A perfect probe: Resonance of underdamped scaled Brownian motion

We numerically investigate the resonance of the underdamped scaled Brownian motion in a bistable system for both cases of a single particle and interacting particles. Through the velocity autocorrelation function (VACF) and mean squared displacement (MSD) of a single particle, we find that for the steady state, diffusions are ballistic at short times and then become normal for most of parameter regimes. However, for certain parameter regimes, both VACF and MSD suggest that the transition between superdiffusion and subdiffusion takes place at intermediate times, and diffusion becomes normal at long times. Via the power spectrum density corresponding to the transitions, we find that there exists a nontrivial resonance. For interacting particles, we find that the interaction between the probe particle and other particles can lead to the resonance, too. Thus we theoretically propose the system with the Brownian particle as a probe, which can detect the temperature of the system and identify the number of the particles or the types of different coupling strengths in the system. The probe is potentially useful for detecting microscopic and nanometer-scale particles and for identifying cancer cells or healthy ones.

Single-cell protein analysis reveals metastable states during the transition to a sensory organ fate

Cell fate decisions can be envisioned as bifurcating dynamical systems, and the decision that Drosophila cells make to undergo sensory organ differentiation has been sucessfully described as such. We have extended these studies by focusing on the Senseless protein, which orchestrates the sensory fate transition. Wing cells contain intermediate Senseless numbers prior to their fate transition, after which they express much greater numbers of Senseless molecules as they differentiate. However, the dynamics are not consistent with it being a simple bistable system. Cells with intermediate Senseless are best modeled as residing in four discrete states, each with a distinct protein number and occupying a specific region of the tissue. Although the four states are stable over time, the number of molecules in each state vary with time. Remarkably, the fold-change in molecule number between adjacent states is invariant and robust to absolute protein number variation. Thus, cells transitioning to sensory fates exhibit metastability with relativistic properties.

Effect of Static Bifurcation on Logical Stochastic Resonance in a Symmetric Bistable System

In previous research works, logical stochastic resonance (LSR) was reported to frequently occur in an asymmetric bistable system, where the bias parameter is the key factor to make the LSR appear. In this work, we investigate the effect of different anharmonic periodic signals on the pitchfork and saddle-node bifurcations in a symmetric bistable system. We focus on the relationship between the static bifurcation and LSR. We use both numerical and circuit simulations to analyze some interesting phenomena. Like the bias parameter, some anharmonic periodic signals also break the symmetry of the symmetric bistable system and lead to the saddle-node bifurcation. The anharmonic periodic signal with a constant term in its expanded Fourier series induces a reliable LSR in the symmetric bistable system. The key factor of LSR is the saddle-node bifurcation which implies the asymmetry of the system. Here, we replace the bias parameter by choosing an anharmonic periodic signal and make the LSR occur in a different way.

Numerical simulation of a class of space fractional bistable systems based on the Fourier spectral method

Nonlinear vibration arises everywhere in a bistable system. The bistable system has been widely applied in physics, biology, and chemistry. In this article, in order to numerically simulate a class of space fractional-order bistable system, we introduce a numerical approach based on the modified Fourier spectral method and fourth-order Runge-Kutta method. The fourth-order Runge-Kutta method is used in time, and the Fourier spectrum is used in space to approximate the solution of the space fractional-order bistable system. Numerical experiments are given to illustrate the effectiveness of this method.

Allosteric mechanism of signal transduction in the two-component system histidine kinase PhoQ

Transmembrane signaling proteins couple extracytosolic sensors to cytosolic effectors. Here, we examine how binding of Mg2+ to the sensor domain of an E. coli two component histidine kinase (HK), PhoQ, modulates its cytoplasmic kinase domain. We use cysteine-crosslinking and reporter-gene assays to simultaneously and independently probe the signaling state of PhoQ's sensor and autokinase domains in a set of over 30 mutants. Strikingly, conservative single-site mutations distant from the sensor or catalytic site strongly influence PhoQ's ligand-sensitivity as well as the magnitude and direction of the signal. Data from 35 mutants are explained by a semi-empirical three-domain model in which the sensor, intervening HAMP, and catalytic domains can adopt kinase-promoting or inhibiting conformations that are in allosteric communication. The catalytic and sensor domains intrinsically favor a constitutively 'kinase-on' conformation, while the HAMP domain favors the 'off' state; when coupled, they create a bistable system responsive to physiological concentrations of Mg2+. Mutations alter signaling by locally modulating domain intrinsic equilibrium constants and interdomain couplings. Our model suggests signals transmit via interdomain allostery rather than propagation of a single concerted conformational change, explaining the diversity of signaling structural transitions observed in individual HK domains.

Multiple molecular events determine stochastic cell fate switching in a eukaryotic bistable system

Eukaryotic transcriptional networks are often large and contain several levels of feedback regulation. Many of these networks exhibit bistability, the ability to generate and stably maintain two distinct transcriptional states and to switch between them. In certain instances, switching between cell states is stochastic, occurring in a small subset of cells of an isogenic population in a seemingly homogenous environment. Given the scarcity and unpredictability of switching in these cases, investigating the determining molecular events is challenging. White-opaque switching in the fungal species Candida albicans is a complex bistable eukaryotic system and can serve as an experimentally accessible model system to study characteristics important for bistability and stochastic cell fate switching. In standard lab media, switching is rare, and genetically identical cells maintain their cellular identity (either “white” or “opaque”) through thousands of cell divisions. By isolating populations of white or opaque cells and measuring switching frequencies, previous studies have elucidated the many differences between the two cell states and identified a set of transcriptional regulators needed for cell type switching. Yet little is known about the molecular events that determine the rare, stochastic switching events that occur in single cells. We use microfluidics combined with fluorescent reporters to directly observe rare switching events between the white and opaque states. We investigate the stochastic nature of switching by beginning with white cells and monitoring the activation of Wor1, a master regulator and marker for the opaque state, in single cells and throughout cell pedigrees. Our results indicate that switching requires two stochastic steps; first an event occurs that predisposes a lineage of cells to switch. In the second step, some but not all, of those predisposed cells rapidly express high levels of Wor1 and commit to the opaque state. To further understand the rapid rise in Wor1, we used a synthetic inducible system in Saccharomyces cerevisiae into which a controllable C. albicans Wor1 and a reporter for its transcriptional control region have been introduced. We document that Wor1 positive autoregulation is highly cooperative (Hill coefficient > 3), leading to rapid activation and producing an “all or none” rather than a graded response. Taken together, our results suggest that reaching a threshold level of a master regulator is sufficient to drive cell type switching in single cells and that an earlier molecular event increases the probability of reaching that threshold in certain small lineages of cells. Quantitative molecular analysis of bistability in the white-opaque circuit can serve as a model for the general understanding of complex circuits.

Elasticity and substitutability of food demand and emerging disease risk on livestock farms

Disease emergence in livestock is a product of environment, epidemiology, and economic forces. The environmental and epidemiological factors contributing to novel pathogen emergence in humans have been studied extensively, but the two-way relationship between farm microeconomics and outbreak risk has received comparably little attention. We introduce a game-theoretic model where farmers produce and sell two goods one of which (e.g. pigs, poultry) is susceptible to infection by a pathogen potentially dangerous to humans. We model market effects and epidemiological effects at both the individual farm level and the community level. The addition of a second good into this modeling framework ensures that producing a unit of livestock has an opportunity cost. We find that in the case of low demand elasticity for livestock meat, the presence of an animal pathogen causing large production losses can lead to a bistable system where two outcomes are possible, depending on the economic inputs into the system. One outcome is succesful disease control. The second outcome, a potentially dangerous one, is a stable equilibrium where farmers slaughter their animals at a low rate, face substantial production losses, but maintain large herds because of the appeal of high meat market prices, therefore maintaining disease circulation. We show the potential epidemiological benefits to (i) policies aimed at stabilizing livestock product prices, (ii) subsidies for alternative agricultural activities during epidemics, and (iii) diversifying agricultural production and sources of proteins available to consumers.

Allosteric mechanism of signal transduction in the two-component system histidine kinase PhoQ

Transmembrane signaling proteins couple extracytosolic sensors to cytosolic effectors. Here, we examine how binding of Mg2+ to the sensor domain of an E. coli two component histidine kinase (HK), PhoQ, modulates its cytoplasmic kinase domain. We use cysteine crosslinking and reporter-gene assays to simultaneously and independently probe the signaling state of PhoQ’s sensor and autokinase domains in a set of over 30 mutants. Strikingly, conservative single-site mutants distant from the sensor or catalytic site strongly influence PhoQ’s ligand-sensitivity as well as the magnitude and direction of the signal, endowing diverse signaling characteristics without need for epistasis. Data from 35 mutants are explained by a semi-empirical 3-domain model in which the sensor, intervening HAMP, and catalytic domains can adopt kinase-promoting or inhibiting conformations, that are in allosteric communication. The catalytic and sensor domains intrinsically favor a constitutively ‘kinase-on’ conformation, while the HAMP favors the ‘off’ state; when coupled, they create a bistable system responsive to physiological [Mg2+]. Mutants alter signaling by locally modulating these intrinsic equilibrium constants and couplings. Our model suggests signals transmit via interdomain allostery rather than propagation of a single concerted conformational change, explaining the diversity of signaling structural transitions observed in individual HK domains.

Emergence of Hidden Attractors through the Rupture of Heteroclinic-Like Orbits of Switched Systems with Self-Excited Attractors

This work is dedicated to the study of an approach that allows the generation of hidden attractors based on a class of piecewise-linear (PWL) systems. The systems produced with the approach present the coexistence of self-excited attractors and hidden attractors such that hidden attractors surround the self-excited attractors. The first part of the approach consists of the generation of self-excited attractors based on pairs of equilibria with heteroclinic orbits. Then, additional equilibria are added to the system to obtain a bistable system with a second self-excited attractor with the same characteristics. It is conjectured that a necessary condition for the existence of the hidden attractor in this class of systems is the rupture of the trajectories that resemble heteroclinic orbits that join the two regions of space that surround the pairs of equilibria; these regions resemble equilibria when seen on a larger scale. With the appearance of a hidden attractor, the system presents a multistable behavior with hidden and self-excited attractors.

The Kinematic Analysis and Bistable Characteristics of the Winding Origami Structure

In the military and aerospace fields, bistable structures with adjustable or adaptive stiffness have been widely applied. Origami structures can be used to design bistable systems due to their unique geometrical characteristics. In this paper, we investigate a special design of winding origami, which consists of a square hub in the center and compactly folded panels around it. This delicate design provides the structure a bistable property. According to its motion characteristics, the folding process of the winding origami can be divided into two stages: the mechanism motion stage and the structural deformation stage. The D-H matrix method and truss transformation method were combined to analyze the kinematic relations, and the winding origami pattern was found to have one degree of freedom. At the structural deformation stage, the mechanical response and the local panel deformation were carefully studied via both experiments and finite element simulations, and a reasonable agreement was reached. It was observed that four creases exhibited a non-uniform folding pattern during the deformation process; that is, a portion of the crease was totally flattened while the rest remained folded. The origami structure’s unique kinematic and bistable features could possibly help provide some new ideas in designing a bistable system in the future.