Dynamic and conformational switching in proteins.

Using bioinformatic methods for treating protein dynamics, developed in earlier work, we study the relationship between sequence mobility and dynamics in proteins. It is shown that sequence mobility drives a transition between two dynamic regimes in proteins, and that the specific details of this transition differ qualitatively between α-helical proteins and those in other structural classes. We examine the possibility that conformational switching is related to dynamic switching, by considering a specific system of sequences which exhibit the switching phenomenon. It is shown that a relationship between dynamic and conformational switching is entirely plausible.

Sequence-specific dynamic information in proteins.

We examine the local and global properties of the average B-factor, 〈B〉, as a residue-specific indicator of protein dynamic characteristics. It has been shown that values of 〈B〉 for the 20 amino acids differ in a statistically significant manner, and that, while strongly determined by the static physical properties of amino acids, they also encode averaged information about the influence of global fold on single-residue dynamics. Therefore, complete sequences of amino acids also encode fold-related global dynamic information, in addition to the local information that arises from static physical properties. We show that the relative magnitudes of these two contributions can be determined using Fourier methods, which represent the global properties of the sequences. It has also been shown that the behavior of Fourier components of 〈B〉 differs, with very high statistical significance, between structural groups, and that this information is not available from a comparable analysis of static amino acid properties.

Tracking the mechanism of fibril assembly by simulated two-dimensional ultraviolet spectroscopy.

Alzheimer's disease (AD) is a neurodegenerative disorder characterized by the accumulation of plaque deposits in the human brain. The main component of these plaques consists of highly ordered structures called amyloid fibrils, formed by the amyloid ß-peptide (Aß). The mechanism connecting Aß and AD is yet undetermined. In a previous study, a coarse-grained united-residue model and molecular dynamics simulations were used to model the growth mechanism of Aß amyloid fibrils. On the basis of these simulations, a dock/lock mechanism was proposed, in which Aß fibrils grow by adding monomers at either end of an amyloid fibril template. To examine the structures in the early time-scale formation and growth of amyloid fibrils, simulated two-dimensional ultraviolet spectroscopy is used. These early structures are monitored in the far ultraviolet regime (λ = 190-250 nm) in which the computed signals originate from the backbone nπ* and ππ* transitions. These signals show distinct cross-peak patterns that can be used, in combination with molecular dynamics, to monitor local dynamics and conformational changes in the secondary structure of Aß-peptides. The protein geometry-correlated chiral xxxy signal and the non-chiral combined signal xyxy-xyyx were found to be sensitive to, and in agreement with, a dock/lock pathway.

Global optimization of clusters, crystals, and biomolecules.

Finding the optimal solution to a complex optimization problem is of great importance in many fields, ranging from protein structure prediction to the design of microprocessor circuitry. Some recent progress in finding the global minima of potential energy functions is described, focusing on applications of the simple "basin-hopping" approach to atomic and molecular clusters and more complicated hypersurface deformation techniques for crystals and biomolecules. These methods have produced promising results and should enable larger and more complex systems to be treated in the future.

Designing potential energy functions for protein folding.

By following a consistent line of physical reasoning, some fundamental understanding about the foldability of proteins has been achieved. In recent years, this has led to the development of a number of successful algorithms for optimizing potential energy functions for folding protein models. The differences between the folding mechanisms of simple, contact-based lattice proteins and more traditional, realistic protein models, however, still call for further development of the potentials in addition to the optimization approaches.

Flexibility of bovine pancreatic trypsin inhibitor.

The native conformation of a protein may be expressed in terms of the dihedral angles, phi's and psi's for the backbone, and kappa's for the side chains, for a given geometry (bond lengths and bond angles). We have developed a method to obtain the dihedral angles for a low-energy structure of a protein, starting with the X-ray structure; it is applied here to examine the degree of flexibility of bovine pancreatic trypsin inhibitor. Minimization of the total energy of the inhibitor (including nonbonded, electrostatic, torsional, hydrogen bonding, and disulfide loop energies) yields a conformation having a total energy of -221 kcal/mol and a root mean square deviation between all atoms of the computed and experimental structures of 0.63 A. The optimal conformation is not unique, however, there being at least two other conformations of low-energy (-222 and -220 kcal/mol), which resemble the experimental one (root mean square deviations of 0.66 and 0.64 A, respectively). These three conformations are located in different positions in phi, psi space, i.e., with a total deviation of 81 degrees, 100 degrees and 55 degrees from each other (with a root mean square deviation of several degrees per dihedral angle from each other). The nonbonded energies of the backbones, calculated along lines in phi, psi space connecting these three conformations, are all negative, without any intervening energy barriers (on an energy contour map in the phi, psi plane). Side chains were attached at several representative positions in this plane, and the total energy was minimized by varying the kappa's. The energies were of approximately the same magnitude as the previous ones, indicating that the conformation of low energy is flexible to some extent in a restricted region of phi, psi space. Interestingly, the difference delta phi i+1 in phi i+1 for the (i + 1)th residue from one conformation to another is approximately the same as -delta psi i for the ith residue; i.e., the plane of the peptide group between the ith and (i + 1)th residues re-orient without significant changes in the positions of the other atoms. The flexibility of the orientations of the planes of the peptide groups is probably coupled in a cooperative manner to the flexibility of the positions of the backbone and side-chain atoms.

Contractility and conformation.

Contractility in fibers can arise from changes of macromolecular conformation caused by changes in some thermodynamic variable such as temperature, pH, or solvent composition. Illustrations are given of contractile processes in fibers and of changes in macromolecular conformation in dilute solution. These may involve order-disorder transitions, e.g. of the type exhibited by the helix-coil transition. A statistical mechanical treatment of the helix-coil transition involves the assignment of statistical weights to various states and the proper counting of these statistical weights in the formation and evaluation of the partition function; the thermodynamic properties of the system are derivable from the partition function. The counting procedure involved in the consideration of the alpha-helix and random coil is described. In addition, the factors affecting the relative stabilities of various helical conformations are discussed. These considerations of macromolecular conformation provide a basis for discussing contractile mechanisms in which changes of conformation are involved.

Lattice neural network minimization. Application of neural network optimization for locating the global-minimum conformations of proteins.

A way of formulating the protein-folding problem in neural network optimization terms is presented in this paper. This is accomplished by representing the conformation of a protein as an array of the amino acid sequence versus position on a three-dimensional face-centered cubic lattice with an energy function defined in terms of the array variables. The method is called lattice neural network minimization (LNNM). Using the neural network minimization method, the energy function is minimized to locate the global minimum energy for the conformation of the protein. The energy function consisted of site exclusion and bond connectivity penalty terms and a pairwise contact energy potential. The contact energy potential used in the procedure is the united-residue potential of Miyazawa, Jernigan and Covell. The LNNM method found the global minimum for a seven-residue peptide in all of the 15 runs carried out. The time for each run was approximately 30 seconds on one processor of an IBM 3090 computer. For a nine-residue peptide, the global minimum was found in 7 out of 15 runs (47%) in approximately 50 seconds per run. For this peptide, LNNM found the global minimum or the second lowest minimum in 10 of the runs. In the same total CPU times (approximately 750 seconds), a Monte Carlo simulated annealing method found the global minimum or the second lowest minimum in only two runs, demonstrating the superiority of LNNM over the standard Monte Carlo simulated annealing method for this nine-residue peptide. Starting from a uniform array for the protein crambin (46 residues) on the lattice, the energy of the crambin array was minimized and a compact low-energy structure was found in approximately 25 minutes of CPU time. Its energy was much lower than that of the native protein, suggesting that there are inadequacies in the Miyazawa-Jernigan-Covell potential. The LNNM method was applied to the prediction of what was previously called nucleation but more properly called chain-folding initiation sites (CFIS) of a protein. LNNM correctly predicted the CFIS for the two proteins examined, RNase S and T4 lysozyme. The LNNM method was also applied to another chain optimization problem, minimization of the root-mean-square distance error (r.m.s.d.) (a measure similar to r.m.s. deviation) in fitting X-ray structures to a lattice, with good results.

Molecular mechanisms for cooperative folding of proteins.

The folding of single-domain globular proteins exhibits the character of first-order or two-state thermodynamics. The origin of such high cooperativity in relatively small polymer systems is still not well understood. Recently, the statistical mechanics of protein folding has been studied extensively with simple protein models such as short cubic-lattice chains with contact-based interactions. While many valuable insights about protein folding were gained with such models, some concerns have also arisen, viz. that they lack the character of protein backbones whose interactions would limit the folding patterns of proteins. Here, a comparative study of the conventional cubic-lattice chain model and a fine-grained more realistic lattice protein model with both backbone and side-chain interactions is carried out. It is found that, even though both types of models exhibit a cooperative two-state folding transition to the native structure with optimized force fields, the character and origin of cooperativity of the two models are different. In the simple contact-based model, the free-energy barrier occurs at the low end of the energy scale, and the cooperativity arises from a concerted formation of native contacts among many residues in a compact state. In the other more complicated model, the free-energy barrier occurs in the intermediate energy region, and the folding cooperativity arises from collective orientational arrangements of locally structured units in semi-open conformational states. On the basis of these results, two limiting molecular mechanisms for protein folding emerge, which can be used for analyzing the folding process of real proteins.

An approach to the multiple-minima problem in protein folding by relaxing dimensionality. Tests on enkephalin.

An algorithm for locating the region in conformational space containing the global energy minimum of a polypeptide is described. Distances are used as the primary variables in the minimization of an objective function that incorporates both energetic and distance-geometric terms. The latter are obtained from geometry and energy functions, rather than nuclear magnetic resonance experiments, although the algorithm can incorporate distances from nuclear magnetic resonance data if desired. The polypeptide is generated originally in a space of high dimensionality. This has two important consequences. First, all interatomic distances are initially at their energetically most favorable values; i.e. the polypeptide is initially at a global minimum-energy conformation, albeit a high-dimensional one. Second, the relaxation of dimensionality constraints in the early stages of the minimization removes many potential energy barriers that exist in three dimensions, thereby allowing a means of escaping from three-dimensional local minima. These features are used in an algorithm that produces short trajectories of three-dimensional minimum-energy conformations. A conformation in the trajectory is generated by allowing the previous conformation in the trajectory to evolve in a high-dimensional space before returning to three dimensions. The resulting three-dimensional structure is taken to be the next conformation in the trajectory, and the process is iterated. This sequence of conformations results in a limited but efficient sampling of conformational space. Results for test calculations on Met-enkephalin, a pentapeptide with the amino acid sequence H-Tyr-Gly-Gly-Phe-Met-OH, are presented. A tight cluster of conformations (in three-dimensional space) is found with ECEPP energies (Empirical Conformational Energy Program for Peptides) lower than any previously reported. This cluster of conformations defines a region in conformational space in which the global-minimum-energy conformation of enkephalin appears to lie.

Calculations on crystal packing of a flexible molecule, Leu-enkephalin.

Crystal packing calculations have been carried out on a substantial number of conformations of Leu-enkephalin; namely, those obtained both from crystal structures and from energy minimizations on isolated molecules, and with and without waters of crystallization. The known crystal structures represent the most energetically stable packings found. The conformations of the enkephalin molecules in the crystal are not the most stable for an isolated molecule; i.e. intermolecular interactions force the isolated molecule to change conformation in order to achieve a small packing volume and an optimal packing energy in the crystal. It is found that the packing energy of an enkephalin molecule is a reasonably smooth function of its molecular volume in the unit cell, if structures with intermolecular hydrogen bonding are excluded, and is substantially independent of other details of the molecular conformation or of the crystal packing. Hydrogen bonding provides additional stabilization of the crystal structure, and would likely permit crystallization of the system if it is sufficiently dense. Solvent molecules further stabilize the structure when they can also provide intermolecular hydrogen bonds.

Catalysis of the oxidative folding of bovine pancreatic ribonuclease A by protein disulfide isomerase.

The major oxidative folding pathways of bovine pancreatic ribonuclease A at pH 8.0 and 25 degrees C involve a pre-equilibrium steady state among ensembles of intermediates with zero, one, two, three and four disulfide bonds. The rate-determining steps are the reshuffling of the unstructured three-disulfide ensemble to two native-like three-disulfide species, des-[65-72] and des-[40-95], that convert to the native structure during oxidative formation of the fourth disulfide bond. Under the same regeneration conditions, with oxidized and reduced DTT, used previously for kinetic oxidative-folding studies of this protein, the addition of 4 microM protein disulfide isomerase (PDI) was found to lead to catalysis of each disulfide-formation step, including the rate-limiting rearrangement steps in which the native-like intermediates des-[65-72] and des-[40-95] are formed. The changes in the distribution of intermediates were also determined in the presence and absence of PDI at three different temperatures (with the DTT redox system) as well as at 25 degrees C (with the glutathione redox system). The results indicate that the acceleration of the formation of native protein by PDI, which we observed earlier, is due to PDI catalysis of each of the intermediate steps without changing the overall pathways or folding mechanism.

Thrombin-bound structures of designed analogs of human fibrinopeptide A determined by quantitative transferred NOE spectroscopy: a new structural basis for thrombin specificity.

The mutation of Gly12 to Val12 in the A alpha chains of human fibrinogen Rouen is associated with a delayed proteolytic release of fibrinopeptide A (FpA or A alpha 1 to 16 of fibrinogen) by thrombin, leading to a bleeding disorder. Analogs of FpA and FpA Rouen have been designed that include a Pro15 to replace Val15 in natural FpA and to mimic the frequent occurrences of a proline residue at equivalent positions of other protein substrates of thrombin. The Pro15 analogs of FpA and FpA Rouen bind specifically to the active site of thrombin as shown by thrombin-induced differential line broadening and transferred nuclear Overhauser effects (transferred NOEs). Pro15 is well tolerated by the thrombin-bound structures of both FpA and FpA Rouen in solution, resulting in enhanced conformational stabilities of the thrombin-FpA complexes. The Val12 mutation in FpA Rouen causes backbone conformational changes in residues Val12 and Gly13 accompanied by an expansion of the hydrophobic cluster of FpA to accommodate the bulky side-chain of Val12. The single turn of helical structure between residues Asp7 and Glu11 is stabilized by hydrogen bonds from the side-chain carboxylate of Asp7 to the exposed backbone NH groups of Ala10 and/or Leu9 (N-capping), and by hydrogen bonds between the exposed backbone carbonyl groups of residues Phe8 and Leu9, and the backbone NH groups of Gly12/Val12 and Gly13 (C-capping). The bound structure of FpA Rouen may be further stabilized by a non-polar (i,i + 4) interaction between the aromatic side-chain of Phe8 and the aliphatic side-chain of Val12. Despite these optimized intrapeptide interactions, the thrombin-peptide interactions are highly dynamic as indicated by the fast rate of dissociation (koff > 100 s-1) of the peptide ligands from the thrombin complexes. Sequence comparison between mammalian fibrinopeptides A and B suggests that the specificity of thrombin is dictated by a four-residue consensus motif, Phe(P4)-Xxx(P3)-Pro(P2)-Arg(P1) or FXPR, when Xxx at P3 can be a charged or a neutral polar residue capable of specific interactions with residues near the active site of thrombin.

Role of interchain interactions in the stabilization of the right-handed twist of beta-sheets.

Conformational energy computations have been carried out for parallel and antiparallel beta-sheets composed of poly-L-Val and poly-L-Ile peptide chains, each consisting of four and of six residues, respectively, with CH3CO- and-NHCH3 end groups. The beta-sheets considered contained three and five equivalent chains, respectively. All computed minimum-energy beta-sheets were found to have a large right-handed twist of a magnitude that corresponds to the mean twist of beta-sheets observed in globular proteins. The twist has the same sign but is much larger than in beta-sheets of poly-L-Ala, because of intra- and interchain interactions between the bulky beta-branched side-chains. While the right-handed twist is a result of intrachain interactions between side-chains in the case of poly-L-Val, these interactions would favor a left-handed twist in poly-L-Ile, and the right-handed twist in the latter is a result of interchain interactions. Parallel beta-sheets are more stable than antiparallel sheets for both poly-L-Val and poly-L-Ile, in contrast to poly-L-Ala. This result agrees with observations on the preferred orientation of the chains in oligopeptides that form beta-structures. It also explains the observed high relative frequencies of occurrence of Val and Ile residues in parallel beta-sheets, as compared with antiparallel sheets, in globular proteins.

Structure of the type I collagen molecule based on conformational energy computations: the triple-stranded helix and the N-terminal telopeptide.

Various studies have implicated a crucial role for the non-helical ends (telopeptides) of the collagen molecule during fibrillogenesis. In this paper, the first extensive conformational analysis of the type I collagen N-terminal telopeptide is reported. The commonly used "build-up" procedure for peptides and proteins has been used, with relevant modifications to take account of all the stereochemical constraints affecting the telopeptide. In particular, consideration was given not only to the interactions among the three chains that constitute the telopeptide, but also to the interactions between the telopeptide and the covalently linked triple helix. The computations led to a limited number of different structures within an energy range of 25 kcal/mol. Comparison of these models clearly shows that the portion of the telopeptide linked to the triple helix is rather rigid whereas its N terminus is more flexible. Furthermore, the lowest-energy structure has an energy that is markedly lower (by 7.75 kcal/mol) than that of other conformations with different structural features. The lowest-energy model of the N-terminal telopeptide, which differs from previous proposed models, has a contracted conformation compared to the triple helix region, in agreement with X-ray and neutron diffraction data on collagen fibers. Finally, the side-chains of the lysine residues of the telopeptide, involved in intermolecular cross-links in mature collagen fibers, are oriented to protrude to the exterior, in positions to interact with adjacent collagen molecules.

Energy of stabilization of the right-handed beta alpha beta crossover in proteins.

An explanation in terms of conformational energies is provided for the observed nearly exclusive preference of the beta alpha beta structure for forming a right-handed, rather than a left-handed, crossover connection. Conformational energy computations have been carried out on a model beta alpha beta structure, consisting of two six-residue Val beta-strands and of a 12-residue Ala alpha-helix, connected by two flexible four-residue Ala links to the strands. The energy of the most favorable right-handed crossover is 15.51 kcal/mol lower than that of the corresponding left-handed cross-over. The right-handed crossover is a strain-free structure. Its energy of stabilization arises largely from the interactions of the two beta-strands with one another and with the alpha-helix. On the other hand, the left-handed crossover is either disrupted after energy minimization or it remains conformationally strained, as indicated by an energetically unfavorable left twisting of the beta-sheet and by the presence of high-energy local residue conformations. In the energetically most favorable right-handed crossover, the right twisting of the beta-sheet and its manner of interacting with the alpha-helix are identical with those computed earlier for isolated beta-sheets and for packed alpha/beta structures. This result supports a proposed principle that it is possible to account for the main features of frequently occurring structural arrangements in globular proteins in terms of the properties of their component structural elements.

On the pH-conformational dependence of the unblocked SYPYD peptide.

Simulations were carried out for an unblocked pentapeptide with the sequence Ser-Tyr-Pro-Tyr-Asp (SYPYD) with explicit consideration of the coupling between the conformation of the molecule and the ionization equilibria at a given pH. The available NMR experimental data indicate a high preference for the cis isomeric turn-like form of Tyr-Pro at intermediate pH (approximately 6) and a destabilization of the cis form at both high (approximately 9) and low (approximately 3) pH. In order to identify the source of the stability of the conformation of this pentapeptide as a function of pH, Monte Carlo simulations were used to generate an ensemble of low-energy conformations at different pH values (viz. 3, 6 and 9). The total free energy function used in these calculations includes terms that account for the solvation free energy and free energy of ionization. These terms are evaluated by means of a fast multigrid boundary element (MBE) method. In good qualitative agreement with the experiments, our results indicate that the Boltzmann averaged population of the cis isomeric form of the pentapeptide has a maximum (45 %) at pH 6 and is significantly smaller (25 % and 23 %) for higher and lower pH values, respectively, following the trend of the experimental data. Also, the degree of charge for the lowest-energy conformations, as well as the contribution of electrostatic interactions to the stability of the preferred conformations, vary widely at the different pH values. Different kinds of packing of the aromatic side-chains of Tyr2 and Tyr4 against the proline ring are observed at different pH values, indicating that their contribution to the stability of the low-energy conformations is also pH-dependent. In summary, our results provide a basis for discussing the nature of the interactions that stabilize turn-like conformations of the peptide SYPYD as a function of pH.

Interactions between two beta-sheets. Energetics of beta/beta packing in proteins.

The analysis of the interactions between regularly folded segments of the polypeptide chain contributes to an understanding of the energetics of protein folding. Conformational energy-minimization calculations have been carried out to determine the favorable ways of packing two right-twisted beta-sheets. The packing of two five-stranded beta-sheets was investigated, with the strands having the composition CH3CO-(L-Ile)6-NHCH3 in one beta-sheet and CH3CO-(L-Val)6-NHCH3 in the other. Two distinct classes of low-energy packing arrangements were found. In the class with lowest energies, the strands of the two beta-sheets are aligned nearly parallel (or antiparallel) with each other, with a preference for a negative orientation angle, because this arrangement corresponds to the best complementary packing of the two twisted saddle-shaped beta-sheets. In the second class, with higher interaction energies, the strands of the two beta-sheets are oriented nearly perpendicular to each other. While the surfaces of the two beta-sheets are not complementary in this arrangement, there is good packing between the corner of one beta-sheet and the interior part of the surface of the other, resulting in a favorable energy of packing. Both classes correspond to frequently observed orientations of beta-sheets in proteins. In proteins, the second class of packing is usually observed when the two beta-sheets are covalently linked, i.e. when a polypeptide strand passes from one beta-sheet to the other, but we have shown here that a large contribution to the stabilization of this packing arrangement arises from noncovalent interactions.

Coupling between folding and ionization equilibria: effects of pH on the conformational preferences of polypeptides.

A new approach to the conformational study of polypeptides is presented. It considers explicitly the coupling between the conformation of the molecule and the ionization equilibria at a given pH value. Calculations of the solvation free energy and free energy of ionization of a 17-residue polypeptide are carried out using a fast multigrid boundary element method (MBE). The MBE method uses an adaptive tessellation of the molecular surface by boundary elements with non-regular size to solve the Poisson equation rapidly, and with a high degree of accuracy. The MBE method is integrated into the ECEPP (Empirical Conformational Energy Program for Peptides) algorithm to compute the coupling between the ionization state and the conformation of the molecule. This approach has been applied to study the conformational preference of a short polypeptide for which the available NMR and CD experimental data indicate that conformations containing a right-handed alpha-helical segment are energetically more favorable at low values of pH. The results of calculations using the present method agree quite well with experiments, in contrast to previous applications with standard techniques (using pre-assigned charges at each pH) that were not able to reproduce the experimental findings. Also, it is shown how the coupling to the conformation leads to different degrees of ionization of a given type of residue, for example glutamic acid, at different positions in the amino acid sequence, at any given pH. The results of this study provide a sound basis to discuss the origin of the stability of polypeptide conformations, and its dependence on the environmental conditions.

Computer-aided discrimination between active and inactive mutants of the N-terminal domain of the bacteriophage lambda repressor.

Binding of the N-terminal domain of the lambda repressor to DNA is coupled to dimerization. Hydrophobic interactions between helix-5 and helix-5' drive the packing at the dimer interface. We have carried out computations of the conformational energy of packing of the fifth helices (and of the helix-4-loop-helix-5 portions) of variants of the lambda repressor operator binding domain, using an ECEPP/3-based packing algorithm. Here, we report the results for 26 mutants chosen among those that hve been characterized experimentally. We find that the relative orientation of the fifth helices for active mutants is very similar to the wild-type. The fifth helices of the inactive mutants have a significantly different relative orientation. This result illustrates that a unique specific orientation pattern of helix-5 relative to helix-5' is required for dimerization-coupled DNA binding activity. This finding is further supported by computational studies of the whole N-terminal domain of ten variants that showed that the active mutants, including the wild-type protein, have similar values of the number of contacts between the two monomers in the dimer, involving two amino acid residues of the fifth helices (positions 84 and 87 in each monomer). A decrease in the number of such contacts abolishes DNA-binding activity. Furthermore, all active mutants have their "DNA-recognition helices", numbers 3 and 3' positioned so that they can fit in the DNA operator like those of the wild-type protein, while some inactive mutants exhibit a substantial change in the relative orientation of their recognition helices.