Microbial metabolism and growth under conditions of starvation modelled as the sliding mode of a differential inclusion

ABSTRACT

We consider a model of bacterial growth with variable internal stores, extended with adaptive resource allocation and investigate the behaviour of this model under conditions of starvation, i.e. severe nutrient shortage, treating the behaviour under the starvation regime in terms of a differential inclusion, and derive Filippov solutions. This Filippov sliding mode representation appears to be simple but sound qualitative description of metabolic ‘shut down’ in response to starvation. We discuss a natural connection between biologically motivated modelling approaches to metabolic ‘shut down’ and numerical regularisation techniques to approximate Filippov solutions.

KEYWORDS:

• Piecewise smooth systems of ordinary differential equations
• Filippov solutions
• sliding modes
• microbial growth and metabolism
• starvation response
• metabolic shut down

MCS/CCS/AMS Classification/CR Category numbers:

• 34A60, 92B05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

O. A. Nev was supported by EU Research Framework programme 7 Marie Curie Actions, grant 316630, Centre for Analytical Science Innovative Doctoral Programme (CAS-IDP).