Exploring the folding free energy surface of a three-helix bundle protein

The multidimensional free energy surface for a small fast folding helical protein is explored based on first-principle calculations. The model represents the 46-residue segment from fragment B of staphylococcal protein A. The relationship between collapse and tertiary structure formation, and the order of collapse and secondary structure formation, are investigated. We find that the initial collapse process gives rise to a transition state with about 30% of the native tertiary structure and 50–70% of the native helix content. We also observe two distinct distributions of native helix in this collapsed state (Rg ≈ 12 Å), one with about 20% of the native helical hydrogen bonds, the other with near 70%. The former corresponds to a local minimum. The barrier from this metastable state to the native state is about 2 kBT. In the latter case, folding is essentially a downhill process involving topological assembly. In addition, the order of formation of secondary structure among the three helices is examined. We observe cooperative formation of the secondary structure in helix I and helix II. Secondary structure in helix III starts to form following the formation of certain secondary structure in both helix I and helix II. Comparisons of our results with those from theory and experiment are made.

Recent improvements in prediction of protein structure by global optimization of a potential energy function

Recent improvements of a hierarchical ab initio or de novo approach for predicting both α and β structures of proteins are described. The united-residue energy function used in this procedure includes multibody interactions from a cumulant expansion of the free energy of polypeptide chains, with their relative weights determined by Z-score optimization. The critical initial stage of the hierarchical procedure involves a search of conformational space by the conformational space annealing (CSA) method, followed by optimization of an all-atom model. The procedure was assessed in a recent blind test of protein structure prediction (CASP4). The resulting lowest-energy structures of the target proteins (ranging in size from 70 to 244 residues) agreed with the experimental structures in many respects. The entire experimental structure of a cyclic α-helical protein of 70 residues was predicted to within 4.3 Å α-carbon (Cα) rms deviation (rmsd) whereas, for other α-helical proteins, fragments of roughly 60 residues were predicted to within 6.0 Å Cα rmsd. Whereas β structures can now be predicted with the new procedure, the success rate for α/β- and β-proteins is lower than that for α-proteins at present. For the β portions of α/β structures, the Cα rmsd's are less than 6.0 Å for contiguous fragments of 30–40 residues; for one target, three fragments (of length 10, 23, and 28 residues, respectively) formed a compact part of the tertiary structure with a Cα rmsd less than 6.0 Å. Overall, these results constitute an important step toward the ab initio prediction of protein structure solely from the amino acid sequence.

Top-down free-energy minimization on protein potential energy landscapes

The hierarchical properties of potential energy landscapes have been used to gain insight into thermodynamic and kinetic properties of protein ensembles. It also may be possible to use them to direct computational searches for thermodynamically stable macroscopic states, i.e., computational protein folding. To this end, we have developed a top-down search procedure in which conformation space is recursively dissected according to the intrinsic hierarchical structure of a landscape's effective-energy barriers. This procedure generates an inverted tree similar to the disconnectivity graphs generated by local minima-clustering methods, but it fundamentally differs in the manner in which the portion of the tree that is to be computationally explored is selected. A key ingredient is a branch-selection algorithm that takes advantage of statistically predictive properties of the landscape to guide searches down the tree branches that are most likely to lead to the physically relevant macroscopic states. Using the computational folding of a β-hairpin-forming peptide as an example, we show that such predictive properties indeed exist and can be used for structure prediction by free-energy global minimization.

From residue matching patterns to protein folding topographies: General model and bovine pancreatic trypsin inhibitor

A coarse-grained model for protein-folding dynamics is introduced based on a discretized representation of torsional modes. The model, based on the Ramachandran map of the local torsional potential surface and the class (hydrophobic/polar/neutral) of each residue, recognizes patterns of both torsional conformations and hydrophobic-polar contacts, with tolerance for imperfect patterns. It incorporates empirical rates for formation of secondary and tertiary structure. The method yields a topological representation of the evolving local torsional configuration of the folding protein, modulo the basins of the Ramachandran map. The folding process is modeled as a sequence of transitions from one contact pattern to another, as the torsional patterns evolve. We test the model by applying it to the folding process of bovine pancreatic trypsin inhibitor, obtaining a kinetic description of the transitions between the contact patterns visited by the protein along the dominant folding pathway. The kinetics and detailed balance make it possible to invert the result to obtain a coarse topographic description of the potential energy surface along the dominant folding pathway, in effect to go backward or forward between a topological representation of the chain conformation and a topographical description of the potential energy surface governing the folding process. As a result, the strong structure-seeking character of bovine pancreatic trypsin inhibitor and the principal features of its folding pathway are reproduced in a reasonably quantitative way.

The photoisomerization of retinal in bacteriorhodopsin: Experimental evidence for a three-state model

The primary events in the all-trans to 13-cis photoisomerization of retinal in bacteriorhodopsin have been investigated with femtosecond time-resolved absorbance spectroscopy. Spectra measured over a broad range extending from 7000 to 22,400 cm−1 reveal features whose dynamics are inconsistent with a model proposed earlier to account for the highly efficient photoisomerization process. Emerging from this work is a new three-state model. Photoexcitation of retinal with visible light accesses a shallow well on the excited state potential energy surface. This well is bounded by a small barrier, arising from an avoided crossing that separates the Franck–Condon region from the nearby reactive region of the photoisomerization coordinate. At ambient temperatures, the reactive region is accessed with a time constant of ≈500 fs, whereupon the retinal rapidly twists and encounters a second avoided crossing region. The protein mediates the passage into the second avoided crossing region and thereby exerts control over the quantum yield for forming 13-cis retinal. The driving force for photoisomerization resides in the retinal, not in the surrounding protein. This view contrasts with an earlier model where photoexcitation was thought to access directly a reactive region of the excited-state potential and thereby drive the retinal to a twisted conformation within 100–200 fs.

Structure-based conformational preferences of amino acids

Proteins can be very tolerant to amino acid substitution, even within their core. Understanding the factors responsible for this behavior is of critical importance for protein engineering and design. Mutations in proteins have been quantified in terms of the changes in stability they induce. For example, guest residues in specific secondary structures have been used as probes of conformational preferences of amino acids, yielding propensity scales. Predicting these amino acid propensities would be a good test of any new potential energy functions used to mimic protein stability. We have recently developed a protein design procedure that optimizes whole sequences for a given target conformation based on the knowledge of the template backbone and on a semiempirical potential energy function. This energy function is purely physical, including steric interactions based on a Lennard-Jones potential, electrostatics based on a Coulomb potential, and hydrophobicity in the form of an environment free energy based on accessible surface area and interatomic contact areas. Sequences designed by this procedure for 10 different proteins were analyzed to extract conformational preferences for amino acids. The resulting structure-based propensity scales show significant agreements with experimental propensity scale values, both for α-helices and β-sheets. These results indicate that amino acid conformational preferences are a natural consequence of the potential energy we use. This confirms the accuracy of our potential and indicates that such preferences should not be added as a design criterion.

Peptide interfacial adsorption is kinetically limited by the thermodynamic stability of self association

We present a study of the adsorption of two peptides at the octane–water interface. The first peptide, Lac21, exists in mixed monomer–tetramer equilibrium in bulk solution with an appreciable monomer concentration. The second peptide, Lac28, exists as a tetramer in solution, with minimal exposed hydrophobic surface. A kinetic limitation to interfacial adsorption exists for Lac28 at moderate to high surface coverage that is not observed for Lac21. We estimate the potential energy barrier for Lac28 adsorption to be 42 kJ/mol and show that this is comparable to the expected free energy barrier for tetramer dissociation. This finding suggests that, at moderate to high surface coverage, adsorption is kinetically limited by the availability of interfacially active monomeric “domains” in the subinterfacial region. We also show how the commonly used empirical equation for protein adsorption dynamics can be used to estimate the potential energy barrier for adsorption. Such an approach is shown to be consistent with a formal description of diffusion–adsorption, provided a large potential energy barrier exists. This work demonstrates that the dynamics of interfacial adsorption depend on protein thermodynamic stability, and hence structure, in a quantifiable way.

Evolution of the folding ability of proteins through functional selection

An evolutionary process is simulated with a simple spin-glass-like model of proteins to examine the origin of folding ability. At each generation, sequences are randomly mutated and subjected to a simulation of the folding process based on the model. According to the frequency of local configurations at the active sites, sequences are selected and passed to the next generation. After a few hundred generations, a sequence capable of folding globally into a native conformation emerges. Moreover, the selected sequence has a distinct energy minimum and an anisotropic funnel on the energy surface, which are the imperative features for fast folding of proteins. The proposed model reveals that the functional selection on the local configurations leads a sequence to fold globally into a conformation at a faster rate.

Pressure-induced protein-folding/unfolding kinetics

We use an off-lattice minimalist model to describe the effects of pressure in slowing down the folding/unfolding kinetics of proteins when subjected to increasingly larger pressures. The potential energy function used to describe the interactions between beads in the model includes the effects of pressure on the pairwise interaction of hydrophobic groups in water. We show that pressure affects the participation of contacts in the transition state. More significantly, pressure exponentially decreases the chain reconfigurational diffusion coefficient. These results are consistent with experimental results on the kinetics of pressure-denaturation of staphylococcal nuclease.

Folding thermodynamics of a model three-helix-bundle protein

The calculated folding thermodynamics of a simple off-lattice three-helix-bundle protein model under equilibrium conditions shows the experimentally observed protein transitions: a collapse transition, a disordered-to-ordered globule transition, a globule to native-state transition, and the transition from the active native state to a frozen inactive state. The cooperativity and physical origin of the various transitions are explored with a single “optimization” parameter and characterized with the Lindemann criterion for liquid versus solid-state dynamics. Below the folding temperature, the model has a simple free energy surface with a single basin near the native state; the surface is similar to that calculated from a simulation of the same three-helix-bundle protein with an all-atom representation [Boczko, E. M. & Brooks III, C. L. (1995) Science 269, 393–396].

Nascent Polypeptide–associated Complex Stimulates Protein Import into Yeast Mitochondria

To identify yeast cytosolic proteins that mediate targeting of precursor proteins to mitochondria, we developed an in vitro import system consisting of purified yeast mitochondria and a radiolabeled mitochondrial precursor protein whose C terminus was still attached to the ribosome. In this system, the N terminus of the nascent chain was translocated across both mitochondrial membranes, generating a translocation intermediate spanning both membranes. The nascent chain could then be completely chased into the mitochondrial matrix after release from the ribosome. Generation of this import intermediate was dependent on a mitochondrial membrane potential, mitochondrial surface proteins, and was stimulated by proteins that could be released from the ribosomes by high salt. The major salt-released stimulatory factor was yeast nascent polypeptide–associated complex (NAC). Purified NAC fully restored import of salt-washed ribosome-bound nascent chains by enhancing productive binding of the chains to mitochondria. We propose that ribosome-associated NAC facilitates recognition of nascent precursor chains by the mitochondrial import machinery.

Folding simulations of a three-stranded antiparallel β-sheet peptide

Protein folding is a grand challenge of the postgenomic era. In this paper, 58 folding events sampled during 47 molecular dynamics trajectories for a total simulation time of more than 4 μs provide an atomic detail picture of the folding of a 20-residue synthetic peptide with a stable three-stranded antiparallel β-sheet fold. The simulations successfully reproduce the NMR solution conformation, irrespective of the starting structure. The sampling of the conformational space is sufficient to determine the free energy surface and localize the minima and transition states. The statistically predominant folding pathway involves the formation of contacts between strands 2 and 3, starting with the side chains close to the turn, followed by association of the N-terminal strand onto the preformed 2–3 β-hairpin. The folding mechanism presented here, formation of a β-hairpin followed by consolidation, is in agreement with a computational study of the free energy surface of another synthetic three-stranded antiparallel β-sheet by Bursulaya and Brooks [(1999) J. Am. Chem. Soc. 121, 9947–9951]. Hence, it might hold in general for antiparallel β-sheets with short turns.

Protein fluctuations are sensed by stimulated infrared echoes of the vibrations of carbon monoxide and azide probes

The correlation functions of the fluctuations of vibrational frequencies of azide ions and carbon monoxide in proteins are determined directly from stimulated photon echoes generated with femtosecond infrared pulses. The asymmetric stretching vibration of azide bound to carbonic anhydrase II exhibits a pronounced evolution of its vibrational frequency distribution on the time scale of a few picoseconds, which is attributed to modifications of the ligand structure through interactions with the nearby Thr-199. When azide is bound in hemoglobin, a more complex evolution of the protein structure is required to interchange the different ligand configurations, as evidenced by the much slower relaxation of the frequency distribution in this case. The time evolution of the distribution of frequencies of carbon monoxide bound in hemoglobin occurs on the ≈10-ps time scale and is very nonexponential. The correlation functions of the frequency fluctuations determine the evolution of the protein structure local to the probe and the extent to which the probe can navigate those parts of the energy landscape where the structural configurations are able to modify the local potential energy function of the probe.

Non-Arrhenius kinetics for the loop closure of a DNA hairpin

Intramolecular chain diffusion is an elementary process in the conformational fluctuations of the DNA hairpin-loop. We have studied the temperature and viscosity dependence of a model DNA hairpin-loop by FRET (fluorescence resonance energy transfer) fluctuation spectroscopy (FRETfs). Apparent thermodynamic parameters were obtained by analyzing the correlation amplitude through a two-state model and are consistent with steady-state fluorescence measurements. The kinetics of closing the loop show non-Arrhenius behavior, in agreement with theoretical prediction and other experimental measurements on peptide folding. The fluctuation rates show a fractional power dependence (β = 0.83) on the solution viscosity. A much slower intrachain diffusion coefficient in comparison to that of polypeptides was derived based on the first passage time theory of SSS [Szabo, A., Schulten, K. & Schulten, Z. (1980) J. Chem. Phys. 72, 4350–4357], suggesting that intrachain interactions, especially stacking interaction in the loop, might increase the roughness of the free energy surface of the DNA hairpin-loop.

Femtochemistry

The topic of femtochemistry is surveyed from both theoretical and experimental points of view. A time-dependent wave packet description of the photodissociation of the O—C—S molecule reveals vibrational motion in the transition-state region and suggests targets for direct experimental observation. Theoretical approaches for treating femtosecond chemical phenomena in condensed phases are featured along with prospects for laser-controlled chemical reactions by using tailored ultrashort chirped pulses. An experimental study of the photoisomerization of retinal in the protein bacteriorhodopsin is discussed with an aim to gain insight into the potential energy surfaces on which this remarkably efficient and selective reactions proceeds. Finally, a prospective view of new frontiers in femtochemistry is given.