Mathematical Model for Growth and Rifampicin-Dependent Killing Kinetics of Escherichia coli Cells.

Antibiotic resistance is a global health threat. We urgently need better strategies to improve antibiotic use to combat antibiotic resistance. Currently, there are a limited number of antibiotics in the treatment repertoire of existing bacterial infections. Among them, rifampicin is a broad-spectrum antibiotic against various bacterial pathogens. However, during rifampicin exposure, the appearance of persisters or resisters decreases its efficacy. Hence, to benefit more from rifampicin, its current standard dosage might be reconsidered and explored using both computational tools and experimental or clinical studies. In this study, we present the mathematical relationship between the concentration of rifampicin and the growth and killing kinetics of Escherichia coli cells. We generated time-killing curves of E. coli cells in the presence of 4, 16, and 32 µg/mL rifampicin exposures. We specifically focused on the oscillations with decreasing amplitude over time in the growth and killing kinetics of rifampicin-exposed E. coli cells. We propose the solution form of a second-order linear differential equation for a damped oscillator to represent the mathematical relationship. We applied a nonlinear curve fitting solver to time-killing curve data to obtain the model parameters. The results show a high fitting accuracy.

Coupling of cell fate selection model enhances DNA damage response and may underlie BE phenomenon.

Double-strand break-induced (DSB) cells send signal that induces DSBs in neighbour cells, resulting in the interaction among cells sharing the same medium. Since p53 network gives oscillatory response to DSBs, such interaction among cells could be modelled as an excitatory coupling of p53 network oscillators. This study proposes a plausible coupling model of three-mode two-dimensional oscillators, which models the p53-mediated cell fate selection in globally coupled DSB-induced cells. The coupled model consists of ATM and Wip1 proteins as variables. The coupling mechanism is realised through ATM variable via a mean-field modelling the bystander signal in the intercellular medium. Investigation of the model reveals that the coupling generates more sensitive DNA damage response by affecting cell fate selection. Additionally, the authors search for the cause-effect relationship between coupled p53 network oscillators and bystander effect (BE) endpoints. For this, they search for the possible values of uncertain parameters that may replicate BE experiments' results. At certain parametric regions, there is a correlation between the outcomes of cell fate and endpoints of BE, suggesting that the intercellular coupling of p53 network may manifest itself as the form of observed BEs.

Two-dimensional polynomial type canonical relaxation oscillator model for p53 dynamics.

p53 network, which is responsible for DNA damage response of cells, exhibits three distinct qualitative behaviours; low state, oscillation and high state, which are associated with normal cell cycle progression, cell cycle arrest and apoptosis, respectively. The experimental studies demonstrate that these dynamics of p53 are due to the ATM and Wip1 interaction. This paper proposes a simple two-dimensional canonical relaxation oscillator model based on the identified topological structure of ATM and Wip1 interaction underlying these qualitative behaviours of p53 network. The model includes only polynomial terms that have the interpretability of known ATM and Wip1 interaction. The introduced model is useful for understanding relaxation oscillations in gene regulatory networks. Through mathematical analysis, we investigate the roles of ATM and Wip1 in forming of these three essential behaviours, and show that ATM and Wip1 constitute the core mechanism of p53 dynamics. In agreement with biological findings, we show that Wip1 degradation term is a highly sensitive parameter, possibly related to mutations. By perturbing the corresponding parameters, our model characterizes some mutations such as ATM deficiency and Wip1 overexpression. Finally, we provide intervention strategies considering our observation that Wip1 seems to be an important target to conduct therapies for these mutations.

Revealing determinants of two-phase dynamics of P53 network under gamma irradiation based on a reduced 2D relaxation oscillator model.

This study proposes a two-dimensional (2D) oscillator model of p53 network, which is derived via reducing the multidimensional two-phase dynamics model into a model of ataxia telangiectasia mutated (ATM) and Wip1 variables, and studies the impact of p53-regulators on cell fate decision. First, the authors identify a 6D core oscillator module, then reduce this module into a 2D oscillator model while preserving the qualitative behaviours. The introduced 2D model is shown to be an excitable relaxation oscillator. This oscillator provides a mechanism that leads diverse modes underpinning cell fate, each corresponding to a cell state. To investigate the effects of p53 inhibitors and the intrinsic time delay of Wip1 on the characteristics of oscillations, they introduce also a delay differential equation version of the 2D oscillator. They observe that the suppression of p53 inhibitors decreases the amplitudes of p53 oscillation, though the suppression increases the sustained level of p53. They identify Wip1 and P53DINP1 as possible targets for cancer therapies considering their impact on the oscillator, supported by biological findings. They model some mutations as critical changes of the phase space characteristics. Possible cancer therapeutic strategies are then proposed for preventing these mutations' effects using the phase space approach.