Lysogenic Propensity in Stressed Environments as a function of Muliplicity of Infection

Description: Research project, undertaken with Supreet Saini, IIT Bombay

Introduction

We are trying to understand the impact of environmental stresses on the coexistence of phage-bacteria systems. A phage-bacteria system can be characterized with the following parameters:

• phage and bacterial populations (jointly expressed using multiplicity of infection (MoI))
• bacterial growth rate: (r)
• phage burst rate: (a)
• bacterial degradation rate: (lambda_b)
• phage degradation rate: (lambda_p)

Some of the pertinent literature in this area covers:

• the impact of the phage degradation rate on coexistence (Heilmann et al., (2010))
• a bet-hedging approach to ensure survival in case of sporadic spikes of degradation rates (Maslov and Sneppen, (2015))
• the stochasticity in the lysogeny-lysis decision at a higher MoI (Avlund et al., (2009))
• a game theoretic approach to investigate the lysogenic propensity for different MoI (Sinha et al., (2017))

We are working on expanding the domain of exploration to include a range of environmental conditions. One possible use case is to simulate the effect of antibiotics on the coexistence of the populations - how the optimal propensity of lysogeny should change in different stress conditions.

Methods

We consider two additional parameters to describe the environment:

• Probability of good environment for phages: (p₁)
• Probability of good environment for bacteria: (p₂)

Our first approach was to observe the result of running Gillespie simulations on fixed curves of Probability of Lysogeny P(lyso) versus Multiplicity of Infection MoI for individual values of p₁ and p₂. The code for this iteration is included in Run1. This approach validated our proposition that for the chosen values, the time for which the phage and the bacteria coexist increases with higher lysogeni propensity.

Our next approach was a slightly novel one - instead of running the entire Gillespie simulation till one of the species went extinct, we chose a novel single echelon method. The idea behind this approach is that the coexistence of the two-species system may be best assured by choosing an action which leads to an MoI closest to 1. We run this simulation for all values of p₁ and p₂ each in the range [0.1,0.2,...,1.0] for five different cases:

• alt_run: lambda_p = 1, lambda_b = 0.1
• alt_run2: lambda_p = 2, lambda_b = 0.1
• alt_run3: lambda_p = 2, lambda_b = 1.0
• alt_run4: lambda_p = 3, lambda_b = 0.1
• alt_run5: lambda_p = 2, lambda_b = 2.0

The table below recapitulates the parameters used along with their description and range of values:

Parameter	Description	Value(s)
MoI	The ratio of total phages to bacteria in the system	[0.01,0.02,...,2.0]
lambdap	The rate of degradation of phages during bad environment	[1,2,3]
lambdab	The rate of degradation of bacteria during bad environment	[0.1,1,2]
r	bacterial rate of growth	[1,2,5]
a	burst factor (phage amplification factor)	[10]
p1	probability of occurence of a good environment period for phages	[0.1,0.2,...,1.0]
p2	probability of occurence of a good environment period for bacteria	[0.1,0.2,...,1.0]

The resulting graphical results have been added here and here.

Current work:

• Visualising the overall trends in a better manner
• Selecting more appropriate values of the parameters and widening the range chosen
• Explaining this phenomenon better through the genetic pathway regulation