epi-scenario-4

[djinnome]

Scenario 4: Microbial Regnets

The human gut microbiome is an increasingly important area of study for multiple infectious diseases and chronic conditions, including COVID-19 and long COVID. However, characterizing the dynamics of microbial ecology, which includes the interactions between microbes and with their environment, is a major challenge. This scenario is a proof-of-concept to demonstrate that ASKEM can utilize regulatory network models to grapple with such questions.

1. Consider a simple system of 4 microbial species with a variety of competitive and mutualistic interactions amongst each other. Given a set of initial microbial populations, a set of inferred growth rates for each species, and an interaction matrix representing the negative (competitive or inhibitory) or positive (mutualistic or beneficial) effects that the presence of one species has on another in the microbial ecosystem… construct a model of the system utilizing the generalized Lotka-Volterra equation below:

$$\frac{dx_i}{dt} = x_i\left(r_i + \sum_{j=1}^n a_{ij}x_j\right)$$

This system represents a community of n species, where $x_i$ is the population of species $i$,
$r_i$ is the intrinsic growth rate of species $i$, and $a_ij$ represents the interaction coefficient between species $i$ and $j$.

2. Simulate the interactions between each species for a 30-day period, with time steps of 1 day. Plot the population size of each species over the 30-day time period. Use the following parameter and initial conditions data to configure the model:

	Species 1	Species 2	Species 3	Species 4
Growth rate (CFU/day)	0.53	0.42	0.49	0.33
Initial conditions (in CFU/arbitrary unit area)	0.51	0.39	0.88	0.4

Interaction Matrix (effect on growth rate, CFU/day)	Species 1	Species 2	Species 3	Species 4
Species 1	-0.5	-0.01	0.002	-0.009
Species 2	0	-0.5	0	-0.169
Species 3	-0.002	-0.003	-0.5	0.02
Species 4	0	-0.226	-0.04	-0.5

The output should match the plot below.

[djinnome]

3. Update the model to reflect a six species model, using the parameter and initial conditions data below:

	Species 1	Species 2	Species 3	Species 4	Species 5	Species 6
Growth rate (CFU/day)	0.53	0.42	0.49	0.33	0.7	0.3
Initial conditions (in CFU/arbitrary unit area)	0.51	0.39	0.88	0.4	0.2	0.8

	Species 1	Species 2	Species 3	Species 4	Species 5	Species 6
Species 1	-0.5	-0.01	0.002	-0.009	-0.002	0.01
Species 2	0	-0.5	0	-0.169	0	0
Species 3	-0.002	-0.003	-0.5	0.02	0.03	-0.04
Species 4	0	-0.226	-0.04	-0.5	0	0.01
Species 5	0	-0.1	-0.02	0	-0.5	0
Species 6	0	-0.04	-0.05	0	0	-0.5

The output should match the plot below: