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Human serum transferrin (hTf) transports ferric ions in the blood stream and inflamed mucosal surfaces with high affinity and delivers them to cells via receptor mediated endocytosis. A typical hTf is folded into two homologous lobes; each lobe is further divided into two similar sized domains. Three different crystal structures of hTf delineate large conformational changes involved in iron binding/dissociation. However, whether the release process follows the same trend at serum (~7.4) and endosomal (~5.6) pH remains unanswered. The specialized role of the two lobes and if communication between them leads to efficient and controlled release is also debated. Here, we study the dynamics of the full structure as well as the separate lobes in different closed, partially open, and open conformations under the nearly neutral pH conditions in the blood serum and the more acidic one in the endosome. The results corroborate experimental observations and underscore the distinguishing effect of pH on the dynamics of hTf. Furthermore, in a total of 2 {\mu}s molecular dynamics simulation of different forms of hTf, residue fluctuations elucidate the cross talk between the two lobes correlated by the peptide linker bridging the two lobes at serum pH, while their correlated motions is lost under endosomal conditions. At serum pH, the presence of even a single iron on either lobe leads C-lobe fluctuations to subside, making it the target for recognition by human cells or hostile bacteria seeking iron sequestration. The N-lobe, on the other hand, has a propensity to open, making iron readily available when needed at regions of serum pH. At endosomal pH, both lobes readily open, making irons available for delivery. The interplay between the relative mobility of the lobes renders efficient mechanism for the recognition and release of hTf at the cell surface, and therefore its recycling in the organism.

We have studied the apo (Fe3+ free) form of periplasmic ferric binding protein (FbpA) under different conditions and we have monitored the changes in the binding and release dynamics of H2PO4- that acts as a synergistic anion in the presence of Fe3+. Our simulations predict a dissociation constant of 2.2$\pm$0.2 mM which is in remarkable agreement with the experimentally measured value of 2.3$\pm$0.3 mM under the same ionization strength and pH conditions. We apply perturbations relevant for changes in environmental conditions as (i) different values of ionic strength (IS), and (ii) protonation of a group of residues to mimic a different pH environment. Local perturbations are also studied by protonation or mutation of a site distal to the binding region that is known to mechanically manipulate the hinge-like motions of FbpA. We find that while the average conformation of the protein is intact in all simulations, the H2PO4- dynamics may be substantially altered by the changing conditions. In particular, the bound fraction which is 20$\%$ for the wild type system is increased to 50$\%$ with a D52A mutation/protonation and further to over 90$\%$ at the protonation conditions mimicking those at pH 5.5. The change in the dynamics is traced to the altered electrostatic distribution on the surface of the protein which in turn affects hydrogen bonding patterns at the active site. The observations are quantified by rigorous free energy calculations. Our results lend clues as to how the environment versus single residue perturbations may be utilized for regulation of binding modes in hFbpA systems in the absence of conformational changes., Comment: 26 pages, 4 figures

We study geometric and energetic factors that partake in modifying properties of polymeric melts via inserting well-dispersed nanoscopic particles (NP). Model systems are polybutadiene melts including 10-150 atom atomic clusters (0.1-1.5% v/v). We tune interactions between chains and particle by van der Waals terms. Using molecular dynamics we study equilibrium fluctuations and dynamical properties at the interface. Effect of bead size and interaction strength both on volume and volumetric fluctuations is manifested in mechanical properties, quantified here by bulk modulus, K. Tuning NP size and non-bonded interactions results in ~15% enhancement in K by addition of a maximum of 1.5% v/v NP., Comment: 25 pages, 7 figures

This study reveals the essence of ligand recognition mechanisms by which calmodulin (CaM) controls a variety of Ca2+ signaling processes. We study eight forms of calcium-loaded CaM each with distinct conformational states. Reducing the structure to two degrees of freedom conveniently describes main features of conformational changes of CaM via simultaneous twist-bend motions of the two lobes. We utilize perturbation-response scanning (PRS) technique, coupled with molecular dynamics simulations to analyze conformational preferences of calcium-loaded CaM, initially in extended form. PRS is comprised of sequential application of directed forces on residues followed by recording the resulting coordinates. We show that manipulation of a single residue, E31 located in one of the EF hand motifs, reproduces structural changes to compact forms, and the flexible linker acts as a transducer of binding information to distant parts of the protein. Independently, using four different pKa calculation strategies, we find E31 to be the charged residue (out of 52), whose ionization state is most sensitive to subtle pH variations in the physiological range. It is proposed that at relatively low pH, CaM structure is less flexible. By gaining charged states at specific sites at a pH value around 7, local conformational changes in the protein will lead to shifts in the energy landscape, paving the way to other conformational states. These findings are in accordance with FRET measured shifts in conformational distributions towards more compact forms with decreased pH. They also corroborate mutational studies and proteolysis results which point to the significant role of E31 in CaM dynamics., Comment: 47 pages, 4 figures

Networks are known to be prone to link failures. In this paper we set out to investigate how networks of varying connectivity patterns respond to different link failure schemes in terms of connectivity, clustering coefficient and shortest path lengths. We then propose a measure, which we call the vulnerability of a network, for evaluating the extent of the damage these failures can cause. Accepting the disconnections of node pairs as a damage indicator, vulnerability simply represents how quickly the failure of the critical links cause the network to undergo a specified damage extent. Analyzing the vulnerabilities under varying damage specifications shows that scale free networks are relatively more vulnerable for small failures, but more efficient; whereas Erd\"os-R\'enyi networks are the least vulnerable despite lacking any clustered structure., Comment: 10 pages, 11 figures

A general 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 derived from spatial atomic/molecular systems exemplified by self-organized residue networks 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. Together, these measures (i) reveal patterns that are common to close-packed clusters of atoms/molecules, (ii) identify the type of surface effects prominent in different systems, and (iii) associate fingerprints that may be used to classify networks with varying types of correlations., Comment: 24 pages, 4 figures

The past decade has witnessed the development and success of coarse-grained network models of proteins for predicting many equilibrium properties related to collective modes of motion. Curiously, the results are usually robust towards the different cutoff distances used for constructing the residue networks from the knowledge of the experimental coordinates. In this study, we present a systematical study of network construction, and their effect on the predicted properties. Probing bond orientational order around each residue, we propose a natural partitioning of the interactions into an essential and a residual set. In this picture the robustness originates from the way with which new contacts are added so that an unusual local orientational order builds up. These residual interactions have a vanishingly small effect on the force vectors on each residue. The stability of the overall force balance then translates into the Hessian as small shifts in the slow modes of motion and an invariance of the corresponding eigenvectors. We introduce a rescaled version of the Hessian matrix and point out a link between the matrix Frobenius norm based on spectral stability arguments. A recipe for the optimal choice of partitioning the interactions into essential and residual components is prescribed. Implications for the study of biologically relevant properties of proteins are discussed with specific examples., Comment: 20 pages, 6 figures

It has been observed that the topology of the native state is an important determinant of protein folding kinetics and there is a significant correlation between folding rate and relative contact order (RCO) in two-state small single-domain proteins. However, as a pure topological property, RCO does not take into account residue interactions that also play an important role in folding kinetics. Using the inter-residue statistical contact potentials, we introduce weight into the residue network of contacts, and therefore define a weighted RCO. Using the weighted RCO, we can capture the folding kinetics of proteins having the same topology, but different sequence information. By constructing essential sub-networks based on the strength of the pairwise interactions, we are able to deduce the features of sequences redundant for folding events. We perform an analysis on 48 two-state proteins and the ultrafast-folding proteins, as well as mutants of the protein CI2, protein G, and protein L. Our results indicate that (i) both the weighted RCO of original residue network and that of essential sub-networks have significant correlations with the folding rate like RCO; (ii) the folding rate is critically dependent on the hydrophobic interactions for two-state folding; and (iii) the sub-networks distinguish the folding rate differences of the mutants and reveal the folding preferences of proteins., Comment: 18 pages, 6 figures

We elucidate the physics of the dynamical transition via 10-100ns molecular dynamics simulations at temperatures spanning 160-300K. By tracking the energy fluctuations, we show that the protein dynamical transition is marked by a cross-over from piecewise stationary to stationary processes that underlie the dynamics of protein motions. A two-time-scale function captures the non-exponential character of backbone structural relaxations. One is attributed to the collective segmental motions and the other to local relaxations. The former is well-defined by a single-exponential, nanosecond decay, operative at all temperatures. The latter is described by a set of processes that display a distribution of time-scales. Though their average remains on the picosecond time-scale, the distribution is markedly contracted at the onset of the transition. The collective motions are shown to impose bounds on time-scales spanned by local dynamical processes. The piecewise stationary character below the transition implicates the presence of a collection of sub-states whose interactions are restricted. At these temperatures, a wide distribution of local motion time-scales, extending beyond that of nanoseconds is observed. At physiological temperatures, local motions are confined to time-scales faster than nanoseconds. This relatively narrow window makes possible the appearance of multiple channels for the backbone dynamics to operate., Comment: 26 pages, 9 figures; suplementary materials added

The past decade has witnessed the development and success of coarse-grained network models of proteins for predicting many equilibrium properties related to collective modes of motion. Curiously, the results are usually robust towards the different methodologies used for constructing the residue networks from knowledge of the experimental coordinates. We present a systematical study of network construction strategies, and their effect on the predicted properties. The analysis is based on the radial distribution function and the spectral dimensions of a large set of proteins as well as a newly defined quantity, the angular distribution function. By partitioning the interactions into an essential and a residual set, we show that the robustness originates from a large number of long-distance interactions belonging to the latter. These residuals have a vanishingly small effect on the force vectors on each residue. The overall force balance then translates into the Hessian as small shifts in the slow modes of motion and an invariance of the corresponding eigenvectors. Implications for the study of biologically relevant properties of proteins are discussed., Comment: 18 pages, 5 figures

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. Furthermore, we model the behavior of the agents through the use of an expression that scores the local attendance states available to the agents. It incorporates a single parameter that weighs the relative contributions that originate from the external and internal limiting factors. Solving this expression analytically as well as numerically using the Metropolis Monte-Carlo technique enables us to attribute statistical-thermodynamical meanings to the essential variables identified with the agent-based model, and to gain physical insight to the bounds observed in the behavior of the agents. The power of the analytical approach is validated by obtaining a one-to-one correspondence between the agent-based model and the analytical approach within a wide range of thresholds using a single parameter for a given selection criterion. The origin of discrepancies between the two models appearing at extreme thresholds is tracked to the shifts in the distributions of algorithm types actively utilized by the adaptive agents., Comment: 16 pages, 4 figures

A protein structure is represented as a network of residues whereby edges are determined by intra-molecular contacts. We introduce inhomogeneity into these networks by assigning each edge a weight that is determined by amino-acid pair potentials. Two methodologies are utilized to calculate the average path lengths (APLs) between pairs: To minimize (i) the maximum weight in the strong APL, and (ii) the total weight in the weak APL. We systematically screen edges that have higher than a cutoff potential and calculate the shortest APLs in these reduced networks, while keeping chain connectivity. Therefore, perturbations introduced at a selected region of the residue network propagate to remote regions only along the non-screened edges that retain their ability to disseminate the perturbation. The shortest APLs computed from the reduced homogeneous networks with only the strongest few non-bonded pairs closely reproduce the strong APLs from the weighted networks. The rate of change in the APL in the reduced residue network as compared to its randomly connected counterpart remains constant until a lower bound. Upon further link removal, this property shows an abrupt increase, towards a random coil behavior. Under different perturbation scenarios, diverse optimal paths emerge for robust residue communication., Comment: 21 pages with 6 figures

This article is concerned with the global behavior of agents in the El Farol bar problem. In particular, we discuss the global attendance in terms of its mean and variance, and show that there is a strong dependence of both on the externally imposed comfort level. We present a possible interpretation for the observed behavior, and propose that the mean attendance converges to the perceived threshold value as opposed to the actually imposed one., Comment: 6 pages, 3 figures

We provide evidence that the energy landscapes of folded proteins do not shift with temperature, but the onset of functional dynamics is associated with its effective sampling. The motion of the backbone is described by three distinct regimes. One is associated with slow time scales of the activity along the envelope of the energy surface defining the folded protein. Another, with fast time scales, is due to activity along the pockets decorating the folded-state envelope. The intermediate regime emerges at temperatures where jumps between the pockets become possible, leading to an active protein., Comment: 13 pages with 4 figures; submitted to Phys. Rev. Lett

It is not merely the position of residues that are of utmost importance in protein function and stability, but the interactions between them. We illustrate, by using a network construction on a set of 595 non-homologous proteins, that regular packing is preserved in short-range interactions, but short average path lengths are achieved through some long-range contacts. Thus, lying between the two extremes of regularity and randomness, residues in folded proteins are distributed according to a "small-world" topology. Using this topology, we show that the core residues have the same local packing arrangements irrespective of protein size. Furthermore, we find that the average shortest path lengths are highly correlated with residue fluctuations, providing a link between the spatial arrangement of the residues and protein dynamics., Comment: 18 pages, 6 figures, submitted to Biophys. J

A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.