Parbati Biswas

Stretch dynamics of flexible dendritic polymers in solution

We study the stretch dynamics of flexible dendritic polymers (dendrimers and stars) under external forces. We work in the framework of the bead-spring model with hydrodynamic interactions (HI) and take spacers of different length into account. The applied fields may, e.g., be of mechanical or electrical origin. We study the motion of a specific monomer, the time evolution of the stretch (the mean distance of the monomer on which the force acts from the center of mass of the polymer) and also the elastic moduli. We analyze how these dynamic properties depend on the underlying topology, i.e., on the number of generations for dendrimers and the length and number of branches for stars. As a special point we assess in how far the HI method utilized here (the Kirkwood–Riseman scheme) is stable for dendritic structures. Characteristic for the topology is the intermediate dynamics (between short and long times). It turns out that, different from stars, for dendrimers the stretch dynamics is for intermediate times close to logarithmic; hence the crossover in behavior at intermediate times is characteristic of the polymer’s topology.

Polymer dynamics and topology: Extension of stars and dendrimers in external fields

e study the influence of topology on the extension of branched polymers subjected to external forces. Such forces can be applied mechanically (by micromanipulation techniques such as laser tweezers) or electrically (in the case of charged polymers). We focus on the unfold dy namics of star and dendrimer type structures. Some of the dynamical quantities of interest are: (i) the structural average of the mean monomer displacement, (ii) the elastic arid the loss moduli and (iii the mean displacement of a specified monomer. In a Gaussian-type approach, (i) and (ii) depend only on the eigenvalues of the adjacency matrix whereas (iii) also requires the knowledge of the eigenvectors. Thus one can sometimes dispense with a full diagonalisation and use efficient recursion procedures. We highlight how the dynamic properties depend on topology: the number of branches and their length for stars and the number of generations for dendrimers. The intermediate time (crossover) behavior turns out to be most revealing of the underlying structure. We compare our results to those for fractal structures in external fields.

Radial dimensions of starburst polymers

Radial properties of starburst polymers are calculated by renormalization group techniques starting from the Edwards model of the chain. The calculations are carried out for a polymer in good solvents grown out to an arbitrary number of generations g and having an arbitrary branch functionality f. Excludd volume effects are modeled by delta function pseudopotentials. Only pair interactions are included in the calculations, which specifically determine the amplitude of the average center-to-end distance R of the starburst for definite values of f and g. Our first order in E estimates of the exponents for R and the number of configurations C coincide with results obtained earlier by direct methods for networks of arbitrary topology in specific limits.

Size, shape, and flexibility of proteins and DNA.

Size, shape, and flexibility are the important topological parameters which characterize the functional specificity and different types of interactions in proteins and DNA. The size of proteins and DNA, often measured by the radius of gyration (R(G)), are determined from the coordinates of their respective structures available in Protein Data Bank and Nucleic Acid Data Bank. The mean square radius of gyration obeys Florys scaling law given by R(G) (2) approximately N(2nu) where N is the number of amino acid residues/nucleotides. The scaling exponent nu reflects the different characteristic features of nonglobular proteins, natively unstructured proteins, and DNA. The asymmetry in the shapes of proteins and DNA are investigated using the asphericity (Delta) parameter and the shape parameter (S), calculated from the eigenvalues of the moment of inertia tensor. The distributions of Delta and S show that most nonglobular proteins and DNA are aspherical and prolate (S>0). Natively unstructured proteins are comparatively spherically symmetrical having both prolate and oblate shapes. The flexibility of these molecules is characterized by the persistence length (l(p)). Persistence length for natively unstructured proteins is determined by fitting the distance distribution function P(r) to the wormlike chain (WLC) model in the limit of r>>R(G). For nonglobular proteins and DNA, l(p) may be computed from the Benoit-Doty approximation for unperturbed radius of gyration of the WLC. The flexibilities of the proteins and DNA increases with the chain length. This is due to an increase in the nonlocal interactions with the increase in N, needed to minimize the conformational fluctuations in the native state. The persistence length of these proteins has not yet been measured directly. Analysis of the two-body contacts for the proteins reveals that the nonglobular proteins are less densely packed compared to the natively unstructured proteins with least side-chain side chain contacts even though side-chain backbone contacts predominate in the two types of proteins.

Structure of hydration water in proteins: a comparison of molecular dynamics simulations and database analysis.

Hydration layer water molecules play important structural and functional roles in proteins. Despite being a critical component in biomolecular systems, characterizing the properties of hydration water poses a challenge for both experiments and simulations. In this context we investigate the local structure of hydration water molecules as a function of the distance from the protein and water molecules respectively in 188 high resolution protein structures and compare it with those obtained from molecular dynamics simulations. Tetrahedral order parameter of water in proteins calculated from previous and present simulation studies show that the potential of bulk water overestimates the average tetrahedral order parameter compared to those calculated from crystal structures. Hydration waters are found to be more ordered at a distance between the first and second solvation shell from the protein surface. The values of the order parameter decrease sharply when the water molecules are located very near or far away from the protein surface. At small water-water distance, the values of order parameter of water are very low. The average order parameter records a maximum value at a distance equivalent to the first solvation layer with respect to the water-water radial distribution and asymptotically approaches a constant value at large distances. Results from present analysis will help to get a better insight into structure of hydration water around proteins. The analysis will also help to improve the accuracy of water models on the protein surface.

Hydrodynamic effects on the extension of stars and dendrimers in external fields

We assess the influence of hydrodynamic interactions on the extension of branched polymers subjected to external forces. We envisage that the macromolecules move under external applied fields, exemplified by mechanical or electrical micromanipulations. We focus our attention on the difference of the results obtained using the Rouse and the Zimm models, both of which represent an extreme situation, so that the realistic behavior is encompassed by the two models. We focus on the mean displacement of a specified monomer, on the shape which the macromolecule attains and on the structural average of the displacements involved. We discuss how these dynamic properties depend on the underlying topology, such as the number of branches and their length for the stars and on the number of generations for the dendrimers. Interestingly, although there exist quantitative differences between the results of the Rouse and of the Zimm model, in both models there appear typical dynamical features which depend on the topology only. This stresses the role of the structure on the dynamics and offers the possibility of tracking it under realistic, experimental conditions.

Conformational transitions in semiflexible dendrimers induced by bond orientations

We theoretically investigate the conformational properties of semiflexible dendrimers where the semiflexibility is implemented by topologically restricting the bond directions and orientations of the respective bond vectors. Molecular size (radius of gyration, R(g) and Wiener index, W), shape factor ρ, configurational free energy F, and the static structure factor, S(q) of semiflexible dendrimers are analyzed as a function of the bond orientation angle, φ. The size of the lower generation dendrimers decreases with increasing φ throughout the entire range of φ, φ ∈ (0, π). The higher generation dendrimers show a non-uniform behavior, for compressed conformations the size decreases with increasing φ, while for the expanded ones it increases with the increase in φ. A conformational transition occurs for the higher generation dendrimers from the limiting value of the hard sphere to an ideal chain with the change in φ. This conformational transition at φ = π∕2 is also reflected in the configurational free energy. The configurational free energy exhibits a discontinuous behavior with the variation of φ, and this discontinuity occurs at φ = π∕2. However, no such conformational transition is observed with the variation of the bond direction angle, θ, generation, G and functionality, f of the semiflexible dendrimers. The flexible dendrimer, i.e., at φ = π∕2 is flanked between the compressed and expanded conformations of the semiflexible dendrimers resembling a hard sphere. The Kratky plot of the structure factor of all conformations quantitatively match with the results obtained from experiments and simulations in the low q-region in respect to the position of the major Kratky peak. For higher wave numbers, the Kratky plots for all conformations of semiflexible dendrimers agree with earlier theoretical results of model dendrimers [R. La Ferla, J. Chem. Phys. 106, 688 (1997); F. Ganazzoli, R. La Ferla, and G. Raffaini, Macromolecules 34, 4222 (2001)] but are in sharp contrast to the experimental [S. Rathgeber et al., J. Chem. Phys. 117, 4047 (2002); S. Rathgeber, T. Pakula, and V. Urban, J. Chem. Phys. 121, 3840 (2004)] and simulated [M. L. Mansfield and L. I. Klushin, Macromolecules 26, 4262 (1993)] scattering curves for the higher generation dendrimers. All compressed conformations (0 < φ < π∕2) behave as compact hard spheres, while the expanded conformations (π∕2 < φ < π) are relatively more open, partially decongesting the steric crowding among the monomers with increasing φ.

Statistical theory for protein ensembles with designed energy landscapes.

Combinatorial protein libraries provide a promising route to investigate the determinants and features of protein folding and to identify novel folding amino acid sequences. A library of sequences based on a pool of different monomer types are screened for folding molecules, consistent with a particular foldability criterion. The number of sequences grows exponentially with the length of the polymer, making both experimental and computational tabulations of sequences infeasible. Herein a statistical theory is extended to specify the properties of sequences having particular values of global energetic quantities that specify their energy landscape. The theory yields the site-specific monomer probabilities. A foldability criterion is derived that characterizes the properties of sequences by quantifying the energetic separation of the target state from low-energy states in the unfolded ensemble and the fluctuations of the energies in the unfolded state ensemble. For a simple lattice model of proteins, excellent agreement is observed between the theory and the results of exact enumeration. The theory may be used to provide a quantitative framework for the design and interpretation of combinatorial experiments.

Diffusion of Hydration Water around Intrinsically Disordered Proteins

Hydration water dynamics around globular proteins have attracted considerable attention in the past decades. This work investigates the hydration water dynamics around partially/fully intrinsically disordered proteins and compares it to that of the globular proteins via molecular dynamics simulations. The translational diffusion of the hydration water is examined by evaluating the mean-square displacement and the velocity autocorrelation function, while the rotational diffusion is probed through the dipole-dipole time correlation function. The results reveal that the translational and rotational motions of water molecules at the surface of intrinsically disordered proteins/regions are less restricted as compared to those around globular proteins/ordered regions, which is reflected in their higher diffusion coefficient and lower orientational relaxation time. The restricted mobility of hydration water in the vicinity of the protein leads to a sublinear diffusion in a heterogeneous interface. A positive correlation between the mean number of hydrogen bonds and the diffusion coefficient of hydration water implies higher mobility of water molecules at the surface of disordered proteins, which is due to their higher number of hydrogen bonds. Enhanced hydration water mobility around disordered proteins/regions is also related to their higher hydration capacity, low hydrophobicity, and increased internal protein motions. Thus, we generalize that the intrinsically disordered proteins/regions are associated with higher hydration water mobility as compared to globular protein/ordered regions, which may help to elucidate their varied functional specificity.

Position-specific propensities of amino acids in the β-strand

BackgroundDespite the importance of β-strands as main building blocks in proteins, the propensity of amino acid in β-strands is not well-understood as it has been more difficult to determine experimentally compared to α-helices. Recent studies have shown that most of the amino acids have significantly high or low propensity towards both ends of β-strands. However, a comprehensive analysis of the sequence dependent amino acid propensities at positions between the ends of the β-strand has not been investigated.ResultsThe propensities of the amino acids calculated from a large non-redundant database of proteins are found to be highly position-specific and vary continuously throughout the length of the β-strand. They follow an unexpected characteristic periodic pattern in inner positions with respect to the cap residues in both termini of β-strands; this periodic nature is markedly different from that of the α-helices with respect to the strength and pattern in periodicity. This periodicity is not only different for different amino acids but it also varies considerably for the amino acids belonging to the same physico-chemical group. Average hydrophobicity is also found to be periodic with respect to the positions from both termini of β-strands.ConclusionsThe results contradict the earlier perception of isotropic nature of amino acid propensities in the middle region of β-strands. These position-specific propensities should be of immense help in understanding the factors responsible for β-strand design and efficient prediction of β-strand structure in unknown proteins.