Reversible jump MCMC for multi-model inference in Metabolic Flux Analysis

Abstract

Motivation The validity of model based inference, as used in systems biology, depends on the underlying model formulation. Often, a vast number of competing models is available, that are built on different assumptions, all consistent with the existing knowledge about the studied biological phenomenon. As a remedy for this, Bayesian Model Averaging (BMA) facilitates parameter and structural inferences based on multiple models simultaneously. However, in fields where a vast number of alternative, high-dimensional and non-linear models are involved, the BMA-based inference task is computationally very challenging. Results Here we use BMA in the complex setting of Metabolic Flux Analysis (MFA) to infer whether potentially reversible reactions proceed uni- or bidirectionally, using 13C labeling data and metabolic networks. BMA is applied on a large set of candidate models with differing directionality settings, using a tailored multi-model Markov Chain Monte Carlo (MCMC) approach. The applicability of our algorithm is shown by inferring the in vivo probability of reaction bidirectionalities in a realistic network setup, thereby extending the scope of 13C MFA from parameter to structural inference. Supplementary information Supplementary data are available at Bioinformatics online.

Bayesian multi-model-based 13C15N-metabolic flux analysis quantifies carbon-nitrogen metabolism in mycobacteria

“…Here, models M i , are structural variants that differ in their bidirectionality setting and, hence, number of flux parameters ( v M i ). Equation (EQ 1) is solved computationally by using a recently developed tailored Markov chain Monte Carlo (MCMC) approach ( 26 ) (see Materials and Methods for details). This results in so-called marginal posterior probability distributions for the net fluxes, as well as the probabilities of reversible reactions being uni- or bidirectional.…”

“…Flux inference with Bayesian Model Averaging: Instead of conventional optimization-based single-model flux inference, in this work metabolic fluxes were estimated using a Bayesian multi-model approach. More precisely, net fluxes and reaction bidirectionalities were inferred simultaneously by employing BMA, implemented using a tailored MCMC approach ( 26 ). Herein, 13CFLUX2 was used for likelihood computation.…”

“…This problem is exacerbated when measurements cannot distinguish between labelling contributions stemming from 13 C and 15 N tracers, such as measurements obtained from single quadrupole MS instruments with insufficient mass resolution. To overcome the impediments of current single-model 13 C-MFA approaches, we used a statistically rigorous multi-model inference approach (26), which we here generalize to 13…”

Quantitative modeling of pentose phosphate pathway response to oxidative stress reveals a cooperative regulatory strategy

“…On the other hand, flux analysis from 13 C-labeling data and parameter estimation from flux and concentration data are based on Monte Carlo sampling methods (Saa and Nielsen, 2016; St. John et al ., 2019; Valderrama-Bahamóndez and Fröhlich, 2019; Theorell and Nöh, 2020) so as generate a representative sample of kinetic models consistent with experimental measurement values and their uncertainties. From such model ensemble, we perform a comprehensive set of analysis regarding parameter distributions, transient dynamical responses, doseresponse properties and gain/loss-of-function phenotypes, which portrays the manner how allosteric regulations contribute to the metabolic response upon oxidative stress.…”

PolyRound: polytope rounding for random sampling in metabolic networks

“…Random sampling of constraint-based models of metabolism is a powerful approach to characterize the potential behaviors of metabolic networks ( Schellenberger and Palsson, 2009 ; Herrmann et al , 2019 ). The field is actively developed, for example, with recent extensions to model inference ( Theorell and Nöh, 2020 ). Algorithmically, Markov Chain Monte Carlo (MCMC) based coordinate hit-and-run with rounding (CHRR) ( Haraldsdóttir et al , 2017 ) showed superior performance in computational benchmarks ( Herrmann et al , 2019 ) and it is available in a highly efficient and modular implementation ( Jadebeck et al , 2021 ).…”