Inferring Microbial Interaction Networks from Metagenomic Data Using SgLV-EKF Algorithm

Abstract

Inferring the microbial interaction networks (MINs) and modeling their dynamics are critical in understanding the mechanisms of the bacterial ecosystem and designing antibiotic and/or probiotic therapies. Recently, several approaches were proposed to infer MINs using the generalized Lotka-Volterra (gLV) model. Main drawbacks of these models include the fact that these models only consider the measurement noise without taking into consideration the uncertainties in the underlying dynamics. Furthermore, inferring the MIN is characterized by the limited number of observations and nonlinearity in the regulatory mechanisms. Therefore, novel estimation techniques are needed to address these challenges. This work proposes SgLV-EKF: a stochastic gLV model that adopts the extended Kalman filter (EKF) algorithm to model the MIN dynamics. In particular, SgLV-EKF employs a stochastic modeling of the MIN by adding a noise term to the dynamical model to compensate for modeling uncertainties. This stochastic modeling is more realistic than the conventional gLV model that assumes that the MIN dynamics are perfectly governed by the gLV equations. After specifying the stochastic model structure, we propose the EKF to estimate the MIN. SgLV-EKF was compared with Nelder's and Stein's algorithm on two synthetic data-sets and two real data-sets. The first data-set models the randomness in measurement data, whereas, the second data-set incorporates uncertainties in the dynamics. The real data-sets were taken from a recent study on antibiotic-mediated Clostridium difficile infection. SgLV-EKF outperforms the existing algorithms in terms of robustness to measurement noise, modeling errors, and tracking the dynamics of the MIN. Particularly, SgLV-EKF provides consistent accuracy irrespective of modeling errors whereas Nelder's algorithm diverges and Stein's algorithm infers parameters that lie in the unstable region of the dynamic system. The execution time of SgLV-EKF is comparable to Stein's algorithm, and is tens of times faster than Nelder's algorithm. Performance analysis demonstrates that the proposed SgLV-EKF algorithm provides a powerful and reliable tool to infer MINs and track their dynamics.