F-Actin Bending Facilitates Net Actomyosin Contraction By Inhibiting Expansion With Plus-End-Located Myosin Motors

We investigate whether a microscopic system of two semi-flexible actin filaments with an attached myosin motor can facilitate contraction. Based on energy minimisation, we derive and analyse a partial differential equation model for a two-filament-motor structure embedded within a dense, two-dimensional network. Our method enables calculation of the plane stress tensor, providing a measure for contractility. After deriving the model, we use a combination of asymptotic analysis and numerical solutions to show how F-actin bending facilitates net contraction as a myosin motor traverses two symmetric filaments. Myosin motors close to the minus-ends facilitate contraction, whereas motors close to the plus-ends facilitate expansion. The leading-order solution for rigid filaments exhibits polarity-reversal symmetry, such that the contractile and expansive components balance to zero. Surprisingly, after introducing bending the first-order correction to stress indicates expansion. However, numerical solutions show that filament bending induces a geometric asymmetry that brings the filaments closer to parallel as a myosin motor approaches their plus-ends. This decreases the effective spring force opposing motion of the motor, enabling it to move faster close to filament plus-ends. This reduces the contribution of expansive stress, giving rise to net contraction. Further numerical solutions confirm that this applies beyond the small bending regime considered in the asymptotic analysis. Our findings confirm that filament bending gives rise to microscopic-scale actomyosin contraction, and provides a possible explanation for network-scale contraction.

Modelling locust foraging: How and why food affects group formation

Locusts are short horned grasshoppers that exhibit two behaviour types depending on their local population density. These are: solitarious, where they will actively avoid other locusts, and gregarious where they will seek them out. It is in this gregarious state that locusts can form massive and destructive flying swarms or plagues. However, these swarms are usually preceded by the aggregation of juvenile wingless locust nymphs. In this paper we attempt to understand how the distribution of food resources affect the group formation process. We do this by introducing a multi-population partial differential equation model that includes non-local locust interactions, local locust and food interactions, and gregarisation. Our results suggest that, food acts to increase the maximum density of locust groups, lowers the percentage of the population that needs to be gregarious for group formation, and decreases both the required density of locusts and time for group formation around an optimal food width. Finally, by looking at foraging efficiency within the numerical experiments we find that there exists a foraging advantage to being gregarious.

Nonlinear Partial Differential Equation Model-Based Coordination Control for a Master–Slave Two-Link Rigid–Flexible Manipulator With Vibration Repression

In this study, vibration control problem is considered for a coordinative master–slave two-link rigid–flexible manipulator. By the help of Hamilton's principle, the dynamic model of the master–slave two-link rigid–flexible manipulator is expressed using nonlinear partial differential equations (PDEs). Based on the nonlinear PDE model, we propose a novel coordination controller for the master–slave system. The proposed controller can achieve the following three objectives: (1) making the master manipulator track the given angles; (2) making the slave manipulator track the angles of the master manipulator; and (3) repressing the deflection and vibration of both the master and the slave flexible manipulators. Stability analysis of the closed-loop system is proven by LaSalle's invariance principle. Two simulation cases are given to validate the effectiveness of the coordination controller.

Geographical Distributions and Equilibrium in Social Norm-Related Behavior in the United States

This research examines the geographical distribution of behavior in line with social norms that are spread and maintained primarily by the effect of social conformity. These include widely held norms that good citizens vote, don’t commit crimes, get flu vaccinations, abstain from binge drinking, and comply with census reporting. A partial differential equation model is used to determine whether such behavior may have attained a geospatial equilibrium in the United States. An equilibrium, as the end state of a diffusion process, has definitive mathematical properties that can be used to test for equilibrium. This is done using recent data for the 48 contiguous states. Results confirm that behavior for several important social norms fits the equilibrium model geographically. Policy implications are briefly discussed.

Vibration control of nonlinear three-dimensional length-varying string with input quantization

This article studies the stability problem for a three-dimensional string with variable length in the case of input quantization. A nonlinear partial differential equation model is used to depict the dynamic characteristics of the length-varying flexible string with distributed variable parameters. The control signals are effectively mapped from a continuous region to a discrete set of numerical signals before being transmitted through communication channels using quantizers. With no information about quantizers, the vibration of the string is eliminated under the proposed adaptive quantized control despite of the actuator degradation, and the stability of the closed-loop system is demonstrated based on the Lyapunov’s direct method. Simulation results are supplied to show the effectiveness of the presented control strategy.