Filtering and inference for stochastic oscillators with distributed delays

Calderazzo, Silvia; Brancaccio, Marco; Finkenstädt, Bärbel

doi:10.1093/bioinformatics/bty782

Cited by 25 publications

(59 citation statements)

References 53 publications

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“…However, using 27 such models involves a compromise: Adding delay can lead to other challenges, as the resulting models are 28 typically non-Markovian. In particular, this complicates the derivation of parameter likelihood functions,Bayesian inference of distributed time delay Choi et al making such models more difficult to analyze and use for parameter inference [35,36]. Thus, developing a 30 general inference framework for biochemical reaction networks with distributed delays that works even when 31 molecule counts are low remains a challenging open problem.…”

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“…Thus, developing a 30 general inference framework for biochemical reaction networks with distributed delays that works even when 31 molecule counts are low remains a challenging open problem. Important progress has been made for certain 32 delay stochastic differential equations [35], and delay linear noise approximations [36]. These approaches 33 rest on the assumption that molecule counts are high enough to allow delay stochastic differential equations 34 to accurately capture system dynamics [31].…”

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confidence: 99%

“…Bayesian inference of distributed time delay Choi et al making such models more difficult to analyze and use for parameter inference [35,36]. Thus, developing a 30 general inference framework for biochemical reaction networks with distributed delays that works even when 31 molecule counts are low remains a challenging open problem.…”

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confidence: 99%

“…In the generative model, we used gamma distributed delay in the birth reactions, assuming that creation 157 of protein is the result of a chain of exponentially distributed monomolecular reaction steps [19,20], 158 approximable by a gamma distribution [21,35,36]. We generated 500 sample trajectories from the model 159 given by Eq.…”

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confidence: 99%

“…Specifically, [35] have developed a Bayesian algorithm using SDE models containing 290 distributed delay, with particular emphasis on oscillations generated by delayed negative feedback loops [55]. 291 Recently, a filtering approach based on LNAs has been developed to infer distributed delays [36]. An 292 interesting avenue for future research is to develop hybrid models, and combine our method with previous 293 SDE or LNA approaches to gain both in computational speed and accuracy.…”

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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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