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Many works confirm the anti-correlations between the default mode network (DMN) and the central-executive network (CEN) in the brain. However, the switching mechanism of the DMN itself is still lack of understanding from the viewpoint of neural network dynamics. Here we simulate the DMN with the Hindmarsh-Rose (HR) neuron model on the small-world network. We model the state of oscillator death and oscillatory firing as the inhibitory state and the activated state, respectively. We find that the DMN can regenerate from the inhibitory state when the input current of only one synapse is cut off at criticality.

Critical physical systems with large numbers of molecules can show universal and scaling behaviors. It is of interest to know whether human societies with large numbers of people can show the same behaviors. Here, we use network theory to analyze Chinese history in periods 209 BCE–23 CE and 515–618 CE) related to the Western Han–Xin Dynasty and the late Northern Wei–Sui Dynasty, respectively. Two persons are connected when they appear in the same historical event. We find that the historical networks from two periods separated about 500 years have interesting universal and scaling behaviors, and they are small-world networks; their average cluster coefficients as a function of degree are similar to the network of movie stars. In the historical networks, the persons with larger degrees prefer to connect with persons with a small degree; however, in the network of movie stars, the persons with larger degrees prefer to connect with persons with large degrees. We also find an interesting similar mechanism for the decline or collapse of historical Chinese dynasties. The collapses of the Xin dynasty (9–23 CE) and the Sui dynasty (581–618 CE) were initiated from their arrogant attitude toward neighboring states.

The objective of this article is to use a recent developed scheme to simulate reaction-diffusion-chemotaxis equations. The solution gradient required for an accurate discretization is computed directly as an additional variable rather than interpolated from solution values around neighboring computational nodes. To achieve this goal, a supplementary equation and its associated control volume are introduced to retain a compact and accurate discretization. Scheme essentials are exposed by the numerical analysis on two-dimensional chemotaxis problems to reveal its formal accuracy. Due to its highly comprehensible and practical features, this formulation can be easily extended to solve problems for other two-dimensional rectangular grid systems. One- and two-dimensional problems are solved to verify its simulation accuracy and to study the possible formation of bacteria bands. We further perform the linearization technique to the reaction term to increase the stability of the current scheme. From the numerical analysis and computational results, it is found that the present formulation is a useful tool to solve reaction-diffusion-chemotaxis equations.

Passenger flight delays, causing much disorder of air traffics, economic losses of airlines, and downgrading the travel quality of millions of people, are ubiquitous phenomena in airports all over the world. Investigation based on real data from the view point of statistical physics is rarely seen. In the present work, big data of such delay records over 20 years accumulated by Bureau of Transportation Statistics in the United States are downloaded and purified by us. We account the departure and arrival records of such flights between certain pair of airports as time series, and rectify them by defining dimensionless velocity of the flights. Furthermore, we find the varying cross-correlations among such time series with the approach of time delay stability, and describe the correlations with temporal networks for correlation states. Deterministic correspondences between the average degrees of temporal networks and delay ratios of passenger flights are verified in different sampling groups of flights with the longest records. The mean degrees of correlation networks usually emerge a peak prior to that of high delay ratios, which serves an indicator for the precaution to serious flight delays.

In this work, the interaction between spherical magnetic nanoparticles and amyloid fibrils as well as formation of self-assembled structures during drying process of such colloidal system were investigated. The final self assembled structures were observed experimentally by atomic force microscopy, scanning electron microscopy and polarizing microscopy. Our results show that the colloidal composites are self-assembled into flower-like patterns after the evaporation of liquid drop. These observations show that a large scale and well-organized multi-branched aggregates are formed during the process of drying. Moreover, observation by polarizing microscopy under crossed polarizers showed birefringence.

Noise has been recognized as an important factor in a range of physical and informational systems, including the elementary physics of life, such as cellular developments and functions. Here we use a stochastic differential equation to study the effects of noise on a typical system of antagonist actors, the Schlogl model. The phenomena of noise-induced bifurcation are observed. Detailed analysis demonstrates that the region revealing bistability can be modulated by the intensity of noise. This suggests that an external noise source can serve as an engineering tool for controlling antagonist inter-reacting systems in general, and in particular, for manipulating biochemical pathways.

We used the Hindmarsh–Rose (HR) model (Hindmarsh and Rose, 1984) to study the effect of time delay on the transition of firing behaviors and desynchronization in neural networks. As time delay is increased, neural networks exhibit diversity of firing behaviors, including regular spiking or bursting and firing patterns transitions (FPTs). Meanwhile, the desynchronization of firing and unstable bursting with decreasing amplitude in neural system, are also increasingly enhanced with the increase of time delay. Furthermore, we also studied the effect of coupling strength and network randomness on these phenomena. Our results imply that time delays can induce transition and desynchronization of firing behaviors in neural networks. These findings provide new insight into the role of time delay in the firing activities of neural networks, and can help to better understand the firing phenomena in complex systems of neural networks. A possible mechanism in brain that can cause the increase of time delay is discussed.

We investigate an integrate-and-fire model of an electronic relaxation oscillator, which can be described by the discontinuous and non-invertible composition of two mapping functions f 1 and f 2 , with f 1 being dissipative. Depending on a control parameter d , f 2 can be conservative (for d = d c = 1 ) or dissipative (for d > d c ). We find a kind of crisis, which is induced by the escape from a riddled-like attraction basin sea in the phase space. The averaged crisis transient lifetime ( 〈 τ 〉 ), the relative measure of the fat fractal forbidden network ( η ), and the measure of the escaping hole ( Δ ) show clear scaling behaviors: 〈 τ 〉 ∝ ( d − d c ) − γ , η ∝ ( d − d c ) σ , and Δ ∝ ( d − d c ) α . Extending an argument by Jiang et al. (2004), we derive γ = σ + α , which agrees well with numerical simulation data.

We have probed small molecule compound CID 9998128 as a potential multitarget drug for the Alzheimer’s disease (AD) using in silico and in vitro experiments. By all-atom simulation and molecular mechanics Poisson–Boltzmann surface area (MM-PBSA) method, we have demonstrated that this compound strongly binds to both amyloid β42 (Aβ42) fibrils and β-secretase, and the van der Waals interaction dominates over the electrostatic interaction in binding affinity. A detailed analysis at the atomic level revealed that indazole in CID 99998128 structure made a major contribution to instability of all studied complexes. In vitro experiments have shown that CID 9998128 inhibits the Aβ42 amyloid fibrillization and is capable to clear Aβ42 fibrils. Moreover, the compound dose-dependently decreases β-site amyloid precursor protein cleaving enzyme (BACE-1) activity with EC50 value in micromolar range. Thus, our study has revealed that CID 9998128 is a good candidate for AD treatment through preventing production of Aβ pe...

Local interneurons (LNs) in the Drosophila olfactory system exhibit neuronal diversity and variability, yet it is still unknown how these features impact information encoding capacity and reliability in a complex LN network. We employed two strategies to construct a diverse excitatory-inhibitory neural network beginning with a ring network structure and then introduced distinct types of inhibitory interneurons and circuit variability to the simulated network. The continuity of activity within the node ensemble (oscillation pattern) was used as a readout to describe the temporal dynamics of network activity. We found that inhibitory interneurons enhance the encoding capacity by protecting the network from extremely short activation periods when the network wiring complexity is very high. In addition, distinct types of interneurons have differential effects on encoding capacity and reliability. Circuit variability may enhance the encoding reliability, with or without compromising encoding capacity. Therefore, we have described how circuit variability of interneurons may interact with excitatory-inhibitory diversity to enhance the encoding capacity and distinguishability of neural networks. In this work, we evaluate the effects of different types and degrees of connection diversity on a ring model, which may simulate interneuron networks in the Drosophila olfactory system or other biological systems.

The second derivative techniques, which are used in spectroscopy to reveal poorly resolved bands, were adjusted for processing of calorimetric melting profiles of DNAs from higher organisms. The procedure strongly increased the sensitivity of the profiles to various distortions of the double helix and allowed clear resolution of the constituents arising from the melting of satellite DNA (minor narrow peaks) and the rest of genome (dominant wide peak). As an illustration of the advantages of the procedure, selective suppression of narrow satellite peaks was demonstrated as DNA was chemically modified by the antitumor drug cisplatin. As the cisplatin/nucleotide molar ratio increased from 0.001 to 0.05, the peaks decreased in height until they fully disappeared. The influence of cisplatin on the shape of the main peak, which corresponds to the rest of the genome, was much weaker. Transplatin, an ineffective analog of cisplatin, suppressed all constituents of the melting profile without selectivity.

We consider an evolution model, in which the mutation rates depend on the structure of population: the mutation rates from lower populated sequences to higher populated sequences are reduced. We have applied the Hamilton–Jacobi equation method to solve the model and calculate the mean fitness. We have found that the modulated mutation rates, directed to increase the mean fitness.

Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic [fine-grained] environment, the time-averaged population frequencies are shown to obey a replicator dynamics with a non-linear fitness that is induced by environmental changes. The non-linear terms in the fitness emerge due to populations tracking their time-dependent environment. These terms can induce a stable polymorphism, though they do not spoil the polymorphism that exists already without them. In this sense polymorphic populations are more robust with respect to their time-dependent environments. The overall fitness of the problem is still given by its time-averaged value, but the emergence of polymorphism during genetic selection can be accompanied by decreasing mean fitness of the population. The impact of the uncovered polymorphism scenario on the models of diversity is examplified via the rock-paper-scissors dynamics, and also via the prisoner's dilemma in a time-periodic environment., 16 pages, 10 figures

There are three possible classifications of the dimer weights on the bonds of the checkerboard lattice and they are denoted as checkerboard $A$, $B$, and $C$ lattices [Phys. Rev. E 91, 062139 (2015)]. The dimer model on the checkerboard $B$ and $C$ lattices has much richer critical behavior compared to the dimer model on the checkerboard $A$ lattice. In this paper we study in full detail the dimer model on the checkerboard $B$ lattice. The dimer model on the checkerboard $B$ lattice has two types of critical behavior. In one limit this model is the anisotropic dimer model on rectangular lattice with algebraic decay of correlators and in another limit it is the anisotropic generalized Kasteleyn model with radically different critical behavior. We analyze the partition function of the dimer model on a $2M\ifmmode\times\else\texttimes\fi{}2N$ checkerboard $B$ lattice wrapped on a torus. We find very unusual behavior of the partition function zeros and the specific heat of the dimer model. Remarkably, the partition function zeros of finite-size systems can have very interesting structures, made of rings, concentric circles, radial line segments, or even arabesque structures. We find out that the number of the specific heat peaks and the number of circles of the partition function zeros increases with the system size. The lattice anisotropy of the model has strong effects on the behavior of the specific heat, dominating the relation between the correlation length exponent $\ensuremath{\nu}$ and the shift exponent $\ensuremath{\lambda}$, and $\ensuremath{\lambda}$ is generally unequal to $1/\ensuremath{\nu}$ ($\ensuremath{\lambda}\ensuremath{\ne}1/\ensuremath{\nu}$).

In some systems, the connecting probability (and thus the percolation process) between two sites depends on the geometric distance between them. To understand such process, we propose gravitationally correlated percolation models for link-adding networks on the two-dimensional lattice $G$ with two strategies $S_{\rm max}$ and $S_{\rm min}$, to add a link $l_{i,j}$ to connect site $i$ and site $j$ with mass $m_i$ and $m_j$, respectively; $m_i$ and $m_j$ are sizes of the clusters which contain site $i$ and site $j$, respectively. The probability to add the link $l_{i,j}$ is related to the generalized gravity $g_{ij} \equiv m_i m_j/r_{ij}^d$, where $r_{ij}$ is the geometric distance between $i$ and $j$, and $d$ is an adjustable decaying exponent. In the beginning of the simulation, all sites of $G$ are occupied and there is no link. In the simulation process, two inter-cluster links $l_{i,j}$ and $l_{k,n}$ are randomly chosen and the generalized gravities $g_{ij}$ and $g_{kn}$ are computed. In the strategy $S_{\rm max}$, the link with larger generalized gravity is added. In the strategy $S_{\rm min}$, the link with smaller generalized gravity is added, which include percolation on the Erd\H os-R\'enyi random graph and the Achlioptas process of explosive percolation as the limiting cases, $d \to \infty$ and $d \to 0$, respectively. Adjustable strategies facilitate or inhibit the network percolation in a generic view. We calculate percolation thresholds $T_c$ and critical exponents $\beta$ by numerical simulations. We also obtain various finite-size scaling functions for the node fractions in percolating clusters or arrival of saturation length with different intervening strategies., Comment: 26 pages, 8 figures, Chinese Journal of Physics, accepted for publication

Polymers are important macromolecules in many physical, chemical, biological and industrial problems. Studies on simple lattice polymer models are very helpful for understanding behaviors of polymers. We develop an efficient algorithm for computing exact partition functions of lattice polymer models, and we use this algorithm and personal computers to obtain exact partition functions of the interacting self-avoiding walks with N monomers on the simple cubic lattice up to N = 28 and on the square lattice up to N = 40 . Our algorithm can be extended to study other lattice polymer models, such as the HP model for protein folding and the charged HP model for protein aggregation. It also provides references for checking accuracy of numerical partition functions obtained by simulations.

Flight delays have negative impacts on passengers, carriers, and airports. To reduce these unpopular influence, we need to find the statistical law of the collective behavior of passenger flights. We use a mean-field approach to analyze big data listing the departure and arrival records of all American domestic passenger flights in 20 years. We treat passenger flights as particle gases and define their dimensionless velocity, quasi-thermodynamic quantities — pressure, volume, temperature, and mole number, respectively. By introducing phenomenological parameters a and b to set up van der Waals-like state equations, we erect a universal gaseous constant R for actually operated passenger flights, their counterparts on schedule, and ”delayor gases” defined as the difference between them. We find that the attractive coefficient of ”delayor gases” positively correlates with the average delay per flight on airports. Rescaling state equations for passenger flights across all 20 years, we find a universal function. This is a significant step toward understanding flight delays and dealing with temporal big data with the tools of statistical physics.

It is widely believed that the brains of human beings work at or near the state of self-organized criticality (SOC). In the present work, we investigate two-dimensional small-world neural networks (2D SWNN) with Bak–Sneppen (BS)-type neurons as their nodes. By taking threshold firing and refractory period as the key features of neurons in the simulations, a few power laws are obtained for suitable range of parameters. The SOC characterized by the power-law distribution of avalanche sizes as well as 1 ∕ f noise emerges in the present model. Moreover, a set of scaling relations are found to exhibit criticality. The exponent for the power spectrum of all return time is α = 0 . 71 , which is comparable with what were found in medical experiments.

Studying gene regulation networks in a single cell is an important, interesting, and hot research topic of molecular biology. Such process can be described by chemical master equations (CMEs). We propose a Hamilton-Jacobi equation method with finite-size corrections to solve such CMEs accurately at the intermediate region of switching, where switching rate is comparable to fast protein production rate. We applied this approach to a model of self-regulating proteins [H. Ge et al., Phys. Rev. Lett. 114, 078101 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.078101] and found that as a parameter related to inducer concentration increases the probability of protein production changes from unimodal to bimodal, then to unimodal, consistent with phenotype switching observed in a single cell.

Shiji prepared by Shima Qian in Western Han Dynasty (202 BC–9 AD) was the most famous historical book in historical China. The current version of Shiji contains 130 chapters, including 10 chapters which contains some parts starting with the sentence “Mr. Chu said … ”; such parts were considered to be written by Chu Shaosun by Chang Yen in the Three Kingdoms Period (220–280 AD), which was widely accepted. We have analyzed the word population in Shiji and books written by Liu Xiang (77 BC–6 BC) in Western Han Dynasty, who was a member of the royal family. Our results and other evidences indicate that the parts of Shiji starting with the sentence “Mr. Chu said … ” were prepared by Liu Xiang. The other evidences include (1) The ending year of the events mentioned in “Mr. Chu said...” was considered to be 47 BC, the second year of Emperor Yuan (as Emperor in 48 BC–32 BC) of Western Han Dynasty, and in the same year Liu Xiang was put into a jail, then left power center for many years. Such coincidence suggests that Liu Xiang wrote the parts “Mr. Chu said … ” in Shiji . (2) Liu Xiang’s education, interest, and writings are quite consistent with the parts with “Mr. Chu said … ” in Shiji . On the other hand, one cannot find such a connection with Chu Shaosun, who did not have any other identified writings for comparison.

Many factors that change the temperature position and interval of the DNA helix-coil transition often also alter the shape of multi-peak differential melting curves (DMCs). For DNAs with a multi-peak DMC, there is no agreement on the most useful definition for the melting temperature, Tm, and temperature melting width, ΔT, of the entire DNA transition. Changes in Tm and ΔT can reflect unstable variation of the shape of the DMC as well as alterations in DNA thermal stability and heterogeneity. Here, experiments and computer modeling for DNA multi-peak DMCs varying under different factors allowed testing of several methods of defining Tm and ΔT. Indeed, some of the methods give unreasonable "jagged" Tm and ΔT dependences on varying relative concentration of DNA chemical modifications (rb), [Na(+)], and GC content. At the same time, Tm determined as the helix-coil transition average temperature, and ΔT, which is proportional to the average absolute temperature deviation from this temperature, are suitable to characterize multi-peak DMCs. They give smoothly varying theoretical and experimental dependences of Tm and ΔT on rb, [Na(+)], and GC content. For multi-peak DMCs, Tm value determined in this way is the closest to the thermodynamic melting temperature (the helix-coil transition enthalpy/entropy ratio).

Here we present the revised and newly rewritten version of our earlier published CAVE package (Busa et al., 2010) which was originally written in FORTRAN. The package has been rewritten in C language, the algorithm has been parallelized and implemented using OpenCL. This makes the program convenient to run on platforms with Graphical Processing Units (GPUs). Improvements include also some modifications/optimizations of the original algorithm. A considerable improvement in the performance of the code has been achieved. A new tool called input_structure has been added which helps the user to make the data input and conversion more easier and universal.

To model the dependence of extreme events on locations, we consider extreme events of Brownian particles in a potential. We find that barring the exception of very large potentials and/or very small regions, in general, the probability of extreme events increases with the potential. Our approach is general and can be useful for studying several complex systems.

Many human or animal diseases are related to aggregation of proteins. A viable biological organism should maintain in non-equilibrium states. How protein aggregate and why biological organisms can maintain in non-equilibrium states are not well understood. As a first step to understand such complex systems problems, we consider simple model systems containing polymer chains and solvent particles. The strength of the spring to connect two neighboring monomers in a polymer chain is controlled by a parameter s with s → ∞ for rigid-bond. The strengths of bending and torsion angle dependent interactions are controlled by a parameter s A with s A → −∞ corresponding to no bending and torsion angle dependent interactions. We find that for very small s A , polymer chains tend to aggregate spontaneously and the trend is independent of the strength of spring. For strong springs, the speed distribution of monomers in the parallel (along the direction of the spring to connect two neighboring monomers) and perpendicular directions have different effective temperatures and such systems are in non-equilibrium states.

The distribution of the geometric distances of connected neurons is a practical factor underlying neural networks in the brain. It can affect the brain’s dynamic properties at the ground level. Karbowski derived a power-law decay distribution that has not yet been verified by experiment. In this work, we check its validity using simulations with a phenomenological model. Based on the in vitro two-dimensional development of neural networks in culture vessels by Ito, we match the synapse number saturation time to obtain suitable parameters for the development process, then determine the distribution of distances between connected neurons under such conditions. Our simulations obtain a clear exponential distribution instead of a power-law one, which indicates that Karbowski’s conclusion is invalid, at least for the case of in vitro neural network development in two-dimensional culture vessels.

At 49 C erythrocytes undergo morphological changes due to an internal force, but the origin of the force that drives changes is not clear. Here we point out that our recent experiments on thermally induced force-release in hemoglobin can provide an explanation for the morphological changes of erythrocytes., 4 pages, 1 figure

Alzheimer's disease is presumed to be caused by the formation of intracellular plaques of amyloid β (Aβ) peptides inside neurons. The most abundant Aβ forms are Aβ40 and Aβ42 comprising, respectively, 40 and 42 residues. Recent experiments showed that the triple Gly33Val-Val36Pro-Gly38Val (VPV) mutation causes Aβ42 to become "super-Aβ42" with elevated aggregation rates and toxicity. Upon VPV mutation, oligomerization pathways of Aβ40 become similar to those of the Aβ42 wild type. It was hypothesized that the super behavior of Aβ42 occurs due to an enhanced content of the β-turn and β-hairpin, centered at residues 36-37, and the similarity in oligomerization pathways of Aβ40-VPV and Aβ42-WT comes from the increased β-turn population. As this is based on simulation of the truncated fragments, this hypothesis may not be valid for the full-length case, motivating us to perform all-atom molecular dynamics simulations for full-length Aβ sequences. We showed that the results obtained for truncated peptides fall short in explaining the similarity of self-assembly pathways of Aβ40-VPV and Aβ42-WT. Instead, we propose that the similarity is due to not only increased β-turn population but also due to the elevated β-structure of the entire sequence. Similar to VPV, the Gly33Val-Val36Asn-Gly38Leu mutation enhances the β-structure and the C-terminal β-turn making the behavior of Aβ40 similar to that of Aβ42-WT.

Urban public traffic networks are typical complex systems. Understanding their evolution mechanism attracts much attention in recent years. Here, we propose that the evolution of urban public traffic network can be considered as a game process between two network manipulators, i.e., passengers and company, and the equilibrium solution to the game determines the steady-state behavior of the network. Both analytical solution and numerical simulations to such game model can well describe the empirical data collected from the urban public traffic systems in four Chinese cities (Beijing, Shanghai, Nanjing, and Hangzhou) and the Boston subway. Our results suggest that the manipulator game model grasps the fundamental characteristics of the evolution mechanism of the urban public traffic systems. Similar idea may be extended to other complex systems which have small number of manipulators.

Antitumor activity of cisplatin is exerted by covalent binding to DNA. For comparison, studies of cisplatin-DNA complexes often employ the very similar but inactive transplatin. In this work, thermal and thermodynamic properties of DNA complexes with these compounds were studied using differential scanning calorimetry (DSC) and computer modeling. DSC demonstrates that cisplatin decreases thermal stability (melting temperature, Tm) of long DNA, and transplatin increases it. At the same time, both compounds decrease the enthalpy and entropy of the helix–coil transition, and the impact of transplatin is much higher. From Pt/nucleotide molar ratio rb = 0.001, both compounds destroy the fine structure of DSC profile and increase the temperature melting range (ΔT). For cisplatin and transplatin, the dependences δTm vs rb differ in sign, while δΔT vs rb are positive for both compounds. The change in the parameter δΔT vs rb demonstrates the GC specificity in the location of DNA distortions. Our experimental results and calculations show that 1) in contrast to [Pt(dien)Cl]Cl, monofunctional adducts formed by transplatin decrease the thermal stability of long DNA at [Na+] > 30 mM; 2) interstrand crosslinks of cisplatin and transplatin only slightly increase Tm; 3) the difference in thermal stability of DNA complexes with cisplatin vs DNA complexes with transplatin mainly arises from the different thermodynamic properties of their intrastrand crosslinks. This type of crosslink appears to be responsible for the antitumor activity of cisplatin. At any [Na+] from interval 10–210 mM, cisplatin and transplatin intrastrand crosslinks give rise to destabilization and stabilization, respectively.

Eigen's quasispecies system with explicit space and global regulation is considered. Limit behavior and stability of the system in a functional space under perturbations of the diffusion matrix with non-negative spectrum are investigated. It is proven that if the diffusion matrix has only positive eigenvalues, then the solutions of the distributed system converge to the equilibrium solution of the corresponding local dynamical system. These results imply that many of the properties of the quasispecies model, including the critical mutation rates that specify the infamous error threshold, do not change if the spatial interactions under the principle of global regulation are taken into account.

We used the Hindmarsh–Rose(HR) model to study the effects of external stimulus on the time delay-induced firing behaviors and synchronization in neural networks with N coupled neurons. As time delay is changed, neural networks exhibit diversity of firing behaviors, we discussed the effect of intensity and frequency of external stimulus on these phenomena. Our results imply that both stimulus intensity and stimulus frequency have a non-trivial impact on firing patterns transitions (FPTs) behaviors and synchronization transitions in neural networks, including the change in the critical value required for time delay-induced FPT behavior and generating new modes of transition between synchronization and desynchronization. These findings provide new insight into the role of external stimulus in the firing activities of neural networks, and can help to better understand the firing phenomena in neural networks.

Dielectric Properties of Lyotropic Magnetic Liquid Crystal P. Kop£anský, L. Tom£o, J. Jadzyn, J. Swiergiel, J. Majoro2ova, M. Kubov£ikova, M. Timko, M. Raj¬ak, K. ’ipo2ova, Z. Gaoova, Z. Bednarikova, N. Toma2ovicova, Chin-Kun Hu, S. Hayryan, I. Studenyak , T.M. Kovalchuk and O.V. Kovalchuk Institute of Experimental Physics, Slovak Academy of Sciences, Ko2ice, Slovakia Faculty of Aeronautics, Technical University, Ko2ice, Slovakia Institute of Molecular Physics, Polish Academy of Sciences, Pozna«, Poland Department of Biochemistry, Institute of Chemistry, P.J. Safarik University in Ko2ice, Slovakia Institute of Physics, Academia Sinica, 128 Sec.2, Academia Rd., Nankang, Taipei 11529, Taiwan Physics Faculty, Uzhhorod National University, Uzhhorod, 88000, Ukraine Institute of Semiconductor Physics, National Academy of Science of Ukraine, Kyiv, Ukraine Kyiv National University of Technologies and Design, Kyiv, Ukraine An important feature of lyotropic liquid crystals is the self-assembly of the amphiphilic molecules as supermolecular structures. We have studied the formation of nematic liquid crystal phase in solutions containing lysozyme amyloid brils and magnetic nanoparticles using oscilloscopic method. Interaction of brils with magnetic nanoparticles under the external magnetic eld resulted in bril re-arrangement. The analysis of the obtained results suggests that the decrease in conductivity of solutions in presence of magnetic eld is due to decrease of the ion mobility caused by re-arrangement of structures in the solution. The obtained results allow determination of the optimum ratio of the components which can lead to preparation of solutions with a more ordered structure in presence of magnetic eld.

Many experiments demonstrate that regions with higher GC-content in natural DNAs unwind at higher temperatures adsorbing more heat than equivalently sized regions with lower GC-content. This simple observation implies that normalized calorimetric melting profiles (calorimetric cDMCs) will not be equivalent differential melting curves (DMCs). We propose simple expressions for long natural and random DNA sequences to reciprocally convert DMCs and corresponding calorimetric cDMCs. The expressions are confirmed by the Poland–Fixman–Freire method and an approach based upon mixtures of homopolymeric duplexes. Using these expressions and experimental calorimetric data, we demonstrate that the average relative deviation between DMC and cDMC is proportional to the temperature melting range of the helix-coil transition Δ T . Corresponding difference between melting temperatures is proportional to Δ T 2 . In general, sequence and ionic conditions influence the deviation through their effect on Δ T . On the basis of the developed approach, we propose a method to determine the thermodynamic melting temperature (ratio of calorimetric enthalpy and entropy of the helix-coil transition) for natural DNAs from optical DMCs without calorimetric experiments.

Lattice models are useful for understanding behaviors of interacting complex many-body systems. The lattice dimer model has been proposed to study the adsorption of diatomic molecules on a substrate. Here we analyze the partition function of the dimer model on an $2 M \times 2 N$ checkerboard lattice wrapped on a torus and derive the exact asymptotic expansion of the logarithm of the partition function. We find that the internal energy at the critical point is equal to zero. We also derive the exact finite-size corrections for the free energy, the internal energy, and the specific heat. Using the exact partition function and finite-size corrections for the dimer model on finite checkerboard lattice we obtain finite-size scaling functions for the free energy, the internal energy, and the specific heat of the dimer model. We investigate the properties of the specific heat near the critical point and find that specific-heat pseudocritical point coincides with the critical point of the thermodynamic limit, which means that the specific-heat shift exponent $\lambda$ is equal to $\infty$. We have also considered the limit $N \to \infty$ for which we obtain the expansion of the free energy for the dimer model on the infinitely long cylinder. From a finite-size analysis we have found that two conformal field theories with the central charges $c = 1$ for the height function description and $c = -2$ for the construction using a mapping of spanning trees can be used to describe the dimer model on the checkerboard lattice., Comment: Physical Review E (2016), in press

The discrete time mathematical models of evolution (the discrete time Eigen model, the Moran model, and the Wright-Fisher model) have many applications in complex biological systems. The discrete time Eigen model rather realistically describes the serial passage experiments in biology. Nevertheless, the dynamics of the discrete time Eigen model is solved in this paper. The 90% of results in population genetics are connected with the diffusion approximation of the Wright-Fisher and Moran models. We considered the discrete time Eigen model of asexual virus evolution and the Wright-Fisher model from population genetics. We look at the logarithm of probabilities and apply the Hamilton-Jacobi equation for the models. We define exact dynamics for the population distribution for the discrete time Eigen model. For the Wright-Fisher model, we express the exact steady state solution and fixation probability via the solution of some nonlocal equation then give the series expansion of the solution via degrees of selection and mutation rates. The diffusion theories result in the zeroth order approximation in our approach. The numeric confirms that our method works in the case of strong selection, whereas the diffusion method fails there. Although the diffusion method is exact for the mean first arrival time, it provides incorrect approximation for the dynamics of the tail of distribution.

We consider the Wright-Fisher model of the finite population evolution on a fitness landscape defined in the sequence space by a path of nearly neutral mutations. We study a specific structure of the fitness landscape: One of the intermediate mutations on the mutation path results in either a large fitness value (climbing up a fitness hill) or a low fitness value (crossing a fitness canyon), the rest of the mutations besides the last one are neutral, and the last sequence has much higher fitness than any intermediate sequence. We derive analytical formulas for the first arrival time of the mutant with two point mutations. For the first arrival problem for the further mutants in the case of canyon crossing, we analytically deduce how the mean first arrival time scales with the population size and fitness difference. The location of the canyon on the path of sequences has a crucial role. If the canyon is at the beginning of the path, then it significantly prolongs the first arrival time; otherwise it just slightly changes it. Furthermore, the fitness hill at the beginning of the path strongly prolongs the arrival time period; however, the hill located near the end of the path shortens it. We optimize the first arrival time by applying a nonzero selection to the intermediate sequences. We extend our results and provide a scaling for the valley crossing time via the depth of the canyon and population size in the case of a fitness canyon at the first position. Our approach is useful for understanding some complex evolution systems, e.g., the evolution of cancer.

Real network data is often incomplete and noisy, where link prediction algorithms and spurious link identification algorithms can be applied. Thus far, it lacks a general method to transform network organizing mechanisms to link prediction algorithms. Here we use an algorithmic framework where a network’s probability is calculated according to a predefined structural Hamiltonian that takes into account the network organizing principles and a non-observed link is scored by the conditional probability of adding the link to the observed network. Extensive numerical simulations show that the proposed algorithm has remarkably higher accuracy than the state-of-the-art methods in uncovering missing links and identifying spurious links in many complex biological and social networks. Such method also finds applications in exploring the underlying network evolutionary mechanisms.

The Poland-Fixman-Freire formalism was adapted for modeling of calorimetric DNA melting profiles, and applied to plasmid pBR 322 and long random sequences. We studied the influence of the difference (HGC -HAT ) between the helix-coil transition enthalpies of AT and GC base pairs on the calorimetric melting profile and on normalized calorimetric melting profile. A strong alteration of DNA calorimetrical profile with HGC -HAT was demonstrated. In contrast, there is a relatively slight change in the normalized profiles and in corresponding ordinary (optical) normalized differential melting curves (DMCs). For fixed HGC -HAT , the average relative deviation (S) between DMC and normalized calorimetric profile, and the difference between their melting temperatures (Tcal -Tm ) are weakly dependent on peculiarities of the multipeak fine structure of DMCs. At the same time, both the deviation S and difference (Tcal -Tm ) enlarge with the temperature melting range of the helix-coil transition. It is shown that the local deviation between DMC and normalized calorimetric profile increases in regions of narrow peaks distant from the melting temperature.

Ideas and methods of statistical physics have been shown to be useful for understanding some interesting problems in physical systems, e.g. universality and scaling in critical systems. The interacting self-avoiding walk (ISAW) on a lattice is the simplest model for homopolymers and serves as the framework of simple models for biopolymers, such as DNA, RNA, and protein, which are important components in complex systems in biology. In this paper, we briefly review our recent work on exact partition functions of ISAW. Based on zeros of these exact partition functions, we have developed a novel method in which both loci of zeros and thermodynamic functions associated with them are considered. With this method, the first zeros can be identified clearly without ambiguity. The critical point of a small system can then be defined as the peak position of the heat capacity component associated with the first zeros. For the system with two phase transitions, two pairs of first zeros corresponding to two phase transitions can be identified and overlapping C υ can be well separated. ISAW on the simple cubic lattice is such a system where in addition to a standard collapse transition, there is another freezing transition occurring at a lower temperature. Our approach can give a clear scenario for the collapse and the freezing transitions.

Introduction of Graphical Processing Units (GPUs) and computing using GPUs in recent years opened possibilities for simple parallelization of programs. In this update, we present the modernized version of program ARVO [J. Busa, J. Dzurina, E. Hayryan, S. Hayryan, C.-K. Hu, J. Plavka, I. Pokorný, J. Skivanek, M.-C. Wu, Comput. Phys. Comm. 165 (2005) 59]. The whole package has been rewritten in the C language andparallelized usingOpenCL. Somenew tricks have been added to the algorithm in order to savememory much needed for efficient usage of graphical cards. A new tool called ‘input_structure’ was added for conversion of pdb files into files suitable for work with the C and OpenCL version of ARVO. New version program summary Program title: ARVO-CL Catalog identifier: ADUL_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADUL_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 11834 No. of bytes in distributed program, including test data, etc.: 182528 Distribution format: tar.gz Programming language: C, OpenCL. Computer: PC Pentium; SPP’2000. Operating system: All OpenCL capable systems. Has the code been vectorized or parallelized?: Parallelized using GPUs. A serial version (non GPU) is also included in the package.

As a continuation of our work, Rozanova et al. (2010) [1] we study possible trajectories of a long time existing vortex in a model of the atmosphere dynamics, where the vortex can be interpreted as a tropical cyclone. The model can be obtained from the system of primitive equations governing the motion of air over the Earth’s surface after averaging over the height. We consider approximations of l -plane and β -plane used in geophysics for modeling of middle scale processes and equations on the whole sphere as well. We associate with a cyclone a special class of smooth solutions having a form of a localized steady non-singular vortex moving with a bearing field. We show that the solutions satisfy the equations of the model either exactly or with a discrepancy which is small in a neighborhood of the trajectory of the center of vortex. We show both analytically and numerically that the trajectory of a localized vortex keeps the features of trajectory of vortex with a linear profile of velocity, where the exact solution can be obtained.

Although many anticancer drugs exert their biological activity by forming DNA interstrand crosslinks (ICLs), the thermodynamics of biologically relevant long crosslinked DNAs has not been intensively studied in contrast to short duplexes. Here, we carry out computer modeling of the shift of melting temperature of long DNAs caused by ICLs taking into account crosslinking effect in itself and concomitant local alterations in the free energy (δG) of the helix-coil transition at sites of ICLs. Depending on δG, DNA interstrand crosslinks at per nucleotide concentration r = 0.05 can change the melting temperature by value from -17 to +47°C, and the influence weakly depends on DNA sequence and GC content. A change in melting temperature caused by introduction of interstrand crosslinking in modified DNA at sites of modifications also depends on δG and varies from 0 to +12°C. Comparison with experiment for the three platinum crosslinking compounds demonstrates utility of the theoretical method for understanding how crosslinking compounds can influence the melting behavior. On the basis of the method, interdependence of local distortions and crosslinking in itself was studied for thermal effect of ICLs. A method for evaluating the nature of the structural alteration that produces a change in thermal stability for short crosslinked DNA is also proposed. The methods can be used for comparative thermodynamic characterization of various DNA crosslinking agents.

We developed a software package (CAVE) in Fortran language to detect internal cavities in proteins which can be applied also to an arbitrary system of balls. The volume, the surface area and other quantitative characteristics of the cavities can be calculated. The code is based on the recently suggested enveloping triangulation algorithm [J. Busa et al., J. Comp. Chem. 30 (2009) 346] for computing volume and surface area of the cavity by analytical equations. Different standard sets of atomic radii can be used. The PDB compatible file containing the atomic coordinates must be stored on the disk in advance. Testing of the code on different proteins and artificial ball systems showed efficiency and accuracy of the algorithm. The program is fast. It can handle a system of several thousands of balls in the order of seconds on contemporary PC's. The code is open source and free.

Excitation of induced coherent Smith–Purcell (SP) radiation by relativistic magnetized electron beam in the absence of the resonator is considered within the framework of the dispersion equation. We have found that the dispersion equation for the SP instability is a quadratic equation for frequency. The first-step approximation for solution of the dispersion equation, giving the SP-spectrum of frequency, corresponds to the mirror boundary case, when the electron beam propagates above a plane metal surface (mirror). It was found that the conditions for both the Thompson and the Raman regimes of excitation do not depend on beam current and depend on the height of the beam above the grating surface. The growth rate of the instability in both cases is proportional to the square root of the electron beam current. No feedback is needed to provide the coherent emission.

We studied the structure of heterogenous DNA in the native state. There are two different regimes in the sample- to-sample fluctuations of the free energy in the native state, which can be interpreted via the concept of local free energy of base pairs. In the first low-temperature frozen regime, local free energies are random and there are large sample-to-sample fluctu- ations for short DNAs. In the high-temperature molten regime, the weakly bounded base pairs are opened and do not give random contribution to the free energy of native DNA. As a result, sample- to-sample fluctuations are suppressed in the molten regime. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 2432-2436, 2010

Kinetic measurement of protein folding is limited by the method used to trigger folding. Traditional methods, such as stopped flow, have a long mixing dead time and cannot be used to monitor fast folding processes. Here, we report a compound, 4-(bromomethyl)6,7-dimethoxycoumarin, that can be used as a ‘‘photolabile cage’’ to study the early stages of protein folding. The folding process of a protein, RD1, including kinetics, enthalpy, and volume change, was studied by the combined use of a phototriggered caging strategy and time-resolved photoacoustic calorimetry. The cage caused unfolding of the photolabile protein, and then a pulse UV laser (� 10 29 s) was used to break the cage, leaving the protein free to refold and allowing the resolving of two folding events on a nanosecond time scale. This strategy is especially good for monitoring fast folding proteins that cannot be studied by traditional methods.

We propose a model based on the primitive system of the Navier–Stokes equations in a bidimensional framework, as the l -plane approximation, which allows us to explain the variety of tracks of tropical cyclones (typhoons). Our idea is to construct special analytical solutions with a linear velocity profile for the Navier–Stokes systems. The evidence of the structure of linear velocity near the center of vortex is provided by the observational data. We study solutions with the linear-velocity property for both barotropic and baroclinic cases and show that they follow the same equations in describing the trajectories of the typhoon eye at the equilibrium state (that relates to the conservative phase of the typhoon dynamics). Moreover, at the equilibrium state, the trajectories can be viewed as a superposition of two circular motions: one has period 2 π / l , the other has period 2 π / b 0 , where l is the Coriolis parameter and b 0 is the height-averaged vorticity at the center of the cyclone. Also, we compare our theoretical trajectories based on initial conditions from the flow with tracks obtained from the observational database. It is worth mentioning that, under certain conditions, our results are still compatible with the observational data, although we did not truly consider the influence of the the ambient pressure field (the “steering” effect). Finally, we propose a parameter-adopting method so that one can correct trajectory prediction in real-time. Examples of our analysis and the use of a parameter-adopting method for the historic trajectories are provided.

Differential scanning calorimetry, circular dichroism spectroscopy, nuclear magnetic resonance spectroscopy, and numerical simulations were used to study the thermostability of the N-terminal RNA-binding domain (RBD) of the SARS-CoV nucleocapsid protein. The transition temperature of the RBD in a mixing buffer, composed of glycine, sodium acetate, and sodium phosphate with 100 mM sodium chloride, at pH 6.8, determined by differential scanning calorimetry and circular dichroism, is 48.74 degrees C. Experimental results showed that the thermal-induced unfolding-folding transition of the RBD follows a two-state model with a reversibility90%. Using a simple Gō-like model and Langevin dynamics we have shown that, in agreement with our experiments, the folding of the RBD is two-state. Theoretical estimates of thermodynamic quantities are in reasonable agreement with the experiments. Folding and thermal unfolding pathways of the RBD also were experimentally and numerically studied in detail. It was shown that the strand beta(1) from the N-terminal folds last and unfolds first, while the remaining beta-strands fold/unfold cooperatively.