JacLy: a Jacobian-based method for the inference of metabolic interactions from the covariance of steady-state metabolome data

Abstract

Reverse engineering metabolome data to infer metabolic interactions is a challenging research topic. Here we introduce JacLy, a Jacobian-based method to infer metabolic interactions of small networks (<20 metabolites) from the covariance of steady-state metabolome data. The approach was applied to two different in silico small-scale metabolome datasets. The power of JacLy lies on the use of steady-state metabolome data to predict the Jacobian matrix of the system, which is a source of information on structure and dynamic characteristics of the system. Besides its advantage of inferring directed interactions, its superiority over correlation-based network inference was especially clear in terms of the required number of replicates and the effect of the use of priori knowledge in the inference. Additionally, we showed the use of standard deviation of the replicate data as a suitable approximation for the magnitudes of metabolite fluctuations inherent in the system.

A closed form for Jacobian reconstruction from time series and its application as an early warning signal in network dynamics

“…Meanwhile the method proposed here may be useful in fields where data are more readily available, such as studies of metabolism, power grids, or economic data. In the study of metabolism Jacobian reconstruction is already frequently used [42], for this application the present work yields an analytic closed-form solution to a problem that is so far solved by machine learning methods. For power grids, reconstructing Jacobians may be particularly interesting because it could yield deeper insights into the functioning of the system in addition to providing an early warning signal.…”

A closed form for Jacobian reconstruction from timeseries and its application as an early warning signal in network dynamics

“…Meanwhile the method proposed here may be useful in fields where data is more readily available, such as studies of metabolism, power grids, or economic data. In the study of metabolism Jacobian reconstruction is already frequently used [36], for this application the present work yields an analytic closed form solution to a problem that is so far solved by machine learning methods. For power grids, reconstructing Jacobians may be particularly interesting because it could yield deeper insights into the functioning of the system in addition to providing an early warning signal.…”

Construction, analysis and assessment of relevance of an algebraic model for a class of biochemical networks

“…The availability of- and accessibility to- empirical- and clinical-datasets has the potential to recreate, without bias, plausible data-driven biochemical networks, infer directionality for a given biochemical network (polynomial equation) or represent an arbitrary state of a modelled network (continuous-time Lyapunov equation) [9-12]. In these approaches perturbations are modelled as stochastic fluctuations and are used to derive the covariance (weak)- or correlation (strong)-interaction matrices for the set of nodes that comprise the modelled biochemical network [13-15]. .…”

“…. This reliance on empirical data both, a priori and a posteriori , along with the computational complexity in computing the Jacobian are limitations in the inferential study of biochemical networks [13-15].…”