Significant influence of four highly conserved amino-acids in lipochaperon-active sHsps on the structure and functions of the Lo18 protein.

To cope with environmental stresses, bacteria have developed different strategies, including the production of small heat shock proteins (sHSP). All sHSPs are described for their role as molecular chaperones. Some of them, like the Lo18 protein synthesized by Oenococcus oeni, also have the particularity of acting as a lipochaperon to maintain membrane fluidity in its optimal state following cellular stresses. Lipochaperon activity is poorly characterized and very little information is available on the domains or amino-acids key to this activity. The aim in this paper is to investigate the importance at the protein structure and function level of four highly conserved residues in sHSP exhibiting lipochaperon activity. Thus, by combining in silico, in vitro and in vivo approaches the importance of three amino-acids present in the core of the protein was shown to maintain both the structure of Lo18 and its functions.

Wild-Type α-Synuclein and Variants Occur in Different Disordered Dimers and Pre-Fibrillar Conformations in Early Stage of Aggregation.

α-Synuclein is a 140 amino-acid intrinsically disordered protein mainly found in the brain. Toxic α-synuclein aggregates are the molecular hallmarks of Parkinson's disease. In vitro studies showed that α-synuclein aggregates in oligomeric structures of several 10th of monomers and into cylindrical structures (fibrils), comprising hundred to thousands of proteins, with polymorphic cross-ß-sheet conformations. Oligomeric species, formed at the early stage of aggregation remain, however, poorly understood and are hypothezised to be the most toxic aggregates. Here, we studied the formation of wild-type (WT) and mutant (A30P, A53T, and E46K) dimers of α-synuclein using coarse-grained molecular dynamics. We identified two principal segments of the sequence with a higher propensity to aggregate in the early stage of dimerization: residues 36-55 and residues 66-95. The transient α-helices (residues 53-65 and 73-82) of α-synuclein monomers are destabilized by A53T and E46K mutations, which favors the formation of fibril native contacts in the N-terminal region, whereas the helix 53-65 prevents the propagation of fibril native contacts along the sequence for the WT in the early stages of dimerization. The present results indicate that dimers do not adopt the Greek key motif of the monomer fold in fibrils but form a majority of disordered aggregates and a minority (9-15%) of pre-fibrillar dimers both with intra-molecular and intermolecular ß-sheets. The percentage of residues in parallel ß-sheets is by increasing order monomer < disordered dimers < pre-fibrillar dimers. Native fibril contacts between the two monomers are present in the NAC domain for WT, A30P, and A53T and in the N-domain for A53T and E46K. Structural properties of pre-fibrillar dimers agree with rupture-force atomic force microscopy and single-molecule Förster resonance energy transfer available data. This suggests that the pre-fibrillar dimers might correspond to the smallest type B toxic oligomers. The probability density of the dimer gyration radius is multi-peaks with an average radius that is 10 Å larger than the one of the monomers for all proteins. The present results indicate that even the elementary α-synuclein aggregation step, the dimerization, is a complicated phenomenon that does not only involve the NAC region.

Missense Mutations Modify the Conformational Ensemble of the α-Synuclein Monomer Which Exhibits a Two-Phase Characteristic.

α-Synuclein is an intrinsically disordered protein occurring in different conformations and prone to aggregate in ß-sheet structures, which are the hallmark of the Parkinson disease. Missense mutations are associated with familial forms of this neuropathy. How these single amino-acid substitutions modify the conformations of wild-type α-synuclein is unclear. Here, using coarse-grained molecular dynamics simulations, we sampled the conformational space of the wild type and mutants (A30P, A53P, and E46K) of α-synuclein monomers for an effective time scale of 29.7 ms. To characterize the structures, we developed an algorithm, CUTABI (CUrvature and Torsion based of Alpha-helix and Beta-sheet Identification), to identify residues in the α-helix and ß-sheet from Cα -coordinates. CUTABI was built from the results of the analysis of 14,652 selected protein structures using the Dictionary of Secondary Structure of Proteins (DSSP) algorithm. DSSP results are reproduced with 93% of success for 10 times lower computational cost. A two-dimensional probability density map of α-synuclein as a function of the number of residues in the α-helix and ß-sheet is computed for wild-type and mutated proteins from molecular dynamics trajectories. The density of conformational states reveals a two-phase characteristic with a homogeneous phase (state B, ß-sheets) and a heterogeneous phase (state HB, mixture of α-helices and ß-sheets). The B state represents 40% of the conformations for the wild-type, A30P, and E46K and only 25% for A53T. The density of conformational states of the B state for A53T and A30P mutants differs from the wild-type one. In addition, the mutant A53T has a larger propensity to form helices than the others. These findings indicate that the equilibrium between the different conformations of the α-synuclein monomer is modified by the missense mutations in a subtle way. The α-helix and ß-sheet contents are promising order parameters for intrinsically disordered proteins, whereas other structural properties such as average gyration radius, R g , or probability distribution of R g cannot discriminate significantly the conformational ensembles of the wild type and mutants. When separated in states B and HB, the distributions of R g are more significantly different, indicating that global structural parameters alone are insufficient to characterize the conformational ensembles of the α-synuclein monomer.

Nanopore sensing of single-biomolecules: a new procedure to identify protein sequence motifs from molecular dynamics.

Solid-state nanopores have emerged as one of the most versatile tools for single-biomolecule detection and characterization. Nanopore sensing is based on the measurement of variations in ionic current as charged biomolecules immersed in an electrolyte translocate through nanometer-sized channels, in response to an external voltage applied across the membrane. The passage of a biomolecule through a pore yields information about its structure and chemical properties, as demonstrated experimentally with sub-microsecond temporal resolution. However, extracting the sequence of a biomolecule without the information about its position remains challenging due to the fact there is a large variability of sensing events recorded. In this paper, we performed microsecond time scale all-atom non-equilibrium Molecular Dynamics (MD) simulations of peptide translocation (motifs of alpha-synuclein, associated with Parkinson's disease) through single-layer MoS2 nanopores. First, we present an analysis based on the current threshold to extract and characterize meaningful sensing events from ionic current time series computed from MD. Second, a mechanism of translocation is established, for which side chains of each amino acid are oriented parallel to the electric field when they are translocating through the pore and perpendicular otherwise. Third, a new procedure based on the permutation entropy (PE) algorithm is detailed to identify protein sequence motifs related to ionic current drop speed. PE is a technique used to quantify the complexity of a given time series and it allows the detection of regular patterns. Here, PE patterns were associated with protein sequence motifs composed of 1, 2 or 3 amino acids. Finally, we demonstrate that this very promising procedure allows the detection of biological mutations and could be tested experimentally, despite the fact that reconstructing the sequence information remains unachievable at this time.

Curvature and Torsion of Protein Main Chain as Local Order Parameters of Protein Unfolding.

Thermal protein unfolding resembles a global (two-state) phase transition. At the local scale, protein unfolding is, however, heterogeneous and probe dependent. Here, we consider local order parameters defined by the local curvature and torsion of the protein main chain. Because chemical shifts (CS's) measured by NMR spectroscopy are extremely sensitive to the local atomic environment, CS has served as a local probe of thermal unfolding of proteins by varying the position of the atomic isotope along the amino acid sequence. The variation of the CS of each Cα atom along the sequence as a function of the temperature defines a local heat-induced denaturation curve. We demonstrate that these local heat-induced denaturation curves mirror the local protein nativeness defined by the free energy landscape of the local curvature and torsion of the protein main chain described by the Cα-Cα virtual bonds. Comparison between molecular dynamics simulations and CS data of the gpW protein demonstrates that some local native states defined by the local curvature and torsion of the main chain, mainly located in secondary structures, are coupled to each other whereas others, mainly located in flexible protein segments, are not. Consequently, CS's of some residues are faithful reporters of global protein unfolding, with heat-induced denaturation curves similar to the average global one, whereas other residues remain silent about the protein unfolded state. For the latter, the local deformation of the protein main chain, characterized by its local curvature and torsion, is not cooperatively coupled to global unfolding.

Molecular Dynamics Investigation of Polylysine Peptide Translocation through MoS2 Nanopores.

Solid-state nanopores (SSN) made of two-dimensional materials such as molybdenum disulfide (MoS2) have emerged as candidate devices for biomolecules sequencing. SSN sequencing is based on measuring the variations in ionic conductance as charged biomolecules translocate through nanometer-sized channels, in response to an external voltage applied across the membrane. Although several experiments on DNA translocation through SSNs have been performed in the past decade, translocation of proteins has been less studied, partly due to small protein size and detection limits. Moreover, the threading of proteins through nanopore channels is challenging, because proteins can exhibit neutral global charge and not be sensitive to the electric field. In this paper, we investigate the translocation of lysine residues and a model protein with polylysine tags through MoS2 nanoporous membranes using molecular dynamics simulations. Adding lysine tags to biological peptides is the method proposed here to promote the entrance of proteins through SSN. Specifically, we study the relationship existing between the translocation events and the ionic conductance signal drops. We show that individual lysine residues translocate easily through MoS2 nanopores, but the translocation speed is extremely fast, which leads to indiscernible ionic conductance drops. To reduce the translocation speed, we demonstrate that increasing the thickness of the membrane from single-layer to bilayer MoS2 reveals a stepwise process of translocation with discernible conductance drops that could be measured experimentally. Finally, a study of the threading of proteins with polylysine tags through MoS2 nanopores is presented. The addition of the positively charged tag to the neutral protein allows the threading and full translocation of the protein through the pore (at least two lysine residues are necessary in this case to observe translocation) and a similar sequence of translocation events is detected, independently of the tag length.

Data on the expression of GSTE1 and GSTE7 in Drosophila chemosensory organs after isothiocyanate exposure.

The data presented in this article are related to the research article entitled "Characterization of a Drosophila glutathione transferase involved in isothiocyanate detoxification." (Gonzalez et al., 2018) [1]. This article includes the expression level of Drosophila melanogaster GSTE1 and GSTE7 in chemosensory male tissues and the expression level of the mRNAs coding for the same enzymes after a PEITC exposure in food.

Characterization of a Drosophila glutathione transferase involved in isothiocyanate detoxification.

Glutathione transferases (GSTs) are ubiquitous key enzymes that catalyse the conjugation of glutathione to xenobiotic compounds in the detoxification process. GSTs have been proposed to play a dual role in the signal termination of insect chemodetection by modifying odorant and tasting molecules and by protecting the chemosensory system. Among the 40 GSTs identified in Drosophila melanogaster, the Delta and Epsilon groups are insect-specific. GSTs Delta and Epsilon may have evolved to serve in detoxification, and have been associated with insecticide resistance. Here, we report the heterologous expression and purification of the D. melanogaster GST Delta 2 (GSTD2). We investigated the capacity of GSTD2 to bind tasting molecules. Among them, we found that isothiocyanates (ITC), insecticidal compounds naturally present in cruciferous plant and perceived as bitter, are good substrates for GSTD2. The X-ray structure of GSTD2 was solved, showing the absence of the classical Ser catalytic residue, conserved in the Delta and Epsilon GSTs. Using molecular dynamics, the interaction of ITC with the GSTD2 three-dimensional structure is analysed and discussed. These findings allow us to consider a biological role for GSTD2 in chemoperception, considering GSTD2 expression in the chemosensory organs and the potential consequences of insect exposure to ITC.

From a Highly Disordered to a Metastable State: Uncovering Insights of α-Synuclein.

α-Synuclein (αS) is a major constituent of Lewy bodies, the insoluble aggregates that are the hallmark of one of the most prevalent neurodegenerative disorders, Parkinson's disease (PD). The vast majority of experiments in vitro and in vivo provide extensive evidence that a disordered monomeric form is the predominant state of αS in water solution, and it undergoes a large-scale disorder-to-helix transition upon binding to vesicles of different types. Recently, another form, tetrameric, of αS with a stable helical structure was identified experimentally. It has been shown that a dynamic intracellular population of metastable αS tetramers and monomers coexists normally; and the tetramer plays an essential role in maintaining αS homeostasis. Therefore, it is of interest to know whether the tetramer can serve as a means of preventing or delaying the start of PD. Before answering this very important question, it is, first, necessary to find out, on an atomistic level, a correlation between tetramers and monomers; what mediates tetramer formation and what makes a tetramer stable. We address these questions here by investigating both monomeric and tetrameric forms of αS. In particular, by examining correlations between the motions of the side chains and the main chain, steric parameters along the amino-acid sequence, and one- and two-dimensional free-energy landscapes along the coarse-grained dihedral angles γ and δ and principal components, respectively, in monomeric and tetrameric αS, we were able to shed light on a fundamental relationship between monomers and tetramers, and the key residues involved in mediating formation of a tetramer. Also, the reasons for the stability of tetrameric αS and inability of monomeric αS to fold are elucidated here.

Statistical Model To Decipher Protein Folding/Unfolding at a Local Scale.

Protein folding/unfolding can be analyzed experimentally at a local scale by monitoring the physical properties of local probes as a function of the temperature, for example, the distance between fluorophores or the values of chemical shifts of backbone atoms. Here, the analytical Lifson-Roig model for the helix-coil transition is modified to analyze local thermal unfolding of the fast-folder W protein of bacteriophage lambda (gpW) simulated by all-atom molecular dynamics (MD) simulations in explicit solvent at 15 different temperatures. The protein structure is described by the coarse-grained dihedral angles (γ) and bond angles (θ) built between successive Cα-Cα virtual bonds. Each (γ,θ) pair serves as a local probe of protein unfolding. Local native/non-native states are defined for each pair of (γ,θ) angles by analyzing the free-energy landscapes Δ G(γ,θ) computed from MD trajectories. The three local elementary equilibrium constants of the model are extracted for each (γ,θ) pair along the sequence from MD simulations, and the model predictions are compared to the MD data. Using only the local equilibrium constants as an input, we show that the local denaturation curves computed from the model partition function fit their MD simulated counterparts in a satisfying manner without any adjustment. In the model and MD simulations, gpW unfolds gradually between 320 and 340 K, with an average native percentage decreasing from 0.8 (320 K) to 0.2 (340 K). In the prism of the model, there is no stable structure at the local scale in this 20 K unfolding temperature range. The enthalpy change upon local unfolding computed from the model and from MD trajectories suggests that the unfolded state between 320 and 340 K corresponds to a dynamical equilibrium between a large ensemble of constantly changing structures. The present results confirm the downhill unfolding of gpW, which does not obey a two-state global folding/unfolding model, and shed light on the interpretation of local denaturation curves.

Serum Gp96 is a chaperone of complement-C3 during graft-versus-host disease.

Better identification of severe acute graft-versus-host disease (GvHD) may improve the outcome of this life-threatening complication of allogeneic hematopoietic stem cell transplantation. GvHD induces tissue damage and the release of damage-associated molecular pattern (DAMP) molecules. Here, we analyzed GvHD patients (n = 39) to show that serum heat shock protein glycoprotein 96 (Gp96) could be such a DAMP molecule. We demonstrate that serum Gp96 increases in gastrointestinal GvHD patients and its level correlates with disease severity. An increase in Gp96 serum level was also observed in a mouse model of acute GvHD. This model was used to identify complement C3 as a main partner of Gp96 in the serum. Our biolayer interferometry, yeast two-hybrid and in silico modeling data allowed us to determine that Gp96 binds to a complement C3 fragment encompassing amino acids 749-954, a functional complement C3 hot spot important for binding of different regulators. Accordingly, in vitro experiments with purified proteins demonstrate that Gp96 downregulates several complement C3 functions. Finally, experimental induction of GvHD in complement C3-deficient mice confirms the link between Gp96 and complement C3 in the serum and with the severity of the disease.

Theoretical Insights into Sub-Terahertz Acoustic Vibrations of Proteins Measured in Single-Molecule Experiments.

Proteins are an important class of nanobioparticles with acoustical modes in the sub-THz frequency range. There is considerable interest to measure and establish the role of these acoustical vibrations for biological function. So far, the technique providing the most detailed information about the acoustical modes of proteins is the very recent Extraordinary Acoustic Raman (EAR) spectroscopy. In this technique, proteins are trapped in nanoholes and excited by two optical lasers of slightly different wavelengths producing an electric field at low frequency (<100 GHz). We demonstrate that the acoustical modes of proteins studied by EAR spectroscopy are both infrared- and Raman-active modes, and we provided interpretation of the spectroscopic fingerprints measured at the single-molecule level. A combination of the present calculations with techniques based on the excitation of a single nanobioparticle by an electric field, such as EAR spectroscopy, should provide a wealth of information on the role of molecular dynamics for biological function.

Fingerprints of Conformational States of Human Hsp70 at Sub-THz Frequencies.

Large multidomain proteins occur in different conformational states to function. Detection and monitoring of these different structural states are of crucial interest for understanding the mechanics of proteins. Using computational methods, we show that different protein conformational states of the two-domain 70 kDa human Heat-shock protein (hHsp70), with similar vibrational density of states, lead to remarkably different far-IR spectra at acoustical frequencies (ν < 300 GHz). We found that the slow damped motions of the positively charged residues of hHsp70 contribute the most to collective IR active modes at low frequencies (ν < 300 GHz). We predicted that different structural states and functional modes of large proteins, such as hHsp70, might be detected in the sub-THz frequency range by single-molecule spectroscopy similar to the recent extraordinary acoustic Raman spectroscopy (Wheaton S.; Nat. Photonics2015, 9, 68-72).

Intrinsic Localized Modes in Proteins.

Protein dynamics is essential for proteins to function. Here we predicted the existence of rare, large nonlinear excitations, termed intrinsic localized modes (ILMs), of the main chain of proteins based on all-atom molecular dynamics simulations of two fast-folder proteins and of a rigid α/ß protein at 300 K and at 380 K in solution. These nonlinear excitations arise from the anharmonicity of the protein dynamics. The ILMs were detected by computing the Shannon entropy of the protein main-chain fluctuations. In the non-native state (significantly explored at 380 K), the probability of their excitation was increased by a factor between 9 and 28 for the fast-folder proteins and by a factor 2 for the rigid protein. This enhancement in the non-native state was due to glycine, as demonstrated by simulations in which glycine was mutated to alanine. These ILMs might play a functional role in the flexible regions of proteins and in proteins in a non-native state (i.e. misfolded or unfolded states).

New Insights into Protein (Un)Folding Dynamics.

A fundamental open problem in biophysics is how the folded structure of the main chain (MC) of a protein is determined by the physics of the interactions between the side chains (SCs). All-atom molecular dynamics simulations of a model protein (Trp-cage) revealed that strong correlations between the motions of the SCs and the MC occur transiently at 380 K in unfolded segments of the protein and during the simulations of the whole amino-acid sequence at 450 K. The high correlation between the SC and MC fluctuations is a fundamental property of the unfolded state and is also relevant to unstructured proteins as intrinsically disordered proteins (IDPs), for which new reaction coordinates are introduced. The presented findings may open a new door as to how functions of IDPs are related to conformations, which play a crucial role in neurodegenerative diseases.

Patients with colorectal tumors with microsatellite instability and large deletions in HSP110 T17 have improved response to 5-fluorouracil­based chemotherapy.

BACKGROUND & AIMS: Patients with colorectal tumors with microsatellite instability (MSI) have better prognoses than patients with tumors without MSI, but have a poor response to 5-fluorouracil­based chemotherapy. A dominant-negative form of heat shock protein (HSP)110 (HSP110DE9) expressed by cancer cells with MSI, via exon skipping caused by somatic deletions in the T(17) intron repeat, sensitizes the cells to 5-fluorouracil and oxaliplatin.We investigated whether HSP110 T(17) could be used to identify patients with colorectal cancer who would benefit from adjuvant chemotherapy with 5-fluorouracil and oxaliplatin. METHODS: We characterized the interaction between HSP110 and HSP110DE9 using surface plasmon resonance. By using polymerase chain reaction and fragment analysis, we examined how the size of somatic allelic deletions in HSP110 T(17) affected the HSP110 protein expressed by tumor cells. We screened 329 consecutive patients with stage II­III colorectal tumors with MSI who underwent surgical resection at tertiary medical centers for HSP110 T(17). RESULTS: HSP110 and HSP110DE9 interacted in a1:1 ratio. Tumor cells with large deletions in T(17) had increased ratios of HSP110DE9:HSP110, owing to the loss of expression of full-length HSP110. Deletions in HSP110 T(17) were mostly biallelic in primary tumor samples with MSI. Patients with stage II­III cancer who received chemotherapy and had large HSP110 T(17) deletions (≥5 bp; 18 of 77 patients, 23.4%) had longer times of relapse-free survival than patients with small or no deletions (≤4 bp; 59 of 77 patients, 76.6%) in multivariate analysis (hazard ratio, 0.16; 95% confidence interval, 0.012­0.8; P = .03). We found a significant interaction between chemotherapy and T17 deletion (P =.009). CONCLUSIONS: About 25% of patients with stages II­III colorectal tumors with MSI have an excellent response to chemotherapy, due to large, biallelic deletions in the T(17) intron repeat of HSP110 in tumor DNA.

Decipher the mechanisms of protein conformational changes induced by nucleotide binding through free-energy landscape analysis: ATP binding to Hsp70.

ATP regulates the function of many proteins in the cell by transducing its binding and hydrolysis energies into protein conformational changes by mechanisms which are challenging to identify at the atomic scale. Based on molecular dynamics (MD) simulations, a method is proposed to analyze the structural changes induced by ATP binding to a protein by computing the effective free-energy landscape (FEL) of a subset of its coordinates along its amino-acid sequence. The method is applied to characterize the mechanism by which the binding of ATP to the nucleotide-binding domain (NBD) of Hsp70 propagates a signal to its substrate-binding domain (SBD). Unbiased MD simulations were performed for Hsp70-DnaK chaperone in nucleotide-free, ADP-bound and ATP-bound states. The simulations revealed that the SBD does not interact with the NBD for DnaK in its nucleotide-free and ADP-bound states whereas the docking of the SBD was found in the ATP-bound state. The docked state induced by ATP binding found in MD is an intermediate state between the initial nucleotide-free and final ATP-bound states of Hsp70. The analysis of the FEL projected along the amino-acid sequence permitted to identify a subset of 27 protein internal coordinates corresponding to a network of 91 key residues involved in the conformational change induced by ATP binding. Among the 91 residues, 26 are identified for the first time, whereas the others were shown relevant for the allosteric communication of Hsp70 s in several experiments and bioinformatics analysis. The FEL analysis revealed also the origin of the ATP-induced structural modifications of the SBD recently measured by Electron Paramagnetic Resonance. The pathway between the nucleotide-free and the intermediate state of DnaK was extracted by applying principal component analysis to the subset of internal coordinates describing the transition. The methodology proposed is general and could be applied to analyze allosteric communication in other proteins.

Conformational dynamics of full-length inducible human Hsp70 derived from microsecond molecular dynamics simulations in explicit solvent.

Human 70 kDa heat shock protein (hHsp70) is an ATP-dependent chaperone and is currently an important target for developing new drugs in cancer therapy. Knowledge of the conformations of hHsp70 is central to understand the interactions between its nucleotide-binding domain (NBD) and substrate-binding domain (SBD) and is a prerequisite to design inhibitors. The conformations of ADP-bound (or nucleotide-free) hHsp70 and ATP-bound hHsp70 was investigated by using unbiased all-atom molecular dynamics (MD) simulations of homology models of hHsp70 in explicit solvent on a timescale of .5 and 2.7 µs, respectively. The conformational heterogeneity of hHsp70 was analyzed by computing effective free-energy landscapes (FELs) and distance distribution between selected pair of residues. These theoretical data were compared with those extracted from single-molecule Förster resonance energy transfer (FRET) experiments and to small-angle X-ray scattering (SAXS) data of Hsp70 homologs. The distance between a pair of residues in FRET is systematically larger than the distance computed in MD which is interpreted as an effect of the size and of the dynamics of the fluorescent probes. The origin of the conformational heterogeneity of hHsp70 in the ATP-bound state is due to different binding modes of the helix B of the SBD onto the NBD. In the ADP-bound (or nucleotide-free) state, it arises from the different closed conformations of the SBD and from the different positions of the SBD relative to the NBD. In each nucleotide-binding state, Hsp70 is better represented by an ensemble of conformations on a µs timescale corresponding to different local minima of the FEL. An animated interactive 3D complement (I3DC) is available in Proteopedia at http://proteopedia.org/w/Journal:JBSD:30.

Anomalous diffusion and dynamical correlation between the side chains and the main chain of proteins in their native state.

Structural fluctuations of a protein are essential for a protein to function and fold. By using molecular dynamics (MD) simulations of the model α/ß protein VA3 in its native state, the coupling between the main-chain (MC) motions [represented by coarse-grained dihedral angles (CGDAs) γ(n) based on four successive C(α) atoms (n - 1, n, n + 1, n + 2) along the amino acid sequence] and its side-chain (SC) motions [represented by CGDAs δ(n) formed by the virtual bond joining two consecutive C(α) atoms (n, n + 1) and the bonds joining these C(α) atoms to their respective C(ß) atoms] was analyzed. The motions of SCs (δ(n)) and MC (γ(n)) over time occur on similar free-energy profiles and were found to be subdiffusive. The fluctuations of the SCs (δ(n)) and those of the MC (γ(n)) are generally poorly correlated on a ps time-scale with a correlation increasing with time to reach a maximum value at about 10 ns. This maximum value is close to the correlation between the δ(n)(t) and γ(n)(t) time-series extracted from the entire duration of the MD runs (400 ns) and varies significantly along the amino acid sequence. High correlations between the SC and MC motions [δ(t) and γ(t) time-series] were found only in flexible regions of the protein for a few residues which contribute the most to the slowest collective modes of the molecule. These results are a possible indication of the role of the flexible regions of proteins for the biological function and folding.

Nonexponential decay of internal rotational correlation functions of native proteins and self-similar structural fluctuations.

Structural fluctuations of a protein are essential for the function of native proteins and for protein folding. To understand how the main chain in the native state of a protein fluctuates on different time scales, we examined the rotational correlation functions (RCFs), C(t), of the backbone N-H bonds and of the dihedral angles γ built on four consecutive C(α) atoms. Using molecular dynamics simulations of a model α/ß protein (VA3) in its native state, we demonstrate that these RCFs decay as stretched exponentials, ln[C(t)] ≈ D(α)t(α) with a constant D(α) and an exponent α (0 < α < 0.35) varying with the free-energy profiles (FEPs) along the amino acid sequence. The probability distributions of the fluctuations of the main chain computed at short time scale (1 ps) were identical to those computed at large time scale (1 ns) if the time is rescaled by a factor depending on α < 1. This self-similar property and the nonexponential decays (α ≠ 1) of the RCFs are described by a rotational diffusion equation with a time-dependent diffusion coefficient D(t) = αD(α)t(α-1). The present findings agree with observations of subdiffusion (α < 1) of fluorescent probes within a protein molecule. The subdiffusion of (15)N-H bonds did not affect the value of the order parameter S(2) extracted from the NMR relaxation data by assuming normal diffusion (α = 1) of (15)N-H bonds on a nanosecond time scale. However, we found that the RCF does not converge to S(2) on the nanosecond time scale for residues with multiple-minima FEPs.