Dynamical Model of Drug Accumulation in Bacteria: Sensitivity Analysis and Experimentally Testable Predictions

Predicting permeation of compounds across the outer membrane of P. aeruginosa using molecular descriptors

The ability Gram-negative pathogens have at adapting and protecting themselves against antibiotics has increasingly become a public health threat. Data-driven models identifying molecular properties that correlate with outer membrane (OM) permeation and growth inhibition while avoiding efflux could guide the discovery of novel classes of antibiotics. Here we evaluate 174 molecular descriptors in 1260 antimicrobial compounds and study their correlations with antibacterial activity in Gram-negative Pseudomonas aeruginosa. The descriptors are derived from traditional approaches quantifying the compounds' intrinsic physicochemical properties, together with, bacterium-specific from ensemble docking of compounds targeting specific MexB binding pockets, and all-atom molecular dynamics simulations in different subregions of the OM model. Using these descriptors and the measured inhibitory concentrations, we design a statistical protocol to identify predictors of OM permeation/inhibition. We find consistent rules across most of our data highlighting the role of the interaction between the compounds and the OM. An implementation of the rules uncovered in our study is shown, and it demonstrates the accuracy of our approach in a set of previously unseen compounds. Our analysis sheds new light on the key properties drug candidates need to effectively permeate/inhibit P. aeruginosa, and opens the gate to similar data-driven studies in other Gram-negative pathogens.

New understanding of multidrug efflux and permeation in antibiotic resistance, persistence, and heteroresistance

Antibiotics effective against Gram-negative ESKAPE pathogens are a critical area of unmet need. Infections caused by these pathogens are not only difficult to treat but finding new therapies to overcome Gram-negative resistance is also a challenge. There are not enough antibiotics in development that target the most dangerous pathogens and there are not enough novel drugs in the pipeline. The major obstacle in the antibiotic discovery pipeline is the lack of understanding of how to breach antibiotic permeability barriers of Gram-negative pathogens. These barriers are created by active efflux pumps acting across both the inner and the outer membranes. Overproduction of efflux pumps alone or together with either modification of the outer membrane or antibiotic-inactivating enzymes and target mutations contribute to clinical levels of antibiotics resistance. Recent efforts have generated significant advances in the rationalization of compound efflux and permeation across the cell envelopes of Gram-negative pathogens. Combined with earlier studies and novel mathematical models, these efforts have led to a multilevel understanding of how antibiotics permeate these barriers and how multidrug efflux and permeation contribute to the development of antibiotic resistance and heteroresistance. Here, we discuss the new developments in this area.

The Extent of Antimicrobial Resistance Due to Efflux Pump Regulation

A key mechanism driving antimicrobial resistance (AMR) stems from the ability of bacteria to up-regulate efflux pumps upon exposure to drugs. The resistance gained by this up-regulation is pliable because of the tight regulation of efflux pump levels. This leads to temporary enhancement in survivability of bacteria due to higher efflux pump levels in the presence of antibiotics, which can be reversed when the cells are no longer exposed to the drug. Knowledge of the extent of resistance thus gained would inform intervention strategies aimed at mitigating AMR. Here, we combine mathematical modeling and experiments to quantify the maximum extent of resistance that efflux pump up-regulation can confer via phenotypic induction in the presence of drugs and genotypic abrogation of regulation. Our model describes the dynamics of drug transport in and out of cells coupled with the associated regulation of efflux pump levels and predicts the increase in the minimum inhibitory concentration (MIC) of drugs due to such regulation. To test the model, we measured the uptake and efflux as well as the MIC of the compound ethidium bromide (EtBr), a substrate of the efflux pump LfrA, in wild-type Mycobacterium smegmatis mc²155, as well as in two laboratory-generated strains. Our model captured the observed EtBr levels and MIC fold-changes quantitatively. Further, the model identified key parameters associated with the resulting resistance, variations in which could underlie the extent to which such resistance arises across different drug-bacteria combinations, potentially offering tunable handles to optimize interventions aimed at minimizing AMR.

Unravelling microbial efflux through mathematical modelling

AbstractMathematical modelling is a useful tool that is increasingly used in the life sciences to understand and predict the behaviour of biological systems. This review looks at how this interdisciplinary approach has advanced our understanding of microbial efflux, the process by which microbes expel harmful substances. The discussion is largely in the context of antimicrobial resistance, but applications in synthetic biology are also touched upon. The goal of this paper is to spark further fruitful collaborations between modellers and experimentalists in the efflux community and beyond.

Mutations in respiratory complex I promote antibiotic persistence through alterations in intracellular acidity and protein synthesis

Antibiotic persistence describes the presence of phenotypic variants within an isogenic bacterial population that are transiently tolerant to antibiotic treatment. Perturbations of metabolic homeostasis can promote antibiotic persistence, but the precise mechanisms are not well understood. Here, we use laboratory evolution, population-wide sequencing and biochemical characterizations to identify mutations in respiratory complex I and discover how they promote persistence in Escherichia coli. We show that persistence-inducing perturbations of metabolic homeostasis are associated with cytoplasmic acidification. Such cytoplasmic acidification is further strengthened by compromised proton pumping in the complex I mutants. While RpoS regulon activation induces persistence in the wild type, the aggravated cytoplasmic acidification in the complex I mutants leads to increased persistence via global shutdown of protein synthesis. Thus, we propose that cytoplasmic acidification, amplified by a compromised complex I, can act as a signaling hub for perturbed metabolic homeostasis in antibiotic persisters.

Microscopic Approach to Intrinsic Antibiotic Resistance

The emergence of multidrug resistance in Gram-negative pathogens is critically determined by the interplay between efflux pumps activity and low permeation outer membrane. Although phenotypic heterogeneity in isogenic cells is recognized as a key factor of treatment failure, a mathematical framework able to integrate growth dynamics and single-cell heterogeneity in antimicrobial resistance, remains absent. Here we provide such framework that bridges single-cell and colony scales in the context of bacterial survival and efficacy against drugs. Using experimental inputs, our approach produces testable outputs and reveals nontrivial collective effects with key implications for fitness and survival of the colony. This framework provides a mathematical tool to test stress response strategies in organisms that can potentially guide experiments in natural and synthetic cellular systems.

Nonnegative Matrix Factorization for identification of unknown number of sources emitting delayed signals

Factor analysis is broadly used as a powerful unsupervised machine learning tool for reconstruction of hidden features in recorded mixtures of signals. In the case of a linear approximation, the mixtures can be decomposed by a variety of model-free Blind Source Separation (BSS) algorithms. Most of the available BSS algorithms consider an instantaneous mixing of signals, while the case when the mixtures are linear combinations of signals with delays is less explored. Especially difficult is the case when the number of sources of the signals with delays is unknown and has to be determined from the data as well. To address this problem, in this paper, we present a new method based on Nonnegative Matrix Factorization (NMF) that is capable of identifying: (a) the unknown number of the sources, (b) the delays and speed of propagation of the signals, and (c) the locations of the sources. Our method can be used to decompose records of mixtures of signals with delays emitted by an unknown number of sources in a nondispersive medium, based only on recorded data. This is the case, for example, when electromagnetic signals from multiple antennas are received asynchronously; or mixtures of acoustic or seismic signals recorded by sensors located at different positions; or when a shift in frequency is induced by the Doppler effect. By applying our method to synthetic datasets, we demonstrate its ability to identify the unknown number of sources as well as the waveforms, the delays, and the strengths of the signals. Using Bayesian analysis, we also evaluate estimation uncertainties and identify the region of likelihood where the positions of the sources can be found.

Modeling the Kinetics of the Permeation of Antibacterial Agents into Growing Bacteria and Its Interplay with Efflux

A mathematical model of the passive permeation of a novel solute into bacteria that explicitly accounts for intracellular dilution through growth was developed. A bacterial cell envelope permeability coefficient of approximately >10^-8 cm² · s^-1 is predicted to ensure passive permeation into rapidly replicating bacterial cells. The relative importance of the permeability coefficients of the cytoplasmic and outer membranes of Gram-negative bacteria in determining the overall envelope permeability coefficient was analyzed quantitatively. A mathematical description of the balance between passive influx and active efflux was also developed and shows that bacterial expansion through growth can usually be neglected for compounds likely to be prepared in antibacterial drug discovery programs and the balance between passive inward permeation and active outwardly directed efflux predominates. A new parameter, efflux efficiency (η, where η is equal to k/P, in which k is the rate coefficient for the efflux pump and P is the permeability coefficient for the membrane across which the pump acts), is introduced, and the consequences for the efficiency of efflux pumping by a single pump, two pumps in parallel across either the cytoplasmic or the outer membrane, and two pumps in series, one across the cytoplasmic membrane and one across the outer membrane of Gram-negative bacteria, are explored. The results, showing additive efficiency for two pumps acting across a single membrane and multiplicative efficiency for two pumps acting in series across the cytoplasmic and outer membranes, can be quantitatively related to the ratios between MICs measured against pump-sufficient and pump deletion strains and agree with those of previous experimental and theoretical studies.