Modeling the correlation functions of conformational motions in proteins

A first principles calculation of the correlation function for conformational motion (CM) in proteins is carried out within the framework of a microscopic model of a protein as a heterogeneous system. The fragments of the protein are assumed to be identical hard spheres undergoing the CM within their conformational potentials about some mean equilibrium positions assigned by the tertiary structure. The memory friction function (MFF) for the generalized Langevin equation describing the CM of the particle is obtained on the basis of the direct calculation which is feasible for the present model of the protein due to the existence of a natural large parameter, viz. the ratio of the minimal distance between the mean equilibrium positions of the particles (approximately 7A) to the amplitude of their CM (<1A). A relationship between the MFF and the correlation functions of the CM of the particles is derived which makes their calculation to be a self-consistent mathematical problem. The general analysis of the MFF is exemplified by a simple model case in which the mean equilibrium positions of the particles form a regular lattice so that the correlation functions for all particles are the same. In this case the MFF is shown to be an infinite series of the powers of the auto-correlation function whose coefficients are independent on temperature. The latter is a result of the abstraction of the interaction potential by that of hard spheres which actually corresponds to the high temperature limit. On the examples of cubic and triangular lattices the coefficients are shown to be non-negative values which increase with the increase of the packing density of the particles and quickly tend to zero with the increase of their index. Thus the MFF can be approximated by a polynomial of the correlation function and the resulting mathematical equation is analogous to the one from the dynamic theory of liquids. The correlation function of the CM is obtained by numerical solution of the equation. At realistic packing densities for proteins it exhibits transparent non-exponential decay and includes two relaxation processes: the first one on the intermediate timescale (tens of picoseconds) and the second on the long timescale (its characteristic time is about tens of nanoseconds at small values of the friction coefficient and increases by orders of the magnitude with the increase of the latter). Thus the present approach provides the microscopic basis for previous phenomenological models of cooperative dynamics in proteins.     

Modeling the Correlation Functions of Conformational Motions in Proteins

Abstract

A first principles calculation of the correlation function for conformational motion (CM) in proteins is carried out within the framework of a microscopic model of a protein as a heterogeneous system. The fragments of the protein are assumed to be identical hard spheres undergoing the CM within their conformational potentials about some mean equilibrium positions assigned by the tertiary structure. The memory friction function (MFF) for the generalized Langevin equation describing the CM of the particle is obtained on the basis of the direct calculation which is feasible for the present model of the protein due to the existence of a natural large parameter, viz. the ratio of the minimal distance between the mean equilibrium positions of the particles (～7A) to the amplitude of their CM (<1A). A relationship between the MFF and the correlation functions of the CM of the particles is derived which makes their calculation to be a self-consistent mathematical problem. The general analysis of the MFF is exemplified by a simple model case in which the mean equilibrium positions of the particles form a regular lattice so that the correlation functions for all particles are the same. In this case the MFF is shown to be an infinite series of the powers of the auto-correlation function whose coefficients are independent on temperature. The latter is a result of the abstraction of the interaction potential by that of hard spheres which actually corresponds to the high temperature limit. On the examples of cubic and triangular lattices the coefficients are shown to be non-negative values which increase with the increase of the packing density of the particles and quickly tend to zero with the increase of their index. Thus the MFF can be approximated by a polynomial of the correlation function and the resulting mathematical equation is analogous to the one from the dynamic theory of liquids. The correlation function of the CM is obtained by numerical solution of the equation. At realistic packing densities for proteins it exhibits transparent non-exponential decay and includes two relaxation processes: the first one on the intermediate timescale (tens of picoseconds) and the second on the long timescale (its characteristic time is about tens of nanoseconds at small values of the friction coefficient and increases by orders of the magnitude with the increase of the latter). Thus the present approach provides the microscopic basis for previous phenomenologi- cal models of cooperative dynamics in proteins.     

Temperature dependence of dynamics of hydrated myoglobin. Comparison of force field calculations with neutron scattering data

Molecular dynamics is used to probe the atomic motions of the carboxy-myoglobin protein as a function of temperature. Simulations of 150 picoseconds in length are carried out on the protein at 20, 60, 100, 180, 220, 240, 260, 280, 300, 320 and 340 K. The simulations attempt to mimic neutron scattering experiments very closely by including a partial hydration shell around the protein. Theoretical elastic, quasielastic and inelastic neutron scattering data are derived from the trajectories and directly compared with experiment. Compared to experiment, the simulation-derived elastic scattering curves show a decrease in intensity as a function of the scattering wavevector, q2. The inelastic and quasielastic spectra show that the inelastic peak is shifted to lower frequency than the experimental value, while quasielastic behavior is in good agreement with experiment. This suggests that the theoretical model is too flexible in the harmonic limit (low temperature), but accurately reproduces high-temperature behavior. Time correlation functions of the intermediate scattering function are determined. At low temperature there is one fast decay process, and at high temperatures there is an additional slow relaxation process that is due to quasielastic scattering. The average atomic fluctuations show that the protein behaves harmonically at low temperatures. At approximately 210 K, a glass-like transition in atomic fluctuations is seen. Above the transition temperature, the atomic fluctuations exhibit both harmonic and anharmonic behavior. Comparison of protein mobility behavior with experiment indicate the fluctuations derived from simulations are larger in the harmonic region. However, the anharmonic region agrees very well with experiment. The anharmonicity is large at all temperatures, with a gradual monotonic increase from 0.5 at 20 K to greater than 0.7 at 340 K without a noticeable change at the glass transition temperature. Heavy-atom dihedral transitions are monitored as a function of temperature. Trends in the type of dihedral transitions that occur with temperature are clearly visible. Dihedral transitions involving backbone atoms occur only above the glass transition temperature. The overall protein behavior results suggest that at low temperatures there is purely vibrational motion with one fast decay process, and above the glass transition temperature there is more anharmonic motion with a fast and a slower relaxation process occurring simultaneously.(ABSTRACT TRUNCATED AT 400 WORDS)     

The protein glass transition as measured by dielectric spectroscopy and differential scanning calorimetry

The glass transition and its related dynamics of myoglobin in water and in a water–glycerol mixture have been investigated by dielectric spectroscopy and differential scanning calorimetry (DSC). For all samples, the DSC measurements display a glass transition that extends over a large temperature range. Both the temperature of the transition and its broadness decrease rapidly with increasing amount of solvent in the system. The dielectric measurements show several dynamical processes, due to both protein and solvent relaxations, and in the case of pure water as solvent the main protein process (which most likely is due to conformational changes of the protein structure) exhibits a dynamic glass transition (i.e. reaches a relaxation time of 100 s) at about the same temperature as the calorimetric glass transition temperature T_g is found. This glass transition is most likely caused by the dynamic crossover and the associated vanishing of the α-relaxation of the main water relaxation, although it does not contribute to the calorimetric T_g. This is in contrast to myoglobin in water–glycerol, where the main solvent relaxation makes the strongest contribution to the calorimetric glass transition. For all samples it is clear that several proteins processes are involved in the calorimetric glass transition and the broadness of the transition depends on how much these different relaxations are separated in time.     

Effect of sucrose and maltodextrin on the physical properties and survival of air-dried Lactobacillus bulgaricus: an in situ fourier transform infrared spectroscopy study

The effect of sucrose, maltodextrin and skim milk on survival of L. bulgaricus after drying was studied. Survival could be improved from 0.01% for cells that were dried in the absence of protectants to 7.8% for cells dried in a mixture of sucrose and maltodextrin. Fourier transform infrared spectroscopy (FTIR) was used to study the effect of the protectants on the overall protein secondary structure and thermophysical properties of the dried cells. Sucrose, maltodextrin and skim milk were found to have minor effects on the membrane phase behavior and the overall protein secondary structure of the dried cells. FTIR was also used to show that the air-dried cell/protectant solutions formed a glassy state at ambient temperature. 1-Palmitoyl 2-oleoyl phosphatidyl choline (POPC) was used in order to determine if sucrose and maltodextrin have the ability to interact with phospholipids during drying. In addition, the glass transition temperature and strength of hydrogen bonds in the glassy state were studied using this model system. Studies using poly-L-lysine were done in order to determine if sucrose and maltodextrin are able to stabilize protein structure during drying. As expected, sucrose depressed the membrane phase transition temperature (Tm) of POPC in the dried state and prevented conformational changes of poly-L-lysine during drying. Maltodextrin, however, did not depress the Tm of dried POPC and was less effective in preventing conformational changes of poly-L-lysine during drying. We suggest that when cells are dried in the presence of sucrose and maltodextrin, sucrose functions by directly interacting with biomolecules, whereas maltodextrin functions as an osmotically inactive bulking compound causing spacing of the cells and strengthening of the glassy matrix.     

Toward minimalist models of larger proteins: a ubiquitin-like protein

Our recently developed off-lattice bead model capable of simulating protein structures with mixed alpha/beta content has been extended to model the folding of a ubiquitin-like protein and provides a means for examining the more complex kinetics involved in the folding of larger proteins. Using trajectories generated from constant-temperature Langevin dynamics simulations and sampling with the multiple multi-histogram method over five-order parameters, we are able to characterize the free energy landscape for folding and find evidence for folding through compact intermediates. Our model reproduces the observation that the C-terminus loop structure in ubiquitin is the last to fold in the folding process and most likely plays a spectator role in the folding kinetics. The possibility of a productive metastable intermediate along the folding pathway consisting of collapsed states with no secondary structure, and of intermediates or transition structures involving secondary structural elements occurring early in the sequence, is also supported by our model. The kinetics of folding remain multi-exponential below the folding temperature, with glass-like kinetics appearing at T/T(f) approximately 0.86. This new physicochemical model, designed to be predictive, helps validate the value of modeling protein folding at this level of detail for genomic-scale studies, and motivates further studies of other protein topologies and the impact of more complex energy functions, such as the addition of solvation forces.     

Dynamics of folding and unfolding transition in a globular protein studied by time correlation functions from computer simulation

A method of calculating time correlation functions from records of computer simulated equilibrium conformational fluctuations in a globular protein is discussed. Use of the calculated time correlation function for discussions of dynamics of folding and unfolding transition in the two-dimensional lattice model of proteins. The time correlation functions can be approximated in general by a sum of two simple exponential terms. The relaxation time of the slower mode does not depend on the nature of the physical quantity with respect to which the time correlation function is calculated. This time characterizes the overall folding and unfolding transition. The relaxation time of the faster mode depends on the nature of the physical quantity and characterizes conformational fluctuations within each of the native and denatured states. The mechanism of a previously observed phenomenon of the acceleration of the folding and unfolding transition by short-range interactions is discussed.     

Aggregation pattern transitions by slightly varying the attractive/repulsive function

Among collective behaviors of biological swarms and flocks, the attractive/repulsive (A/R) functional links between particles play an important role. By slightly changing the cutoff distance of the A/R function, a drastic transition between two distinct aggregation patterns is observed. More precisely, a large cutoff distance yields a liquid-like aggregation pattern where the particle density decreases monotonously from the inside to the outwards within each aggregated cluster. Conversely, a small cutoff distance produces a crystal-like aggregation pattern where the distance between each pair of neighboring particles remains constant. Significantly, there is an obvious spinodal in the variance curve of the inter-particle distances along the increasing cutoff distances, implying a legible transition pattern between the liquid-like and crystal-like aggregations. This work bridges the aggregation phenomena of physical particles and swarming of organisms in nature upon revealing some common mechanism behind them by slightly varying their inter-individual attractive/repulsive functions, and may find its potential engineering applications, for example, in the formation design of multi-robot systems and unmanned aerial vehicles (UAVs).     

Conformational fluctuation of native-like and molten-globule-like cytochrome c observed by time-resolved hole burning

Nanosecond to millisecond conformational fluctuations of Zn-substituted cytochrome c (ZnCytc) have been studied by the time-resolved transient hole-burning method. The investigation of low-temperature dynamics has been made on the ZnCytc solution sample in a water-glycerol mixture. The conformational fluctuations in the native-like and the molten-globule (MG)-like states have been compared for the aqueous solution samples at room temperature. ZnCytc in the MG-like state has been prepared by adding 200 mM NaClO4 to the protein solution with a pH of 2.1, and the formation of the MG-like state has been confirmed by both the far-UV CD and the visible absorption spectra. The hole spectrum of ZnCytc has been found to consist of two nearly degenerate components, that is, the Qx and Qy bands. The temporal change in the Qx component hole spectrum has been extracted by fitting the observed hole spectrum to the three-Gaussian form. The experimental results for ZnCytc dissolved in a water-glycerol mixture have revealed that the conformational fluctuation of ZnCytc is suppressed around 200 K, which is nearly the same temperature as the glass-like transition point of Zn-substituted myoglobin (ZnMb) and also as the glass-transition point of the solvent. This supports the idea of the solvent-induced glass-like transition of a protein. It has been also found that at physiological temperatures the time scale of the conformational fluctuation of ZnCytc lies around a few tens of nanoseconds, which is 2-3 orders of magnitude faster than that of ZnMb. The experimental results for the aqueous solution samples have shown that the difference between the native-like and the MG-like states is not conspicuous. However, they are indicative of the appearance of the slower conformational fluctuation in the MG-like state.     

Temperature and compositional dependence of the structure of hydrated dimyristoyl lecithin.

Differential scanning calorimetry and x-ray diffraction techniques have been used to investigate the structure and phase behavior of hydrated dimyristoyl lecithin (DML) in the hydration range 7.5 to 60 weight % water and the temperature range -10 to +60 degrees C. Four different calorimetric transitions have been observed: T1, a low enthalpy transition (deltaH approximately equal to 1 kcal/mol of DML) at 0 degrees C between lamellar phases (L leads to Lbeta); T2, the low enthalpy "pretransition" at water contents greater than 20 weight % corresponding to the transition Lbeta leads to Pbeta; T3, the hydrocarbon chain order-disorder transition (deltaH = 6 to 7 kcal/mol of DML) representing the transition of the more ordered low temperature phases (Lbeta, Pbeta, or crystal C, depending on the water content) to the lamellar Lalpha phase; T4, a transition occurring at 25--27 degrees C at low water contents representing the transition from the lamellar Lbeta phase to a hydrated crystalline phase C. The structures of the Lbeta, Pbeta, C, and Lalpha phases have been examined as a function of temperature and water content. The Lbeta structure has a lamellar bilayer organization with the hydrocarbon chains fully extended and tilted with respect to the normal to the bilayer plane, but packed in a distorted quasihexagonal lattice. The Pbeta structure consists of lipid bilayer lamellae distorted by a periodic "ripple" in the plane of the lamellae; the hydrocarbon chains are tilted but appear to be packed in a regular hexagonal lattice. The diffraction pattern from the crystalline phase C indexes according to an orthorhombic cell with a = 53.8 A, b = 9.33 A, c = 8.82 A. In the lamellae bilayer Lalpha strucure, the hydrocarbon chains adopt a liquid-like conformation. Analysis of the hydration characteristics and bilayer parameters (lipid thickness, surface area/molecule) of synthetic lecithins permits an evaluation of the generalized hydration and structural behavior of this class of lipids.     

Possible configuration of dimers of Gua-Cyt bases. Computation by molecular mechanic models and density functional theory

The energies of interactions between guanine and cytosine in various mutual positions were calculated by the methods of molecular mechanics with refined atom-atom potential functions and the quantum mechanics theory of density functional. Both methods indicate three types of mutual positions of bases in local energy minima. These types correspond to (1) nearly coplanar base positions with intermolecular hydrogen bond formation (base pairing); (2) arrangements of two bases in nearly parallel planes one above another (base stacking); and (3) nearly perpendicular positions of base planes. According to the calculations, the global energy minimum corresponds to the Watson-Crick base pair with three hydrogen bonds. A specific feature of the pair is a transition from many positions of type (2) to positions of type (1) without any energy barrier. This feature is revealed by both methods. Another special feature of this pair is a deviation, for most of mutual base positions, of the amine group atoms from the ring plane, the deviation being more pronounced for Gua. These features are important for understanding the conformational behavior of DNA fragments and the RNA structure.     

Exploring the relationship between funneled energy landscapes and two-state protein folding

It should take an astronomical time span for unfolded protein chains to find their native state based on an unguided conformational random search. The experimental observation that folding is fast can be rationalized by assuming that protein energy landscapes are sloped towards the native state minimum, such that rapid folding can proceed from virtually any point in conformational space. Folding transitions often exhibit two-state behavior, involving extensively disordered and highly structured conformers as the only two observable kinetic species. This study employs a simple Brownian dynamics model of "protein particles" moving in a spherically symmetrical potential. As expected, the presence of an overall slope towards the native state minimum is an effective means to speed up folding. However, the two-state nature of the transition is eradicated if a significant energetic bias extends too far into the non-native conformational space. The breakdown of two-state cooperativity under these conditions is caused by a continuous conformational drift of the unfolded proteins. Ideal two-state behavior can only be maintained on surfaces exhibiting large regions that are energetically flat, a result that is supported by other recent data in the literature (Kaya and Chan, Proteins: Struct Funct Genet 2003;52:510-523). Rapid two-state folding requires energy landscapes exhibiting the following features: (i) A large region in conformational space that is energetically flat, thus allowing for a significant degree of random sampling, such that unfolded proteins can retain a random coil structure; (ii) a trapping area that is strongly sloped towards the native state minimum.     

Tryptophan residues at subunit interfaces used as fluorescence probes to investigate homotropic and heterotropic regulation of aspartate transcarbamylase

The homotropic and heterotropic interactions in Escherichia coli aspartate transcarbamylase (EC 2.1.3.2) are accompanied by various structure modifications. The large quaternary structure change associated with the T to R transition, promoted by substrate binding, is accompanied by different local conformational changes. These tertiary structure modifications can be monitored by fluorescence spectroscopy, after introduction of a tryptophan fluorescence probe at the site of investigation. To relate unambiguously the fluorescence signals to structure changes in a particular region, both naturally occurring Trp residues in positions 209c and 284c of the catalytic chains were previously substituted with Phe residues. The regions of interest were the so-called 240's loop at position Tyr240c, which undergoes a large conformational change upon substrate binding, and the interface between the catalytic and regulatory chains in positions Asn153r and Phe145r supposed to play a role in the different regulatory processes. Each of these tryptophan residues presents a complex fluorescence decay with three to four independent lifetimes, suggesting that the holoenzyme exists in slightly different conformational states. The bisubstrate analogue N-phosphonacetyl-L-aspartate affects mostly the environment of tryptophans at position 240c and 145r, and the fluorescence signals were related to ligand binding and the quaternary structure transition, respectively. The binding of the nucleotide activator ATP slightly affects the distribution of the conformational substates as probed by tryptophan residues at position 240c and 145r, whereas the inhibitor CTP modifies the position of the C-terminal residues as reflected by the fluorescence properties of Trp153r. These results are discussed in correlation with earlier mutagenesis studies and mechanisms of the enzyme allosteric regulation.     

Hydration dependence of conformational dielectric relaxation of lysozyme

Dielectric response of hen egg white lysozyme is measured in the far infrared (5-65 cm-1, 0.15-1.95 THz, 0.6-8.1 meV) as a function of hydration. The frequency range is associated with collective vibrational modes of protein tertiary structure. The observed frequency dependence of the absorbance is broad and glass-like. For the entire frequency range, there is a slight increase in both the absorbance and index of refraction with increasing hydration for <0.27 h (mass of H2O per unit mass protein). At 0.27 h, the absorbance and index begin to increase more rapidly. This transition corresponds to the point where the first hydration shell is filled. The abrupt increase in dielectric response cannot be fully accounted for by the additional contribution to the dielectric response due to bulk water, suggesting that the protein has not yet achieved its fully hydrated state. The broad, glass-like response suggests that at low hydrations, the low frequency conformational hen egg white lysozyme dynamics can be described by a dielectric relaxation model where the protein relaxes to different local minima in the conformational energy landscape. However, the low frequency complex permittivity does not allow for a pure relaxational mechanism. The data can best be modeled with a single low frequency resonance (nu approximately 120 GHz=4 cm-1) and a single Debye relaxation process (tau approximately .03-.04 ps). Terahertz dielectric response is currently being considered as a possible biosensing technique and the results demonstrate the required hydration control necessary for reliable biosensor applications.     

Evolutionary Conserved Positions Define Protein Conformational Diversity

Conformational diversity of the native state plays a central role in modulating protein function. The selection paradigm sustains that different ligands shift the conformational equilibrium through their binding to highest-affinity conformers. Intramolecular vibrational dynamics associated to each conformation should guarantee conformational transitions, which due to its importance, could possibly be associated with evolutionary conserved traits. Normal mode analysis, based on a coarse-grained model of the protein, can provide the required information to explore these features. Herein, we present a novel procedure to identify key positions sustaining the conformational diversity associated to ligand binding. The method is applied to an adequate refined dataset of 188 paired protein structures in their bound and unbound forms. Firstly, normal modes most involved in the conformational change are selected according to their corresponding overlap with structural distortions introduced by ligand binding. The subspace defined by these modes is used to analyze the effect of simulated point mutations on preserving the conformational diversity of the protein. We find a negative correlation between the effects of mutations on these normal mode subspaces associated to ligand-binding and position-specific evolutionary conservations obtained from multiple sequence-structure alignments. Positions whose mutations are found to alter the most these subspaces are defined as key positions, that is, dynamically important residues that mediate the ligand-binding conformational change. These positions are shown to be evolutionary conserved, mostly buried aliphatic residues localized in regular structural regions of the protein like β-sheets and α-helix.     

The HPV16 E7 viral oncoprotein self-assembles into defined spherical oligomers

Despite the fact that E7 is a major transforming oncoprotein in papillomavirus, its structure and precise molecular mechanism of action remain puzzling to date. E7 proteins share sequence homology and proteasome targeting properties of tumor suppressors with adenovirus E1A and SV40 T antigen, two other paradigmatic oncoproteins from DNA tumor viruses. High-risk HPV16 E7, a nonglobular dimer with some properties of intrinsically disordered proteins, is capable of undergoing pH-dependent conformational transitions that expose hydrophobic surfaces to the solvent. We found that treatment with a chelating agent produced a protein that can readily assemble into homogeneous spherical particles with an average molecular mass of 790 kDa and a diameter of 50 nm, as determined from dynamic light scattering and electron microscopy. The protein undergoes a substantial conformational transition from coil to beta-sheet structure, with concomitant consolidation of tertiary structure as judged by circular dichroism and fluorescence. The assembly process is very slow, in agreement with a substantial energy barrier caused by structural rearrangements. The resulting particles are highly stable, cooperatively folded, and capable of binding both Congo Red and thioflavin T, reporters of repetitive beta-sheet structures similar to those found in amyloids, although no fibrillar or insoluble material was observed under our experimental conditions.     

Large-scale,pH-dependent,quaternary structure changes in an RNA virus capsid are reversible in the absence of subunit autoproteolysis

The assembly and maturation of the coat protein of a T=4, nonenveloped, single-stranded RNA virus, Nudaurelia capensis omega virus (N omega V), was examined by using a recombinant baculovirus expression system. At pH 7.6, the coat protein assembles into a stable particle called the procapsid, which is 450 A in diameter and porous. Lowering the pH to 5.0 leads to a concerted reorganization of the subunits into a 410-A-diameter particle called the capsid, which has no obvious pores. This conformational change is rapid but reversible until slow, autoproteolytic cleavage occurs in at least 15% of the subunits at the lower pH. In this report, we show that expression of subunits with replacement of Asn-570, which is at the cleavage site, with Thr results in assembly of particles with expected morphology but that are cleavage defective. The conformational change from procapsid to capsid is reversible in N570T mutant virus-like particles, in contrast to wild-type particles, which are locked into the capsid conformation after cleavage of the coat protein. The reexpanded procapsids display slightly different properties than the original procapsid, suggesting hysteretic effects. Because of the stability of the procapsid under near-neutral conditions and the reversible properties of the cleavage-defective mutant, N omega V provides an excellent model for the study of pH-induced conformational changes in macromolecular assemblies. Here, we identify the relationship between cleavage and the conformational change and propose a pH-dependent helix-coil transition that may be responsible for the structural rearrangement in N omega V.     

The glass transition behavior of the globular protein bovine serum albumin

The glass-like transition behavior of concentrated aqueous solutions of bovine serum albumin was examined using rheological techniques. At mass fractions >0.4, there was a marked concentration dependence of viscosity with a glass-like kinetic arrest observed at mass fractions in the region of 0.55. At mass fractions >0.6 the material behaved as a solid with a Young's modulus rising from approximately 20 MPa at a mass fraction of 0.62-1.1 GPa at 0.86. The solid was viscoelastic and exhibited stress relaxation with relaxation times increasing from 33 to 610 s over the same concentration range. The concentration dependence of the osmotic pressure was measured, at intermediate concentrations, using an osmotic stress technique and could be described using a hard sphere model, indicating that the intermolecular interactions were predominantly repulsive. In summary, a major structural relaxation results from the collective motion of the globules at the supra-globule length scale and, at 20 degrees C, this is arrested at water contents of 40% w/w. This appears to be analogous to the glass transition in colloidal hard spheres.     

Protein conformational transitions explored by mixed elastic network models

We develop a mixed elastic network model (MENM) to study large-scale conformational transitions of proteins between two (or more) known structures. Elastic network potentials for the beginning and end states of a transition are combined, in effect, by adding their respective partition functions. The resulting effective MENM energy function smoothly interpolates between the original surfaces, and retains the beginning and end structures as local minima. Saddle points, transition paths, potentials of mean force, and partition functions can be found efficiently by largely analytic methods. To characterize the protein motions during a conformational transition, we follow "transition paths" on the MENM surface that connect the beginning and end structures and are invariant to parameterizations of the model and the mathematical form of the mixing scheme. As illustrations of the general formalism, we study large-scale conformation changes of the motor proteins KIF1A kinesin and myosin II. We generate possible transition paths for these two proteins that reveal details of their conformational motions. The MENM formalism is computationally efficient and generally applicable even for large protein systems that undergo highly collective structural changes.     

Correlation between local structural dynamics of proteins inferred from NMR ensembles and evolutionary dynamics of homologues of known structure

Conformational changes in proteins are extremely important for their biochemical functions. Correlation between inherent conformational variations in a protein and conformational differences in its homologues of known structure is still unclear. In this study, we have used a structural alphabet called Protein Blocks (PBs). PBs are used to perform abstraction of protein 3-D structures into a 1-D strings of 16 alphabets (a–p) based on dihedral angles of overlapping pentapeptides. We have analyzed the variations in local conformations in terms of PBs represented in the ensembles of 801 protein structures determined using NMR spectroscopy. In the analysis of concatenated data over all the residues in all the NMR ensembles, we observe that the overall nature of inherent local structural variations in NMR ensembles is similar to the nature of local structural differences in homologous proteins with a high correlation coefficient of .94. High correlation at the alignment positions corresponding to helical and β-sheet regions is only expected. However, the correlation coefficient by considering only the loop regions is also quite high (.91). Surprisingly, segregated position-wise analysis shows that this high correlation does not hold true to loop regions at the structurally equivalent positions in NMR ensembles and their homologues of known structure. This suggests that the general nature of local structural changes is unique; however most of the local structural variations in loop regions of NMR ensembles do not correlate to their local structural differences at structurally equivalent positions in homologues.