Comparison of parameter estimation methods in stochastic chemical kinetic models: Examples in systems biology

Gupta, Ankur; Rawlings, James B.

doi:10.1002/aic.14409

Cited by 33 publications

(30 citation statements)

References 37 publications

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“…For example, Lipniacki et al [14,64] proposed a hybrid stochastic-deterministic model of the TNFα-induced NFκB signaling pathway that was able to reproduce the heterogeneous responses observed in the single-cell measurements [14,65] and identify possible origins of the heterogeneity. However, stochastic simulation algorithms are computationally expensive, and they are difficult to fit to experimental measurements for model validation [7,66,67]. A more viable method is a semi-stochastic model, which uses deterministic modeling with model parameters that have distributions [5][6][7], to reduce the computational cost while still studying the cell-to-cell variability.…”

Section: Discussionmentioning

confidence: 99%

Mathematical Modeling and Parameter Estimation of Intracellular Signaling Pathway: Application to LPS-induced NFκB Activation and TNFα Production in Macrophages

et al. 2018

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Due to the intrinsic stochasticity, the signaling dynamics in a clonal population of cells exhibit cell-to-cell variability at the single-cell level, which is distinct from the population-average dynamics. Frequently, flow cytometry is widely used to acquire the single-cell level measurements by blocking cytokine secretion with reagents such as Golgiplug ™ . However, Golgiplug ™ can alter the signaling dynamics, causing measurements to be misleading. Hence, we developed a mathematical model to infer the average single-cell dynamics based on the flow cytometry measurements in the presence of Golgiplug ™ with lipopolysaccharide (LPS)-induced NFκB signaling as an example. First, a mathematical model was developed based on the prior knowledge. Then, average single-cell dynamics of two key molecules (TNFα and IκBα) in the NFκB signaling pathway were measured through flow cytometry in the presence of Golgiplug ™ to validate the model and maximize its prediction accuracy. Specifically, a parameter selection and estimation scheme selected key model parameters and estimated their values. Unsatisfactory results from the parameter estimation guided subsequent experiments and appropriate model improvements, and the refined model was calibrated again through the parameter estimation. The inferred model was able to make predictions that were consistent with the experimental measurements, which will be used to construct a semi-stochastic model in the future.

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Section: Discussionmentioning

confidence: 99%

Mathematical Modeling and Parameter Estimation of Intracellular Signaling Pathway: Application to LPS-induced NFκB Activation and TNFα Production in Macrophages

et al. 2018

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“…The theory of stochastic systems with random delays is well-understood [31,32]. The Gillespie algorithm,…”

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confidence: 99%

Bayesian inference of distributed time delay in transcriptional and translational regulation

Choi

Cheng

Cinar

et al. 2019

Preprint

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Motivation: Advances in experimental and imaging techniques have allowed for unprecedented insights into the dynamical processes within individual cells. However, many facets of intracellular dynamics remain hidden, or can be measured only indirectly. This makes it challenging to reconstruct the regulatory networks that govern the biochemical processes underlying various cell functions. Current estimation techniques for inferring reaction rates frequently rely on marginalization over unobserved processes and states. Even in simple systems this approach can be computationally challenging, and can lead to large uncertainties and lack of robustness in parameter estimates. Therefore we will require alternative approaches to efficiently uncover the interactions in complex biochemical networks.Results: We propose a Bayesian inference framework based on replacing uninteresting or unobserved reactions with time delays. Although the resulting models are non-Markovian, recent results on stochastic systems with random delays allow us to rigorously obtain expressions for the likelihoods of model parameters. In turn, this allows us to extend MCMC methods to efficiently estimate reaction rates, and delay distribution parameters, from single-cell assays. We illustrate the advantages, and potential pitfalls, of the approach using a birth-death model with both synthetic and experimental data, and show that we can robustly infer model parameters using a relatively small number of measurements. We demonstrate how to do so even when only the relative molecule count within the cell is measured, as in the case of fluorescence microscopy. Introduction 1The dynamics of intracellular processes are determined by the structure and rates of interactions between 2 different molecular species. However, stochasticity and limitations of experimental methods make it difficult 3 to infer the characteristics of these interactions from data. On the single-cell level, different molecular 4 species can occur in small number, correlate with phenotype, and localize within different parts of the cell. 5The resulting dynamics can thus be highly variable over time, and across the population. Averaging over 6 such fluctuations can lead to inaccurate representations of the underlying biology [1], and inference methods 7 therefore need to account for stochasticity within individual cells, and variability across the population [2-5].8 Different statistical approaches have been developed to fit stochastic models to data from single-cell 9 assays, offering a window into the dynamical processes within individual cells [6][7][8][9][10][11][12][13]. Among these, Bayesian 10 methods have been particularly promising. To apply Bayesian techniques, one typically assumes a model 11 for the network of interactions, postulates a prior over model parameters, and uses experimental data to 12 determine a posterior and estimates of unknown parameters [6,[13][14][15]. However, Bayesian approaches can 13 suffer from the curse of dimensionality [16], and are thus difficult to i...

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“…MCMC sampling can be combined with importance sampling to reduce computational complexity and simulation times (Golightly et al, 2015). Conditional density importance sampling (CDIS) is introduced in (Gupta and Rawlings, 2014) as an alternative to MCMC parameter estimation. MCMC methods for high-dimensional systems are compared in (Septier and Peters, 2016).…”

Section: Monte Carlo Methodsmentioning

confidence: 99%

“…Parameter likelihoods can be updated assuming increments and decrements of the species counts (Lecca et al, 2009). Probabilistic state space representation of BRNs as dynamic systems was considered in (Andreychenko et al, 2011;Gupta and Rawlings, 2014;McGoff et al, 2015;Schnoerr et al, 2017). Augmented state space representation of BRN from ordinary differential equations (ODEs) is obtained in (Baker et al, 2013).…”

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confidence: 99%

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

2019

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The key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their non-linear dynamics. The model dynamics are crucially dependent on the parameter values which are often estimated from observations. Over the past decade, the interest in parameter and state estimation in models of (bio-) chemical reaction networks (BRNs) grew considerably. The related inference problems are also encountered in many other tasks including model calibration, discrimination, identifiability, and checking, and optimum experiment design, sensitivity analysis, and bifurcation analysis. The aim of this review paper is to examine the developments in literature to understand what BRN models are commonly used, and for what inference tasks and inference methods. The initial collection of about 700 documents concerning estimation problems in BRNs excluding books and textbooks in computational biology and chemistry were screened to select over 270 research papers and 20 graduate research theses. The paper selection was facilitated by text mining scripts to automate the search for relevant keywords and terms. The outcomes are presented in tables revealing the levels of interest in different inference tasks and methods for given models in the literature as well as the research trends are uncovered. Our findings indicate that many combinations of models, tasks and methods are still relatively unexplored, and there are many new research opportunities to explore combinations that have not been considered—perhaps for good reasons. The most common models of BRNs in literature involve differential equations, Markov processes, mass action kinetics, and state space representations whereas the most common tasks are the parameter inference and model identification. The most common methods in literature are Bayesian analysis, Monte Carlo sampling strategies, and model fitting to data using evolutionary algorithms. The new research problems which cannot be directly deduced from the text mining data are also discussed.

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Comparison of parameter estimation methods in stochastic chemical kinetic models: Examples in systems biology

Cited by 33 publications

References 37 publications

Mathematical Modeling and Parameter Estimation of Intracellular Signaling Pathway: Application to LPS-induced NFκB Activation and TNFα Production in Macrophages

Mathematical Modeling and Parameter Estimation of Intracellular Signaling Pathway: Application to LPS-induced NFκB Activation and TNFα Production in Macrophages

Bayesian inference of distributed time delay in transcriptional and translational regulation

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

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