  The generalized Lotka-Volterra (gLV) equations are a mathematical proxy for
ecological dynamics. We focus on a gLV model of the gut microbiome, in which
the evolution of the gut microbial state is determined in part by pairwise
inter-species interaction parameters that encode environmentally-mediated
resource competition between microbes. We develop an in silico method that
controls the steady-state outcome of the system by adjusting these interaction
parameters. This approach is confined to a bistable region of the gLV model.
The two steady states of interest are idealized as either a "healthy" or
"diseased" steady state of the gut microbiome. In this method, a dimensionality
reduction technique called steady-state reduction (SSR) is first used to
generate a two-dimensional (2D) gLV model that approximates the
high-dimensional dynamics on the 2D subspace spanned by the two steady states.
Then a bifurcation analysis of the 2D model analytically determines parameter
modifications that drive a disease-prone initial condition to the healthy
steady state. This parameter modification of the reduced 2D model guides
parameter modifications of the original high-dimensional model, resulting in a
change of steady-state outcome in the high-dimensional model. This control
method, called SPARC (SSR-guided parameter change), bypasses the computational
challenge of directly determining parameter modifications in the original
high-dimensional system. SPARC could guide the development of indirect
bacteriotherapies, which seek to change microbial compositions by deliberately
modifying gut environmental variables such as gut acidity or macronutrient
availability.
