Signatures of small-world and scale-free properties in large computer programs

A large computer program is typically divided into many hundreds or even thousands of smaller units, whose logical connections define a network in a natural way. This network reflects the internal structure of the program, and defines the ``information flow'' within the program. We show that, (1) due to its growth in time this network displays a scale-free feature in that the probability of the number of links at a node obeys a power-law distribution, and (2) as a result of performance optimization of the program the network has a small-world structure. We believe that these features are generic for large computer programs. Our work extends the previous studies on growing networks, which have mostly been for physical networks, to the domain of computer software.Comment: 4 pages, 1 figure, to appear in Phys. Rev.

Effect of monovalent salt on cationic lipid membranes as revealed by molecular dynamics simulations

An atomic-scale understanding of cationic lipid membranes is required for development of gene delivery agents based on cationic liposomes. To address this problem, we recently performed molecular dynamics (MD) simulations of mixed lipid membranes comprised of cationic dimyristoyltrimethylammonium propane (DMTAP) and zwitterionic dimyristoylphosphatidylcholine (DMPC) (Biophys. J. 2004, 86, 3461-3472). Given that salt ions are always present under physiological conditions, here we focus on the effects of monovalent salt (NaCl) on cationic (DMPC/DMTAP) membranes. Using atomistic MD simulations, we found that salt-induced changes in membranes depend strongly on their composition. When the DMTAP mole fraction is small (around 6%), the addition of monovalent salt leads to a considerable compression of the membrane and to a concurrent enhancement of the ordering of lipid acyl chains. That is accompanied by reorientation of phosphatidylcholine headgroups in the outward normal direction and slight changes in electrostatic properties. We attribute these changes to complexation of DMPC lipids with Na+ ions which penetrate deep into the membrane and bind to the carbonyl region of the DMPC lipids. In contrast, at medium and high molar fractions of cationic DMTAP (50 and 75%) a substantial positive surface charge density of the membranes prevents the binding of Na+ ions, making such membranes almost insensitive to monovalent salt. Finally, we compare our results to the Poisson-Boltzmann theory. With the exception of the immediate vicinity of the bilayer plane, we found excellent agreement with the theory. This is as expected since unlike in the theoretical description the surface is now structured due to its atomic scale nature

Effect of monovalent salt on cationic lipid membranes as revealed by molecular dynamics simulations

An atomic-scale understanding of cationic lipid membranes is required for development of gene delivery agents based on cationic liposomes. To address this problem, we recently performed molecular dynamics (MD) simulations of mixed lipid membranes comprised of cationic dimyristoyltrimethylammonium propane (DMTAP) and zwitterionic dimyristoylphosphatidylcholine (DMPC) (Biophys. J. 2004, 86, 3461-3472). Given that salt ions are always present under physiological conditions, here we focus on the effects of monovalent salt (NaCl) on cationic (DMPC/DMTAP) membranes. Using atomistic MD simulations, we found that salt-induced changes in membranes depend strongly on their composition. When the DMTAP mole fraction is small (around 6%), the addition of monovalent salt leads to a considerable compression of the membrane and to a concurrent enhancement of the ordering of lipid acyl chains. That is accompanied by reorientation of phosphatidylcholine headgroups in the outward normal direction and slight changes in electrostatic properties. We attribute these changes to complexation of DMPC lipids with Na+ ions which penetrate deep into the membrane and bind to the carbonyl region of the DMPC lipids. In contrast, at medium and high molar fractions of cationic DMTAP (50 and 75%) a substantial positive surface charge density of the membranes prevents the binding of Na+ ions, making such membranes almost insensitive to monovalent salt. Finally, we compare our results to the Poisson-Boltzmann theory. With the exception of the immediate vicinity of the bilayer plane, we found excellent agreement with the theory. This is as expected since unlike in the theoretical description the surface is now structured due to its atomic scale nature

Atomic-scale structure and electrostatics of anionic palmitoyloleoylphosphatidylglycerol lipid bilayers with Na+ counterions

Anionic palmitoyloleoylphosphatidylglycerol (POPG) is one of the most abundant lipids in nature, yet its atomic-scale properties have not received significant attention. Here we report extensive 150-ns molecular dynamics simulations of a pure POPG lipid membrane with sodium counterions. It turns out that the average area per lipid of the POPG bilayer under physiological conditions is ~19% smaller than that of a bilayer built from its zwitterionic phosphatidylcholine analog, palmitoyloleoylphosphatidylcholine. This suggests that there are strong attractive interactions between anionic POPG lipids, which overcome the electrostatic repulsion between negative charges of PG headgroups. We demonstrate that interlipid counterion bridges and strong intra- and intermolecular hydrogen bonding play a key role in this seemingly counterintuitive behavior. In particular, the substantial strength and stability of ion-mediated binding between anionic lipid headgroups leads to complexation of PG molecules and ions and formation of large PG-ion clusters that act in a concerted manner. The ion-mediated binding seems to provide a possible molecular-level explanation for the low permeability of PG-containing bacterial membranes to organic solvents: highly polar interactions at the water/membrane interface are able to create a high free energy barrier for hydrophobic molecules such as benzene

Microsecond atomic-scale molecular dynamics simulations of polyimides

We employ microsecond atomic-scale molecular dynamics simulations to get insight into the structural and thermal properties of heat-resistant bulk polyimides. As electrostatic interactions are essential for the polyimides considered, we propose a two-step equilibration protocol that includes long (microsecond-scale) MD simulations of polymer melt with partial atomic charges switched off, followed by relatively short runs (100 ns) of the polymer system with full electrostatics. We demonstrate that macroscopic characteristics of a polyimide sample (such as the glass transition temperature and density) are not particularly sensitive to the degree of equilibration. However, great caution should be paid when local structural characteristics are considered: proper equilibration of the local polymer structure (monitored through the radius of gyration and the end-to-end distance of individual chains) is found to require simulations on a microsecond time scale. Finally, we found a dramatic impact of electrostatic interactions on the properties of the bulk polyimides considered: when intra- and intermolecular dipole–dipole interactions come into play we witness compaction of individual polymer coils and eventually an increase in the glass transition temperature and polymer density

Role of phosphatidylglycerols in the stability of bacterial membranes

Abstract An extensive 100-ns molecular dynamics simulation of lipid bilayer composed of mixture of phosphatidylethanolamine (PE) and phosphatidylglycerol (PG) was performed to elucidate the role of PGs to the stability of bacterial membranes. In addition, a control simulation of pure PE over 150 ns was performed. We observed that PGs decrease both the PE headgroup protrusions into the water phase, and the PE headgroup motion along bilayer normal. The above effects are caused by stronger inter-lipid interactions in the mixed bilayer: the number of hydrogen bonds created by PEs is 34% higher in the mixed than in the pure bilayer. Another contribution is due to the numerous ion-mediated inter-lipid links, which strongly enhance interface stability. That provides a plausible mechanism for preventing lipid desorption from the membrane, for example, under the influence of an organic solvent. A more compact and less dynamic interface structure also decreases membrane permeability. That provides a possible mechanism for stabilizing, e.g., bacterial membranes. Keywords: Phospholipids; Molecular dynamics; Bacterial membranes; Interactions Abbreviations: PC, phosphatidylcholine; PE, phosphatidylethanolamine; PG, phosphatidylglycerol; POPC, palmitoyloleoylphosphatidylcholine; POPE, palmitoyloleoylphosphatidylethanolamine; POPG, palmitoyloleoylphosphatidylglycerol; MD, molecular dynamic

Molecular dynamics simulations of uniaxial deformation of thermoplastic polyimides

The results of atomistic molecular-dynamics simulations of mechanical properties of heterocyclic polymer subjected to uniaxial deformation are reported. A new amorphous thermoplastic polyimide R-BAPO with a repeat unit consisting of dianhydride 1,3-bis-(3',4,-dicarboxyphenoxy)diphenyl (dianhydride R) and diamine 4,4'-bis-(4''-aminophenoxy)diphenyloxide (diamine BAPO) was chosen for the simulations. Our primary goal was to establish the impact of various factors (sample preparation method, molecular mass, and cooling and deformation rates) on the elasticity modulus. In particular, we found that the elasticity modulus was only slightly affected by the degree of equilibration, the molecular mass and the size of the simulation box. This is most likely due to the fact that the main contribution to the elasticity modulus is from processes on scales smaller than the entanglement length. Essentially, our simulations reproduce the logarithmic dependence of the elasticity modulus on cooling and deformation rates, which is normally observed in experiments. With the use of the temperature dependence analysis of the elasticity modulus we determined the flow temperature of R-BAPO to be 580 K in line with the experimental data available. Furthermore, we found that the application of high external pressure to the polymer sample during uniaxial deformation can improve the mechanical properties of the polyimide. Overall, the results of our simulations clearly demonstrate that atomistic molecular-dynamics simulations represent a powerful and accurate tool for studying the mechanical properties of heterocyclic polymers and can therefore be useful for the virtual design of new materials, thereby supporting cost-effective synthesis and experimental research

Molecular-dynamics simulation of polyimide matrix pre-crystallization near the surface of a single-walled carbon nanotube

Polyimide-based composite materials with a single-walled carbon nanotube as filler were studied by means of extensive fully-atomistic molecular-dynamics simulations. Polyimides (PI) were considered based on 1,3-bis-(3',4-dicarboxyphenoxy)-benzene (dianhydride R) and various types of diamines: 4,4'-bis-(4''-aminophenoxy)-diphenylsulfone (diamine BAPS) and 4,4'-bis-(4''-aminophenoxy)-diphenyl (diamine BAPB). The influence of the chemical structure of the polyimides on the microstructure of the composite matrix near the filler surface and away from it was investigated. The formation of subsurface layers close to the nanotube surface was found for all composites considered. In the case of R–BAPB-based composites, the formation of an organized structure was shown that could be the initial stage of the matrix crystallization process observed experimentally. Similar structural features were not observed in the R–BAPS composites. Carbon nanotubes induce the elongation of R–BAPB chains in composites whereas R–BAPS chains become more compact similar to what is observed for EXTEM™ polyimide. It was shown that electrostatic interactions do not influence the microstructure of composites but slow down significantly the dynamics of PI chains in composites

Influence of the electrostatic interactions on the thermophysical properties of polyimides: molecular-dynamics simulations

Revealing the way of how modification of the chemical structure of a polymer affects its macroscopic physical properties offers an opportunity to develop novel polymer materials with pre-defined characteristics. To address this problem two thermoplastic polyimides, ULTEM™ and EXTEM™, were simulated with small difference in chemical structures of monomer units, namely, the phenyl ring in ULTEM™ was replaced by the diphenylsulphone group in EXTEM™. It is shown that such a small modification results in a drastic difference of the thermal properties: the glass transition temperature of EXTEM™ is higher than that of ULTEM™. Our molecular-dynamics simulations clearly demonstrated that it is the electrostatic interactions that are responsible for the observed difference in thermal properties of ULTEM™ and EXTEM™: large partial charges of the sulphone group in the EXTEM™ lead to strong dipole–dipole intra- and intermolecular interactions and correspondingly to an elevated glass transition temperature. © 2014 Wiley Periodicals, Inc. J. Polym. Sci. Part B: Polym. Phys. 2014, 52, 640–64

Effect of the SO2 group in the diamine fragment of polyimides on their structural, thermophysical and mechanical properties

Experimental and theoretical investigations, including an all-atom computer simulation, are performed for block samples of thermoplastic polyimides, amorphous R-BAPS (based on R dianhydride 1,3-bis(3',4-dicarboxyphenoxy)benzene and diamine BAPS 4,4'-bis(4¿-aminophenoxy)biphenyl sulfone), and crystallizable R-BAPB (based on R dianhydride and diamine BAPB 4,4’-bis(4¿-aminophenoxy)biphenyl), which differ in either the presence or absence of the sulfone group in the repeating unit of the polyimide macromolecule. The features of thermophysical, structural, and mechanical properties of R-BAPS and R-BAPB are related to the formation of associates from sulfur and oxygen atoms of the sulfone group that are stabilized by electrostatic interactions