Identification of microbiota dynamics using robust parameter estimation methods

Abstract

The compositions of in-host microbial communities (microbiota) play a significant role in host health, and a better understanding of the microbiota’s role in a host’s transition from health to disease or vice versa could lead to novel medical treatments. One of the first steps toward this understanding is modeling interaction dynamics of the microbiota, which can be exceedingly challenging given the complexity of the dynamics and difficulties in collecting sufficient data. Methods such as principal differential analysis, dynamic flux estimation, and others have been developed to overcome these challenges. Despite their advantages, these methods are still vastly underutilized in fields such as mathematical biology, and one potential reason for this is their sophisticated implementation. While this paper focuses on applying principal differential analysis to microbiota data, we also provide comprehensive details regarding the derivation and numerics of this method and include a functional implementation for readers’ benefit. For further validation of these methods, we demonstrate the feasibility of principal differential analysis using simulation studies and then apply the method to intestinal and vaginal microbiota data. In working with these data, we capture experimentally confirmed dynamics while also revealing potential new insights into the system dynamics.

Dynamic interaction network inference from longitudinal microbiome data

“…The main drawback of this approach is that individual microbiome entities are treated as independent outcomes, hence, potential relationships between these entities are ignored. An alternative approach involves the use of dynamical systems such as the generalized Lotka-Volterra (gLV) models [6–10]. While gLV and other dynamical systems can help in studying the stability of temporal bacterial communities, they are not well-suited for temporally sparse and non-uniform high-dimensional microbiome time series data (e.g., limited frequency and number of samples), as well as noisy data [3, 10].…”

Parameter and Uncertainty Estimation for Dynamical Systems Using Surrogate Stochastic Processes

“…Solving ordinary differential equation (ODE) model-constrained parameter estimation problems may be computationally challenging for various reasons, including having a limited number of observations, high levels of noise in the data, chaotic system dynamics, nonlinear system models, and large numbers of unknown parameters. Many of these challenges appear in biological systems [71, 3]; hence, parameter estimation for dynamical systems for biological applications is of high interest and an active area of research [72, 9, 50, 51, 19].…”

“…Parameter estimation for the setup described in Figure 1 and (1) amounts to solving an inverse problem . Our inferential scheme is tailored to the setting where one has repeated observations d = [ d 1 ,…, d N ] ⊤ of the states given at discrete time points t = [ t 1 ,…, t N ] ⊤ , as such a setup appears frequently in a diverse set of biological applications (e.g., as in [19, 27, 58, 60, 63]). However, even with such regularity in the data, establishing a coherent parameter and uncertainty estimation scheme with underlying dynamical systems for such observations is challenging.…”

np2QTL: networking phenotypic plasticity quantitative trait loci across heterogeneous environments

“…In the meanwhile, increasing availability of genomewide genotypic data has greatly motivated and inspired the systematic characterization of how each and every QTL interacts with all possible other QTLs in a genetic network. Networks are central to the functionality of complex systems (Newman, 2003) and network reconstruction, aimed at recovering properties of the underlying interconnections of the network in the complex system, have been widely used as an approach for understanding, diagnosing, and controlling the dynamics of diverse networked systems in physics, engineering, biology, and medicine (Bonneau, 2008;Arianos et al, 2009;Stein et al, 2013;Chung et al, 2017). The reconstruction of the most informative network relies on dynamic data, i.e., phenotypic values measured repeatedly at a series of times, although this type of data are not always available.…”