Universality and scaling in complex networks from periods of Chinese history.

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.

Polymorphism in rapidly changing cyclic environment.

Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric payoffs 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 nonlinear fitness that is induced by environmental changes. The nonlinear 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 exemplified via the rock-paper-scissors dynamics, and also via the prisoner's dilemma in a time-periodic environment.

Specific heat and partition function zeros for the dimer model on the checkerboard B lattice: Finite-size effects.

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)PLEEE81539-375510.1103/PhysRevE.91.062139]. 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×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 ν and the shift exponent λ, and λ is generally unequal to 1/ν (λ≠1/ν).

Dependence of extreme events on spatial location.

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.

Compound CID 9998128 Is a Potential Multitarget Drug for Alzheimer's Disease.

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 ß42 (Aß42) fibrils and ß-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 Aß42 amyloid fibrillization and is capable to clear Aß42 fibrils. Moreover, the compound dose-dependently decreases ß-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 Aß peptides and degrading their aggregates. For drug design, we predict that the chemical structure of potent AD multitarget inhibitors should not contain indazole.

Circuit variability interacts with excitatory-inhibitory diversity of interneurons to regulate network encoding capacity.

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.

Accurate analytic solution of chemical master equations for gene regulation networks in a single cell.

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.

Crossing fitness canyons by a finite population.

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.

Physical mechanism for biopolymers to aggregate and maintain in non-equilibrium states.

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.

Relationship between calorimetric profiles and differential melting curves for natural DNAs.

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 ΔT. Corresponding difference between melting temperatures is proportional to ΔT2. In general, sequence and ionic conditions influence the deviation through their effect on ΔT. 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.

Impact of Mutations at C-Terminus on Structures and Dynamics of Aß40 and Aß42: A Molecular Simulation Study.

Alzheimer's disease is presumed to be caused by the formation of intracellular plaques of amyloid ß (Aß) peptides inside neurons. The most abundant Aß forms are Aß40 and Aß42 comprising, respectively, 40 and 42 residues. Recent experiments showed that the triple Gly33Val-Val36Pro-Gly38Val (VPV) mutation causes Aß42 to become "super-Aß42" with elevated aggregation rates and toxicity. Upon VPV mutation, oligomerization pathways of Aß40 become similar to those of the Aß42 wild type. It was hypothesized that the super behavior of Aß42 occurs due to an enhanced content of the ß-turn and ß-hairpin, centered at residues 36-37, and the similarity in oligomerization pathways of Aß40-VPV and Aß42-WT comes from the increased ß-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 Aß sequences. We showed that the results obtained for truncated peptides fall short in explaining the similarity of self-assembly pathways of Aß40-VPV and Aß42-WT. Instead, we propose that the similarity is due to not only increased ß-turn population but also due to the elevated ß-structure of the entire sequence. Similar to VPV, the Gly33Val-Val36Asn-Gly38Leu mutation enhances the ß-structure and the C-terminal ß-turn making the behavior of Aß40 similar to that of Aß42-WT.

Finite-size corrections and scaling for the dimer model on the checkerboard lattice.

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 a 2M×2N 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 a 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 the specific-heat pseudocritical point coincides with the critical point of the thermodynamic limit, which means that the specific-heat shift exponent λ is equal to ∞. We have also considered the limit N→∞ 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.

Solution of classical evolutionary models in the limit when the diffusion approximation breaks down.

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.

The rich phase structure of a mutator model.

We propose a modification of the Crow-Kimura and Eigen models of biological molecular evolution to include a mutator gene that causes both an increase in the mutation rate and a change in the fitness landscape. This mutator effect relates to a wide range of biomedical problems. There are three possible phases: mutator phase, mixed phase and non-selective phase. We calculate the phase structure, the mean fitness and the fraction of the mutator allele in the population, which can be applied to describe cancer development and RNA viruses. We find that depending on the genome length, either the normal or the mutator allele dominates in the mixed phase. We analytically solve the model for a general fitness function. We conclude that the random fitness landscape is an appropriate choice for describing the observed mutator phenomenon in the case of a small fraction of mutators. It is shown that the increase in the mutation rates in the regular and the mutator parts of the genome should be set independently; only some combinations of these increases can push the complex biomedical system to the non-selective phase, potentially related to the eradication of tumors.

Noise-induced multistability in the regulation of cancer by genes and pseudogenes.

We extend a previously introduced model of stochastic gene regulation of cancer to a nonlinear case having both gene and pseudogene messenger RNAs (mRNAs) self-regulated. The model consists of stochastic Boolean genetic elements and possesses noise-induced multistability (multimodality). We obtain analytical expressions for probabilities for the case of constant but finite number of microRNA molecules which act as a noise source for the competing gene and pseudogene mRNAs. The probability distribution functions display both the global bistability regime as well as even-odd number oscillations for a certain range of model parameters. Statistical characteristics of the mRNA's level fluctuations are evaluated. The obtained results of the extended model advance our understanding of the process of stochastic gene and pseudogene expressions that is crucial in regulation of cancer.

Discovery of DNA dyes Hoechst 34580 and 33342 as good candidates for inhibiting amyloid beta formation: in silico and in vitro study.

Combining Lipinski's rule with the docking and steered molecular dynamics simulations and using the PubChem data base of about 1.4 million compounds, we have obtained DNA dyes Hoechst 34580 and Hoechst 33342 as top-leads for the Alzheimer's disease. The binding properties of these ligands to amyloid beta (Aß) fibril were thoroughly studied by in silico and in vitro experiments. Hoechst 34580 and Hoechst 33342 prefer to locate near hydrophobic regions with binding affinity mainly governed by the van der Waals interaction. By the Thioflavin T assay, it was found that the inhibition constant IC50 ≈ 0.86 and 0.68 µM for Hoechst 34580 and Hoechst 33342, respectively. This result qualitatively agrees with the binding free energy estimated using the molecular mechanic-Poisson Boltzmann surface area method and all-atom simulations with the AMBER-f99SB-ILDN force field and water model TIP3P. In addition, DNA dyes have the high capability to cross the blood brain barrier. Thus, both in silico and in vitro experiments have shown that Hoechst 34580 and 33342 are good candidates for treating the Alzheimer's disease by inhibiting Aß formation.

On the adsorption of magnetite nanoparticles on lysozyme amyloid fibrils.

An adsorption of magnetic nanoparticles (MNP) from electrostatically stabilized aqueous ferrofluids on amyloid fibrils of hen egg white lysozyme (HEWL) in 2mg/mL acidic dispersions have been detected for the MNP concentration range of 0.01-0.1vol.%. The association of the MNP with amyloid fibrils has been characterized by transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS) and magneto-optical measurements. It has been observed that the extent of adsorption is determined by the MNP concentration. When increasing the MNP concentration the formed aggregates of magnetic particles repeat the general rod-like structure of the fibrils. The effect is not observed when MNP are mixed with the solution of lysozyme monomers. The adsorption has been investigated with the aim to clarify previously found disaggregation activity of MNP in amyloid fibrils dispersions and to get deeper insight into interaction processes between amyloids and MNP. The observed effect is also discussed with respect to potential applications for ordering lysozyme amyloid fibrils in a liquid crystal phase under external magnetic fields.

Estimation of the diversity between DNA calorimetric profiles, differential melting curves and corresponding melting temperatures.

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.

Correction: Structural Perturbations to Population Skeletons: Transient Dynamics, Coexistence of Attractors and the Rarity of Chaos.

[This corrects the article DOI: 10.1371/journal.pone.0024200.].

Predicting missing links and identifying spurious links via likelihood analysis.

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.