Pathways to folding, nucleation events, and native geometry

We perform extensive Monte Carlo simulations of a lattice model and the Gō potential [N. Gō and H. Taketomi, Proc. Natl. Acad. Sci. U.S.A. 75, 559563 (1978)] to investigate the existence of folding pathways at the level of contact cluster formation for two native structures with markedly different geometries. Our analysis of folding pathways revealed a common underlying folding mechanism, based on nucleation phenomena, for both protein models. However, folding to the more complex geometry (i.e., that with more nonlocal contacts) is driven by a folding nucleus whose geometric traits more closely resemble those of the native fold. For this geometry folding is clearly a more cooperative process.     

Chemical reaction rates using the semiclassical Van Vleck initial value representation

A semiclassical initial value representation formulation using the Van Vleck [Proc. Natl. Acad. Sci. U.S.A. 14, 178 (1928)] propagator has been used to calculate the flux correlation function and thereby reaction rate constants. This Van Vleck formulation of the flux-flux correlation function is computationally as simple as the classical Wigner [Trans. Faraday Soc. 34, 29 (1938)] model. However, unlike the latter, it has the ability to capture quantum interference/coherence effects. Classical trajectories are evolved starting from the dividing surface that separates reactants and products, and are evolved negatively in time. This formulation has been tested on model problems ranging from the Eckart barrier, double well to the collinear H+H2.     

Stretched versus compressed exponential kinetics in α-helix folding

In a recent paper (J. Bredenbeck, J. Helbing, J.R. Kumita, G.A. Woolley, P. Hamm, α-helix formation in a photoswitchable peptide tracked from picoseconds to microseconds by time resolved IR spectroscopy, Proc. Natl. Acad. Sci USA 102 (2005) 2379), we have investigated the folding of a photo-switchable α-helix with a kinetics that could be fit by a stretched exponential function exp(−(t/τ)^β). The stretching factor β became smaller as the temperature was lowered, a result which has been interpreted in terms of activated diffusion on a rugged energy surface. In the present paper, we discuss under which conditions diffusion problems occur with stretched exponential kinetics (β < 1) and under which compressed exponential kinetics is obtained (β > 1). We show that diffusion problems do have a strong tendency to yield stretched exponential kinetics, yet, that there are conditions (strong perturbation from equilibrium, performing the experiment in the folding direction) under which compressed exponential kinetics would be expected instead. We discuss the kinetics on free energy surfaces predicted by simple initiation-propagation models (zipper models) of α-helix folding, as well as by folding funnel models. We show that our recent experiment has been performed under condition for which models with strong downhill driving force, such as the zipper model, would predict compressed, rather than stretched exponential kinetics, in disagreement with the experimental observation. We therefore propose that the free energy surface along a reaction coordinate that governs the folding kinetics must be relatively flat and has a shape similar to a 1D golf course. We discuss how this conclusion can be unified with the thermodynamically well established zipper model by introducing an additional kinetic reaction coordinate.     

Folding kinetics of a lattice protein via a forward flux sampling approach

We implement a forward flux sampling approach [R. J. Allen et al., J. Chem. Phys. 124, 194111 (2006)] for calculating transition rate constants and for sampling paths of protein folding events. The algorithm generates trajectories for the transition between the unfolded and folded states as chains of partially connected paths, which can be used to obtain the transition-state ensemble and the properties that characterize these intermediates. We apply this approach to Monte Carlo simulations of a model lattice protein in open space and in confined spaces of varying dimensions. We study the effect of confinement on both protein thermodynamic stability and folding kinetics; the former by mapping free-energy landscapes and the latter by the determination of rate constants and mechanistic details of the folding pathway. Our results show that, for the range of temperatures where the native state is stable, confinement of a protein destabilizes the unfolded state by reducing its entropy, resulting in increased thermodynamic stability of the folded state. Relative to the folding in open space, we find that the kinetics can be accelerated at temperatures above the temperature at which the unconfined protein folds fastest and that the rate constant increases with the number of constrained dimensions. By examining the statistical properties of the transition-state ensemble, we detect signs of a classical nucleation folding mechanism for a core of native contacts formed at an early stage of the process. This nucleus acts as folding foci and is composed of those residues that have higher probability to form native contacts in the transition-state intermediates, which can vary depending on the confinement conditions of the system.     

Exploring the free energy surfaces of clusters using reconnaissance metadynamics

A new approach is proposed for exploring the low-energy structures of small to medium-sized aggregates of atoms and molecules. This approach uses the recently proposed reconnaissance metadynamics method [G. A. Tribello, M. Ceriotti, and M. Parrinello. Proc. Natl. Acad. Sci. U.S.A. 107(41), 17509 (2010)] in tandem with collective variables that describe the average structure of the coordination sphere around the atoms/molecules. We demonstrate this method on both Lennard-Jones and water clusters and show how it is able to quickly find the global minimum in the potential energy surface, while exploring the finite temperature free energy surface.     

Are defect models consistent with the entropy and specific heat of glass formers?

We show that pointlike defect model of glasses cannot explain the thermodynamic properties of glass formers, as for example, the excess specific heat close to the glass transition, contrary to the claim of Garrahan and Chandler [Proc. Natl. Acad. Sci. U.S.A. 100, 9710 (2003)]. More general models and approaches in terms of extended defects are also discussed.     

A photocontrolled beta-hairpin peptide

Beta-hairpins constitute the smallest beta-type structures in peptides and proteins. The development of highly stable, yet monomeric beta-hairpins based on the tryptophan zipper motif was therefore a remarkable success [A. G. Cochran, N. J. Skelton, M. A. Starovasnik, Proc. Natl. Acad. Sci USA 2001, 98, 5578-5583]. We have been able to design, synthesize and characterize a hairpin based on this motif which incorporates an azobenzene-based photoswitch, that allows for time-resolved folding studies of beta-structures with unprecedented time resolution. At room temperature the trans-azo isomer exhibits a mostly disordered structure; however, light-induced isomerization to the cis-azo form leads to a predominantly extended and parallel conformation of the two peptide parts, which are linked by the novel photoswitch, [3-(3-aminomethyl)phenylazo]phenylacetic acid (AMPP). While in the original sequence the dipeptide Asn-Gly forms a type I' beta-turn which connects the two strands of the hairpin, this role is adopted by the AMPP chromophore in our photoresponsive beta-hairpin that can apparently act as a beta I'-turn mimetic. The beta-hairpin structure was determined and confirmed by NMR spectroscopy, but the folding process can be monitored by pronounced changes in the CD, IR and fluorescence spectra. Finally, incorporation of the structurally and functionally important beta-hairpin motif into proteins by chemical ligation might allow for the photocontrol of protein structures and/or functions.     

Inverse Monte Carlo procedure for conformation determination of macromolecules

A novel numerical method for determining the conformational structure of macromolecules is applied to idealized biomacromolecules in solution. The method computes effective inter-residue interaction potentials solely from the corresponding radial distribution functions, such as would be obtained from experimental data. The interaction potentials generate conformational ensembles that reproduce thermodynamic properties of the macromolecule (mean energy and heat capacity) in addition to the target radial distribution functions. As an evaluation of its utility in structure determination, we apply the method to a homopolymer and a heteropolymer model of a three-helix bundle protein [Zhou, Y.; Karplus, M. Proc Natl Acad Sci USA 1997, 94, 14429; Zhou, Y. et al. J Chem Phys 1997, 107, 10691] at various thermodynamic state points, including the ordered globule, disordered globule, and random coil states.     

Mapping potential energy surfaces

A recently proposed dynamical method [A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002)] allows us to globally sample the free energy surface. This approach uses a coarse-grained non-Markovian dynamics to bias microscopic atomic trajectories. After a sufficiently long simulation time, the global free energy surface can be reconstructed from the non-Markovian dynamics. Here we apply this scheme to study the T=0 free energy surface, i.e., the potential energy surface in coarse-grained space. We show that the accuracy of the reconstructed potential energy surface can be dramatically improved by a simple postprocessing procedure with only minor computational overhead. We illustrate this approach by conducting conformational analysis on a small organic molecule, demonstrating its superiority over traditional unbiased approaches in sampling potential energy surfaces in coarse-grained space.     

Rapid on-membrane proteolytic cleavage for Edman sequencing and mass spectrometric identification of proteins

A method for the rapid limited enzymatic cleavage of PVDF membrane-immobilized proteins is described. This method allows the fast characterization of PVDF blotted proteins by peptide mass fingerprinting (Henzel, W. J., Billeci, T. M., Stults, J. T., Wong, S. C., Grimley, C., Wantanabe, C., Proc. Natl. Acad. Sci. USA 1993, 90, 5011-5015), LC-MS/MS, or N-terminal sequencing and has been demonstrated on a range of proteins using a full complement of proteolytic enzymes. This technique allows the generation of proteolytic fragments between 5 and 60 min (depending on the enzyme employed), which is significantly faster than previously reported on-membrane digestion methods. To date, this on-membrane rapid digestion protocol has aided in the identification and confirmation of mutation sites in over 200 recombinant proteins.     

Correction factors for boundary diffusion in reaction-diffusion master equations

The reaction-diffusion master equation (RDME) has been widely used to model stochastic chemical kinetics in space and time. In recent years, RDME-based trajectorial approaches have become increasingly popular. They have been shown to capture spatial detail at moderate computational costs, as compared to fully resolved particle-based methods. However, finding an appropriate choice for the discretization length scale is essential for building a reasonable RDME model. Moreover, it has been recently shown [R. Erban and S. J. Chapman, Phys. Biol. 4, 16 (2007); R. Erban and S. J. Chapman, Phys. Biol. 6, 46001 (2009); D. Fange, O. G. Berg, P. Sjo?berg, and J. Elf, Proc. Natl. Acad. Sci. U.S.A. 107, 46 (2010)] that the reaction rates commonly used in RDMEs have to be carefully reassessed when considering reactive boundary conditions or binary reactions, in order to avoid inaccurate--and possibly unphysical--results. In this paper, we present an alternative approach for deriving correction factors in RDME models with reactive or semi-permeable boundaries. Such a correction factor is obtained by solving a closed set of equations based on the moments at steady state, as opposed to modifying probabilities for absorption or reflection. Lastly, we briefly discuss existing correction mechanisms for bimolecular reaction rates both in the limit of fast and slow diffusion, and argue why our method could also be applied for such purpose.     

Context-dependent effects of asparagine glycosylation on Pin WW folding kinetics and thermodynamics

Asparagine glycosylation is one of the most common and important post-translational modifications of proteins in eukaryotic cells. N-glycosylation occurs when a triantennary glycan precursor is transferred en bloc to a nascent polypeptide (harboring the N-X-T/S sequon) as the peptide is cotranslationally translocated into the endoplasmic reticulum (ER). In addition to facilitating binding interactions with components of the ER proteostasis network, N-glycans can also have intrinsic effects on protein folding by directly altering the folding energy landscape. Previous work from our laboratories (Hanson et al. Proc. Natl. Acad. Sci. U.S.A. 2009, 109, 3131-3136; Shental-Bechor, D.; Levy, Y. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 8256-8261) suggested that the three sugar residues closest to the protein are sufficient for accelerating protein folding and stabilizing the resulting structure in vitro; even a monosaccharide can have a dramatic effect. The highly conserved nature of these three proximal sugars in N-glycans led us to speculate that introducing an N-glycosylation site into a protein that is not normally glycosylated would stabilize the protein and increase its folding rate in a manner that does not depend on the presence of specific stabilizing protein-saccharide interactions. Here, we test this hypothesis experimentally and computationally by incorporating an N-linked GlcNAc residue at various positions within the Pin WW domain, a small β-sheet-rich protein. The results show that an increased folding rate and enhanced thermodynamic stability are not general, context-independent consequences of N-glycosylation. Comparison between computational predictions and experimental observations suggests that generic glycan-based excluded volume effects are responsible for the destabilizing effect of glycosylation at highly structured positions. However, this reasoning does not adequately explain the observed destabilizing effect of glycosylation within flexible loops. Our data are consistent with the hypothesis that specific, evolved protein-glycan contacts must also play an important role in mediating the beneficial energetic effects on protein folding that glycosylation can confer.     

Design and synthesis of peptides that bind alpha-bungarotoxin with high affinity

BACKGROUND: Alpha-bungarotoxin (alpha-BTX) is a highly toxic snake venom alpha-neurotoxin that binds to acetylcholine receptor (AChR) at the neuromuscular junction, and is a potent inhibitor of this receptor. We describe the design and synthesis of peptides that bind alpha-BTX with high affinity, and inhibit its interaction with AChR with an IC(50) of 2 nM. The design of these peptides was based on a lead peptide with an IC(50) of 3x10(-7) M, previously identified by us [M. Balass et al., Proc. Natl. Acad. Sci. USA 94 (1997) 6054] using a phage-display peptide library. RESULTS: Employing nuclear magnetic resonance-derived structural information [T. Scherf et al., Proc. Natl. Acad. Sci. USA 94 (1997) 6059] of the complex of alpha-BTX with the lead peptide, as well as structure-function analysis of the ligand-binding site of AChR, a systematic residue replacement of the lead peptide, one position at a time, yielded 45 different 13-mer peptides. Of these, two peptides exhibited a one order of magnitude increase in inhibitory potency in comparison to the lead peptide. The design of additional peptides, with two or three replacements, resulted in peptides that exhibited a further increase in inhibitory potency (IC(50) values of 2 nM), that is more than two orders of magnitude better than that of the original lead peptide, and better than that of any known peptide derived from AChR sequence. The high affinity peptides had a protective effect on mice against alpha-BTX lethality. CONCLUSIONS: Synthetic peptides with high affinity to alpha-BTX may be used as potential lead compounds for developing effective antidotes against alpha-BTX poisoning. Moreover, the procedure employed in this study may serve as a general approach for the design and synthesis of peptides that interact with high affinity with any desired biological target.     

Mechanisms of selenium-mediated protection from photocarcinogenesis and cell death are not solely p53-dependent

Recent studies published in Oncogene and Proc. Natl. Acad. Sci. USA ascribe a role for selenium, acting through wild type p53, in protecting skin cells in culture from ultraviolet radiation-induced death. While selenium clearly protects cells against ultraviolet radiation-induced death, data that we present and discuss in this letter shows that wild type p53 is not required for such protection. Moreover the non-physiologically high levels of selenium used in some studies leads us to question the relevance of such effects for selenium-induced photoprotection.     

Evaluation of Solvent Accessibility to the [Fe(4)S(4)] Binding Pocket in Native and Tyr19 Mutant High Potential Iron Proteins by (1)H-(15)N HMQC and (19)F NMR Experiments

The solvent accessibility of Chromatium vinosumhigh potential iron protein (HiPIP) has been investigated by use of (1)H-(15)N HMQC, and (19)F NMR spectroscopy. These NMR experiments indicate that solvent accessibility to the cluster core is similar, and minimal, for the reduced and oxidized states of native HiPIP, but increases significantly for mutant proteins (Tyr19Leu and Tyr19His). These results support a proposed role [Agarwal, A.; Li, D.; Cowan, J. A. Proc. Natl. Acad. Sci. U.S.A. 1995, 92, 9440-9444] for Tyr19 in maintaining hydrolytic stability of the [Fe(4)S(4)] cluster, and demonstrate a general strategy for mapping out the solvent accessibility of protein-bound metalloredox prosthetic centers.     

Conformational equilibrium in alanine-rich peptides probed by reversible stretching simulations

Reversible stretching of the alanine-rich peptide 3K (Proc. Natl. Acad. Sci. USA 1989, 86, 5286-5290) and its analogue MW (Nature 1992, 359, 653-655) is examined using molecular dynamics simulations in explicit water. In both cases, sampling of the extension pathway is obtained on the 10 ns time scale by applying an adaptive biasing force. The free energy profile reveals a single minimum associated with a contiguous alpha-helix. Short 3(10)-helical motifs are observed in folded as well as extended conformations, in accordance with their proposed role as folding intermediates. The native 3(10)-helical content of both peptides is found, however, to be no higher than a few percent. Difficulties in both the definition and the detection of secondary structure motifs, most notably in relation to bifurcated hydrogen bonds, are proposed to account for the discrepancy between 3(10)-helical propensities reported by several authors, based on experimental and computational results.     

Identification of [PtCl2(phen)] binding modes in amyloid-β peptide and the mechanism of aggregation inhibition

Platinum phenanthroline complexes inhibit amyloid-β (Aβ) aggregation and reduce Aβ-caused neurotoxicity [Proc. Natl. Acad. Sci., 2008, 105, 6813-6818]. In this study, we investigated the interactions of Aβ(1-16) with [PtCl(2)(phen)] (phen=1,10-phenanthroline) using HPLC, ESI-MS, and NMR spectroscopy , and characterized the identity of products using tandem mass spectrometry. Results indicated that the phenanthroline ligand could induce noncovalent interactions between Aβ peptide and platinum complexes, leading to rapid Aβ platination. Multiple products were generated in the reaction, in which His6/His14 chelation was preferentially formed. Coordination of Asp7, His13, and Lys16 was also detected in other products. The majority of products were monoplatinated adducts with binding of the {Pt(phen)} scaffold, which impeded intermolecular interactions between Aβ peptides. Moreover, noncovalent interactions were confirmed by the interaction between Aβ peptide and [Pt(phen)(2)]Cl(2). The synergistic roles of the phen ligand and platinum(II) atom in the inhibition of Aβ aggregation are discussed.