Antibiotic treatments often fail to eliminate bacterial populations due to heterogeneity in how individual cells respond to the drug. In structured bacterial populations such as biofilms, bacterial metabolism and environmental transport processes lead to an emergent phenotypic structure and self-generated nutrient gradients toward the interior of the colony, which can affect cell growth, gene expression and susceptibility to the drug. Even in single cells, survival depends on a dynamic interplay between the drug’s action and the expression of resistance genes. How expression of resistance is coordinated across populations in the presence of such spatiotemporal environmental coupling remains elusive. Using a custom microfluidic device, we observe the response of spatially extended microcolonies of tetracycline-resistant E. coli to precisely defined dynamic drug regimens. We find an intricate interplay between drug-induced changes in cell growth and growth-dependent expression of resistance genes, resulting in the redistribution of metabolites and the reorganization of growth patterns. This dynamic environmental feedback affects the regulation of drug resistance differently across the colony, generating dynamic phenotypic structures that maintain colony growth during exposure to high drug concentrations and increase population-level resistance to subsequent exposures. A mathematical model linking metabolism and the regulation of gene expression is able to capture the main features of spatiotemporal colony dynamics. Uncovering the fundamental principles that govern collective mechanisms of antibiotic resistance in spatially extended populations will allow the design of optimal drug regimens to counteract them.
Many countries worldwide that were successful in containing the first wave of the COVID-19 epidemic are faced with the seemingly impossible choice between the resurgence of infections and endangering the economic and mental well-being of their citizens. While blanket measures are slowly being lifted and infection numbers are monitored, a systematic strategy for balancing contact restrictions and the freedom necessary for a functioning society long-term in the absence of a vaccine is currently lacking. Here, we propose a regional strategy with locally triggered containment measures that can largely circumvent this trade-off and substantially lower the magnitude of restrictions the average individual will have to endure in the near future. For the simulation of future disease dynamics and its control, we use current data on the spread of COVID-19 in Germany, Italy, England, New York State and Florida, taking into account the regional structure of each country and their past lockdown efficiency. Overall, our analysis shows that tight regional control in the short term can lead to long-term net benefits due to small-number effects which are amplified by the regional subdivision and crucially depend on the rate of cross-regional contacts. We outline the mechanisms and parameters responsible for these benefits and suggest possible was to gain access to them, simultaneously achieving more freedom for the population and successfully containing the epidemic. Our open-source simulation code is freely available and can be readily adapted to other countries. We hope that our analysis will help create sustainable, theory-driven long-term strategies for the management of the COVID-19 epidemic until therapy or immunization options are available.
Dynamical billiards are paradigmatic examples of chaotic Hamiltonian dynamical systems with widespread applications in physics. We study how well their Lyapunov exponent, characterizing the chaotic dynamics, and its dependence on external parameters can be estimated from phase space volume arguments, with emphasis on billiards with mixed regular and chaotic phase spaces. We show that in the very diverse billiards considered here the leading contribution to the Lyapunov exponent is inversely proportional to the chaotic phase space volume, and subsequently discuss the generality of this relationship. We also extend the well established formalism by Dellago, Posch, and Hoover to calculate the Lyapunov exponents of billiards to include external magnetic fields and provide a software implementation of it.From the foundations of statistical physics to transport properties of electronic devices, in many areas of physics billiard models are an important tool for understanding complex dynamics. In a billiard model a point particle is moving freely (and frictionless) on a flat (or constantly curved) surface until it hits the boundary of the billiard where it is specularly reflected. Chaotic dynamics in the billiard are characterized by a positive Lyapunov exponent, measuring how initially close trajectories separate exponentially fast. Obtaining its value so far usually requires detailed numerical simulations of the chaotic dynamics. In our paper we assess how well the Lyapunov exponent can be estimated from quite general considerations. Especially we study how parameter changes that vary the phase space structure of the billiard get reflected in the Lyapunov exponent. For example the application of an external magnetic field can force some trajectories in the billiard on closed cyclotron orbits. We show how the mere existence of such orbits varies the Lyapunov exponent of the chaotic dynamics through the phase space volume they occupy . The knowledge of this connection will be helpful to understand physical mechanisms in many systems like the magneto-transport in graphene nanostructures.
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