Biomedical subjects

Sergey V Buldyrev

Publications and source records attributed to Sergey V Buldyrev.

At least 19 recordsLinked to original sources

PubMed2005

Structural order for one-scale and two-scale potentials.

We perform molecular dynamics simulations to investigate the relationship between structural order and waterlike dynamic and thermodynamic anomalies in spherically symmetric potentials having either one or two characteristic length scales. Structural order is characterized by translational and orientational order parameters. We find that (i) dynamic and thermodynamic anomalies exist for both one-scale and two-scale ramp potentials, and (ii) waterlike structural order anomalies exist only for the two-scale ramp potential. Our findings suggest that the waterlike relationship between structural order and anomalies is related to the presence of two different length scales in the potential.

Journal Article↗

PubMed2005

Scaling of optimal-path-lengths distribution in complex networks.

We study the distribution of optimal path lengths in random graphs with random weights associated with each link ("disorder"). With each link i we associate a weight tau(i) = exp (a r(i)), where r(i) is a random number taken from a uniform distribution between 0 and 1, and the parameter a controls the strength of the disorder. We suggest, in an analogy with the average length of the optimal path, that the distribution of optimal path lengths has a universal form that is controlled by the expression (1/p(c)) (l(infinity)/a), where l(infinity) is the optimal path length in strong disorder (a --> infinity) and p(c) is the percolation threshold. This relation is supported by numerical simulations for Erdos-Rényi and scale-free graphs. We explain this phenomenon by showing explicitly the transition between strong disorder and weak disorder at different length scales in a single network.

Journal Article↗

PubMed2005

Static and dynamic anomalies in a repulsive spherical ramp liquid: theory and simulation.

We compare theoretical and simulation results for static and dynamic properties for a model of particles interacting via a spherically symmetric repulsive ramp potential. The model displays anomalies similar to those found in liquid water, namely, expansion upon cooling and an increase of diffusivity upon compression. In particular, we calculate the state points P (rho,T) from the simulation and successfully compare it with the state points P (rho,T) obtained using the Rogers-Young (RY) closure for the Ornstein-Zernike (OZ) equation. Both the theoretical and the numerical calculations confirm the presence of a line of isobaric density maxima, and lines of compressibility minima and maxima. Indirect evidence of a liquid-liquid critical point is found. Dynamic properties also show anomalies. Along constant temperature paths, as the density increases, the dynamics alternate between slowing down and speeding up, and we associate this behavior with the progressive structuring and destructuring of the liquid. Finally we confirm that mode coupling theory successfully predicts the nonmonotonic behavior of dynamics and the presence of multiple glass phases, providing strong evidence that structure (the only input of mode coupling theory) controls dynamics.

Journal Article↗

PubMed2005

Clusters of mobile molecules in supercooled water.

We study the spatially heterogeneous dynamics in water via molecular dynamics simulations using the extended simple point charge potential. We identify clusters formed by mobile molecules and study their properties. We find that these clusters grow in size and become more compact as temperature decreases. We analyze the probability density function of cluster size, and we study the cluster correlation length. We find that clusters appear to be characterized by a fractal dimension consistent with that of lattice animals. We relate the cluster size and correlation length to the configurational entropy, S(conf). We find that these quantities depend weakly on 1/ S(conf). In particular, the linearity found between the cluster mass n(*) and 1/ S(conf) suggests that n(*) may be interpreted as the mass of the cooperatively rearranging regions that form the basis of the Adam-Gibbs approach to the dynamics of supercooled liquids. We study the motion of molecules within a cluster, and find that each molecule preferentially follows a neighboring molecule in the same cluster. Based on this finding we hypothesize that stringlike cooperative motion may be a general mechanism for molecular rearrangement of complex, as well as simple liquids. By mapping each equilibrium configuration onto its corresponding local potential energy minimum or inherent structure (IS), we are able to compare the mobile molecule clusters in the equilibrium system with the molecules forming the clusters identified in the transitions between IS. We find that (i) mobile molecule clusters obtained by comparing different system configurations and (ii) clusters obtained by comparing the corresponding IS are completely different for short time scales, but are the same on the longer time scales of diffusive motion.

Journal Article↗

PubMed2005

Anomalous transport in scale-free networks.

To study transport properties of scale-free and Erdos-Rényi networks, we analyze the conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k)-k(-lambda) in which all links have unit resistance. We predict a broad range of values of G, with a power-law tail distribution phi(SF)(G)-G(-g(G)), where g(G)=2lambda-1, and confirm our predictions by simulations. The power-law tail in phi(SF)(G) leads to large values of G, signaling better transport in scale-free networks compared to Erdos-Rényi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical "transport backbone" picture we show that the conductances of scale-free and Erdos-Rényi networks are well approximated by ck(A)k(B)/(k(A)+k(B)) for any pair of nodes A and B with degrees k(A) and k(B), where c emerges as the main parameter characterizing network transport.

Computer Systems↗

PubMed2005

Liquid-liquid phase transition for an attractive isotropic potential with wide repulsive range.

We investigate how the phase diagram of a repulsive soft-core attractive potential, with a liquid-liquid phase transition in addition to the standard gas-liquid phase transition, changes by varying the parameters of the potential. We extend our previous work on short soft-core ranges to the case of large soft-core ranges, by using an integral equation approach in the hypernetted-chain approximation. We show, using a modified van der Waals equation we recently introduced, that if there is a balance between the attractive and repulsive part of the potential this potential has two fluid-fluid critical points well separated in temperature and in density. This implies that for the repulsive (attractive) energy U(R)(U(A)) and the repulsive (attractive) range w(R)(w(A)) the relation U(R)/U(A) proportional to w(R)/w(A) holds for short soft-core ranges, while U(R)/U(A) proportional to 3w(R)/w(A) holds for large soft-core ranges.

Journal Article↗

PubMed2005

Folding events in the 21-30 region of amyloid beta-protein (Abeta) studied in silico.

Oligomeric assemblies of the amyloid beta-protein (Abeta) have been implicated in the pathogenesis of Alzheimer's disease as a primary source of neurotoxicity. Recent in vitro studies have suggested that a 10-residue segment, Ala-21-Ala-30, forms a turn-like structure that nucleates the folding of the full-length Abeta. To gain a mechanistic insight, we simulated Abeta(21-30) folding by using a discrete molecular dynamics algorithm and a united-atom model incorporating implicit solvent and a variable electrostatic interaction strength (EIS). We found that Abeta(21-30) folds into a loop-like conformation driven by an effective hydrophobic attraction between Val-24 and the butyl portion of the Lys-28 side chain. At medium EIS [1.5 kcal/mol (1 cal = 4.18 J)], unfolded conformations almost disappear, in agreement with experimental observations. Under optimal conditions for folding, Glu-22 and Asp-23 form transient electrostatic interactions (EI) with Lys-28 that stabilize the loop conformations. Glu-22-Lys-28 is the most favored interaction. High EIS, as it occurs in the interior of proteins and aggregates, destabilizes the packing of Val-24 and Lys-28. Analysis of the unpacked structures reveals strong EI with predominance of the Asp-23-Lys-28 interaction, in agreement with studies of molecular modeling of full-length Abeta fibrils. The binary nature of the EI involving Lys-28 provides a mechanistic explanation for the linkage of amino acid substitutions at Glu-22 with Alzheimer's disease and cerebral amyloid angiopathy. Substitutions may alter the frequency of Glu-22 or Asp-23 involvement in contact formation and affect the stability of the folding nucleus formed in the Abeta(21-30) region.

Algorithms↗

PubMed2005

Current flow in random resistor networks: the role of percolation in weak and strong disorder.

We study the current flow paths between two edges in a random resistor network on a L X L square lattice. Each resistor has resistance e(ax) , where x is a uniformly distributed random variable and a controls the broadness of the distribution. We find that: (a) The scaled variable u identical with u congruent to L/a(nu) , where nu is the percolation connectedness exponent, fully determines the distribution of the current path length l for all values of u . For u >> 1, the behavior corresponds to the weak disorder limit and l scales as l approximately L, while for u << 1 , the behavior corresponds to the strong disorder limit with l approximately L(d(opt) ), where d(opt) =1.22+/-0.01 is the optimal path exponent. (b) In the weak disorder regime, there is a length scale xi approximately a(nu), below which strong disorder and critical percolation characterize the current path.

Journal Article↗

PubMed2005

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.

Animals↗

PubMed2005

Static and dynamic heterogeneities in water.

The thermodynamic behaviour of water seems to be related to static heterogeneities. These static heterogeneities are related to the local structure of water molecules and, when properly characterized, may offer an economical explanation of thermodynamic data. 'What matters' most in determining some of the unusual properties of liquid water may be the fact that the local geometry of the liquid molecules is not spherical or oblong, but rather tetrahedral. In respect to static heterogeneities, this local geometry is critical. The dynamic behaviour of water seems to be related to dynamic heterogeneities, which seem to explain the dynamics of supercooled liquid water well.

Anisotropy↗

PubMed2004

Folding Trp-cage to NMR resolution native structure using a coarse-grained protein model.

We develop a coarse-grained protein model with a simplified amino acid interaction potential. Using this model, we perform discrete molecular dynamics folding simulations of a small 20-residue protein--Trp-cage--from a fully extended conformation. We demonstrate the ability of the Trp-cage model to consistently reach conformations within 2-angstroms backbone root-mean-square distance from the corresponding NMR structures. The minimum root-mean-square distance of Trp-cage conformations in simulations can be <1 angstroms. Our findings suggest that, at least in the case of Trp-cage, a detailed all-atom protein model with a molecular mechanics force field is not necessary to reach the native state of a protein. Our results also suggest that the success of folding Trp-cage in our simulations and in the reported all-atom molecular mechanics simulation studies may be mainly due to the special stabilizing features specific to this miniprotein.

Algorithms↗

PubMed2004

Effect of disorder strength on optimal paths in complex networks.

We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path l(opt) in a disordered Erdos-Rényi (ER) random network and scale-free (SF) network. Each link i is associated with a weight tau(i) identical withexp (a r(i) ) , where r(i) is a random number taken from a uniform distribution between 0 and 1 and the parameter a controls the strength of the disorder. We find that for any finite a , there is a crossover network size N* (a) at which the transition occurs. For N< /=4 , and l(opt) approximately N (lambda-3) (/ (lambda-1) ) for SF networks with 3 >N* (a) the scaling behavior is in the weak disorder regime, with l(opt) approximately ln N for ER networks and SF networks with lambda>3 . In order to study the transition we propose a measure which indicates how close or far the disordered network is from the limit of strong disorder. We propose a scaling ansatz for this measure and demonstrate its validity. We proceed to derive the scaling relation between N* (a) and a . We find that N* (a) approximately a(3) for ER networks and for SF networks with lambda>/=4 , and N* (a) approximately a (lambda-1) (/ (lambda-3) ) for SF networks with 3<lambda<4 .

Journal Article↗

PubMed2004

Universality of the optimal path in the strong disorder limit.

We study numerically the optimal paths in two and three dimensions on various disordered lattices in the limit of strong disorder. We find that the length l of the optimal path scales with geometric distance r , as l approximately r (d(opt) ) with d(opt) =1.22+/-0.01 for d=2 and 1.44+/-0.02 for d=3 , independent of whether the optimization is on a path of weighted bonds or sites, and independent of the lattice or its coordination number. Our finding suggests that the exponent d(opt) is universal, depending only on the dimension of the system.

Journal Article↗

PubMed2004

Multiple folding pathways of the SH3 domain.

Experimental observations suggest that proteins follow different folding pathways under different environmental conditions. We perform molecular dynamics simulations of a model of the c-Crk SH3 domain over a broad range of temperatures, and identify distinct pathways in the folding transition. We determine the kinetic partition temperature-the temperature for which the c-Crk SH3 domain undergoes a rapid folding transition with minimal kinetic barriers-and observe that below this temperature the model protein may undergo a folding transition by multiple folding pathways via only one or two intermediates. Our findings suggest the hypothesis that the SH3 domain, a protein fold for which only two-state folding kinetics was observed in previous experiments, may exhibit intermediate states under conditions that strongly stabilize the native state.

Animals↗

PubMed2003

Dynamical robustness of Lévy search strategies.

We study the role of dynamical constraints in the general problem of finding the best statistical strategy for random searching when the targets can be detected only in the limited vicinity of the searcher. We find that the optimal search strategy depends strongly on the delay time tau during which a previously visited site becomes unavailable. We also find that the optimal search strategy is always described for large step lengths l by a power-law distribution P(l) approximately l(-mu), with 1<mu(tau)</=2. Our findings appear to remain valid even if arbitrary energy costs of locomotion are considered.

Feeding Behavior↗

PubMed2003

Optimal paths in disordered complex networks.

We study the optimal distance in networks, l(opt), defined as the length of the path minimizing the total weight, in the presence of disorder. Disorder is introduced by assigning random weights to the links or nodes. For strong disorder, where the maximal weight along the path dominates the sum, we find that l(opt) approximately N(1/3) in both Erdos-Rényi (ER) and Watts-Strogatz (WS) networks. For scale-free (SF) networks, with degree distribution P(k) approximately k(-lambda), we find that l(opt) scales as N((lambda-3)/(lambda-1)) for 3 or =4. Thus, for these networks, the small-world nature is destroyed. For 2<lambda<3, our numerical results suggest that l(opt) scales as ln(lambda-1N. We also find numerically that for weak disorder l(opt) approximately ln(N for both the ER and WS models as well as for SF networks.

Communication↗

PubMed2003

Perimeter growth of a branched structure: application to crackle sounds in the lung.

We study an invasion percolation process on Cayley trees and find that the dynamics of perimeter growth is strongly dependent on the nature of the invasion process, as well as on the underlying tree structure. We apply this process to model the inflation of the lung in the airway tree, where crackling sounds are generated when airways open. We define the perimeter as the interface between the closed and opened regions of the lung. In this context we find that the distribution of time intervals between consecutive openings is a power law with an exponent beta approximately 2. We generalize the binary structure of the lung to a Cayley tree with a coordination number Z between 2 and 4. For Z=4, beta remains close to 2, while for a chain, Z=2 and beta=1, exactly. We also find a mean field solution of the model.

Airway Resistance↗

PubMed2003

Postbreakthrough behavior in flow through porous media.

We numerically simulate the traveling time of a tracer in convective flow between two points (injection and extraction) separated by a distance r in a model of porous media, d=2 percolation. We calculate and analyze the traveling time probability density function for two values of the fraction of connecting bonds p: the homogeneous case p=1 and the inhomogeneous critical threshold case p=p(c). We analyze both constant current and constant pressure conditions at p=p(c). The homogeneous p=1 case serves as a comparison base for the more complicated p=p(c) situation. We find several regions in the probability density of the traveling times for the homogeneous case (p=1) and also for the critical case (p=p(c)) for both constant pressure and constant current conditions. For constant pressure, the first region I(P) corresponds to the short times before the flow breakthrough occurs, when the probability distribution is strictly zero. The second region II(P) corresponds to numerous fast flow lines reaching the extraction point, with the probability distribution reaching its maximum. The third region III(P) corresponds to intermediate times and is characterized by a power-law decay. The fourth region IV(P) corresponds to very long traveling times, and is characterized by a different power-law decaying tail. The power-law characterizing region IV(P) is related to the multifractal properties of flow in percolation, and an expression for its dependence on the system size L is presented. The constant current behavior is different from the constant pressure behavior, and can be related analytically to the constant pressure case. We present theoretical arguments for the values of the exponents characterizing each region and crossover times. Our results are summarized in two scaling assumptions for the traveling time probability density; one for constant pressure and one for constant current. We also present the production curve associated with the probability of traveling times, which is of interest to oil recovery.

Journal Article↗