Hydrogen-Bond Driven Loop-Closure Kinetics in Unfolded Polypeptide Chains

Characterization of the length dependence of end-to-end loop-closure kinetics in unfolded polypeptide chains provides an understanding of early steps in protein folding. Here, loop-closure in poly-glycine-serine peptides is investigated by combining single-molecule fluorescence spectroscopy with molecular dynamics simulation. For chains containing more than 10 peptide bonds loop-closing rate constants on the 20–100 nanosecond time range exhibit a power-law length dependence. However, this scaling breaks down for shorter peptides, which exhibit slower kinetics arising from a perturbation induced by the dye reporter system used in the experimental setup. The loop-closure kinetics in the longer peptides is found to be determined by the formation of intra-peptide hydrogen bonds and transient β-sheet structure, that accelerate the search for contacts among residues distant in sequence relative to the case of a polypeptide chain in which hydrogen bonds cannot form. Hydrogen-bond-driven polypeptide-chain collapse in unfolded peptides under physiological conditions found here is not only consistent with hierarchical models of protein folding, that highlights the importance of secondary structure formation early in the folding process, but is also shown to speed up the search for productive folding events.     

Importance of context in protein folding: secondary structural propensities versus tertiary contact-assisted secondary structure formation

Molecular dynamics simulations can be used to reveal the detailed conformational behaviors of peptides and proteins. By comparing fragment and full-length protein simulations, we can investigate the role of each peptide segment in the folding process. Here, we take advantage of information regarding the helix formation process from our previous simulations of barnase and protein A as well as new simulations of four helical fragments from these proteins at three different temperatures, starting with both helical and extended structures. Segments with high helical propensity began the folding process by tethering the chain through side chain interactions involving either polar interactions, such as salt bridges, or hydrophobic staples. These tethers were frequently nonnative (i.e., not i --> i + 4 spacing) and provided a scaffold for other residues, thereby limiting the conformational search. The helical structure then propagated on both sides of the tether. Segments with low stability and propensity formed later in the folding process and utilized contacts with other portions of the protein when folding. These helices formed via a tertiary contact-assisted mechanism, primarily via hydrophobic contacts between residues distant in sequence. Thus, segments with different helical propensities appear to play different roles during protein folding. Furthermore, the active role of nonlocal side chains in helix formation highlights why we must move beyond simple hierarchical models of protein folding.     

Helix nucleation kinetics from molecular simulations in explicit solvent

We study the reversible folding/unfolding of short Ala and Gly-based peptides by molecular dynamics simulations of all-atom models in explicit water solvent. A kinetic analysis shows that the formation of a first alpha-helical turn occurs within 0.1-1 ns, in agreement with the analyses of laser temperature jump experiments. The unfolding times exhibit Arrhenius temperature dependence. For a rapidly nucleating all-Ala peptide, the helix nucleation time depends only weakly on temperature. For a peptide with enthalpically competing turn-like structures, helix nucleation exhibits an Arrhenius temperature dependence, corresponding to the unfolding of enthalpic traps in the coil ensemble. An analysis of structures in a "transition-state ensemble" shows that helix-to-coil transitions occur predominantly through breaking of hydrogen bonds at the helix ends, particularly at the C-terminus. The temperature dependence of the transition-state ensemble and the corresponding folding/unfolding pathways illustrate that folding mechanisms can change with temperature, possibly complicating the interpretation of high-temperature unfolding simulations. The timescale of helix formation is an essential factor in molecular models of protein folding. The rapid helix nucleation observed here suggests that transient helices form early in the folding event.     

Molecular dynamics simulation of the folding of single alkane chains with different lengths on single-walled carbon nanotubes and graphene

Chain folding is an important step during polymer crystallization. In order to study the effects of the surface on chain folding, molecular dynamics simulations of the folding of different alkane chains on three kinds of single-walled carbon nanotubes (SWCNTs) and graphene were performed. The folding behaviors of the single alkane chains on these surfaces were found to be different from their folding behaviors in vacuum. The end-to-end distances of the chains were calculated to explore the chain folding. An increasing tendency to fold into two or more stems with increasing alkane chain length was observed. This result indicates that the occurrence and the stability of chain folding are related to the surface curvature, the diameter of the SWCNT, and surface texture. In addition, the angle between the direction of the alkane chain segment and the direction of the surface texture was measured on different surfaces.     

The determinants of hydrophobic mismatch response for transmembrane helices

Hydrophobic mismatch arises from a difference in the hydrophobic thickness of a lipid membrane and a transmembrane protein segment, and is thought to play an important role in the folding, stability and function of membrane proteins. We have investigated the possible adaptations that lipid bilayers and transmembrane α-helices undergo in response to mismatch, using fully-atomistic molecular dynamics simulations totaling 1.4 μs. We have created 25 different tryptophan-alanine-leucine transmembrane α-helical peptide systems, each composed of a hydrophobic alanine–leucine stretch, flanked by 1–4 tryptophan side chains, as well as the β-helical peptide dimer, gramicidin A. Membrane responses to mismatch include changes in local bilayer thickness and lipid order, varying systematically with peptide length. Adding more flanking tryptophan side chains led to an increase in bilayer thinning for negatively mismatched peptides, though it was also associated with a spreading of the bilayer interface. Peptide tilting, bending and stretching were systematic, with tilting dominating the responses, with values of up to ~ 45° for the most positively mismatched peptides. Peptide responses were modulated by the number of tryptophan side chains due to their anchoring roles and distributions around the helices. Potential of mean force calculations for local membrane thickness changes, helix tilting, bending and stretching revealed that membrane deformation is the least energetically costly of all mismatch responses, except for positively mismatched peptides where helix tilting also contributes substantially. This comparison of energetic driving forces of mismatch responses allows for deeper insight into protein stability and conformational changes in lipid membranes.     

Nucleation and propagation of the collagen triple helix in single-chain and trimerized peptides: transition from third to first order kinetics

The kinetics of triple helix formation from single non-crosslinked peptide chains were studied for the collagen models (ProProGly)10 and (ProHypGly)10 in a broad concentration range and compared with those in nucleated trimers. At very low peptide concentrations the reaction order is 3 but decreases at higher concentrations. For (ProProGly)10 the third order rate constant is 800 M(-2) x s(-1) at 7 degrees C, which corresponds to a very long half time of 15 hours at 60 microM chain concentration. For (ProHypGly)10 the rate constant is about 1000-fold higher, which is consistent with the stabilizing effect of 4-hydroxyproline in collagens. The concentration dependence of the reaction order is explained by a nucleation mechanism in which a very unstable dimer is in fast equilibrium with the monomeric chains and addition of the third chain occurs in a rate-limiting step. At high concentrations nucleation is faster than propagation of helix formation and propagation becomes rate-limiting. To test this hypothesis an artificial nucleus was introduced by fusion of (ProProGly)10 with the trimeric foldon domain of T4 phage or the crosslinking domain of collagen III GlyProProGlyProCysCysGlyGlyGly. These domains were recombinantly attached to the C terminus of (GlyProPro)10 and link the three chains in a similar way to the C-terminal propeptide domain in collagen III. This results in a local intrinsic chain concentration of about 1 M. A first order reaction is observed for the folding of the triple helix in (GlyProPro)10foldon with a half time of 8.3 minutes, which approximately matches the rate of folding from single chains at 1 M peptide concentration. A high activation energy of 54 kJ/mol is found for this reaction, whereas the temperature dependence of the nucleation step is close to zero, confirming earlier findings on natural collagens that cis-trans isomerization of peptide bonds is the rate-limiting step in propagation.     

Dynamics of unfolded polypeptide chains as model for the earliest steps in protein folding

The rate of formation of intramolecular interactions in unfolded proteins determines how fast conformational space can be explored during folding. Characterization of the dynamics of unfolded proteins is therefore essential for the understanding of the earliest steps in protein folding. We used triplet-triplet energy transfer to measure formation of intrachain contacts in different unfolded polypeptide chains. The time constants (1/k) for contact formation over short distances are almost independent of chain length, with a maximum value of about 5 ns for flexible glycine-rich chains and of 12 ns for stiffer chains. The rates of contact formation over longer distances decrease with increasing chain length, indicating different rate-limiting steps for motions over short and long chain segments. The effect of the amino acid sequence on local chain dynamics was probed by using a series of host-guest peptides. Formation of local contacts is only sixfold slower around the stiffest amino acid (proline) compared to the most flexible amino acid (glycine). Good solvents for polypeptide chains like EtOH, GdmCl and urea were found to slow intrachain diffusion and to decrease chain stiffness. These data allow us to determine the time constants for formation of the earliest intrachain contacts during protein folding.     

Folding of oligoglutamines: a theoretical approach based upon thermodynamics and molecular mechanics

Folding of oligoglutamine chains of different lengths is of crucial interest for exploring the molecular mechanisms of Huntington's disease. A simple oligoglutamine model based upon the Flory-Huggins theory of polymer solutions demonstrates a random coil instability in chains containing more than 40 glutamine residues with respect to beta-sheet formation. This is in striking quantitative agreement with biochemical results on the chain length dependence of polyglutamine aggregation in vivo and in vitro, as well as with clinical data on the polyglutamine chain length dependence of the onset of Huntington's disease. Furthermore, a detailed molecular-mechanical investigation of a polypeptide chain carrying 40 glutamine residues was performed. Two possible folding modes of such an oligoglutamine chain were revealed: a) a beta-hairpin and b) a highly compact random coil entity stabilized by a wealth of H-bonds among the glutamine side chains. A possible role of these folding modes in polyglutamine aggregation, as well as in the onset of Huntington's disease, is discussed.     

Simulation of α-helix–coil transitions in simplified polyvaline: Equilibrium properties and brownian dynamics

A quantitative understanding of helix–coil dynamics will help explain their role in protein folding and in folded proteins. As a contribution to the understanding, the equilibrium and dynamical aspects of the helix–coil transition in polyvaline have been studied by computer simulation using a simplified model of the polypeptide chain. Each amino acid residue is treated as a single quasiparticle in an effective potential that approximates the potential of mean force in solution. The equilibrium properties examined include the helix–coil transition and its dependence on chain position and well depth at the coil–helix interface. A stochastic simulation of the Brownian motion of the chain in its solvent surroundings has been used to investigate dynamical properties. Time histories of the dihedral angles have been used to study the behavior of the helical structure. Auto and cross-correlation functions have been calculated from the time histories and from the state (helix or coil) functions of the residues with relaxation times of tens to hundreds of picoseconds. Helix–coil rate constants of tens of ns^?1 were found for both directions of the transition. © 1993 John Wiley & Sons, Inc.     

Molecular dynamics simulations of synthetic peptide folding

Because the time scale of protein folding is much greater than that of the widely used simulations of native structures, a detailed report of molecular dynamics simulations of folding has not been available. In this study, we Included the average solvent effect in the potential functions to simplify the calculation of the solvent effect and carried out long molecular dynamics simulations of the alanine-based synthetic peptides at 274 K. From either an extended or a randomly generated conformation, the simulations approached a helix-coil equilibrium in about 3 ns. The multiple minima problem did not prevent helix folding. The calculated helical ratio of Ac-AAQAAAAQAAAAQAAY-NH₂ was 47%, in good agreement with the circular dichroism measurement (about 50%). A helical segment with frayed ends was the most stable conformation, but the hydrophobic interaction favored the compact, distorted helix-turn-helix conformations. The transition between the two types of conformations occurred in a much larger time scale than helix propagation. The transient hydrogen bonds between the glutamine side chain and the backbone carbonyl group could reduce the free energy barrier of helix folding and unfolding. The substitution of a single alanine residue in the middle of the peptide with valine or glycine decreased the average helical ratio significantly, in agreement with experimental observations. © 1996 Wiley-Liss, Inc.     

Helix folding simulations with various initial conformations.

Using a solvent-referenced energy calculation, a 16-residue peptide with alanine side chains folded into predominantly alpha-helical conformations during constant temperature (274 K) simulations. From different initial conformations, helical conformations were reached and the multiple energy minima did not become a serious problem. Under the same conditions, the simulation did not indiscriminately fold a sequence such as polyglycine into stable helices. Interesting observations from the simulations relate to the folding mechanism. The electrostatic interactions between the successive amides favored extended conformations (or beta strands) and caused energy barriers to helix folding. beta-bends were observed as intermediates during helix nucleation. The helix propagation toward the C-terminus seemed faster than that toward the N-terminus. In helical conformations, hydrogen bond oscillation between the i,i+ 4 and the i,i+3 patterns was observed. The i,i+3 hydrogen bonds occurred more frequently during helix propagation and deformation near both ends of the helical segment.     

An all-atom structure-based potential for proteins: bridging minimal models with all-atom empirical forcefields

Protein dynamics take place on many time and length scales. Coarse-grained structure-based (Go) models utilize the funneled energy landscape theory of protein folding to provide an understanding of both long time and long length scale dynamics. All-atom empirical forcefields with explicit solvent can elucidate our understanding of short time dynamics with high energetic and structural resolution. Thus, structure-based models with atomic details included can be used to bridge our understanding between these two approaches. We report on the robustness of folding mechanisms in one such all-atom model. Results for the B domain of Protein A, the SH3 domain of C-Src Kinase, and Chymotrypsin Inhibitor 2 are reported. The interplay between side chain packing and backbone folding is explored. We also compare this model to a C(alpha) structure-based model and an all-atom empirical forcefield. Key findings include: (1) backbone collapse is accompanied by partial side chain packing in a cooperative transition and residual side chain packing occurs gradually with decreasing temperature, (2) folding mechanisms are robust to variations of the energetic parameters, (3) protein folding free-energy barriers can be manipulated through parametric modifications, (4) the global folding mechanisms in a C(alpha) model and the all-atom model agree, although differences can be attributed to energetic heterogeneity in the all-atom model, and (5) proline residues have significant effects on folding mechanisms, independent of isomerization effects. Because this structure-based model has atomic resolution, this work lays the foundation for future studies to probe the contributions of specific energetic factors on protein folding and function.     

Folding of Oligoglutamines: A Theoretical Approach Based Upon Thermodynamics and Molecular Mechanics

Abstract

Folding of oligoglutamine chains of different lengths is of crucial interest for exploring the molecular mechanisms of Huntington's disease. A simple oligoglutamine model based upon the Flory-Huggins theory of polymer solutions demonstrates a random coil instability in chains containing more than 40 glutamine residues with respect to β-sheet formation. This is in striking quantitative agreement with biochemical results on the chain length dependence of polyglutamine aggregation in vivo and in vitro, as well as with clinical data on the polyglutamine chain length dependence of the onset of Huntington's disease. Furthermore, a detailed molecular-mechanical investigation of a polypeptide chain carrying 40 glutamine residues was performed. Two possible folding modes of such an oligoglutamine chain were revealed: a) a β-hairpin and b) a highly compact random coil entity stabilized by a wealth of H-bonds among the glutamine side chains. A possible role of these folding modes in polyglutamine aggregation, as well as in the onset of Huntington's disease, is discussed.     

Unit-vector RMS (URMS) as a tool to analyze molecular dynamics trajectories

The Unit-vector RMS (URMS) is a new technique to compare protein chains and to detect similarities of chain segments. It is limited to comparison of C(alpha) chains. However, it has a number of unique features that include exceptionally weak dependence on the length of the chain and efficient detection of substructure similarities. Two molecular dynamics simulations of proteins in the neighborhood of their native states are used to test the performance of the URMS. The first simulation is of a solvated myoglobin and the second is of the protein MHC. In accord with previous studies the secondary structure elements (helices or sheets) are found to be moving relatively rigidly among flexible loops. In addition to these tests, folding trajectories of C peptides are analyzed, revealing a folding nucleus of seven amino acids.     

Molecular dynamics simulations predict a tilted orientation for the helical region of dynorphin A(1-17) in dimyristoylphosphatidylcholine bilayers

The structural properties of the endogenous opioid peptide dynorphin A(1-17) (DynA), a potential analgesic, were studied with molecular dynamics simulations in dimyristoylphosphatidylcholine bilayers. Starting with the known NMR structure of the peptide in dodecylphosphocholine micelles, the N-terminal helical segment of DynA (encompassing residues 1-10) was initially inserted in the bilayer in a perpendicular orientation with respect to the membrane plane. Parallel simulations were carried out from two starting structures, systems A and B, that differ by 4 A in the vertical positioning of the peptide helix. The complex consisted of approximately 26,400 atoms (dynorphin + 86 lipids + approximately 5300 waters). After >2 ns of simulation, which included >1 ns of equilibration, the orientation of the helical segment of DynA had undergone a transition from parallel to tilted with respect to the bilayer normal in both the A and B systems. When the helix axis achieved a approximately 50 degrees angle with the bilayer normal, it remained stable for the next 1 ns of simulation. The two simulations with different starting points converged to the same final structure, with the helix inserted in the bilayer throughout the simulations. Analysis shows that the tilted orientation adopted by the N-terminal helix is due to specific interactions of residues in the DynA sequence with phospholipid headgroups, water, and the hydrocarbon chains. Key elements are the "snorkel model"-type interactions of arginine side chains, the stabilization of the N-terminal hydrophobic sequence in the lipid environment, and the specific interactions of the first residue, Tyr. Water penetration within the bilayer is facilitated by the immersed DynA, but it is not uniform around the surface of the helix. Many water molecules surround the arginine side chains, while water penetration near the helical surface formed by hydrophobic residues is negligible. A mechanism of receptor interaction is proposed for DynA, involving the tilted orientation observed from these simulations of the peptide in the lipid bilayer.     

Dependence on the dielectric model and pH in a synthetic helical peptide studied by Monte Carlo simulated annealing

Monte Carlo simulated annealing is applied to the tertiary structure prediction of a 17-residue synthetic peptide, which is known by experiment to exhibit high helical content at low pH. Two dielectric models are considered: sigmoidal distance-dependent dielectric function and a constant dielectric function (? = 2). Starting from completely random initial conformations, our simulations for both dielectric models at low pH gave many helical conformations. The obtained low-energy conformations are compared with the nuclear Overhauser effect spectroscopy cross-peak data for both main chain and side chains, and it is shown that the results for the sigmoidal dielectric function are in remarkable agreement with the experimental data. The results predict the existence of two disjoint helices around residues 5–9 and 11–16, while nmr experiments imply significant α-helix content between residues 5 and 14. Simulations with high pH, on the other hand, hardly gave a helical conformation, which is also in accord with the experiment. These findings indicate that when side chains are charged, electrostatic interactions due to these charges play a major role in the helix stability. Our results are compared with the previous 500 ps molecular dynamics simulations of the same peptide. It is argued that simulated annealing is superior to molecular dynamics in two respects: (1) direct folding of α-helix from completely random initial conformations is possible for the former, whereas only unfolding of an α-helix can be studied by the latter; (2) while both methods predict high helix content for low pH, the results for high pH agree with experiment (low helix content) only for the former method. © 1994 John Wiley & Sons, Inc.     

Molecular basis for the effect of urea and guanidinium chloride on the dynamics of unfolded polypeptide chains

Chemical denaturants are frequently used to unfold proteins and to characterize mechanisms and transition states of protein folding reactions. The molecular basis of the effect of urea and guanidinium chloride (GdmCl) on polypeptide chains is still not well understood. Models for denaturant--protein interaction include both direct binding and indirect changes in solvent properties. Here we report studies on the effect of urea and GdmCl on the rate constants (k(c)) of end-to-end diffusion in unstructured poly(glycine-serine) chains of different length. Urea and GdmCl both lead to a linear decrease of lnk(c) with denaturant concentration, as observed for the rate constants for protein folding. This suggests that the effect of denaturants on chain dynamics significantly contributes to the denaturant-dependence of folding rate constants for small proteins. We show that this linear dependency is the result of two additive non-linear effects, namely increased solvent viscosity and denaturant binding. The contribution from denaturant binding can be quantitatively described by Schellman's weak binding model with binding constants (K) of 0.62(+/-0.01)M(-1) for GdmCl and 0.26(+/-0.01)M(-1) for urea. In our model peptides the number of binding sites and the effect of a bound denaturant molecule on chain dynamics is identical for urea and GdmCl. The results further identify the polypeptide backbone as the major denaturant binding site and give an upper limit of a few nanoseconds for residence times of denaturant molecules on the polypeptide chain.     

Molecular modeling of vimentin filament assembly

Intermediate-filament forming proteins are known to form rod-shaped dimers that are calculated to be 45 nm in length. Molecular modeling indicates that the dimerization is promoted by interchain hydrophobic interactions between sections of α helix β and helix. Further aggregation involves the formation of tetramers in which two dimers are anti-parallel and staggered to two characteristic degrees of overlap. Modeling indicated that the degrees of stagger are dictated by the association of sections of α helix in 4-chain bundles, in which hydrophobic side chains are sequestered from contact with water. The staggered arrangement of two dimers produces a tetramer having sections of 2-chain rod in which hydrophobic side chains are exposed to water. Extension of the tetramer to form protofilaments may be driven by associations with the 2-chain regions that reduce aqueous exposure of the hydrophobic side chains. Exposure of hydrophobic groups may be reduced by the 2-chain regions folding back upon themselves so that the entire tetramer becomes a 4-chain conformation. This prediction is in line with electron microscope data showing that mixtures of the lower oligomers contain rods of uniform thickness ranging upwards from 45 nm in a series having incremental increases in length. Data from previous chemical crosslinking studies support this model and also the idea that the completed intermediate filaments each consist of seven 4-chain protofilaments. Proteins 26:472–478 © 1996 Wiley-Liss, Inc.     

Core formation in apomyoglobin: probing the upper reaches of the folding energy landscape

An acid-destabilized form of apomyoglobin, the so-called E state, consists of a set of heterogeneous structures that are all characterized by a stable hydrophobic core composed of 30-40 residues at the intersection of the A, G, and H helices of the protein, with little other secondary structure and no other tertiary structure. Relaxation kinetics studies were carried out to characterize the dynamics of core melting and formation in this protein. The unfolding and/or refolding response is induced by a laser-induced temperature jump between the folded and unfolded forms of E, and structural changes are monitored using the infrared amide I' absorbance at 1648-1651 cm(-1) that reports on the formation of solvent-protected, native-like helix in the core and by fluorescence emission changes from apomyoglobin's Trp14, a measure of burial of the indole group of this residue. The fluorescence kinetics data are monoexponential with a relaxation time of 14 micros. However, infrared kinetics data are best fit to a biexponential function with relaxation times of 14 and 59 micros. These relaxation times are very fast, close to the limits placed on folding reactions by diffusion. The 14 micros relaxation time is weakly temperature dependent and thus represents a pathway that is energetically downhill. The appearance of this relaxation time in both the fluorescence and infrared measurements indicates that this folding event proceeds by a concomitant formation of compact secondary and tertiary structures. The 59 micros relaxation time is much more strongly temperature dependent and has no fluorescence counterpart, indicating an activated process with a large energy barrier wherein nonspecific hydrophobic interactions between helix A and the G and H helices cause some helix burial but Trp14 remains solvent exposed. These results are best fit by a multiple-pathway kinetic model when U collapses to form the various folded core structures of E. Thus, the results suggest very robust dynamics for core formation involving multiple folding pathways and provide significant insight into the primary processes of protein folding.     

Amino Acid Insertion Reveals a Necessary Three-Helical Intermediate in the Folding Pathway of the Colicin E7 Immunity Protein Im7

The small (87-residue) α-helical protein Im7 (an inhibitor protein for colicin E7 that provides immunity to cells producing colicin E7) folds via a three-state mechanism involving an on-pathway intermediate. This kinetic intermediate contains three of four native helices that are oriented in a non-native manner so as to minimise exposed hydrophobic surface area at this point in folding. The short (6-residue) helix III has been shown to be unstructured in the intermediate ensemble and does not dock onto the developing hydrophobic core until after the rate-limiting transition state has been traversed. After helix III has docked, it adopts an α-helical secondary structure, and the side chains of residues within this region provide contacts that are crucial to native-state stability. In order to probe further the role of helix III in the folding mechanism of Im7, we created a variant that contains an eight-amino-acid polyalanine-like helix stabilised by a Glu-Arg salt bridge and an Asn-Pro-Gly capping motif, juxtaposed C-terminal to the natural 6-residue helix III. The effect of this insertion on the structure of the native protein and its folding mechanism were studied using NMR and ?-value analysis, respectively. The results reveal a robust native structure that is not perturbed by the presence of the extended helix III. Mutational analysis performed to probe the folding mechanism of the redesigned protein revealed a conserved mechanism involving the canonical three-helical intermediate. The results suggest that folding via a three-helical species stabilised by both native and non-native interactions is an essential feature of Im7 folding, independent of the helical propensity of helix III.