Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca dynamics

We present a bidomain threshold model of intracellular calcium (Ca²⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca²⁺ liberation is modulated by the Ca²⁺ concentration in the releasing compartment. We explicitly construct stationary fronts and determine their stability using an Evans function approach. Our results show that a biologically motivated choice of a dynamic threshold, as opposed to a constant threshold, can pin stationary fronts that would otherwise be unstable. This illustrates a novel mechanism to stabilise pinned interfaces in continuous excitable systems. Our framework also allows us to compute travelling pulse solutions in closed form and systematically probe the wave speed as a function of physiologically important parameters. We find that the existence of travelling wave solutions depends on the time scale of the threshold dynamics, and that facilitating release by lowering the cytosolic threshold increases the wave speed. The construction of the Evans function for a travelling pulse shows that of the co-existing fast and slow solutions the slow one is always unstable.     

The dynamics of cargo driven by molecular motors in the context of asymmetric simple exclusion processes

We consider the dynamics of cargo driven by a collection of interacting molecular motors in the context of an asymmetric simple exclusion process (ASEP). The model is formulated to account for (i) excluded-volume interactions, (ii) the observed asymmetry of the stochastic movement of individual motors and (iii) interactions between motors and cargo. Items (i) and (ii) form the basis of ASEP models and have already been considered to study the behavior of motor density profile [A. Parmeggiani, T. Franosch, E. Frey, Phase Coexistence in driven one-dimensional transport, Phys. Rev. Lett. 90 (2003) 086601-1-086601-4]. Item (iii) is new. It is introduced here as an attempt to describe explicitly the dependence of cargo movement on the dynamics of motors in this context. The steady-state solutions of the model indicate that the system undergoes a phase transition of condensation type as the motor density varies. We study the consequences of this transition to the behavior of the average cargo velocity.     

Signal-to-noise analysis of Hopfield neural networks with a formulation of the dynamics in terms of transition probabilities

We study Hopfield neural networks with infinite connectivity using signal-to-noise analysis with a formulation of the dynamics in terms of transition probabilities. We focus our study on models where the strongest effects of the feedback correlations appear. We introduce an analysis of the path probability of one neuron in order to obtain the contribution of all feedback correlations to the dynamics of this neuron. In this way, we obtain a complete theory for dynamics with order parameter equations identical to those obtained with general functional analysis for finite temperature. In the first part of this work, we present our method in the fully connected Little-Hopfield neural network. We obtain, in a simple and direct way, the order parameter equations found by general functional analysis. In the second part, the exposed method is applied to the fully connected Ashkin-Teller neural network. It is shown that the retrieval quality is improved by introducing four-spin couplings. Simulation results support our theoretical predictions.     

3-D maps and coupling numbers for protein sequences

Based on a five-letter model of the 20 amino acids, we propose a new 3-D graphical representation of protein sequence. Then we derive from the graphical representation, numerical indices called 3-D coupling numbers, to characterize protein sequences. The examination of the similarities/dissimilarities among the β-globin proteins of 15 species illustrates the utility of the approach.     

Granger causality for circular variables

In this Letter we discuss the use of Granger causality to the analyze systems of coupled circular variables, by modifying a recently proposed method for multivariate analysis of causality. We show the application of the proposed approach on several Kuramoto systems, in particular one living on networks built by preferential attachment and a model for the transition from deeply to lightly anaesthetized states. Granger causalities describe the flow of information among variables.     

Consensus problem in directed networks of multi-agents via nonlinear protocols

In this Letter, the consensus problem via distributed nonlinear protocols for directed networks is investigated. Its dynamical behaviors are described by ordinary differential equations (ODEs). Based on graph theory, matrix theory and the Lyapunov direct method, some sufficient conditions of nonlinear protocols guaranteeing asymptotical or exponential consensus are presented and rigorously proved. The main contribution of this work is that for nonlinearly coupled networks, we generalize the results for undirected networks to directed networks. Consensus under pinning control technique is also developed here. Simulations are also given to show the validity of the theories.     

Electric Field-Induced Fluid Velocity Field Distribution in DNA Solution

We present an analytical solution for fluid velocity field distribution of polyelectrolyte DNA. Both the electric field force and the viscous force in the DNA solution are considered under a suitable boundary condition. The solution of electric potential is analytically obtained by using the linearized Poisson-Boltzmann equation. The fluid velocity along the electric field is dependent on the cylindrical radius and concentration. It is shown that the electric field-induced fluid velocity will be increased with the increasing cylindrical radius, whose distribution also varies with the concentration     

Effect of Laser Field and Mechanical Force on Deoxyribonucleic Acid Melting

We propose a physics method to study the effect of laser field and mechanical force on the melting process of double-stranded deoxyribonucleic acid （DNA）. A two-dimensional lattice model is established for DNA molecules stuck on the surface, and the stretching energy of the hydrogen bond and stacking energy for each DNA molecule are calculated by using a nonlinear potential. A real-time algorithm is employed to deal with the dynamics process of DNA melting. Numerical results explain the experimental observations. The spatial distribution of the laser field determines the sequences of DNA melting. The simulation has shown the dependence of the final number of melted DNA on the laser field and mechanical force.     

Genetic code evolution as an initial driving force for molecular evolution

There is an intrinsic relationship between the molecular evolution in primordial period and genomic or proteomic properties of contemporary species. The genomic data may help us understand the driving force of evolution of life at a molecular level. In the absence of evidence, numerous problems in molecular evolution had to fall into a twilight zone of speculation and controversy in the past. Here we show that delicate variation patterns of genomic base compositions and amino acid frequencies resulted from the genetic code evolution, which underlies the molecular evolution. The theoretical results agree with the experimental observations very well, not only in the evolutionary trends of amino acid frequencies and genomic base compositions but also in many detailed characters. Inversely, the genomic data of contemporary species can help us unravel the genetic code chronology and amino acid chronology. Our results may shed light on the intrinsic mechanism of molecular evolution and the genetic code evolution.     

Local Magnetic Nanoparticle Delivery in Microvasculature

The transport and capture of therapeutic magnetic nanoparticles in human microvasculature is studied numerically. The nanoparticles are injected into a vascular system upstream from malignant tissue, and are captured at the tumour site with the aid of a local applied magnetic field positioned outside the body. Taking into account the dominant magnetic and fluidic forces on the particles, our study shows that the nanoparticles can be directed to and concentrated at the desired zone that is within a few centimetres from the surface of the body. In addition, influence of the particles size, average blood flow velocity and the diameter of the blood vessel on the captured efficiency are parametrically analysed.     

Asymmetric coupling in two-lane simple exclusion processes: Effect of unequal injection rates

This Letter investigates the effect of unequal injection rates on two-lane simple exclusion processes with asymmetric coupling. It is a generalization of the work of Pronina and Kolomeisky [E. Pronina, A.B. Kolomeisky, Physica A 372 (2006) 12], in which the injection rates of two lanes are equal. With the injection rate α₁ increases, the (1,LD), (1,HD), (1,MC) and (MC,MC) phase region do not change, while the (LD,0) phase regions shrink and the (HD,0) and (MC,0) phase regions expand. Interestingly, domain walls are observed in both lanes when the system is in the (MC,MC) phase. However, the unequal injection rates have little effect on the domain wall dynamics. The phase diagram and the density profiles are investigated by using Monte Carlo simulations and mean-field approximation. The analytical results are in good agreement with simulations.     

Comparison of the energetic properties and the dynamical stability in a mathematical model of the stretch reflex

The previous studies on finite-time thermodynamic engines have shown that some of the parameters affecting their thermodynamic performance also affect their stability. Moreover, such parameters have to be tuned to reach an optimal trade-off between these two generic properties. In the present work we carry out a similar analysis on a mathematical model of the stretch reflex regulatory pathway, which is a simplified version of a previously published model. We show that the model has a unique stable fixed point in the absence of time delays. However, when the system inherent time delays are considered, they can destabilize the fixed point and engender a stable limit cycle. We further explore the parameter space to analyse the sensitivity of the system stability to variations in the parameter values. Particular attention is paid to the parameter here denoted as α, which has been shown to determine the muscle thermodynamic properties during steady-state contractions: larger values of α mean more powerful and less efficient muscles. Our results indicate that the stretch reflex pathway is less stable in the more powerful and less efficient muscles. We finally compare these observations with those obtained on thermal engines.     

Leader--Follower Consensus Problems of Multi-agent Systems with Noise Perturbation and Time Delays

In light of the stability theory for stochastic differential delay equations, the leader--followerconsensus problem with noise perturbation and communication time delays is investigated. Communication among agents is modelled as a weighted directed graph and the weights are stochastically perturbed with white noise. It is analytically proven that the consensus could be achieved almost surely with the perturbation of noise and communication time delays. Furthermore, numerical examples are provided to illustrate the effectiveness of the theoretical results     

A computational model for cancer growth by using complex networks

In this work we propose a computational model to investigate the proliferation of cancerous cell by using complex networks. In our model the network represents the structure of available space in the cancer propagation. The computational scheme considers a cancerous cell randomly included in the complex network. When the system evolves the cells can assume three states: proliferative, non-proliferative, and necrotic. Our results were compared with experimental data obtained from three human lung carcinoma cell lines. The computational simulations show that the cancerous cells have a Gompertzian growth. Also, our model simulates the formation of necrosis, increase of density, and resources diffusion to regions of lower nutrient concentration. We obtain that the cancer growth is very similar in random and small-world networks. On the other hand, the topological structure of the small-world network is more affected. The scale-free network has the largest rates of cancer growth due to hub formation. Finally, our results indicate that for different average degrees the rate of cancer growth is related to the available space in the network.     

Two mechanisms of spiral-pair-source creation in excitable media

Two new modes of generating spiral pairs in an excitable medium have been found. They depend on a geometrical structure (GS) inside the medium. This may be formed e.g. as a result of scars or fibrosis in the heart tissue, or artificially built in a chemical reaction substrate. Both sources involve a GS composed of a circular “convergent lens” bounded by two opaque “walls”. One mode can be induced by a single wave and behaves as a “flip-flop” type of a limit cycle. The other mode is generated by a train of plane waves impinging on the GS, and is created at the focus of the converging wave-fragments.     

Defect-induced transitions in synchronous asymmetric exclusion processes

The effects of a single local defect in synchronous asymmetric exclusion processes are investigated via theoretical analysis and Monte Carlo simulations. Our theoretical analysis shows that there are four possible stationary phases, i.e., the (low density, low density), (low density, high density), (high density, low density) and (high density, high density) in the system. In the (high density, low density) phase, the system can reach a maximal current which is determined by the local defect, but independent of boundary conditions. A phenomenological domain wall approach is developed to predict dynamic behavior at phase boundaries. The effects of defective hopping probability p on density profiles and currents are investigated. Our investigation shows that the value of p determines phase transitions when entrance rate α and exit rate β are fixed. Density profiles and currents obtained from theoretical calculations are in agreement with Monte Carlo simulations.     

A flower-like Ising model. Thermodynamic properties

We consider a flower-like Ising model, in which there are some additional bonds (in the “flower-core”) compared to a pure Ising chain. To understand the behaviour of this system and particularly the competition between ferromagnetic (usual) bonds along the chain and antiferromagnetic (additional) bonds across the chain, we study analytically and iteratively the main thermodynamic quantities. Very interesting is, in the zero-field and zero-temperature limit, the behaviour of the magnetization and the susceptibility, closely related to the ground state configurations and their degeneracies. This degeneracy explains the existence of non-zero entropy at zero temperature, in our results. Also, this model could be useful for the experimental investigations in studying the saturation curves for the enzyme kinetics or the melting curves for DNA-denaturation in some flower-like configurations.     

The zone strong coupling two-channel totally asymmetric simple exclusion processes

This article investigates the zone strong coupling two-channel totally asymmetric simple exclusion processes (TASEPs). The study is based on Pronina and Kolomeisky’s work [J. Phys. A-Math. Gen. 37, 9907 (2004)], in which the coupling exists within two whole parallel channels. Zone strong coupling two-channel TASEPs focuses on the behavior and the effect of a particular segment rather than the whole channel. The study shows that there are five possible stationary phases; LD/LD, HD/HD, MC/LD, LD/HD, and MC/HD. The phase diagrams and the density profiles are investigated using computer Monte Carlo simulations and mean-field approximation. The outcomes of the simulations match agreeably with the analytical predictions.