Regional surname affinity: A spatial network approach

Objective

We investigate surname affinities among areas of modern‐day China, by constructing a spatial network, and making community detection. It reports a geographical genealogy of the Chinese population that is result of population origins, historical migrations, and societal evolutions.

Materials and methods

We acquire data from the census records supplied by China's National Citizen Identity Information System, including the surname and regional information of 1.28 billion registered Chinese citizens. We propose a multilayer minimum spanning tree (MMST) to construct a spatial network based on the matrix of isonymic distances, which is often used to characterize the dissimilarity of surname structure among areas. We use the fast unfolding algorithm to detect network communities.

Results

We obtain a 10‐layer MMST network of 362 prefecture nodes and 3,610 edges derived from the matrix of the Euclidean distances among these areas. These prefectures are divided into eight groups in the spatial network via community detection. We measure the partition by comparing the inter‐distances and intra‐distances of the communities and obtain meaningful regional ethnicity classification.

Discussion

The visualization of the resulting communities on the map indicates that the prefectures in the same community are usually geographically adjacent. The formation of this partition is influenced by geographical factors, historic migrations, trade and economic factors, as well as isolation of culture and language. The MMST algorithm proves to be effective in geo‐genealogy and ethnicity classification for it retains essential information about surname affinity and highlights the geographical consanguinity of the population.

Cascading Failures in Interdependent Networks with Multiple Supply-Demand Links and Functionality Thresholds

Various social, financial, biological and technological systems can be modeled by interdependent networks. It has been assumed that in order to remain functional, nodes in one network must receive the support from nodes belonging to different networks. So far these models have been limited to the case in which the failure propagates across networks only if the nodes lose all their supply nodes. In this paper we develop a more realistic model for two interdependent networks in which each node has its own supply threshold, i.e., they need the support of a minimum number of supply nodes to remain functional. In addition, we analyze different conditions of internal node failure due to disconnection from nodes within its own network. We show that several local internal failure conditions lead to similar nontrivial results. When there are no internal failures the model is equivalent to a bipartite system, which can be useful to model a financial market. We explore the rich behaviors of these models that include discontinuous and continuous phase transitions. Using the generating functions formalism, we analytically solve all the models in the limit of infinitely large networks and find an excellent agreement with the stochastic simulations.

Publisher's Note: Cascading failures in interdependent networks with finite functional components [Phys. Rev. E 94, 042304 (2016)]

This corrects the article DOI: 10.1103/PhysRevE.94.042304.

Cascading failures in interdependent networks with finite functional components

We present a cascading failure model of two interdependent networks in which functional nodes belong to components of size greater than or equal to s. We find theoretically and via simulation that in complex networks with random dependency links the transition is first order for s≥3 and continuous for s=2. We also study interdependent lattices with a distance constraint r in the dependency links and find that increasing r moves the system from a regime without a phase transition to one with a second-order transition. As r continues to increase, the system collapses in a first-order transition. Each regime is associated with a different structure of domain formation of functional nodes.

The cost of attack in competing networks

Real-world attacks can be interpreted as the result of competitive interactions between networks, ranging from predator-prey networks to networks of countries under economic sanctions. Although the purpose of an attack is to damage a target network, it also curtails the ability of the attacker, which must choose the duration and magnitude of an attack to avoid negative impacts on its own functioning. Nevertheless, despite the large number of studies on interconnected networks, the consequences of initiating an attack have never been studied. Here, we address this issue by introducing a model of network competition where a resilient network is willing to partially weaken its own resilience in order to more severely damage a less resilient competitor. The attacking network can take over the competitor's nodes after their long inactivity. However, owing to a feedback mechanism the takeovers weaken the resilience of the attacking network. We define a conservation law that relates the feedback mechanism to the resilience dynamics for two competing networks. Within this formalism, we determine the cost and optimal duration of an attack, allowing a network to evaluate the risk of initiating hostilities.

Recovery of Interdependent Networks

Recent network research has focused on the cascading failures in a system of interdependent networks and the necessary preconditions for system collapse. An important question that has not been addressed is how to repair a failing system before it suffers total breakdown. Here we introduce a recovery strategy for nodes and develop an analytic and numerical framework for studying the concurrent failure and recovery of a system of interdependent networks based on an efficient and practically reasonable strategy. Our strategy consists of repairing a fraction of failed nodes, with probability of recovery γ, that are neighbors of the largest connected component of each constituent network. We find that, for a given initial failure of a fraction 1 − p of nodes, there is a critical probability of recovery above which the cascade is halted and the system fully restores to its initial state and below which the system abruptly collapses. As a consequence we find in the plane γ − p of the phase diagram three distinct phases. A phase in which the system never collapses without being restored, another phase in which the recovery strategy avoids the breakdown, and a phase in which even the repairing process cannot prevent system collapse.

Epidemic Model with Isolation in Multilayer Networks

The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the propagation of such airborne diseases as influenza A (H1N1). Although the SIR model has recently been studied in a multilayer networks configuration, in almost all the research the isolation of infected individuals is disregarded. Hence we focus our study in an epidemic model in a two-layer network, and we use an isolation parameter w to measure the effect of quarantining infected individuals from both layers during an isolation period tw. We call this process the Susceptible-Infected-Isolated-Recovered (SIIR) model. Using the framework of link percolation we find that isolation increases the critical epidemic threshold of the disease because the time in which infection can spread is reduced. In this scenario we find that this threshold increases with w and tw. When the isolation period is maximum there is a critical threshold for w above which the disease never becomes an epidemic. We simulate the process and find an excellent agreement with the theoretical results.

Network risk and forecasting power in phase-flipping dynamical networks

To model volatile real-world network behavior, we analyze a phase-flipping dynamical scale-free network in which nodes and links fail and recover. We investigate how stochasticity in a parameter governing the recovery process affects phase-flipping dynamics, and we find the probability that no more than q% of nodes and links fail. We derive higher moments of the fractions of active nodes and active links, fn(t) and fℓ(t), and we define two estimators to quantify the level of risk in a network. We find hysteresis in the correlations of fn(t) due to failures at the node level, and we derive conditional probabilities for phase-flipping in networks. We apply our model to economic and traffic networks.

Triple point in correlated interdependent networks

Many real-world networks depend on other networks, often in nontrivial ways, to maintain their functionality. These interdependent "networks of networks" are often extremely fragile. When a fraction 1-p of nodes in one network randomly fails, the damage propagates to nodes in networks that are interdependent and a dynamic failure cascade occurs that affects the entire system. We present dynamic equations for two interdependent networks that allow us to reproduce the failure cascade for an arbitrary pattern of interdependency. We study the "rich club" effect found in many real interdependent network systems in which the high-degree nodes are extremely interdependent, correlating a fraction α of the higher-degree nodes on each network. We find a rich phase diagram in the plane p-α, with a triple point reminiscent of the triple point of liquids that separates a nonfunctional phase from two functional phases.

Optimal transport exponent in spatially embedded networks

The imposition of a cost constraint for constructing the optimal navigation structure surely represents a crucial ingredient in the design and development of any realistic navigation network. Previous works have focused on optimal transport in small-world networks built from two-dimensional lattices by adding long-range connections with Manhattan length r(ij) taken from the distribution P(ij)~r(ij)(-α), where α is a variable exponent. It has been shown that, by introducing a cost constraint on the total length of the additional links, regardless of the strategy used by the traveler (independent of whether it is based on local or global knowledge of the network structure), the best transportation condition is obtained with an exponent α=d+1, where d is the dimension of the underlying lattice. Here we present further support, through a high-performance real-time algorithm, on the validity of this conjecture in three-dimensional regular as well as in two-dimensional critical percolation clusters. Our results clearly indicate that cost constraint in the navigation problem provides a proper theoretical framework to justify the evolving topologies of real complex network structures, as recently demonstrated for the networks of the US airports and the human brain activity.

Robustness of a network formed by n interdependent networks with a one-to-one correspondence of dependent nodes

Many real-world networks interact with and depend upon other networks. We develop an analytical framework for studying a network formed by n fully interdependent randomly connected networks, each composed of the same number of nodes N. The dependency links connecting nodes from different networks establish a unique one-to-one correspondence between the nodes of one network and the nodes of the other network. We study the dynamics of the cascades of failures in such a network of networks (NON) caused by a random initial attack on one of the networks, after which a fraction p of its nodes survives. We find for the fully interdependent loopless NON that the final state of the NON does not depend on the dynamics of the cascades but is determined by a uniquely defined mutual giant component of the NON, which generalizes both the giant component of regular percolation of a single network (n=1) and the recently studied case of the mutual giant component of two interdependent networks (n=2). We also find that the mutual giant component does not depend on the topology of the NON and express it in terms of generating functions of the degree distributions of the network. Our results show that, for any n≥2 there exists a critical p=p(c)>0 below which the mutual giant component abruptly collapses from a finite nonzero value for p≥p(c) to zero for p<p(c), as in a first-order phase transition. This behavior holds even for scale-free networks where p(c)=0 for n=1. We show that, if at least one of the networks in the NON has isolated or singly connected nodes, the NON completely disintegrates for sufficiently large n even if p=1. In contrast, in the absence of such nodes, the NON survives for any n for sufficiently large p. We illustrate this behavior by comparing two exactly solvable examples of NONs composed of Erdős-Rényi (ER) and random regular (RR) networks. We find that the robustness of n coupled RR networks of degree k is dramatically higher compared to the n-coupled ER networks of the same average degree k[over ¯]=k. While for ER NONs there exists a critical minimum average degree k[over ¯]=k[over ¯](min)∼lnn below which the system collapses, for RR NONs k(min)=2 for any n (i.e., for any k>2, a RR NON is stable for any n with p(c)<1). This results arises from the critical role played by singly connected nodes which exist in an ER NON and enhance the cascading failures, but do not exist in a RR NON.

Epidemics on interconnected networks

Populations are seldom completely isolated from their environment. Individuals in a particular geographic or social region may be considered a distinct network due to strong local ties but will also interact with individuals in other networks. We study the susceptible-infected-recovered process on interconnected network systems and find two distinct regimes. In strongly coupled network systems, epidemics occur simultaneously across the entire system at a critical infection strength β(c), below which the disease does not spread. In contrast, in weakly coupled network systems, a mixed phase exists below β(c) of the coupled network system, where an epidemic occurs in one network but does not spread to the coupled network. We derive an expression for the network and disease parameters that allow this mixed phase and verify it numerically. Public health implications of communities comprising these two classes of network systems are also mentioned.

Fragile-to-strong crossover coupled to the liquid-liquid transition in hydrophobic solutions

Using discrete molecular dynamics simulations we study the relation between the thermodynamic and diffusive behaviors of a primitive model of aqueous solutions of hydrophobic solutes consisting of hard spheres in the Jagla particles solvent, close to the liquid-liquid critical point of the solvent. We find that the fragile-to-strong dynamic transition in the diffusive behavior is always coupled to the low-density-high-density liquid transition. Above the liquid-liquid critical pressure, the diffusivity crossover occurs at the Widom line, the line along which the thermodynamic response functions show maxima. Below the liquid-liquid critical pressure, the diffusivity crossover occurs when the limit of mechanical stability lines are crossed, as indicated by the hysteresis observed when going from high to low temperature and vice versa. These findings show that the strong connection between dynamics and thermodynamics found in bulk water persists in hydrophobic solutions for concentrations from low to moderate, indicating that experiments measuring the relaxation time in aqueous solutions represent a viable route for solving the open questions in the field of supercooled water.

Hydrophobic nanoconfinement suppresses fluctuations in supercooled water

We perform very efficient Monte Carlo simulations to study the phase diagram of a water monolayer confined in a fixed disordered matrix of hydrophobic nanoparticles between two hydrophobic plates. We consider different hydrophobic nanoparticle concentrations c. We adopt a coarse-grained model of water that, for c = 0, displays a first-order liquid-liquid phase transition (LLPT) line with negative slope in the pressure-temperature (P-T) plane, ending in a liquid-liquid critical point at about 174 K and 0.13 GPa. We show that upon increase of c the liquid-gas spinodal and the temperature of the maximum density line are shifted with respect to the c = 0 case. We also find dramatic changes in the region around the LLPT. In particular, we observe a substantial (more than 90%) decrease of isothermal compressibility, thermal expansion coefficient and constant-pressure specific heat upon increasing c, consistent with recent experiments. Moreover, we find that a hydrophobic nanoparticle concentration as small as c = 2.4% is enough to destroy the LLPT for P ≥ 0.16 GPa. The fluctuations of volume apparently diverge at P ≈ 0.16 GPa, suggesting that the LLPT line ends in an LL critical point at 0.16 GPa. Therefore, nanoconfinement reduces the range of P-T where the LLPT is observable. By increasing the hydrophobic nanoparticle concentration c, the LLPT becomes weaker and its P-T range smaller. The model allows us to explain these phenomena in terms of a proliferation of interfaces among domains with different local order, promoted by the hydrophobic effect of the water-hydrophobic-nanoparticle interfaces.

The role of the dynamic crossover temperature and the arrest in glass-forming fluids

We discuss the role of the dynamic glass-forming fragile-to-strong crossover (FSC) in supercooled liquids. In the FSC, significant dynamic changes such as the decoupling (the violation of the Stokes-Einstein relation) of homologous transport parameters, e.g., the density relaxation time τ and the viscosity η, occur at a characteristic temperature T(c). We study the FSC using a scaling law approach. In particular, we use both forms of the mode-coupling theory (MCT): the original (ideal) and the extended form, which explicitly describes energy hopping processes. We demonstrate that T(c) plays the most important physical role in understanding dynamic arrest processes.

Quarantine-generated phase transition in epidemic spreading

We study the critical effect of quarantine on the propagation of epidemics on an adaptive network of social contacts. For this purpose, we analyze the susceptible-infected-recovered model in the presence of quarantine, where susceptible individuals protect themselves by disconnecting their links to infected neighbors with probability w and reconnecting them to other susceptible individuals chosen at random. Starting from a single infected individual, we show by an analytical approach and simulations that there is a phase transition at a critical rewiring (quarantine) threshold w(c) separating a phase (w<w(c)) where the disease reaches a large fraction of the population from a phase (w≥w(c)) where the disease does not spread out. We find that in our model the topology of the network strongly affects the size of the propagation and that w(c) increases with the mean degree and heterogeneity of the network. We also find that w(c) is reduced if we perform a preferential rewiring, in which the rewiring probability is proportional to the degree of infected nodes.

Phase transitions and dynamics of bulk and interfacial water

New experiments on water at the surface of proteins at very low temperature display intriguing dynamic behaviors. The extreme conditions of these experiments make it difficult to explore the wide range of thermodynamic state points needed to offer a suitable interpretation. Detailed simulations suffer from the same problem, where equilibration times at low temperature become extremely long. We show how Monte Carlo simulations and mean field calculations using a tractable model of water help interpret the experimental results. Here we summarize the results for bulk water and investigate the thermodynamic and dynamic properties of supercooled water at an interface.

Liquid polymorphism: water in nanoconfined and biological environments

We demonstrate some recent progress in understanding the anomalous behavior of liquid water, by combining information provided by recent experiments and simulations on water in bulk, nanoconfined, and biological environments. We interpret evidence from recent experiments designed to test the hypothesis that liquid water may display 'polymorphism' in that it can exist in two different phases--and discuss recent work on water's transport anomalies as well as the unusual behavior of water in biological environments. Finally, we will discuss how the general concept of liquid polymorphism may prove useful in understanding anomalies in other liquids, such as silicon, silica, and carbon, as well as metallic glasses which have in common that they are characterized by two characteristic length scales in their interactions.

Electrostatic and steric effects in the selective complexation of cations in nonactin

The ester carbonyl stretch frequencies of complexes of the macrotetrolide nonactin with Na(+), K(+), Rb(+), Cs(+), Tl(+), NH(4)(+), NH(3)OH(+), and (NH(2))(2)CNH(2)(+) have been measured. For the larger alkali cations and the polyatomic cations, the ester carbonyl stretch frequency is linearly proportional to the cation-ester carbonyl electrostatic interaction energy. This constitutes direct evidence that the cation-nonactin interaction is primarily electrostatic, rather than mechanical (steric).

Hemoglobin kinetics and the effect of organic phosphates

A kinetic model based on allosteric mechanisms of cooperativity fits the experimentally observed phosphate dependence of hemoglobin reactions. Subunit inequivalence is found to be important in analyzing hemoglobin kinetics. The observed increase in the rate of deoxygenation in the presence of organic phosphates is primarily related to the increased rate of dissociation of the second oxygen molecule.

Towards design principles for optimal transport networks

We investigate the navigation problem in lattices with long-range connections and subject to a cost constraint. Our network is built from a regular two-dimensional (d=2) square lattice to be improved by adding long-range connections (shortcuts) with probability P(ij) approximately r(ij)(-alpha), where r(ij) is the Manhattan distance between sites i and j, and alpha is a variable exponent. We introduce a cost constraint on the total length of the additional links and find optimal transport in the system for alpha=d+1 established here for d=1 and d=2. Remarkably, this condition remains optimal, regardless of the strategy used for navigation, being based on local or global knowledge of the network structure, in sharp contrast with the results obtained for unconstrained navigation using global or local information, where the optimal conditions are alpha=0 and alpha=d, respectively. The validity of our results is supported by data on the U.S. airport network.

Heterogeneities in confined water and protein hydration water

We report recent efforts to understand a broad range of experiments on confined water and protein hydration water, many initiated by a collaboration between workers at the University of Messina and MIT-the editors of this special issue. Preliminary calculations are not inconsistent with one tentative interpretation of these experiments as resulting from the system passing from the high-temperature high-pressure 'HDL' side of the Widom line (where the liquid might display non-Arrhenius behavior) to the low-temperature low-pressure 'LDL' side of the Widom line (where the liquid might display Arrhenius behavior). The Widom line-defined to be the line in the pressure-temperature plane where the correlation length has its maximum-arises if there is a critical point. Hence, interpreting the Messina-MIT experiments in terms of a Widom line is of potential relevance to testing, experimentally, the hypothesis that water displays a liquid-liquid critical point.

Unusual phase behavior of one-component systems with two-scale isotropic interactions

We study the phase behavior of systems of particles interacting through pair potentials with a hard core plus a soft repulsive component. We consider several different forms of soft repulsion, including a square shoulder, a linear ramp and a quasi-exponential tail. The common feature of these potentials is the presence of two repulsive length scales, which may be the origin of unusual phase behaviors such as polyamorphism both in the equilibrium liquid phase and in the glassy state, water-like anomalies in the liquid state and anomalous melting at very high pressures.

Understanding Static and Dynamic Heterogeneities in Confined Water

We report recent efforts to understand the new MIT-Messina experimental discovery of a dynamic crossover at low temperatures in confined water. Preliminary calculations are not inconsistent with one tentative interpretation of this dynamic crossover as resulting from the system passing from the high-temperature high-pressure "HDL" side of the Widom line (where the liquid might display fragile behavior) to the low-temperature low-pressure "LDL" side of the Widom line (where the liquid might display strong behavior). The Widom line - defined to be the line in the pressure-temperature plane where the correlation length has its maximum - arises only if there is a critical point. Hence interpreting the MIT experiments in terms of a Widom line is of potential relevance to testing experimentally, for confined water, the liquid-liquid critical point hypothesis.

Effects of the Arctic (E22-->G) mutation on amyloid beta-protein folding: discrete molecular dynamics study

The 40-42 residue amyloid beta-protein (Abeta) plays a central role in the pathogenesis of Alzheimer's disease (AD). Of the two main alloforms, Abeta40 and Abeta42, the longer Abeta42 is linked particularly strongly to AD. Despite the relatively small two amino acid length difference in primary structure, in vitro studies demonstrate that Abeta40 and Abeta42 oligomerize through distinct pathways. Recently, a discrete molecular dynamics (DMD) approach combined with a four-bead protein model recapitulated the differences in Abeta40 and Abeta42 oligomerization and led to structural predictions amenable to in vitro testing. Here, the same DMD approach is applied to elucidate folding of Abeta40, Abeta42, and two mutants, [G22]Abeta40 and [G22]Abeta42, which cause a familial ("Arctic") form of AD. The implicit solvent in the DMD approach is modeled by amino acid-specific hydropathic and electrostatic interactions. The strengths of these effective interactions are chosen to best fit the temperature dependence of the average beta-strand content in Abeta42 monomer, as determined using circular dichroism (CD) spectroscopy. In agreement with these CD data, we show that at physiological temperatures, the average beta-strand content in both alloforms increases with temperature. Our results predict that the average beta-strand propensity should decrease in both alloforms at temperatures higher than approximately 370 K. At physiological temperatures, both Abeta40 and Abeta42 adopt a collapsed-coil conformation with several short beta-strands and a small (<1%) amount of alpha-helical structure. At slightly above physiological temperature, folded Abeta42 monomers display larger amounts of beta-strand than do Abeta40 monomers. At increased temperatures, more extended conformations with a higher amount of beta-strand (approximately < 30%) structure are observed. In both alloforms, a beta-hairpin at A21-A30 is a central folding region. We observe three additional folded regions: structure 1, a beta-hairpin at V36-A42 that exists in Abeta42 but not in Abeta40; structure 2, a beta-hairpin at R5-H13 in Abeta42 but not in Abeta40; and structure 3, a beta-strand A2-F4 in Abeta40 but not Abeta42. At physiological temperatures, the Arctic mutation, E22G, disrupts contacts in the A21-A30 region of both [G22]Abeta peptides, resulting in a less stable main folding region relative to the wild type peptides. The Arctic mutation induces a significant structural change at the N-terminus of [G22]Abeta40 by preventing the formation of structure 3 observed in Abeta40 but not Abeta42, thereby reducing the structural differences between [G22]Abeta40 and [G22]Abeta42 at the N-terminus. [G22]Abeta40 is characterized by a significantly increased amount of average beta-strand relative to the other three peptides due to an induced beta-hairpin structure at R5-H13, similar to structure 2. Consequently, the N-terminal folded structure of the Arctic mutants closely resembles the N-terminal structure of Abeta42, suggesting that both Arctic Abeta peptides might assemble into structures similar to toxic Abeta42 oligomers.

Age-related reduction in microcolumnar structure correlates with cognitive decline in ventral but not dorsal area 46 of the rhesus monkey

The age-related decline in cognitive function that is observed in normal aging monkeys and humans occurs without significant loss of cortical neurons. This suggests that cognitive impairment results from subtle, sub-lethal changes in the cortex. Recently, changes in the structural coherence in mini- or microcolumns without loss of neurons have been linked to loss of function. Here we use a density map method to quantify microcolumnar structure in both banks of the sulcus principalis (prefrontal cortical area 46) of 16 (ventral) and 19 (dorsal) behaviorally tested female rhesus monkeys from 6 to 33 years of age. While total neuronal density does not change with age in either of these banks, there is a significant age-related reduction in the strength of microcolumns in both regions on the order of 40%. This likely reflects a subtle but definite loss of organization in the structure of the cortical microcolumn. The reduction in strength in ventral area 46 correlates with cognitive impairments in learning and memory while the reduction in dorsal area 46 does not. This result is congruent with published data attributing cognitive functions to ventral area 46 that are similar to our particular cognitive battery which does not optimally tap cognitive functions attributed to dorsal area 46. While the exact mechanisms underlying this loss of microcolumnar organization remain to be determined, it is plausible that they reflect age-related alterations in dendritic and/or axonal organization which alter connectivity and may contribute to age-related declines in cognitive performance.

NMR evidence of a sharp change in a measure of local order in deeply supercooled confined water

Using NMR, we measure the proton chemical shift delta, of supercooled nanoconfined water in the temperature range 195 K < T < 350 K. Because delta is directly connected to the magnetic shielding tensor, we discuss the data in terms of the local hydrogen bond geometry and order. We argue that the derivative -( partial differential ln delta/ partial differentialT)(P) should behave roughly as the constant pressure specific heat C(P)(T), and we confirm this argument by detailed comparisons with literature values of C(P)(T) in the range 290-370 K. We find that -( partial differential ln delta/ partial differentialT)(P) displays a pronounced maximum upon crossing the locus of maximum correlation length at approximately 240 K, consistent with the liquid-liquid critical point hypothesis for water, which predicts that C(P)(T) displays a maximum on crossing the Widom line.

Automated identification of neurons and their locations

Individual locations of many neuronal cell bodies (>10(4)) are needed to enable statistically significant measurements of spatial organization within the brain such as nearest-neighbour and microcolumnarity measurements. In this paper, we introduce an Automated Neuron Recognition Algorithm (ANRA) which obtains the (x, y) location of individual neurons within digitized images of Nissl-stained, 30 microm thick, frozen sections of the cerebral cortex of the Rhesus monkey. Identification of neurons within such Nissl-stained sections is inherently difficult due to the variability in neuron staining, the overlap of neurons, the presence of partial or damaged neurons at tissue surfaces, and the presence of non-neuron objects, such as glial cells, blood vessels, and random artefacts. To overcome these challenges and identify neurons, ANRA applies a combination of image segmentation and machine learning. The steps involve active contour segmentation to find outlines of potential neuron cell bodies followed by artificial neural network training using the segmentation properties (size, optical density, gyration, etc.) to distinguish between neuron and non-neuron segmentations. ANRA positively identifies 86 +/- 5% neurons with 15 +/- 8% error (mean +/- SD) on a wide range of Nissl-stained images, whereas semi-automatic methods obtain 80 +/- 7%/17 +/- 12%. A further advantage of ANRA is that it affords an unlimited increase in speed from semi-automatic methods, and is computationally efficient, with the ability to recognize approximately 100 neurons per minute using a standard personal computer. ANRA is amenable to analysis of huge photo-montages of Nissl-stained tissue, thereby opening the door to fast, efficient and quantitative analysis of vast stores of archival material that exist in laboratories and research collections around the world.

Generating a model of the three-dimensional spatial distribution of neurons using density maps

Microcolumns are a vertical arrangement of neocortical neurons that may constitute a fundamental computational ensemble but have been difficult to study morphologically because of the challenges of determining the three-dimensional (3D) spatial arrangements of individual neurons in the ensemble. Previously, a statistical density map method was developed to characterize microcolumns using two-dimensional (2D) coordinates of neurons from thin tissue sections. Here we extend this approach to derive the relationship between these 2D density maps and the actual 3D properties of microcolumns by creating a theoretical 3D model of cortical neurons. In seven steps, we transform a 3D initial arrangement of neurons from a crystalline lattice, with distances and neuron numbers approximating the idealized cortical microcolumn as assayed by our 2D density map analysis, into a model whose neuronal locations represent a plausible 3D arrangement of neurons in the brain. Because we constrain the transformations on the 3D model by the 2D density map properties, the transformed 3D model will exhibit properties that are consistent with experimental findings regarding microcolumnar anatomy in the brain. Moreover, because our methodology only requires the x,y locations of neurons from thin sections, it is readily accessible to any set of input data regardless of preparation or staining, from human or animals. By generating 3D model neuronal arrangements and comparing between control, aged, and diseased brain, our method can be used to test hypotheses about the effects of neurological diseases as well as normal aging on the 3D structure of microcolumns in the brain.

Parallel folding pathways in the SH3 domain protein

The transition-state ensemble (TSE) is the set of protein conformations with an equal probability to fold or unfold. Its characterization is crucial for an understanding of the folding process. We determined the TSE of the src-SH3 domain protein by using extensive molecular dynamics simulations of the Go model and computing the folding probability of a generated set of TSE candidate conformations. We found that the TSE possesses a well-defined hydrophobic core with variable enveloping structures resulting from the superposition of three parallel folding pathways. The most preferred pathway agrees with the experimentally determined TSE, while the two least preferred pathways differ significantly. The knowledge of the different pathways allows us to design the interactions between amino acids that guide the protein to fold through the least preferred pathway. This particular design is akin to a circular permutation of the protein. The finding motivates the hypothesis that the different experimentally observed TSEs in homologous proteins and circular permutants may represent potentially available pathways to the wild-type protein.

Relation between the Widom line and the breakdown of the Stokes–Einstein relation in supercooled water

Supercooled water exhibits a breakdown of the Stokes–Einstein relation between the diffusion constant D and the alpha relaxation time τα. For water simulated with two different potentials, TIP5P and ST2, we find that the temperature of the decoupling of diffusion and alpha relaxation correlates with the temperature of the maximum in specific heat that corresponds to crossing the Widom line T W(P ). Specifically, we find that our results for D τα/T collapse onto a single “master curve” if temperature is replaced by T − T W(P ). We further find that the size of the mobile molecule clusters (dynamical heterogeneities) increases sharply near T W(P ). Moreover, our calculations of mobile particle cluster size w for different pressures, where t * is the time for which the mobile particle cluster size is largest, also collapse onto a single master curve if T is replaced by T − T W(P ). The crossover to a more locally structured low density liquid (LDL) as T → T W(P ) appears to be well correlated both with the breakdown of the Stokes–Einstein relation and with the growth of dynamic heterogeneities. Our results are consistent with the possibility that the breakdown of the SE relation in supercooled water at low pressures is associated with the hypothesized liquid–liquid phase transition.

Role of electrostatic interactions in amyloid beta-protein (A beta) oligomer formation: a discrete molecular dynamics study

Pathological folding and oligomer formation of the amyloid beta-protein (A beta) are widely perceived as central to Alzheimer's disease. Experimental approaches to study A beta self-assembly provide limited information because most relevant aggregates are quasi-stable and inhomogeneous. We apply a discrete molecular dynamics approach combined with a four-bead protein model to study oligomer formation of A beta. We address the differences between the two most common A beta alloforms, A beta 40 and A beta 42, which oligomerize differently in vitro. Our previous study showed that, despite simplifications, our discrete molecular dynamics approach accounts for the experimentally observed differences between A beta 40 and A beta 42 and yields structural predictions amenable to in vitro testing. Here we study how the presence of electrostatic interactions (EIs) between pairs of charged amino acids affects A beta 40 and A beta 42 oligomer formation. Our results indicate that EIs promote formation of larger oligomers in both A beta 40 and A beta 42. Both A beta 40 and A beta 42 display a peak at trimers/tetramers, but A beta 42 displays additional peaks at nonamers and tetradecamers. EIs thus shift the oligomer size distributions to larger oligomers. Nonetheless, the A beta 40 size distribution remains unimodal, whereas the A beta 42 distribution is trimodal, as observed experimentally. We show that structural differences between A beta 40 and A beta 42 that already appear in the monomer folding, are not affected by EIs. A beta 42 folded structure is characterized by a turn in the C-terminus that is not present in A beta 40. We show that the same C-terminal region is also responsible for the strongest intermolecular contacts in A beta 42 pentamers and larger oligomers. Our results suggest that this C-terminal region plays a key role in the formation of A beta 42 oligomers and the relative importance of this region increases in the presence of EIs. These results suggest that inhibitors targeting the C-terminal region of A beta 42 oligomers may be able to prevent oligomer formation or structurally modify the assemblies to reduce their toxicity.

Glass transition in biomolecules and the liquid-liquid critical point of water

Using molecular dynamics simulations, we investigate the relation between the dynamic transitions of biomolecules (lysozyme and DNA) and the dynamic and thermodynamic properties of hydration water. We find that the dynamic transition of the macromolecules, sometimes called a "protein glass transition," occurs at the temperature of dynamic crossover in the diffusivity of hydration water and also coincides with the maxima of the isobaric specific heat C_{P} and the temperature derivative of the orientational order parameter. We relate these findings to the hypothesis of a liquid-liquid critical point in water. Our simulations are consistent with the possibility that the protein glass transition results from crossing the Widom line, which is defined as the locus of correlation length maxima emanating from the hypothesized second critical point of water.

Relation between the Widom line and the dynamic crossover in systems with a liquid-liquid phase transition

We investigate, for two water models displaying a liquid-liquid critical point, the relation between changes in dynamic and thermodynamic anomalies arising from the presence of the liquid-liquid critical point. We find a correlation between the dynamic crossover and the locus of specific heat maxima C(P)(max) ("Widom line") emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesized liquid-liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between C(P)(max) and dynamic crossover is not limited to the case of water, a hydrogen bond network-forming liquid, but is a more general feature of crossing the Widom line. Specifically, we also study the Jagla potential, a spherically symmetric two-scale potential known to possess a liquid-liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactions.

Optimization of network robustness to waves of targeted and random attacks

We study the robustness of complex networks to multiple waves of simultaneous (i) targeted attacks in which the highest degree nodes are removed and (ii) random attacks (or failures) in which fractions p(t) and p(r) , respectively, of the nodes are removed until the network collapses. We find that the network design which optimizes network robustness has a bimodal degree distribution, with a fraction r of the nodes having degree k2 = ((k)-1+r)/r and the remainder of the nodes having degree k1=1, where k is the average degree of all the nodes. We find that the optimal value of r is of the order of p(t)/p(r) for p(t)/p(r) << 1.

Molecular dynamics simulation of amyloid beta dimer formation

Recent experiments with amyloid beta (Abeta) peptide indicate that formation of toxic oligomers may be an important contribution to the onset of Alzheimer's disease. The toxicity of Abeta oligomers depends on their structure, which is governed by assembly dynamics. Due to limitations of current experimental techniques, a detailed knowledge of oligomer structure at the atomic level is missing. We introduce a molecular dynamics approach to study Abeta dimer formation. 1), We use discrete molecular dynamics simulations of a coarse-grained model to identify a variety of dimer conformations; and 2), we employ all-atom molecular mechanics simulations to estimate thermodynamic stability of all dimer conformations. Our simulations of a coarse-grained Abeta peptide model predicts 10 different planar beta-strand dimer conformations. We then estimate the free energies of all dimer conformations in all-atom molecular mechanics simulations with explicit water. We compare the free energies of Abeta(1-42) and Abeta(1-40) dimers. We find that 1), dimer conformations have higher free energies compared to their corresponding monomeric states; and 2), the free-energy difference between the Abeta(1-42) and the corresponding Abeta(1-40) dimer conformation is not significant. Our results suggest that Abeta oligomerization is not accompanied by the formation of thermodynamically stable planar beta-strand dimers.

A statistically based density map method for identification and quantification of regional differences in microcolumnarity in the monkey brain

We present a statistical density map method derived from condensed matter physics to quantify microcolumns, the fundamental computational unit of the cerebral cortex. This method provides measures for microcolumnar strength, width, spacing, length, and periodicity. We applied this method to Nissl-stained 30 microm thick frozen sections from areas 46, TE, and TL of rhesus monkey brains, areas that differ visually in microcolumnarity and are associated with different cognitive functions. Our results indicate that microcolumns in these areas are similar in width, spacing, and periodicity, but are stronger (possess a higher neuronal density) in area TE, as compared to areas TL and 46. We modeled the effect of section orientation on microcolumnar spacing and demonstrated that this method provides an adequate estimate of spacing. We also modeled disruption of microcolumnarity by performing simulations that randomly displace neurons and demonstrated that displacements of only one neuronal diameter effectively eliminate microcolumnar organization. These results indicate that our density map method is sensitive enough to detect and quantify subtle differences in microcolumnar organization that may occur in the context of development, aging, and neuropathology, as well as between areas and species.

In silico study of amyloid beta-protein folding and oligomerization

Experimental findings suggest that oligomeric forms of the amyloid beta protein (Abeta) play a critical role in Alzheimer's disease. Thus, elucidating their structure and the mechanisms of their formation is critical for developing therapeutic agents. We use discrete molecular dynamics simulations and a four-bead protein model to study oligomerization of two predominant alloforms, Abeta40 and Abeta42, at the atomic level. The four-bead model incorporates backbone hydrogen-bond interactions and amino acid-specific interactions mediated through hydrophobic and hydrophilic elements of the side chains. During the simulations we observe monomer folding and aggregation of monomers into oligomers of variable sizes. Abeta40 forms significantly more dimers than Abeta42, whereas pentamers are significantly more abundant in Abeta42 relative to Abeta40. Structure analysis reveals a turn centered at Gly-37-Gly-38 that is present in a folded Abeta42 monomer but not in a folded Abeta40 monomer and is associated with the first contacts that form during monomer folding. Our results suggest that this turn plays an important role in Abeta42 pentamer formation. Abeta pentamers have a globular structure comprising hydrophobic residues within the pentamer's core and hydrophilic N-terminal residues at the surface of the pentamer. The N termini of Abeta40 pentamers are more spatially restricted than Abeta42 pentamers. Abeta40 pentamers form a beta-strand structure involving Ala-2-Phe-4, which is absent in Abeta42 pentamers. These structural differences imply a different degree of hydrophobic core exposure between pentamers of the two alloforms, with the hydrophobic core of the Abeta42 pentamer being more exposed and thus more prone to form larger oligomers.

Age-related reduction in microcolumnar structure in area 46 of the rhesus monkey correlates with behavioral decline

Many age-related declines in cognitive function are attributed to the prefrontal cortex, area 46 being especially critical. Yet in normal aging, studies indicate that neurons are not lost in area 46, suggesting that impairments result from more subtle processes. One cortical feature that is functionally important, but that has not been examined in normal aging because of a lack of efficient quantitative methods, is the vertical arrangement of neurons into microcolumns, a fundamental computational unit of the cortex. By using a density-map method derived from condensed-matter physics, we quantified microcolumns in area 46 of seven young and seven aged rhesus monkeys that had been cognitively tested. This analysis demonstrated that there is no age-related reduction in total neuronal density or in microcolumn width, length, or periodicity. There was, however, a statistically significant decrease in the strength of microcolumns, indicating microcolumnar disorganization. This reduction in strength was significantly correlated with age-related cognitive decline on tests of spatial working memory and recognition memory independent of the effect of age. Modeling demonstrated that random neuron displacements of approximately 30% of a neuronal diameter (<3 mum) produced the observed reduction in strength. Hence, it is possible that, with changes in dendrites and myelinated axons, subtle displacements of neurons occur that alter microcolumnar structure and correlate with age-induced dysfunction. Therefore, quantitative measurement of microcolumnar structure may provide a sensitive morphological method to assay microcolumnar function in aging and other conditions.

Liquid-liquid phase transitions for soft-core attractive potentials

Using event-driven molecular dynamics simulations, we study a three-dimensional one-component system of spherical particles interacting via a discontinuous potential combining a repulsive square soft core and an attractive square well. In the case of a narrow attractive well, it has been shown that this potential has two metastable gas-liquid critical points. Here we systematically investigate how the changes of the parameters of this potential affect the phase diagram of the system. We find a broad range of potential parameters for which the system has both a gas-liquid critical point C1 and a liquid-liquid critical point C2. For the liquid-gas critical point we find that the derivatives of the critical temperature and pressure, with respect to the parameters of the potential, have the same signs: they are positive for increasing width of the attractive well and negative for increasing width and repulsive energy of the soft core. This result resembles the behavior of the liquid-gas critical point for standard liquids. In contrast, for the liquid-liquid critical point the critical pressure decreases as the critical temperature increases. As a consequence, the liquid-liquid critical point exists at positive pressures only in a finite range of parameters. We present a modified van der Waals equation which qualitatively reproduces the behavior of both critical points within some range of parameters, and gives us insight on the mechanisms ruling the dependence of the two critical points on the potential's parameters. The soft-core potential studied here resembles model potentials used for colloids, proteins, and potentials that have been related to liquid metals, raising an interesting possibility that a liquid-liquid phase transition may be present in some systems where it has not yet been observed.

Discrete molecular dynamics simulations of peptide aggregation

We study the aggregation of peptides using the discrete molecular dynamics simulations. Specifically, at temperatures above the alpha-helix melting temperature of a single peptide, the model peptides aggregate into a multilayer parallel beta-sheet structure. This structure has an interstrand distance of 4.8 A and an intersheet distance of 10 A, which agree with experimental observations. Our model explains these results as follows: hydrogen-bond interactions give rise to the interstrand spacing in beta sheets, while Gō interactions between side chains make beta strands parallel to each other and allow beta sheets to pack into layers. An important feature of our results is that the aggregates contain free edges, which may allow for further aggregation of model peptides to form elongated fibrils.

Analysis of clusters formed by the moving average of a long-range correlated time series

We analyze the stochastic function C(n)(i) identical with y(i)-y(n)(i), where y(i) is a long-range correlated time series of length N(max) and y(n)(i) identical with (1/n) Sigma(n-1)(k=0)y(i-k) is the moving average with window n. We argue that C(n)(i) generates a stationary sequence of self-affine clusters C with length l, lifetime tau, and area s. The length and the area are related to the lifetime by the relationships l approximately tau(psi(l)) and s approximately tau(psi(s)), where psi(l)=1 and psi(s)=1+H. We also find that l, tau, and s are power law distributed with exponents depending on H: P(l) approximately l(-alpha), P(tau) approximately tau(-beta), and P(s) approximately s(-gamma), with alpha=beta=2-H and gamma=2/(1+H). These predictions are tested by extensive simulations on series generated by the midpoint displacement algorithm of assigned Hurst exponent H (ranging from 0.05 to 0.95) of length up to N(max)=2(21) and n up to 2(13).

Neuron recognition by parallel Potts segmentation

Identifying neurons and their spatial coordinates in images of the cerebral cortex is a necessary step in the quantitative analysis of spatial organization in the brain. This is especially important in the study of Alzheimer's disease (AD), in which spatial neuronal organization and relationships are highly disrupted because of neuronal loss. To automate neuron recognition by using high-resolution confocal microscope images from human brain tissue, we propose a recognition method based on statistical physics that consists of image preprocessing, parallel image segmentation, and cluster selection on the basis of shape, optical density, and size. We segment a preprocessed digital image into clusters by applying Monte Carlo simulations of a q-state inhomogeneous Potts model. We then select the range of Potts segmentation parameters to yield an ideal recognition of simplified objects in the test image. We apply our parallel segmentation method to control individuals and to AD patients and achieve recognition of 98% (for a control) and 93% (for an AD patient), with at most 3% false clusters.

Water and its energy landscape

We present an overview of the recent studies on the properties of the potential energy surface for a simple model of water. We emphasize the relations between PES properties and dynamics in supercooled states for the model and discuss possible future application of the PES studies.