Theoretical investigation of stochastic clearance of bacteria: first-passage analysis

Abstract

<jats:p>Understanding mechanisms of bacterial eradication is critically important for overcoming failures of antibiotic treatments. Current studies suggest that the clearance of large bacterial populations proceeds deterministically, while for smaller populations, the stochastic effects become more relevant. Here, we develop a theoretical approach to investigate the bacterial population dynamics under the effect of antibiotic drugs using a method of first-passage processes. It allows us to explicitly evaluate the most important characteristics of bacterial clearance dynamics such as extinction probabilities and extinction times. The new meaning of minimal inhibitory concentrations for stochastic clearance of bacterial populations is also discussed. In addition, we investigate the effect of fluctuations in population growth rates on the dynamics of bacterial eradication. It is found that extinction probabilities and extinction times generally do not correlate with each other when random fluctuations in the growth rates are taking place. Unexpectedly, for a significant range of parameters, the extinction times increase due to these fluctuations, indicating a slowing in the bacterial clearance dynamics. It is argued that this might be one of the initial steps in the pathway for the development of antibiotic resistance. Furthermore, it is suggested that extinction times is a convenient measure of bacterial tolerance.</jats:p>

Resist or perish: fate of a microbial population subjected to a periodic presence of antimicrobial

“…So far, we considered antimicrobial drugs above the MIC, allowing deterministic extinction 295 in the absence of resistance for long enough drug exposure times. However, sub-MIC drugs 296 can also have a major impact on the evolution of resistance, by selecting for resistance 297 without killing large microbial populations, and moreover by facilitating stochastic 298 extinctions in finite-sized microbial populations [18][19][20]. In the sub-MIC regime where 299 f S > g S , the population has a nonzero deterministic equilibrium size N = K(1 − g S /f S ) 300 in the presence of antimicrobial.…”

Resist or perish: Fate of a microbial population subjected to a periodic presence of antimicrobial

“…However, it is particularly crucial to address both of them when studying the evolution of antimicrobial resistance, because the aim of an antimicrobial treatment is to eradicate a microbial population, or at least to substantially decrease its size, while the evolution of resistance corresponds to a change in the genetic makeup of the population. Our general model allows us to fully incorporate the stochasticity of mutation occurrence and establishment [13][14][15][16][17], as well as that of population extinction, whose practical importance was recently highlighted [18][19][20].…”

Adapt or perish: Evolutionary rescue in a gradually deteriorating environment

“…Conversely, for 330 t 0 > θ, mutants are fitter than wild-type organisms, and S mutants are fitter than G mutants: hence, S mutants 331 are always more extreme than G mutants. Because of this, intuition based on the fixation times within the Moran 332 process [57,62,66] with constant population size make us expect that S mutants will have their fates sealed faster, 333 and thus will get extinct faster provided that they are destined for extinction. This is indeed what we obtain (see 334 Fig.…”

“…Intuitively, mutants that are strongly deleterious or beneficial have their fates sealed faster than 223 neutral ones. Furthermore, in the framework of the Moran process (with constant population size and fitnesses), 224 extinction times are longest for neutral mutants [57,62,66]. While the time to extinction is not crucial to our study 225 of rescue by a single mutation, it can become relevant to more complex processes involving several mutations, e.g.…”

“…In principle, the time variability of the division rates imposes a difficulty [56], but the 81 sort duration of time intervals between individual events allows us to neglect rate variations between events (see 82 Supporting Information, section 8 for details). Our model allows us to fully account for the stochasticity of mutation 83 occurrence and establishment [57][58][59][60][61], as well as that of population extinction [16,62,63].…”