Likelihood-free nested sampling for parameter inference of biochemical reaction networks

Abstract

The development of mechanistic models of biological systems is a central part of Systems Biology. One major challenge in developing these models is the accurate inference of model parameters. In recent years, nested sampling methods have gained increased attention in the Systems Biology community due to the fact that they are parallelizable and provide error estimates with no additional computations. One drawback that severely limits the usability of these methods, however, is that they require the likelihood function to be available, and thus cannot be applied to systems with intractable likelihoods, such as stochastic models. Here we present a likelihood-free nested sampling method for parameter inference which overcomes these drawbacks. This method gives an unbiased estimator of the Bayesian evidence as well as samples from the posterior. We derive a lower bound on the estimators variance which we use to formulate a novel termination criterion for nested sampling. The presented method enables not only the reliable inference of the posterior of parameters for stochastic systems of a size and complexity that is challenging for traditional methods, but it also provides an estimate of the obtained variance. We illustrate our approach by applying it to several realistically sized models with simulated data as well as recently published biological data. We also compare our developed method with the two most popular other likelioodfree approaches: pMCMC and ABC-SMC. The C++ code of the proposed methods, together with test data, is available at the github web page https://github.com/Mijan/LFNS_paper.

Optogenetic actuator/ERK biosensor circuits identify MAPK network nodes that shape ERK dynamics

“…For the parameter inference, we used a Nested Sampling algorithm as described in (Mikelson and Khammash 2020). The inference was performed on the ETH High-performance Cluster Euler and was done using the parallel implementation on 48 cores.…”

“…For the modeling of the two smaller models (without feedback (Figure S3E) or without endocytosis (Figure S3H)), we set the corresponding parameters ( IYZ and >,[ ) to zero. For the parameter inference we used a Nested Sampling algorithm as described in (Mikelson and Khammash, 2020). The inference was performed on the ETH Highperformance Cluster Euler and was done using the parallel implementation on 48 cores.…”

“…We also included a receptor level inactivation process for EGFR, but not for optoFGFR, to account for EGF-dependent regulatory mechanisms. We used a Bayesian inference approach (Mikelson and Khammash 2020) to infer the model parameters from averaged ERK trajectories in response to sustained low optoFGFR input with or without sustained EGFR pre-stimulation (Figure 3E). After identification of parameters that allowed the model to capture the training dataset (Figure 3F), we simulated ERK dynamics evoked by low EGFR input (adaptative, oscillatory ERK dynamics), high EGFR input (adaptative ERK dynamics without oscillation) and sustained high optoFGFR input (sustained ERK dynamics) (Figure 3G).…”

“…The inference was performed on the ETH Highperformance Cluster Euler and was done using the parallel implementation on 48 cores. The algorithm was run for 24 hours or until the algorithm stopped because the termination criterion 𝛥 -./0 (see (Mikelson and Khammash 2020) for details) was −∞.…”

Nested sampling for materials

“…The NS technique has been quickly taken up in the field of astrophysics [31][32][33][34][35] and gravitational wave data analysis [36,37], and has gradually been adapted to explore the parameter space in a wide range of disciplines, such as data analysis [38], signal processing [39], phylogenetics [40], and systems biology [41,42].…”