Bayesian model discovery for reverse-engineering biochemical networks from data

Abstract

The reverse engineering of gene regulatory networks based on gene expression data is a challenging inference task. A related problem in computational systems biology lies in identifying signalling networks that perform particular functions, such as adaptation. Indeed, for many research questions, there is an ongoing search for efficient inference algorithms that can identify the simplest model among a larger set of related models. To this end, in this paper, we introduce SLInG, a Bayesian sparse likelihood-free inference method using Gibbs sampling. We demonstrate that SLInG can reverse engineer stochastic gene regulatory networks from single-cell data with high accuracy, outperforming state-of-the-art correlation-based methods. Furthermore, we show that SLInG can successfully identify signalling networks that execute adaptation. Sparse hierarchical Bayesian inference thus provides a versatile tool for model discovery in systems biology and beyond.

Inference of the core gene regulatory network underlying seam cell development inCaenorhabditis elegans

“…To constrain the parameters of our 20 model variants to data, we use the recently developed Bayesian model discovery approach, SLING. In short, SLING attempts to find the simplest model that explains the data by fitting parameters of the model, setting parameters associated with regulatory links not required to explain the data to zero (see Jørgensen et al, 2023, and Methods for more details). This approach helps to avoid overfitting complex models and encourages simpler models that can explain the data.…”

“…The adaptation of the MRA algorithm (Kholodenko et al, 2002) to genetic hypomorphs has given us the flexibility to work without gene knockouts, which was necessary in this case as two out of the three core factors represent essential genes. The MRA produced an initial quantitative description of the network, which we built on by searching among a series of ODE models, using the recently proposed Bayesian model discovery approach, SLI n G (Jørgensen et al, 2023). This also allowed us to narrow down which interactions are essential to explain the data resulting in several candidate ODE models using different regulatory logics.…”

“…This kind of inference problem is sometimes called equation or model discovery (Brunton et al, 2016; Alahmadi et al, 2020; Both et al, 2021). A novel Bayesian model discovery approach called SLING (Sparse Likelihood-free Inference using Gibbs) uses sparsity-inducing priors to find the simplest model among a library of related models that can explain a given set of data (Jørgensen et al, 2023). This approach, which is simulation-based and related to Approximate Bayesian Computation (ABC) (Beaumont, 2019), is applicable to non-linear or stochastic models of biochemical networks.…”

“…This approach, which is simulation-based and related to Approximate Bayesian Computation (ABC) (Beaumont, 2019), is applicable to non-linear or stochastic models of biochemical networks. The method has been used for the inference of GRNs based on synthetic data (Jørgensen et al, 2023), but it remains to be applied to real data.…”

“…Based on the MRA results, we construct a detailed ODE model of the GRN, including all possible regulatory links. We then use the recently developed Bayesian model discovery tool SLING (Jørgensen et al, 2023) to both estimate the parameter values and assess which links are necessary for the gene network to explain and predict experimental data. Taken together, we propose a new network architecture for the core seam cell gene regulatory network.…”