A specialized ODE integrator for the efficient computation of parameter sensitivities

Gonnet, Pedro; Dimopoulos, Sotiris; Widmer, Lukas A.; Stelling, Jörg

doi:10.1186/1752-0509-6-46

Cited by 16 publications

(14 citation statements)

References 44 publications

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“…AMIGO [6], Data2Dynamics [7], MEIGO [54] and SBtoolbox2 [55] could be extended to exploit adjoint sensitivity analysis. In addition to adjoint sensitivity analysis, these MATLAB toolboxes could exploit forward sensitivity analysis available via AMICI, as AMICI yields computation times comparable to those of tailored numerical methods such as odeSD [56] (S1 Supporting Information Section 5 ) or Data2Dynamics [7]. Moreover AMICI comes with detailed documentation and is already now used by several research labs.…”

Section: Discussionmentioning

confidence: 99%

Scalable Parameter Estimation for Genome-Scale Biochemical Reaction Networks

et al. 2017

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Mechanistic mathematical modeling of biochemical reaction networks using ordinary differential equation (ODE) models has improved our understanding of small- and medium-scale biological processes. While the same should in principle hold for large- and genome-scale processes, the computational methods for the analysis of ODE models which describe hundreds or thousands of biochemical species and reactions are missing so far. While individual simulations are feasible, the inference of the model parameters from experimental data is computationally too intensive. In this manuscript, we evaluate adjoint sensitivity analysis for parameter estimation in large scale biochemical reaction networks. We present the approach for time-discrete measurement and compare it to state-of-the-art methods used in systems and computational biology. Our comparison reveals a significantly improved computational efficiency and a superior scalability of adjoint sensitivity analysis. The computational complexity is effectively independent of the number of parameters, enabling the analysis of large- and genome-scale models. Our study of a comprehensive kinetic model of ErbB signaling shows that parameter estimation using adjoint sensitivity analysis requires a fraction of the computation time of established methods. The proposed method will facilitate mechanistic modeling of genome-scale cellular processes, as required in the age of omics.

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Section: Discussionmentioning

confidence: 99%

Scalable Parameter Estimation for Genome-Scale Biochemical Reaction Networks

et al. 2017

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“…where the approximation ignores second-order terms and is based on the sensitivities S ijk : = v vb i m ijk of the k-th observable at time t ij (Marsili-Libelli et al, 2003;Seber and Wild, 2005). We computed the first-and second-order model sensitivities using forward sensitivities during the integration of the ODE system with either CVODES (using the AMICI toolbox: http://ICB-DCM.github.io/ AMICI/) or odeSD (Gonnet et al, 2012).…”

Section: Two-stage Estimation Proceduresmentioning

confidence: 99%

“…We integrated the ODE system with absolute and relative tolerances set to 10 À8 and 10 À4 , respectively, and simultaneously computed the first-order sensitivities with respect to the parameters using the odeSD solver (Gonnet et al, 2012). The sensitivity of the output f(t) with respect to the kinetic parameters k m , g m , and g p was calculated via the chain rule using the first order parameter sensitivities of pðt À tÞ.…”

Section: Estimation For Osmotic Shock Modelmentioning

confidence: 99%

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A Simple and Flexible Computational Framework for Inferring Sources of Heterogeneity from Single-Cell Dynamics

et al. 2019

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Graphical AbstractHighlights d Dynamic single-cell data pose opportunities and challenges for mechanistic models d Non-linear mixed-effects models disentangle sources of cellular heterogeneity d Methods for flexible, scalable parameter inference and for sub-process identification d Several sub-processes contribute dynamically to heterogeneity in yeast endocytosis SUMMARY Single-cell time-lapse data provide the means for disentangling sources of cell-to-cell and intracellular variability, a key step for understanding heterogeneity in cell populations. However, single-cell analysis with dynamic models is a challenging open problem: current inference methods address only single-gene expression or neglect parameter correlations. We report on a simple, flexible, and scalable method for estimating cell-specific and populationaverage parameters of non-linear mixed-effects models of cellular networks, demonstrating its accuracy with a published model and dataset. We also propose sensitivity analysis for identifying which biological sub-processes quantitatively and dynamically contribute to cell-to-cell variability. Our application to endocytosis in yeast demonstrates that dynamic models of realistic size can be developed for the analysis of single-cell data and that shifting the focus from single reactions or parameters to nuanced and time-dependent contributions of subprocesses helps biological interpretation. Generality and simplicity of the approach will facilitate customized extensions for analyzing single-cell dynamics.

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“…The biggest hurdle is most likely the increased computational cost associated with the evaluation of the Jacobian. The matrix D a F pâq can found by various methods ranging from exact to approximate [58,20,30,41,18].…”

Section: Tablementioning

confidence: 99%

On the Importance of the Jacobian Determinant in Parameter Inference for Random Parameter and Random Measurement Error Models

Swigon¹,

Stanhope²,

Zenker³

et al. 2019

SIAM/ASA J. Uncertainty Quantification

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Random parameter models are used to describe natural phenomena governed by deterministic processes in situations where such descriptions require randomness in the parameters of the model (such as model coefficients and initial conditions). Such scenarios arise, for example, due to variability across a spectrum of sources from which data are extracted or across conditions under which data are collected. Random measurement error models describe phenomena that are governed by deterministic processes with fixed parameters, but for which the relation between model outputs and the data is obscured by random errors in the observation process that differ from one observation to the next. Here we revisit the problem of parameter inference for such models and point out the importance of the determinant of the Jacobian of the solution map for the process. The Jacobian deteminant appears in the random parameter model inference as a factor in a transformation of measure formula, and in the random measurement error case as a noninformative prior density that is invariant to parameter space transformations. We use numerical examples to illustrate that, although computationally expensive, the Jacobian determinant is important for accurate parameter density estimates in both cases. We also show that in special cases good approximations can be obtained with less expensive priors as alternatives. Finally, we survey some efficient methods for Jacobian computation.Key words. dynamical systems, parameter distribution, Bayesian inference, prior, inverse map AMS subject classifications. 34A55, 34F05, 37H10, 62F15, 93B30 1. Introduction. Dynamical models of physical or biological systems often include parameters that are not known a priori and cannot be directly measured. Instead, one uses observations of the system and the ability to compute model trajectories for arbitrary parameter sets to deduce information about the parameters via various estimation techniques. These techniques depend on how uncertainty affects the observations of the system, which can be captured by statistical extensions of the model.One common situation is that in which the system can be represented by a deterministic dynamical system with a unique parameter vector but the observed quantities associated with the system are subject to measurement errors. A popular technique of parameter estimation for such random measurement error models is Bayesian inference. It seeks to find a distribution on the space of parameters, called the posterior distribution, that defines the plausibility that any particular parameter set describes the system, given the available data [24,60,50,52,14]. Bayesian parameter estimation requires the prescription of the prior density, which reflects ¦ Submitted to the editors DATE. ).1 The term Jacobian prior has appeared previously [62], in the computation of a marginal with a change of variables, however the context of that usage is different and it does not appear to be a commonly used term.

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A specialized ODE integrator for the efficient computation of parameter sensitivities

Cited by 16 publications

References 44 publications

Scalable Parameter Estimation for Genome-Scale Biochemical Reaction Networks

Scalable Parameter Estimation for Genome-Scale Biochemical Reaction Networks

A Simple and Flexible Computational Framework for Inferring Sources of Heterogeneity from Single-Cell Dynamics

On the Importance of the Jacobian Determinant in Parameter Inference for Random Parameter and Random Measurement Error Models

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