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.

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.

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.

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.

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.

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.

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.

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.

Single-pair fluorescence resonance energy transfer on freely diffusing molecules: Observation of Förster distance dependence and subpopulations

Photon bursts from single diffusing donor-acceptor labeled macromolecules were used to measure intramolecular distances and identify subpopulations of freely diffusing macromolecules in a heterogeneous ensemble. By using DNA as a rigid spacer, a series of constructs with varying intramolecular donor-acceptor spacings were used to measure the mean and distribution width of fluorescence resonance energy transfer (FRET) efficiencies as a function of distance. The mean single-pair FRET efficiencies qualitatively follow the distance dependence predicted by Förster theory. Possible contributions to the widths of the FRET efficiency distributions are discussed, and potential applications in the study of biopolymer conformational dynamics are suggested. The ability to measure intramolecular (and intermolecular) distances for single molecules implies the ability to distinguish and monitor subpopulations of molecules in a mixture with different distances or conformational states. This is demonstrated by monitoring substrate and product subpopulations before and after a restriction endonuclease cleavage reaction. Distance measurements at single-molecule resolution also should facilitate the study of complex reactions such as biopolymer folding. To this end, the denaturation of a DNA hairpin was examined by using single-pair FRET.

Factors controlling the competition among rotational and vibrational energy transfer channels in glyoxal

The state-to-state transfer of rotational and vibrational energy has been studied for S1 glyoxal (CHOCHO) in collisions with D2, N2, CO and C2H4 using crossed molecular beams. A laser is used to pump glyoxal seeded in He to its S1 zero point level with zero angular momentum about its top axis (K′ = 0). The inelastic scattering to each of at least 26 S1 glyoxal rotational and rovibrational levels is monitored by dispersed S1–S0 fluorescence. Various collision partners are chosen to investigate the relative influences of reduced mass and the collision pair interaction potential on the competition among the energy transfer channels. When the data are combined with that obtained previously from other collision partners whose masses range from 2 to 84 amu, it is seen that the channel competition is controlled primarily by the kinematics of the collisional interaction. Variations in the intermolecular potential play strictly a secondary role.

Linking topography of its potential surface with the dynamics of folding of a protein model

The “3-color, 46-bead” model of a folding polypeptide is the vehicle for adapting to proteins a mode of analysis used heretofore for atomic clusters, to relate the topography of the potential surface to the dynamics that lead to formation of selected structures. The analysis is based on sequences of stationary points—successive minima, joined by saddles—that rise monotonically in energy from basin bottoms. Like structure-seeking clusters, the potential surface of the model studied here is staircase-like, rather than sawtooth-like, with highly collective motions required for passage from one minimum to the next. The surface has several deep basins whose minima correspond to very similar structures, but which are separated by high energy barriers.

Acute decrease in net glutamate uptake during energy deprivation

The extracellular glutamate concentration ([glu]o) rises during cerebral ischemia, reaching levels capable of inducing delayed neuronal death. The mechanisms underlying this glutamate accumulation remain controversial. We used N-methyl-d-aspartate receptors on CA3 pyramidal neurons as a real-time, on-site, glutamate sensor to identify the source of glutamate release in an in vitro model of ischemia. Using glutamate and l-trans-pyrrolidine-2,4-dicarboxylic acid (tPDC) as substrates and dl-threo-β-benzyloxyaspartate (TBOA) as an inhibitor of glutamate transporters, we demonstrate that energy deprivation decreases net glutamate uptake within 2–3 min and later promotes reverse glutamate transport. This process accounts for up to 50% of the glutamate accumulation during energy deprivation. Enhanced action potential-independent vesicular release also contributes to the increase in [glu]o, by ≈50%, but only once glutamate uptake is inhibited. These results indicate that a significant rise in [glu]o already occurs during the first minutes of energy deprivation and is the consequence of reduced uptake and increased vesicular and nonvesicular release of glutamate.

Energy-based de novo protein folding by conformational space annealing and an off-lattice united-residue force field: Application to the 10-55 fragment of staphylococcal protein A and to apo calbindin D9K

The conformational space annealing (CSA) method for global optimization has been applied to the 10-55 fragment of the B-domain of staphylococcal protein A (protein A) and to a 75-residue protein, apo calbindin D9K (PDB ID code 1CLB), by using the UNRES off-lattice united-residue force field. Although the potential was not calibrated with these two proteins, the native-like structures were found among the low-energy conformations, without the use of threading or secondary-structure predictions. This is because the CSA method can find many distinct families of low-energy conformations. Starting from random conformations, the CSA method found that there are two families of low-energy conformations for each of the two proteins, the native-like fold and its mirror image. The CSA method converged to the same low-energy folds in all cases studied, as opposed to other optimization methods. It appears that the CSA method with the UNRES force field, which is based on the thermodynamic hypothesis, can be used in prediction of protein structures in real time.

Relationship between the oxidation potential and electron spin density of the primary electron donor in reaction centers from Rhodobacter sphaeroides

The primary electron donor in bacterial reaction centers is a dimer of bacteriochlorophyll a molecules, labeled L or M based on their proximity to the symmetry-related protein subunits. The electronic structure of the bacteriochlorophyll dimer was probed by introducing small systematic variations in the bacteriochlorophyll–protein interactions by a series of site-directed mutations that replaced residue Leu M160 with histidine, tyrosine, glutamic acid, glutamine, aspartic acid, asparagine, lysine, and serine. The midpoint potentials for oxidation of the dimer in the mutants showed an almost continuous increase up to ≈60 mV compared with wild type. The spin density distribution of the unpaired electron in the cation radical state of the dimer was determined by electron–nuclear–nuclear triple resonance spectroscopy in solution. The ratio of the spin density on the L side of the dimer to the M side varied from ≈2:1 to ≈5:1 in the mutants compared with ≈2:1 for wild type. The correlation between the midpoint potential and spin density distribution was described using a simple molecular orbital model, in which the major effect of the mutations is assumed to be a change in the energy of the M half of the dimer, providing estimates for the coupling and energy levels of the orbitals in the dimer. These results demonstrate that the midpoint potential can be fine-tuned by electrostatic interactions with amino acids near the dimer and show that the properties of the electronic structure of a donor or acceptor in a protein complex can be directly related to functional properties such as the oxidation–reduction midpoint potential.