Robert L. Jernigan

Structure-derived potentials and protein simulations

There has recently been an explosion in the number of structure-derived potential functions that are based on the increasing number of high-resolution protein crystal structures. These functions differ principally in their reference states; the usual two classes correspond either to initial solvent exposure or to residue exposure of residues. Reference states are critically important for applications of these potentials functions. Inspection of the potential functions and their derivation can tell us not only about protein interaction strengths themselves, but can also provide suggestions for the design of better folding simulations. An appropriate goal in this field is achieving self-consistency between the details in the derivation of potentials and the applied simulations.

Dynamics of large proteins through hierarchical levels of coarse-grained structures

Elastic network models have been successful in elucidating the largest scale collective motions of proteins. These models are based on a set of highly coupled springs, where only the close neighboring amino acids interact, without any residue specificity. Our objective here is to determine whether the equivalent cooperative motions can be obtained upon further coarse‐graining of the protein structure along the backbone. The influenza virus hemagglutinin A (HA), composed of N=1509 residues, is utilized for this analysis. Elastic network model calculations are performed for coarse‐grained HA structures containing only N/2, N/10, N/20, and N/40 residues along the backbone. High correlations (>0.95) between residue fluctuations are obtained for the first dominant (slowest) mode of motion between the original model and the coarse‐grained models. In the case of coarse‐graining by a factor of 1/40, the slowest mode shape for HA is reconstructed for all residues by successively selecting different subsets of residues, shifting one residue at a time. The correlation for this reconstructed first mode shape with the original all‐residue case is 0.73, while the computational time is reduced by about three orders of magnitude. The reduction in computational time will be much more significant for larger targeted structures. Thus, the dominant motions of protein structures are robust enough to be captured at extremely high levels of coarse‐graining. And more importantly, the dynamics of extremely large complexes are now accessible with this new methodology.

Proteins with Similar Architecture Exhibit Similar Large-Scale Dynamic Behavior

We have investigated the similarities and differences in the computed dynamic fluctuations exhibited by six members of a protein fold family with a coarse-grained Gaussian network model. Specifically, we consider the cofactor binding fragment of CysB; the lysine/arginine/ornithine-binding protein (LAO); the enzyme porphobilinogen deaminase (PBGD); the ribose-binding protein (RBP); the N-terminal lobe of ovotransferrin in apo-form (apo-OVOT); and the leucine/isoleucine/valine-binding protein (LIVBP). All have domains that resemble a Rossmann fold, but there are also some significant differences. Results indicate that similar global dynamic behavior is preserved for the members of a fold family, and that differences usually occur in regions only where specific function is localized. The present work is a computational demonstration that the scaffold of a protein fold may be utilized for diverse purposes. LAO requires a bound ligand before it conforms to the large-scale fluctuation behavior of the three other members of the family, CysB, PBGD, and RBP, all of which contain a substrate (cofactor) at the active site cleft. The dynamics of the ligand-free enzymes LIVBP and apo-OVOT, on the other hand, concur with that of unliganded LAO. The present results suggest that it is possible to construct structure alignments based on dynamic fluctuation behavior.

Self-consistent estimation of inter-residue protein contact energies based on an equilibrium mixture approximation of residues

Pairwise contact energies for 20 types of residues are estimated self‐consistently from the actual observed frequencies of contacts with regression coefficients that are obtained by comparing “input” and predicted values with the Bethe approximation for the equilibrium mixtures of residues interacting. This is premised on the fact that correlations between the “input” and the predicted values are sufficiently high although the regression coefficients themselves can depend to some extent on protein structures as well as interaction strengths. Residue coordination numbers are optimized to obtain the best correlation between “input” and predicted values for the partition energies. The contact energies self‐consistently estimated this way indicate that the partition energies predicted with the Bethe approximation should be reduced by a factor of about 0.3 and the intrinsic pairwise energies by a factor of about 0.6. The observed distribution of contacts can be approximated with a small relative error of only about 0.08 as an equilibrium mixture of residues, if many proteins were employed to collect more than 20,000 contacts. Including repulsive packing interactions and secondary structure interactions further reduces the relative errors. These new contact energies are demonstrated by threading to have improved their ability to discriminate native structures from other non‐native folds. Proteins 1999;34:49–68.

Understanding the recognition of protein structural classes by amino acid composition

Knowledge of amino acid composition, alone, is verified here to be sufficient for recognizing the structural class, α, β, α+β, or α/β of a given protein with an accuracy of 81%. This is supported by results from exhaustive enumerations of all conformations for all sequences of simple, compact lattice models consisting of two types (hydrophobic and polar) of residues. Different compositions exhibit strong affinities for certain folds. Within the limits of validity of the lattice models, two factors appear to determine the choice of particular folds: 1) the coordination numbers of individual sites and 2) the size and geometry of non‐bonded clusters. These two properties, collectively termed the distribution of non‐bonded contacts, are quantitatively assessed by an eigenvalue analysis of the so‐called Kirchhoff or adjacency matrices obtained by considering the non‐bonded interactions on a lattice. The analysis permits the identification of conformations that possess the same distribution of non‐bonded contacts. Furthermore, some distributions of non‐bonded contacts are favored entropically, due to their high degeneracies. Thus, a competition between enthalpic and entropic effects is effective in determining the choice of a distribution for a given composition. Based on these findings, an analysis of non‐bonded contacts in protein structures was made. The analysis shows that proteins belonging to the four distinct folding classes exhibit significant differences in their distributions of non‐bonded contacts, which more directly explains the success in predicting structural class from amino acid composition. Proteins 29:172–185, 1997. Published 1997 Wiley‐Liss, Inc. This article is a US Goverment work and, as such, is in the public domain in the United States of America.

Relating molecular flexibility to function: a case study of tubulin.

Microtubules (MT), along with a variety of associated motor proteins, are involved in a range of cellular functions including vesicle movement, chromosome segregation, and cell motility. MTs are assemblies of heterodimeric proteins, alpha beta-tubulins, the structure of which has been determined by electron crystallography of zinc-induced, pacilitaxel-stabilized tubulin sheets. These data provide a basis for examining relationships between structural features and protein function. Here, we study the fluctuation dynamics of the tubulin dimer with the aim of elucidating its functional motions relevant to substrate binding, polymerization/depolymerization and MT assembly. A coarse-grained model, harmonically constrained according to the crystal structure, is used to explore the global dynamics of the dimer. Our results identify six regions of collective motion, comprised of structurally close but discontinuous sequence fragments, observed only in the dimeric form, dimerization being a prerequisite for domain identification. Boundaries between regions of collective motions appear to act as linkages, found primarily within secondary-structure elements that lack sequence conservation, but are located at minima in the fluctuation curve, at positions of hydrophobic residues. Residue fluctuations within these domains identify the most mobile regions as loops involved in recognition of the adjacent regions. The least mobile regions are associated with nucleotide binding sites where lethal mutations occur. The functional coupling of motions between and within regions identifies three global motions: torsional and wobbling movements, en bloc, between the alpha- and beta-tubulin monomers, and stretching longitudinally. Further analysis finds the antitumor drug pacilitaxel (TaxotereR) to reduce flexibility in the M loop of the beta-tubulin monomer; an effect that may contribute to tightening lateral interactions between protofilaments assembled into MTs. Our analysis provides insights into relationships between intramolecular tubulin movements of MT organization and function.

Short-Range Conformational Energies, Secondary Structure Propensities, and Recognition of Correct Sequence-Structure Matches

A statistical analysis of known structures is made for an assessment of the utility of short‐range energy considerations. For each type of amino acid, the potentials governing (1) the torsions and bond angle changes of virtual Cα‐Cα bonds and (2) the coupling between torsion and bond angle changes are derived. These contribute approximately −2 RT per residue to the stability of native proteins, approximately half of which is due to coupling effects. The torsional potentials for the α‐helical states of different residues are verified to be strongly correlated with the free‐energy change measurements made upon single‐site mutations at solvent‐exposed regions. Likewise, a satisfactory correlation is shown between the β‐sheet potentials of different amino acids and the scales from free‐energy measurements, despite the role of tertiary context in stabilizing β‐sheets. Furthermore, there is excellent agreement between our residue‐specific potentials for α‐helical state and other thermodynamic based scales. Threading experiments performed by using an inverse folding protocol show that 50 of 62 test structures correctly recognize their native sequence on the basis of short‐range potentials. The performance is improved to 55, upon simultaneous consideration of short‐range potentials and the nonbonded interaction potentials between sequentially distant residues. Interactions between near residues along the primary structure, i.e., the local or short‐range interactions, are known to be insufficient, alone, for understanding the tertiary structural preferences of proteins alone. Yet, knowledge of short‐range conformational potentials permits rationalizing the secondary structure propensities and aids in the discrimination between correct and incorrect tertiary folds. Proteins 29:292–308, 1997.

AN EMPIRICAL ENERGY POTENTIAL WITH A REFERENCE STATE FOR PROTEIN FOLD AND SEQUENCE RECOGNITION

We consider modifications of an empirical energy potential for fold and sequence recognition to represent approximately the stabilities of proteins in various environments. A potential used here includes a secondary structure potential representing short‐range interactions for secondary structures of proteins, and a tertiary structure potential consisting of a long‐range, pairwise contact potential and a repulsive packing potential. This potential is devised to evaluate together the total conformational energy of a protein at the coarse grained residue level. It was previously estimated from the observed frequencies of secondary structures, from contact frequencies between residues, and from the distributions of the number of residues in contact in known protein structures by regarding those distributions as the equilibrium distributions with the Boltzmann factor of these interaction energies. The stability of native structures is assumed as a primary requirement for proteins to fold into their native structures. A collapse energy is subtracted from the contact energies to remove the protein size dependence and to represent protein stabilities for monomeric and multimeric states. The free energy of the whole ensemble of protein conformations that is subtracted from the conformational energy to represent protein stability is approximated as the average energy expected for a typical native structure with the same amino acid composition. This term may be constant in fold recognition but essentially varies in sequence recognition. A simple test of threading sequences into structures without gaps is employed to demonstrate the importance of the present modifications that permit the same potential to be utilized for both fold and sequence recognition. Proteins 1999;36:357–369. Published 1999 Wiley‐Liss, Inc.

Coordination geometry of nonbonded residues in globular proteins

BACKGROUNDnTwo opposite views have been advanced for the packing of sidechains in globular proteins. The first is the jigsaw puzzle model, in which the complementarity of size and shape is essential. The second, the nuts-and-bolts model, suggests that constraints induced by steric complementarity or pairwise specificity have little influence. Here, the angular distributions of sidechains around amino acids of different types are analyzed, in order to capture the preferred (if any) coordination loci in the neighborhood of a given type of amino acid.nnnRESULTSnSome residue pairs select specific coordination states with probabilities about ten times higher than expected for random distributions. This selectivity becomes more pronounced at closer separations leading to an effective free energy of stabilization as large as -2 RT for some sidechain pairs. A list of the most probable coordination sites around each residue type is presented, along with their statistical weights.nnnCONCLUSIONSnThese data provide guidance as to how to pack selectively the nonbonded sidechains in the neighborhood of a central residue for computer generation of unknown protein structures.

Myosin flexibility: structural domains and collective vibrations.

The movement of the myosin motor along an actin filament involves a directed conformational change within the cross‐bridge formed between the protein and the filament. Despite the structural data that has been obtained on this system, little is known of the mechanics of this conformational change. We have used existing crystallographic structures of three conformations of the myosin head, containing the motor domain and the lever arm, for structural comparisons and mechanical studies with a coarse‐grained elastic network model. The results enable us to define structurally conserved domains within the protein and to better understand myosin flexibility. Notably they point to the role of the light chains in rigidifying the lever arm and to changes in flexibility as a consequence of nucleotide binding. Proteins 2004;54:000–000.