Highly inclined light sheet allows volumetric super-resolution imaging of efflux pumps distribution in bacterial biofilms.

Bacterial biofilms are highly complex communities in which isogenic bacteria display different gene expression patterns and organize in a three-dimensional mesh gaining enhanced resistance to biocides. The molecular mechanisms behind such increased resistance remain mostly unknown, also because of the technical difficulties in biofilm investigation at the sub-cellular and molecular level. In this work we focus on the AcrAB-TolC protein complex, a multidrug efflux pump found in Enterobacteriaceae, whose overexpression is associated with most multiple drug resistance (MDR) phenotypes occurring in Gram-negative bacteria. We propose an optical method to quantify the expression level of the AcrAB-TolC pump within the biofilm volume at the sub-cellular level, with single-molecule sensitivity. Through a combination of super-resolution PALM with single objective light sheet and precision genome editing, we can directly quantify the spatial distribution of endogenous AcrAB-TolC pumps expressed in both planktonic bacteria and, importantly, within the bacterial biofilm volume. We observe a gradient of pump density within the biofilm volume and over the course of biofilm maturation. Notably, we propose an optical method that could be broadly employed to achieve volumetric super-resolution imaging of thick samples.

Exchange Rate Dynamics and Central Bank Interventions: On the (De)Stabilizing Nature of Targeting Long-Run Fundamentals Interventions.

We develop a foreign exchange market model in which a market maker adjusts the exchange rate with respect to the trading behavior of chartists, fundamentalists and a central bank. While chartists bet on the persistence of bull and bear markets, fundamentalists speculate on mean reversion. The central bank seeks to stabilize the foreign exchange market by placing buy (sell) orders when the undervaluation (overvaluation) of the exchange rate exceeds a certain threshold. Since a one-dimensional piecewise-linear discontinuous map with three branches determines the evolution of the exchange rate, we use a combination of analytical and numerical tools to explore the extent to which the central bank is able to tame the behavior of the foreign exchange market.

Border collision bifurcation of a resonant closed invariant curve.

This paper contributes to studying the bifurcations of closed invariant curves in piecewise-smooth maps. Specifically, we discuss a border collision bifurcation of a repelling resonant closed invariant curve (a repelling saddle-node connection) colliding with the border by a point of the repelling cycle. As a result, this cycle becomes attracting and the curve is destroyed, while a new repelling closed invariant curve appears (not in a neighborhood of the previously existing invariant curve), being associated with quasiperiodic dynamics. This leads to a global restructuring of the phase portrait since both curves mentioned above belong to basin boundaries of coexisting attractors.

α-catenin switches between a slip and an asymmetric catch bond with F-actin to cooperatively regulate cell junction fluidity.

α-catenin is a crucial protein at cell junctions that provides connection between the actin cytoskeleton and the cell membrane. At adherens junctions (AJs), α-catenin forms heterodimers with ß-catenin that are believed to resist force on F-actin. Outside AJs, α-catenin forms homodimers that regulates F-actin organization and directly connect the cell membrane to the actin cytoskeleton, but their mechanosensitive properties are inherently unknown. By using ultra-fast laser tweezers we found that a single α-ß-catenin heterodimer does not resist force but instead slips along F-actin in the direction of force. Conversely, the action of 5 to 10 α-ß-catenin heterodimers together with force applied toward F-actin pointed end engaged a molecular switch in α-catenin, which unfolded and strongly bound F-actin as a cooperative catch bond. Similarly, an α-catenin homodimer formed an asymmetric catch bond with F-actin triggered by protein unfolding under force. Our data suggest that α-catenin clustering together with intracellular tension engage a fluid-to-solid phase transition at the membrane-cytoskeleton interface.

Dissecting Mechanoenzymatic Properties of Processive Myosins with Ultrafast Force-Clamp Spectroscopy.

Ultrafast force-clamp spectroscopy (UFFCS) is a single molecule technique based on laser tweezers that allows the investigation of the chemomechanics of both conventional and unconventional myosins under load with unprecedented time resolution. In particular, the possibility to probe myosin motors under constant force right after the actin-myosin bond formation, together with the high rate of the force feedback (200 kHz), has shown UFFCS to be a valuable tool to study the load dependence of fast dynamics such as the myosin working stroke. Moreover, UFFCS enables the study of how processive and non-processive myosin-actin interactions are influenced by the intensity and direction of the applied force. By following this protocol, it will be possible to perform ultrafast force-clamp experiments on processive myosin-5 motors and on a variety of unconventional myosins. By some adjustments, the protocol could also be easily extended to the study of other classes of processive motors such as kinesins and dyneins. The protocol includes all the necessary steps, from the setup of the experimental apparatus to sample preparation, calibration procedures, data acquisition and analysis.

Memory effects on binary choices with impulsive agents: Bistability and a new BCB structure.

After the seminal works by Schelling, several authors have considered models representing binary choices by different kinds of agents or groups of people. The role of the memory in these models is still an open research argument, on which scholars are investigating. The dynamics of binary choices with impulsive agents has been represented, in the recent literature, by a one-dimensional piecewise smooth map. Following a similar way of modeling, we assume a memory effect which leads the next output to depend on the present and the last state. This results in a two-dimensional piecewise smooth map with a limiting case given by a piecewise linear discontinuous map, whose dynamics and bifurcations are investigated. The map has a particular structure, leading to trajectories belonging only to a pair of straight lines. The system can have, in general, only attracting cycles, but the related periods and periodicity regions are organized in a complex structure of the parameter space. We show that the period adding structure, characteristic for the one-dimensional case, also persists in the two-dimensional one. The considered cycles have a symbolic sequence which is obtained by the concatenation of the symbolic sequences of cycles, which play the role of basic cycles in the bifurcation structure. Moreover, differently from the one-dimensional case, the coexistence of two attracting cycles is now possible. The bistability regions in the parameter space are investigated, evidencing the role of different kinds of codimension-two bifurcation points, as well as in the phase space and the related basins of attraction are described.

High-Speed Optical Tweezers for the Study of Single Molecular Motors.

Mechanical transitions in molecular motors often occur on a submillisecond time scale and rapidly follow binding of the motor with its cytoskeletal filament. Interactions of nonprocessive molecular motors with their filament can be brief and last for few milliseconds or fraction of milliseconds. The investigation of such rapid events and their load dependence requires specialized single-molecule tools. Ultrafast force-clamp spectroscopy is a constant-force optical tweezers technique that allows probing such rapid mechanical transitions and submillisecond kinetics of biomolecular interactions, which can be particularly valuable for the study of nonprocessive motors, single heads of processive motors, or stepping dynamics of processive motors. Here we describe a step-by-step protocol for the application of ultrafast force-clamp spectroscopy to myosin motors. We give indications on optimizing the optical tweezers setup, biological constructs, and data analysis to reach a temporal resolution of few tens of microseconds combined with subnanometer spatial resolution. The protocol can be easily generalized to other families of motor proteins.

A piecewise smooth model of evolutionary game for residential mobility and segregation.

The paper proposes an evolutionary version of a Schelling-type dynamic system to model the patterns of residential segregation when two groups of people are involved. The payoff functions of agents are the individual preferences for integration which are empirically grounded. Differently from Schelling's model, where the limited levels of tolerance are the driving force of segregation, in the current setup agents benefit from integration. Despite the differences, the evolutionary model shows a dynamics of segregation that is qualitatively similar to the one of the classical Schelling's model: segregation is always a stable equilibrium, while equilibria of integration exist only for peculiar configurations of the payoff functions and their asymptotic stability is highly sensitive to parameter variations. Moreover, a rich variety of integrated dynamic behaviors can be observed. In particular, the dynamics of the evolutionary game is regulated by a one-dimensional piecewise smooth map with two kink points that is rigorously analyzed using techniques recently developed for piecewise smooth dynamical systems. The investigation reveals that when a stable internal equilibrium exists, the bimodal shape of the map leads to several different kinds of bifurcations, smooth, and border collision, in a complicated interplay. Our global analysis can give intuitions to be used by a social planner to maximize integration through social policies that manipulate people's preferences for integration.

2D discontinuous piecewise linear map: Emergence of fashion cycles.

We consider a discrete-time version of the continuous-time fashion cycle model introduced in Matsuyama, 1992. Its dynamics are defined by a 2D discontinuous piecewise linear map depending on three parameters. In the parameter space of the map periodicity, regions associated with attracting cycles of different periods are organized in the period adding and period incrementing bifurcation structures. The boundaries of all the periodicity regions related to border collision bifurcations are obtained analytically in explicit form. We show the existence of several partially overlapping period incrementing structures, that is, a novelty for the considered class of maps. Moreover, we show that if the time-delay in the discrete time formulation of the model shrinks to zero, the number of period incrementing structures tends to infinity and the dynamics of the discrete time fashion cycle model converges to those of continuous-time fashion cycle model.