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We modify the Peyrard–Bishop–Holstein model and bring out the influence of the torsion and solvent interactions on charge transport in DNA. Through the linear stability analysis, we detect regions of instability and we compare the results with those of the standard Peyrard–Bishop–Holstein model. There are two regimes where modulated charge patterns can occur: the undertwisted and the overtwisted conformations. Numerical simulations are used to confirm our analytical predictions. Charge patterns are obtained and propagate more easily in an overwinded helix than in an underwinded one. The effects of dissipation and thermal fluctuations are also studied, which confirm the robustness of the obtained modulated patterns. On the one hand, we argue that in the absence of twisting, temperature can lead to the breaking of the hydrogen bonds between bases and prevent charges from propagating. On the other hand, when the molecule is overtwisted, the solvent and the temperature will rather enhance charge spreading patterns with random features. [ABSTRACT FROM AUTHOR]

Modulational instability is utilized to investigate intercellular Ca 2+ wave propagation in an array of diffusively coupled cells. Cells are supposed to be connected via paracrine signaling, where long-range effects, due to the presence of extracellular messengers, are included. The multiple-scale expansion is used to show that the whole dynamics of Ca 2+ waves, from the endoplasmic reticulum to the cytosol, can be reduced to a single differential-difference nonlinear equation whose solutions are assumed to be plane waves. Their linear stability analysis is studied, with emphasis on the impact of long-range coupling, via the range parameter s . It is shown that s , as well as the number of interacting cells, importantly modifies the features of modulational instability, as small values of s imply a strong coupling, and increasing its value rather reduces the problem to a first-neighbor one. Our theoretical findings are numerically tested, as the generic equations are fully integrated, leading to the emergence of nonlinear patterns of Ca 2+ waves. Strong long-range coupling is pictured by extended trains of breather-like structures whose frequency decreases with increasing s . We also show numerically that the number of interacting cells plays on the spatio-temporal formation of Ca 2+ patterns, whilst the quasi-perfect intercellular communication depends on the paracrine coupling parameter. [ABSTRACT FROM AUTHOR]

The elimination of spiral waves is numerically studied in a network of Hindmarsh–Rose neurons in presence of long-range diffusive interactions and external frequency excitations. Some features of membrane potential, including time series, spatiotemporal and spatial diagrams are discussed. It is found that at low frequency excitations, weak and strong long-range couplings sustain target wave propagation and spiral wave formation. However, ultra-long-range connections fully suppress such patterns, especially in the case of a Kac–Baker-like long-range coupling. In addition, increase in the excitation frequency supports the transition from stable robust spiral waves to spiral turbulence at weak or strong long-range connections. The interplay between hyper-high-frequency excitation and Kac–Baker-like long-range interaction completely eliminates spiral waves and only regenerates target wave propagation. Our results suggest that both frequency excitation regimes and long-range interaction may efficiently regulate the electrical activity of thalamus neurons and effectively prevent some brain disorders such as epileptic seizures. • A network of Hindmarsh–Rose neurons is used to numerically study the elimination of spiral waves in presence of long-range interactions and external frequency excitations. • Low frequency excitations, weak and strong long-range couplings sustain target waves propagation and spiral waves formation. • Ultra-long-range connections fully suppress such patterns. • High excitation frequency supports transition from stable spiral waves to spiral turbulence for weak/strong long-range connections. [ABSTRACT FROM AUTHOR]

Abstract A system for three-strand α -helix proteins, with long-range dispersive interactions among polypeptide units, is considered. The associate improved Davydov model is shown to be fully described by a set of modified coupled discrete nonlinear Schrödinger equations, which involve long-range interactions between peptide groups along the protein strands. By means of the modulational instability theory, the competition between nonlinearity and long-range intermolecular interactions are shown to modify the domain of instability of plane waves. The impact of the competition between nonlinearity and long-range interactions, on the process of energy transport and storage, is also addressed numerically. It is shown that nonlinearity and the long-range couplings conspire to the emergence of trains of solitonic structures, when parameters are well chosen within the domain of instability of plane waves. The relevance of the improved model as well as the biological implications of the account of long-range intermolecular interactions, are discussed in the contexts of energy transport and storage in hydrogen-bonded molecular structures in general, and in α -helix proteins in particular. Highlights • Long-range dispersive interactions are considered in a tridimensional model of α -helix proteins. • Model equations are derived in the form of discrete and coupled nonlinear Schrödinger equations. • Modulational instability analysis gives rise to trains of solitonic structures. • Trains of solitons and their characteristics are sensitive to nonlinear and LR coupling effects. [ABSTRACT FROM AUTHOR]

The underdamped Brownian motion of particles in a deformable potential in response to a constant external force is investigated. Using the matrix continued fraction method, we compute the diffusion coefficient of Brownian particles via the dynamics factor structure at low temperature and intermediate values of friction coefficient. It is numerically found that the transport properties of Brownian particles such as the effective diffusion coefficient, the average velocity and the distribution probability are sensitive to the shape parameter r of the modified nonsinusoidal Remoissenet–Peyrard deformable potential. The bistable behaviour and the distribution of velocity which also shed light on the diffusion anomalies are discussed for some values of the shape parameter. We show that for the negative values of the shape parameter (r < 0), the average velocity versus the external tilting of Brownian particles is optimized, while for the positive values (r > 0), the average velocity of Brownian particles collapses due to the geometry of the system combined with the friction. Finally, the mechanism of enhancement of the effective diffusion coefficient for a range of the external force is discussed as a function of the shape parameter. We find a power law for the effective diffusion coefficient in terms of the shape parameter r , and show that, it evolves as D t h ∼ ∣ r ∣ 2 . • Transport properties of Brownian particles in deformable potential. • The average velocity and the effective diffusion coefficient of particles is affected by the geometry of the system. • The average velocity of Brownian particles is optimized for some values of the shape parameter than others. • The distribution probability of Brownian particles is affected by the geometry. • The low transitions between locked and running states promotes excess diffusion peak. [ABSTRACT FROM AUTHOR]