was faster than the other inference methods. We then applied the proposed method to actual expression data of the bacterial SOS DNA repair system, and succeeded in finding several reasonable regulations. When our method inferred the genetic network from the actual data, it required about 4.7 min on a single-CPU personal computer.ConclusionThe proposed method has an ability to obtain reasonable networks with a short computational time. As a high performance computer is not always available at every laboratory, the short computational time of our method is a preferable feature. There does not seem to be a perfect model for the inference of genetic networks yet. Therefore, in order to extract reliable information from the observed gene expression data, we should infer genetic networks using multiple inference methods based on different models. Our approach could be used as one of the promising inference methods.
| S-EPMC2258286 | biostudies-literature
Project description:In cognitive neuroscience, computational modeling can formally adjudicate between theories and affords quantitative fits to behavioral/brain data. Pragmatically, however, the space of plausible generative models considered is dramatically limited by the set of models with known likelihood functions. For many models, the lack of a closed-form likelihood typically impedes Bayesian inference methods. As a result, standard models are evaluated for convenience, even when other models might be superior. Likelihood-free methods exist but are limited by their computational cost or their restriction to particular inference scenarios. Here, we propose neural networks that learn approximate likelihoods for arbitrary generative models, allowing fast posterior sampling with only a one-off cost for model simulations that is amortized for future inference. We show that these methods can accurately recover posterior parameter distributions for a variety of neurocognitive process models. We provide code allowing users to deploy these methods for arbitrary hierarchical model instantiations without further training.
| S-EPMC8102064 | biostudies-literature
Project description:BackgroundStochastic effects can be important for the behavior of processes involving small population numbers, so the study of stochastic models has become an important topic in the burgeoning field of computational systems biology. However analysis techniques for stochastic models have tended to lag behind their deterministic cousins due to the heavier computational demands of the statistical approaches for fitting the models to experimental data. There is a continuing need for more effective and efficient algorithms. In this article we focus on the parameter inference problem for stochastic kinetic models of biochemical reactions given discrete time-course observations of either some or all of the molecular species.ResultsWe propose an algorithm for inference of kinetic rate parameters based upon maximum likelihood using stochastic gradient descent (SGD). We derive a general formula for the gradient of the likelihood function given discrete time-course observations. The formula applies to any explicit functional form of the kinetic rate laws such as mass-action, Michaelis-Menten, etc. Our algorithm estimates the gradient of the likelihood function by reversible jump Markov chain Monte Carlo sampling (RJMCMC), and then gradient descent method is employed to obtain the maximum likelihood estimation of parameter values. Furthermore, we utilize flux balance analysis and show how to automatically construct reversible jump samplers for arbitrary biochemical reaction models. We provide RJMCMC sampling algorithms for both fully observed and partially observed time-course observation data. Our methods are illustrated with two examples: a birth-death model and an auto-regulatory gene network. We find good agreement of the inferred parameters with the actual parameters in both models.ConclusionsThe SGD method proposed in the paper presents a general framework of inferring parameters for stochastic kinetic models. The method is computationally efficient and is effective for both partially and fully observed systems. Automatic construction of reversible jump samplers and general formulation of the likelihood gradient function makes our method applicable to a wide range of stochastic models. Furthermore our derivations can be useful for other purposes such as using the gradient information for parametric sensitivity analysis or using the reversible jump samplers for full Bayesian inference. The software implementing the algorithms is publicly available at http://cbcl.ics.uci.edu/sgd.
| S-EPMC2914651 | biostudies-literature