Bayesian parameter estimation for nonlinear modelling of biological pathways

Ghasemi, Omid; Lindsey, Merry L.; Yang, Tianyi; Nguyen, Nguyen K.; Huang, Yufei; Jin, Yufang

doi:10.1186/1752-0509-5-s3-s9

Cited by 32 publications

(41 citation statements)

References 16 publications

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Section: Introductionmentioning

confidence: 99%

“…It allows us to directly estimate parameter uncertainties, interpret them intuitively as probabilities about parameters conditioned on the data and we are able to seamlessly include prior knowledge. Due to these benefits, Bayesian parameter estimation has seen a strong comeback and is becoming ever so popular (Cronin et al, 2010;Ghasemi et al, 2011).In order to use Bayesian estimation we need to understand three concepts: the likelihood, the prior and the posterior. The likelihood tells us how likely it is, that our data are generated by a given set of parameter-values.…”

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Understanding melanopsin using bayesian generative models − an Introduction

Ehinger

Eickelbeck

Spoida

et al. 2016

Preprint

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Understanding biological processes implies a quantitative description. In recent years a new tool set, Bayesian hierarchical modeling, has seen rapid development. We use these methods to model kinetics of a specific protein in a neuroscience context: melanopsin. Melanopsin is a photoactive protein in retinal ganglion cells. Due to its photoactivity, melanopsin is widely used in optogenetic experiments and an important component in the elucidation of neuronal interactions. Thus it is important to understand the relevant processes and develop mechanistic models. Here, with a focus on methodological aspects, we develop, implement, fit and discuss Bayesian generative models of melanopsin dynamics.We start with a sketch of a basic model and then translate it into formal probabilistic language. As melanopsin occurs in at least two states, a resting and a firing state, a basic model is defined by a non-stationary two state hidden Markov process. Subsequently we add complexities in the form of (1) a hierarchical extension to fit multiple cells; (2) a wavelength dependency, to investigate the response at different color of light stimulation; (3) an additional third state to investigate whether melanopsin is bi-or tri-stable; (4) differences between different sub-types of melanopsin as found in different species. This application of modeling melanopsin dynamics demonstrates several benefits of Bayesian methods. They directly model uncertainty of parameters, are flexible in the distributions and relations of parameters in the modeling, and allow including prior knowledge, for example parameter values based on biochemical data.. CC-BY 4.0 International license not peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was . http://dx.doi.org/10.1101/043273 doi: bioRxiv preprint first posted online Mar. 11, 2016; IntroductionTime-varying data can be analyzed with a multitude of statistical methods. Integrating ordinary or partial differential equations is one of the major tools in the natural sciences. For example in order to analyze the morphology of an action potential we could model the rise and fall by a system of two coupled differential equations. In a linear approximation this results in two exponential functions, where the time-constants of the exponential describe the rise and fall.Alternatively we could use the more complex Hodgkin-Huxley model (Hodgkin and Huxley, 1952). This system of equations does not only better describe the data, but allows a direct interpretation of model variables in terms of molecular and cellular properties. Furthermore, in many experiments, multiple factors influence the dependent variable concurrently and the process of interest is non-stationary. In that case, extracting single time constants can be biased and unable to explain the data. And consequently the mechanistic model should be preferred.The benefit of such generative models is the ability to generate 'fake-data' using previously fitted parameters. It allows t...

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Understanding melanopsin using bayesian generative models − an Introduction

Ehinger

Eickelbeck

Spoida

et al. 2016

Preprint

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“…, n of the trajectory X * , made at time t i . Estimation can be done by classical estimators such as Nonlinear Least Squares (NLS), Maximum Likelihood Estimator (MLE) [27] or Bayesian approaches ( [21], [14], [6] and [15] for example). Nevertheless, the statistical estimation of an ODE model by NLS leads to a difficult nonlinear estimation problem.…”

Section: Such a Model Is Called An Initial Value Problem (Ivp) The Smentioning

confidence: 99%

A tracking approach to parameter estimation in linear ordinary differential equations

Brunel

Clairon

2015

Electron. J. Statist.

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Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data. Classical statistical approaches (nonlinear least squares, maximum likelihood estimator) can give unsatisfactory results because of computational difficulties and ill-posedness of the statistical problem. New estimation methods that use some nonparametric devices have been proposed to circumvent these issues. We present a new estimator that shares properties with Two-Step estimator and Generalized Smoothing (introduced by Ramsay et al. [34]). We introduce a perturbed model and we use optimal control theory for constructing a criterion that aims at minimizing the discrepancy with data and the model. Here, we focus on the case of linear Ordinary Differential Equations as our criterion has a closed-form expression that permits a detailed analysis. Our approach avoids the use of a nonparametric estimator of the derivative, which is one of the main cause of inaccuracy in Two-Step estimators. Moreover, we take into account model discrepancy and our estimator is more robust to model misspecification than classical methods. The discrepancy with the parametric ODE model correspond to the minimum perturbation (or control) to apply to the initial model. Its qualitative analysis can be informative for misspecification diagnosis. In the case of well-specified model, we show the consistency of our estimator and that we reach the parametric √ n− rate when regression splines are used in the first step.

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“…The difficulties of these methods are the estimation of the dimensionality and ill-posed problems and computational inefficiency. Non-linear differential equation based approaches have been also applied to genetic, biochemical network data (Chen et al, 2005;Jones and West, 2005;Ghasemi et al, 2011). For instance, Chen et al developed a stochastic differential equation model for quantifying transcriptional regulatory network in Saccharomyces cerevisiae Jones and West).…”

Section: Introductionmentioning

confidence: 99%

“…Various network and pathway based computational approaches have been developed for modeling time course genomic data to infer and predict the dynamic profiles and gene-gene interactions (Friedman et al, 2000;Gilks and Berzuini, 2001;Kimm et al, 2002;Perrin et al, 2003;Friedman, 2004;Liang and Kelemen, 2004;Yu et al, 2004;Chen et al, 2005;Jones and West, 2005;Dojer et al, 2006;Carvalho and West, 2007;Carvalho et al, 2007a;Li et al, 2007;Shmulevich and Dougherty, 2009;Ghasemi et al, 2011;Grzegorczyk and Husmeier, 2011;Mitra et al, 2013;Peterson et al, 2014). Probabilistic Boolean Networks were developed as models of gene regulatory networks and are able to cope with uncertainty and discover the relative sensitivity of genes in their interactions with other genes (Li et al, 2007;Shmulevich and Dougherty, 2009).…”

Section: Introductionmentioning

confidence: 99%

Bayesian state space models for dynamic genetic network construction across multiple tissues

Liang

Kelemen

2016

Statistical Applications in Genetics and Molecular Biology

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Construction of gene-gene interaction networks and potential pathways is a challenging and important problem in genomic research for complex diseases while estimating the dynamic changes of the temporal correlations and non-stationarity are the keys in this process. In this paper, we develop dynamic state space models with hierarchical Bayesian settings to tackle this challenge for inferring the dynamic profiles and genetic networks associated with disease treatments. We treat both the stochastic transition matrix and the observation matrix time-variant and include temporal correlation structures in the covariance matrix estimations in the multivariate Bayesian state space models. The unevenly spaced short time courses with unseen time points are treated as hidden state variables. Hierarchical Bayesian approaches with various prior and hyper-prior models with Monte Carlo Markov Chain and Gibbs sampling algorithms are used to estimate the model parameters and the hidden state variables. We apply the proposed Hierarchical Bayesian state space models to multiple tissues (liver, skeletal muscle, and kidney) Affymetrix time course data sets following corticosteroid (CS) drug administration. Both simulation and real data analysis results show that the genomic changes over time and gene-gene interaction in response to CS treatment can be well captured by the proposed models. The proposed dynamic Hierarchical Bayesian state space modeling approaches could be expanded and applied to other large scale genomic data, such as next generation sequence (NGS) combined with real time and time varying electronic health record (EHR) for more comprehensive and robust systematic and network based analysis in order to transform big biomedical data into predictions and diagnostics for precision medicine and personalized healthcare with better decision making and patient outcomes.

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Bayesian parameter estimation for nonlinear modelling of biological pathways

Cited by 32 publications

References 16 publications

Understanding melanopsin using bayesian generative models − an Introduction

Understanding melanopsin using bayesian generative models − an Introduction

A tracking approach to parameter estimation in linear ordinary differential equations

Bayesian state space models for dynamic genetic network construction across multiple tissues

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