Generalizing Gillespie’s Direct Method to Enable Network-Free Simulations

Suderman, Ryan; Mitra, Eshan D.; Lin, Yen Ting; Erickson, Keesha E.; Feng, Song; Hlavacek, William S.

doi:10.1007/s11538-018-0418-2

Cited by 15 publications

(17 citation statements)

References 72 publications

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“…It could be a system of nonlinear ODEs that are numerically integrated to generate deterministic time courses for each chemical species. It could also be a stochastic model simulated using Gillespie's direct method [18], for example, or a network-free method [19], such as that implemented in NFsim [20]. In network-free methods, the system state is tracked in terms of the set of molecules currently present in the system, without enumerating all possible chemical species and reactions (which could be too many to practically enumerate).…”

Section: Model Formulationmentioning

confidence: 99%

Parameter estimation and uncertainty quantification for systems biology models

Mitra

Hlavacek

2019

Current Opinion in Systems Biology

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Mathematical models can provide quantitative insight into immunoreceptor signaling, but require parameterization and uncertainty quantification before making reliable predictions. We review currently available methods and software tools to address these problems. We consider gradient-based and gradient-free methods for point estimation of parameter values, and methods of profile likelihood, bootstrapping, and Bayesian inference for uncertainty quantification. We consider recent and potential future applications of these methods to systems-level modeling of immune-related phenomena. Highlights• Models of immunoreceptor signaling often contain parameters that must be fit to data.• New tools including PyBioNetFit and AMICI support automated parameter estimation.• Optimization algorithms can be used to obtain point estimates of parameter values.• Parameter estimation can incorporate both quantitative and qualitative data.• Uncertainty quantification assesses confidence in parameter values and model predictions.

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Section: Model Formulationmentioning

confidence: 99%

Parameter estimation and uncertainty quantification for systems biology models

Mitra

Hlavacek

2019

Current Opinion in Systems Biology

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“…KMC procedures are also useful for studying systems, such as cell signaling networks, that have large state spaces 4 arising from the combinatorial number of chemical species that can be generated by biomolecular interactions of interest 5 . For such systems, it may be impracticable, even with the aid of a computer, to enumerate the chemical species that are potentially populated.…”

Section: Introductionmentioning

confidence: 99%

“…For such systems, it may be impracticable, even with the aid of a computer, to enumerate the chemical species that are potentially populated. Nonetheless, simulations can be performed by formulating rules to represent biomolecular interactions 5 and then using these rules as event generators in a so-called network-free simulation algorithm 4 , such as that implemented in the NFsim software package 6,7 . In a networkfree simulation (of cell signaling dynamics), stochastic effects may be negligible 8 .…”

Section: Introductionmentioning

confidence: 99%

Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks

Lin

Hlavacek

2019

The Journal of Chemical Physics

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Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. Here, we present a new acceleration algorithm based on adaptive and heterogeneous scaling of reaction rates and stoichiometric coefficients. The algorithm is conceptually related to the commonly used idea of accelerating a stochastic simulation by considering a sub-volume λΩ (0 < λ < 1) within a system of interest, which reduces the number of reaction events per unit time occurring in a simulation by a factor 1/λ at the cost of greater error in unbiased estimates of first moments and biased overestimates of second moments. Our new approach offers two unique benefits. First, scaling is adaptive and heterogeneous, which eliminates the pitfall of overaggressive scaling. Second, there is no need for an a priori classification of populations as discrete or continuous (as in a hybrid method), which is problematic when discreteness of a chemical species changes during a simulation. The method requires specification of only a single algorithmic parameter, N c , a global critical population size above which populations are effectively scaled down to increase simulation efficiency. The method, which we term partial scaling, is implemented in the open-source BioNetGen software package. We demonstrate that partial scaling can significantly accelerate simulations without significant loss of accuracy for several published models of biological systems. These models characterize activation of the mitogen-activated protein kinase ERK, prion protein aggregation, and T-cell receptor signaling. arXiv:1903.08615v2 [q-bio.QM]

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“…However, if the state of one tyrosine residue does not influence the state of others, then the same system of interactions could be fully captured with only 2 n equations. One way to overcome the combinatorial explosion problem is with network-free simulation algorithms that avoid the explicit specification or derivation of all possible states [32–36]. A second option is model reduction, in which an approximate model is derived by neglecting sparsely populated species [37].…”

Section: Introductionmentioning

confidence: 99%

Modeling cell line-specific recruitment of signaling proteins to the insulin-like growth factor 1 receptor

et al. 2019

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Receptor tyrosine kinases (RTKs) typically contain multiple autophosphorylation sites in their cytoplasmic domains. Once activated, these autophosphorylation sites can recruit downstream signaling proteins containing Src homology 2 (SH2) and phosphotyrosine-binding (PTB) domains, which recognize phosphotyrosine-containing short linear motifs (SLiMs). These domains and SLiMs have polyspecific or promiscuous binding activities. Thus, multiple signaling proteins may compete for binding to a common SLiM and vice versa. To investigate the effects of competition on RTK signaling, we used a rule-based modeling approach to develop and analyze models for ligand-induced recruitment of SH2/PTB domain-containing proteins to autophosphorylation sites in the insulin-like growth factor 1 (IGF1) receptor (IGF1R). Models were parameterized using published datasets reporting protein copy numbers and site-specific binding affinities. Simulations were facilitated by a novel application of model restructuration, to reduce redundancy in rule-derived equations. We compare predictions obtained via numerical simulation of the model to those obtained through simple prediction methods, such as through an analytical approximation, or ranking by copy number and/or KD value, and find that the simple methods are unable to recapitulate the predictions of numerical simulations. We created 45 cell line-specific models that demonstrate how early events in IGF1R signaling depend on the protein abundance profile of a cell. Simulations, facilitated by model restructuration, identified pairs of IGF1R binding partners that are recruited in anti-correlated and correlated fashions, despite no inclusion of cooperativity in our models. This work shows that the outcome of competition depends on the physicochemical parameters that characterize pairwise interactions, as well as network properties, including network connectivity and the relative abundances of competitors.

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Generalizing Gillespie’s Direct Method to Enable Network-Free Simulations

Cited by 15 publications

References 72 publications

Parameter estimation and uncertainty quantification for systems biology models

Parameter estimation and uncertainty quantification for systems biology models

Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks

Modeling cell line-specific recruitment of signaling proteins to the insulin-like growth factor 1 receptor

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