Background: The ability to rapidly adapt to adverse environmental conditions represents the key of success of many pathogens and, in particular, of Mycobacterium tuberculosis. Upon exposition to heat shock, antibiotics or other sources of stress, appropriate responses in terms of genes transcription and proteins activity are activated leading part of a genetically identical bacterial population to express a different phenotype, namely to develop persistence. When the stress response network is mathematically described by an ordinary differential equations model, development of persistence in the bacterial population is associated with bistability of the model, since different emerging phenotypes are represented by different stable steady states. Results: In this work, we develop a mathematical model of SigE stress response network that incorporates interactions not considered in mathematical models currently available in the literature. We provide, through involved analytical computations, accurate approximations of the system’s nullclines, and exploit the obtained expressions to determine, in a reliable though computationally efficient way, the number of equilibrium points of the system. Conclusions: Theoretical analysis and perturbation experiments point out the crucial role played by the degradation pathway involving RseA, the anti-sigma factor of SigE, for coexistence of two stable equilibria and the emergence of bistability. Our results also indicate that a fine control on RseA concentration is a necessary requirement in order for the system to exhibit bistability.
Mathematical modelling of SigE regulatory network reveals new insights into bistability of mycobacterial stress response
Zorzan I.;Del Favero S.;Giaretta A.;Manganelli R.;Di Camillo B.;Schenato L.
2021
Abstract
Background: The ability to rapidly adapt to adverse environmental conditions represents the key of success of many pathogens and, in particular, of Mycobacterium tuberculosis. Upon exposition to heat shock, antibiotics or other sources of stress, appropriate responses in terms of genes transcription and proteins activity are activated leading part of a genetically identical bacterial population to express a different phenotype, namely to develop persistence. When the stress response network is mathematically described by an ordinary differential equations model, development of persistence in the bacterial population is associated with bistability of the model, since different emerging phenotypes are represented by different stable steady states. Results: In this work, we develop a mathematical model of SigE stress response network that incorporates interactions not considered in mathematical models currently available in the literature. We provide, through involved analytical computations, accurate approximations of the system’s nullclines, and exploit the obtained expressions to determine, in a reliable though computationally efficient way, the number of equilibrium points of the system. Conclusions: Theoretical analysis and perturbation experiments point out the crucial role played by the degradation pathway involving RseA, the anti-sigma factor of SigE, for coexistence of two stable equilibria and the emergence of bistability. Our results also indicate that a fine control on RseA concentration is a necessary requirement in order for the system to exhibit bistability.
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