Assortative mixing in close-packed spatial networks

Background In recent years, there is aroused interest in expressing complex systems as networks of interacting nodes. Using descriptors from graph theory, it has been possible to classify many diverse systems derived from social and physical sciences alike. In particular, folded proteins as examples of self-assembled complex molecules have also been investigated intensely using these tools. However, we need to develop additional measures to classify different systems, in order to dissect the underlying hierarchy. Methodology and Principal Findings In this study, a general analytical relation for the dependence of nearest neighbor degree correlations on degree is derived. Dependence of local clustering on degree is shown to be the sole determining factor of assortative versus disassortative mixing in networks. The characteristics of networks constructed from spatial atomic/molecular systems exemplified by self-organized residue networks built from folded protein structures and block copolymers, atomic clusters and well-compressed polymeric melts are studied. Distributions of statistical properties of the networks are presented. For these densely-packed systems, assortative mixing in the network construction is found to apply, and conditions are derived for a simple linear dependence. Conclusions Our analyses (i) reveal patterns that are common to close-packed clusters of atoms/molecules, (ii) identify the type of surface effects prominent in different close-packed systems, and (iii) associate fingerprints that may be used to classify networks with varying types of correlations

Driving calmodulin protein towards conformational shift by changing ionization states of selected residues

Proteins are complex systems made up of many conformational sub-states which are mainly determined by the folded structure. External factors such as solvent type, temperature, pH and ionic strength play a very important role in the conformations sampled by proteins. Here we study the conformational multiplicity of calmodulin (CaM) which is a protein that plays an important role in calcium signaling pathways in the eukaryotic cells. CaM can bind to a variety of other proteins or small organic compounds, and mediates different physiological processes by activating various enzymes. Binding of calcium ions and proteins or small organic molecules to CaM induces large conformational changes that are distinct to each interacting partner. In particular, we discuss the effect of pH variation on the conformations of CaM. By using the pKa values of the charged residues as a basis to assign protonation states, the conformational changes induced in CaM by reducing the pH are studied by molecular dynamics simulations. Our current view suggests that at high pH, barrier crossing to the compact form is prevented by repulsive electrostatic interactions between the two lobes. At reduced pH, not only is barrier crossing facilitated by protonation of residues, but also conformations which are on average more compact are attained. The latter are in accordance with the fluorescence resonance energy transfer experiment results of other workers. The key events leading to the conformational change from the open to the compact conformation are (i) formation of a salt bridge between the N-lobe and the linker, stabilizing their relative motions, (ii) bending of the C-lobe towards the N-lobe, leading to a lowering of the interaction energy between the two-lobes, (iii) formation of a hydrophobic patch between the two lobes, further stabilizing the bent conformation by reducing the entropic cost of the compact form, (iv) sharing of a Ca+2 ion between the two lobes

Long-range structural regularities and collectivity of folded proteins

Coarse-grained network models of proteins successfully predict equilibrium properties related to collective modes of motion. In this study, the network construction strategies and their systematic application to proteins are used to explain the role of network models in defining the collective properties of the system. The analysis is based on the radial distribution function, a newly defined angular distribution function and the spectral dimensions of a large set of globular proteins. Our analysis shows that after reaching a certain threshold for cut-off distance, network construction has negligible effect on the collective motions and the fluctuation patterns of the residues

Effect of van der Waals interaction strength and nanocluster size on the dynamical and mechanical properties of 1,4-cis-polybutadiene melts

Using molecular dynamics simulations, we have investigated the effect of embedding nanoclusters of radius 3-7 Å on the dynamical and mechanical properties of 1,4-cispolybutadiene melts. To see the effect of polymer-nanocluster interaction strength on the bulk modulus, the van der Waals interactions (vdW) between the polymer chain and nanocluster have been varied from weak to very stong while keeping polymer-polymer and nanocluster-nanocluster interactions constant. The modulus depends on the interaction strength, but not on nanocluster size. Residence time of chains on the surface of the nanocluster (τr) has an increasing trend that reaches to a plateau as the vdW strength is increased. τr also doubles from 100 ps to 200 ps as the nanocluster size is increased from 3 to 7 Å. Our findings give clues on how the properties of polymeric materials may be controlled by nanoparticles of different chemistry and size

Collective behavior of El Farol attendees

Arthur’s paradigm of the El Farol bar for modeling bounded rationality and inductive behavior is undertaken. The memory horizon available to the agents and the selection criteria they utilize for the prediction algorithm are the two essential variables identified to represent the heterogeneity of agent strategies. The latter is enriched by including various rewarding schemes during decision making. Though the external input of comfort level is not explicitly coded in the algorithm pool, it contributes to each agent’s decision process. Playing with the essential variables, one can maneuver the overall outcome between the comfort level and the endogenously identified limiting state. The distribution of algorithm clusters significantly varies for shorter agent memories. This in turn affects the long-term aggregated dynamics of attendances. We observe that a transition occurs in the attendance distribution at the critical memory horizon where the correlations of the attendance deviations take longer time to decay to zero. A larger part of the crowd becomes more comfortable while the rest of the bar-goers still feel the congestion for long memories. Agents’ confidence on their algorithms and the delayed feedback of attendance data increase the overall collectivity of the system behavior

Molecular recognition mechanisms of calmodulin examined by perturbation-response scanning

We analyze the apo and holo calmodulin (CaM) structures by sequentially inserting a perturbation on every residue of the protein, and monitoring the linear response. Residue crosscorrelation matrices obtained from 20 ns long molecular dynamics simulation of the apo-form are used as the kernel in the linear response. We determine two residues whose perturbation equivalently yields the experimentally determined displacement profiles of CaM, relevant to the binding of the trifluoperazine (TFP) ligand. They reside on structurally equivalent positions on the N- and C-terminus lobes of CaM, and are not in direct contact with the binding region. The direction of the perturbation that must be inserted on these residues is an important factor in recovering the conformational change, implying that highly selective binding must occur near these sites to invoke the necessary conformational change

Assortative Mixing in Close-Packed Spatial Networks

Background: In recent years, there is aroused interest in expressing complex systems as networks of interacting nodes. Using descriptors from graph theory, it has been possible to classify many diverse systems derived from social and physical sciences alike. In particular, folded proteins as examples of self-assembled complex molecules have also been investigated intensely using these tools. However, we need to develop additional measures to classify different systems, in order to dissect the underlying hierarchy. Methodology and Principal Findings: In this study, a general analytical relation for the dependence of nearest neighbor degree correlations on degree is derived. Dependence of local clustering on degree is shown to be the sole determining factor of assortative versus disassortative mixing in networks. The characteristics of networks constructed from spatial atomic/molecular systems exemplified by self-organized residue networks built from folded protein structures and block copolymers, atomic clusters and well-compressed polymeric melts are studied. Distributions of statistical properties of the networks are presented. For these densely-packed systems, assortative mixing in the network construction is found to apply, and conditions are derived for a simple linear dependence. Conclusions: Our analyses (i) reveal patterns that are common to close-packed clusters of atoms/molecules, (ii) identify the type of surface effects prominent in different close-packed systems, and (iii) associate fingerprints that may be used t