Calculations of Conformations of Polypeptides

Protein structure prediction from the complementary science perspective

A comparative analysis between two problems-apparently unrelated-which are solved in a period of ~400 years, viz., the accurate prediction of both the planetary orbits and the protein structures, leads to inferred conjectures that go far beyond the existence of a common path in their resolution, i.e., observation → pattern recognition → modeling. The preliminary results from this analysis indicate that complementary science, together with a new perspective on protein folding, may help us discover common features that could contribute to a more in-depth understanding of still-unsolved problems such as protein folding.

Proteins' Evolution upon Point Mutations

As the reader must be already aware, state-of-the-art protein folding prediction methods have reached a smashing success in their goal of accurately determining the three-dimensional structures of proteins. Yet, a solution to simple problems such as the effects of protein point mutations on their (i) native conformation; (ii) marginal stability; (iii) ensemble of high-energy nativelike conformations; and (iv) metamorphism propensity and, hence, their evolvability, remains as an unsolved problem. As a plausible solution to the latter, some properties of the amide hydrogen-deuterium exchange, a highly sensitive probe of the structure, stability, and folding of proteins, are assessed from a new perspective. The preliminary results indicate that the protein marginal stability change upon point mutations provides the necessary and sufficient information to estimate, through a Boltzmann factor, the evolution of the amide hydrogen exchange protection factors and, consequently, that of the ensemble of folded conformations coexisting with the native state. This work contributes to our general understanding of the effects of point mutations on proteins and may spur significant progress in our efforts to develop methods to determine the appearance of new folds and functions accurately.

Hydrogen bonds in molecular mechanics force fields

This chapter reviews formulation and parametrization of molecular mechanics force fields with special attention to technical and inherent problems. Most striking among the shortcomings is the inadequacy of the simple point charge description as a means to describe energy and forces of interactions between polar molecules and between polar groups in macromolecules, including hydrogen bonds. The current state of efforts to improve the description of polar interactions is discussed.

Hydration shells of molecules in molecular association: A mechanism for biomolecular recognition

It has become clear that water should not be treated as an inert environment, but rather as an integral and active component of molecules. Here, we consider molecules and their hydration shells together as single entities. We show that: (1) the rate of association of molecules should be determined by the energetic barriers arising from interactions between their hydration shells; (2) replacing non-polar atoms of molecular surfaces with polar atoms increases these barriers; (3) reduction of the hydration shells during molecular association is the driving force for association not only of non-polar, but of polar molecules as well; (4) in most cases the dehydration of polar atoms during molecular association thermodynamically counteracts association; (5) on balance the thermodynamic stability of associated complexes is basically determined by the action of these two opposing factors: reduction of the hydration shells and dehydration of polar atoms; (6) molecular crowding reduces the energetic barriers counteracting association and changes the thermodynamic stability of associated complexes. These results lead to a mechanism for biomolecular recognition in the context of which the formation of unique structures is provided by rapidly forming kinetic traps with a biologically necessary lifetime but with a marginal thermodynamic stability. The mechanism gives definitive answers to questions concerning the heart of specific interactions between biomolecules, their folding and intracellular organization. Predictions are given that can be subjected to direct experimental tests.

Overview of computer modeling of cellulose

Although it has a deceptively simple primary structure, the collective organization of bulk cellulose, particularly as it exists in cellulose fibers in the cell walls of living plants and other organisms, is quite diverse and complex. While some experimental techniques, such as vibrational spectroscopy and diffraction from partially crystalline samples, are able to provide insights into the organization of bulk cellulose, its intrinsic complexity has left many questions still unanswered. For this reason, additional probes of cellulose structure would be highly desirable. With the continuing advances in computer power through massive parallelization, and the steady progress in computer codes and force fields for modeling carbohydrate systems, molecular mechanics simulations have become an attractive means of studying cellulosic systems at the atomic and molecular level. The coming decade will almost certainly see remarkable advances in the understanding of cellulose using such simulations.

Respice, adspice, and prospice

The title, "Look to the past, Look to the present, and Look to the future," the motto of City College of New York, expresses how my family life and education led me to an academic career in physical chemistry and ultimately to a study of proteins. The economic depression of the 1930s left a lasting impression on my outlook and career aspirations. With fortunate experiences at several stages in my life, I was able to participate in the great adventure of the last half of the twentieth century: the revolution in biology that advanced the field of protein chemistry to so great an extent. The future is bright and limitless, with greater understanding of biology yet to come.

Coarse-grained force field: general folding theory

We review the coarse-grained UNited RESidue (UNRES) force field for the simulations of protein structure and dynamics, which is being developed in our laboratory over the last several years. UNRES is a physics-based force field, the prototype of which is defined as a potential of mean force of polypeptide chains in water, where all the degrees of freedom except the coordinates of α-carbon atoms and side-chain centers have been integrated out. We describe the initial implementation of UNRES to protein-structure prediction formulated as a search for the global minimum of the potential-energy function and its subsequent molecular dynamics and extensions of molecular-dynamics implementation, which enabled us to study protein-folding pathways and thermodynamics, as well as to reformulate the protein-structure prediction problem as a search for the conformational ensemble with the lowest free energy at temperatures below the folding-transition temperature. Applications of UNRES to study biological problems are also described.

Loop simulations

Loop modeling is crucial for high-quality homology model construction outside conserved secondary structure elements. Dozens of loop modeling protocols involving a range of database and ab initio search algorithms and a variety of scoring functions have been proposed. Knowledge-based loop modeling methods are very fast and some can successfully and reliably predict loops up to about eight residues long. Several recent ab initio loop simulation methods can be used to construct accurate models of loops up to 12-13 residues long, albeit at a substantial computational cost. Major current challenges are the simulations of loops longer than 12-13 residues, the modeling of multiple interacting flexible loops, and the sensitivity of the loop predictions to the accuracy of the loop environment.

CHARMM: the biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

Spinach on the ceiling: a theoretical chemist's return to biology

I was born in Vienna and came to the United States as a refugee in October 1938. This experience played an important role in my view of the world and my approach to science: It contributed to my realization that it was safe to stop working in fields that I felt I understood and to focus on different areas of research by asking questions that would teach me and others something new. I describe my experiences that led me from chemistry and physics back to my first love, biology, and outline some of the contributions I have made as part of my ongoing learning experience.

Ribosomal Elongation Cycle: Energetic, Kinetic and Stereochemical Aspects

As a preface to an analysis of the ribosomal elongation cycle, we examine the energetics of macromolecular structural transformations. We show that the kinetic barriers and changes of the energetic levels during these transformations are essentially determined by disruption of hydrogen and cation-ligand bonds, and by uncompensated losses of these bonds (ULBs). The disruption of a hydrogen or cation-ligand bond increases the heights of kinetic barriers by the energy of these bonds. The association and dissociation of macromolecules, and conformational transitions within macromolecules, can change the numbers of ULBs but cannot completely eliminate them. Two important general conclusions are drawn from this analysis. First, occupation of enzyme active centers by substrates should be accompanied by a reduction in the number of ULBs. This reduction decreases the activation barriers in enzyme reactions, and is a major contributor to catalysis. Second, the enzymic reactions of the ribosomal cycle (structural changes caused by transpeptidation and by GTP hydrolyses in EF-Tu and EF-G) disrupt kinetic traps that prevent tRNAs from dissociating into solution during their motion within the ribosome and are necessary for progression of the cycle. These results are general purpose structural-functional blocks for building a molecular model of the ribosomal elongation cycle. Here, we demonstrate the utility of these blocks for analysis of acceptance of cognate tRNAs into the ribosomal elongation cycle.

Analysis of recognition of transfer-messenger RNA by the ribosomal decoding center

Bacterial ribosomes stalled on defective mRNAs are rescued by tmRNA that functions as both tRNA and mRNA. The first ribosomal elongation cycle on tmRNA where tmRNA functions as tRNA is highly unusual: occupation of the ribosomal A site by tmRNA occurs without codon:anticodon pairing. Our analysis shows that in this case the role of a codon:anticodon duplex should be accomplished by a single unpaired triplet. In order that tmRNA could participate in the ribosomal elongation cycle, a triplet preceding the mRNA portion of tmRNA (the -1triplet) should be in the A-form and this form should be recognized by the ribosomal decoding center. A rule is derived that determines what triplets cannot be used as the -1triplet. The rule was tested with the -1triplets of all known 414 tmRNA species. All 23 observed -1triplets follow the formulated rule. The rule is also supported by the available data on base substitutions within the -1triplet.

Algorithm for normal mode analysis with general internal coordinates

A technique for performing normal vibrational analysis for biological macromolecules using general internal coordinates is proposed. The technique is based on the conventional algorithm for calculating the second derivatives of potential and kinetic energies using intramolecular dihedral angles, intermolecular translation, and rotation as variables [Braun, W. et al., J Phys Soc Jpn 1984, 53, 3269]. We extend the algorithm to include more general internal coordinates, bond stretching, angle bending, and so forth, without assuming two-body interactions. The essential point is the separation of the variables for potential functions and vibrational analysis. With our technique, we can arbitrarily choose any combination of internal coordinates as variables, free from the functional form of potential energy. We can analyze complex systems such as a multiple molecular system including solvents or a transition state of chemical reactions. In addition, mixed use of the potentials of molecular mechanics and quantum chemistry is possible.

Protein folding: from the levinthal paradox to structure prediction

This article is a personal perspective on the developments in the field of protein folding over approximately the last 40 years. In addition to its historical aspects, the article presents a view of the principles of protein folding with particular emphasis on the relationship of these principles to the problem of protein structure prediction. It is argued that despite much that is new, the essential elements of our current understanding of protein folding were anticipated by researchers many years ago. These elements include the recognition of the central importance of the polypeptide backbone as a determinant of protein conformation, hierarchical protein folding, and multiple folding pathways. Important areas of progress include a detailed characterization of the folding pathways of a number of proteins and a fundamental understanding of the physical chemical forces that determine protein stability. Despite these developments, fold prediction algorithms still encounter difficulties in identifying the correct fold for a given sequence. This may be due to the possibility that the free energy differences between at least a few alternate conformations of many proteins are not large. Significant progress in protein structure prediction has been due primarily to the explosive growth of sequence and structural databases. However, further progress is likely to depend in part on the ability to combine information available from databases with principles and algorithms derived from physical chemical studies of protein folding. An approach to the integration of the two areas is outlined with specific reference to the PrISM program that is a fully integrated sequence/structural-analysis/fold-recognition/homology model building software system.

Rigid-body oscillations of α-helices: implications for protein thermal stability

A quasi-continuity model protein consisting of two alpha-helices undergoing rigid-body torsional oscillations demonstrates that factors stabilizing the model protein, such as increased helix rigidity and hydrophobicity, are the same factors that stabilize thermophilic proteins relative to their mesophilic analogs. The model predicts oscillatory motions with frequencies in the microwave (10(10) Hz) range. These oscillations decrease in frequency with increasing helix rigidity because of compensating increases in the force constant and moment of inertia, thus explaining the retention of activity in the more rigid thermophilic enzymes. Implications for protein design, based on the predictions of the model, are discussed.

Recent developments in the theory of protein folding: searching for the global energy minimum

Statistical mechanical theories and computer simulation are being used to gain an understanding of the fundamental features of protein folding. A major obstacle in the computation of protein structures is the multiple-minima problem arising from the existence of many local minima in the multidimensional energy landscape of the protein. This problem has been surmounted for small open-chain and cyclic peptides, and for regular-repeating sequences of models of fibrous proteins. Progress is being made in resolving this problem for globular proteins.

Towards an understanding of the arginine-aspartate interaction

We have made a comparison of the geometries of intra- and intermolecular arginine-aspartate interactions by extracting orientation information from protein co-ordinate data. The results show a pronounced difference, with both types of interaction preferring to form twin N-H . . . O = C hydrogen bonds, but involving different nitrogen atoms. In intramolecular interactions, the aspartate favours a "side on" geometry, forming hydrogen bonds with N epsilon and N eta 2; in the intermolecular case, however, "end on" contacts involving N eta 1 and N eta 2 of the arginine are preferred. We have used Distributed Multipole Analysis of the methylguanidinium-acetate system to model the electrostatic component of the arginine-aspartate ion pair interaction in vacuo. We find, in agreement with the experimental arginine-aspartate distribution, that side on and end on doubly N-H . . . O = C hydrogen-bonded configurations are clearly the most favourable, with the side on being marginally lower in energy. Thus, despite the many competing side-chain interactions in proteins, many arginine-aspartate pairs adopt one of the minimum electrostatic energy conformations, or one close to a minimum. Within each of the two regions (side on and end on) we find only a small energy gap between the "symmetric" doubly hydrogen-bonded and slightly displaced "staggered" structures, again in agreement with the crystal structure data. Further calculations of the total ab initio interaction energy show that this follows the electrostatic term in its orientational variation, this phenomenon of "electrostatic domination" being well known in hydrogen-bonded systems. The end on arginine nitrogen atoms are observed to be more surface-exposed than N epsilon, as demonstrated by their greater accessibilities over a large sample of proteins. This helps explain the side on and end on preferences of intra- and intermolecular interactions, respectively. We also note the effect of short sequence intervals, particularly i in equilibrium with i + 2 relationships, in forcing many intramolecular contacts to be side on.

A comparison of the CHARMM, AMBER and ECEPP potentials for peptides. II. Phi-psi maps for N-acetyl alanine N'-methyl amide: comparisons, contrasts and simple experimental tests

phi-psi maps of N-acetyl alanine N'-methyl amide have been computed using the CHARMM potential, the all-atom AMBER potential, and the ECEPP/2 potential, before and after adiabatic relaxation. Maps using the CHARMM and AMBER potentials were determined with values of 1.0 and 4.0 for the dielectric constant epsilon, and with a distance dependent dielectric constant. Adiabatic relaxation was carried out using flexible geometry for the CHARMM and AMBER potentials, and using rigid geometry for the AMBER and ECEPP potentials. In all cases, the lowest energy was found in the C7eq region (phi approximately -70 degrees, psi approximately 70 degrees). The maps with CHARMM and AMBER with epsilon = 4.0 and with ECEPP, without adiabatic relaxation, were broadly similar but differed in the relative energies allotted to high-energy regions of the map. After adiabatic relaxation with rigid geometry, the map with ECEPP, and the map with AMBER using a distance-dependent dielectric constant, agreed fairly well apart from differences in the relative energies of the alpha R, alpha L, and C7ax regions. After adiabatic relaxation with flexible geometry, the maps with CHARMM and AMBER became very similar; the lowest energies were observed in the C7eq region, the C5 region (phi approximately -150 degrees, psi approximately 150 degrees) and the C7ax region (phi approximately 70 degrees, psi approximately -70 degrees). Breakdown of the energies, after adiabatic relaxation, into electrostatic, nonbonded, and geometric (including torsional) contributions, showed that (1) with fixed geometry, the nonbonded and torsional contribution to the ECEPP and AMBER potentials were very similar, but the electrostatic contributions were markedly different; (2) with flexible geometry, the nonbonded contribution to the CHARMM and AMBER potentials did not vary greatly over the whole map. The phi-psi maps were subjected to three simple comparisons with experiment. (1) The maps were used to predict the characteristic ratio for poly-L-alanine, and the results were compared with experimental findings (D.A. Brant and P.J. Flory, J. Amer. Chem. Soc. 87, 2788-2791, 1965). The agreement with experiment was acceptable for ECEPP, and for CHARMM after adiabatic relaxation, marginal for AMBER after adiabatic relaxation, and unsatisfactory for CHARMM or AMBER without adiabatic relaxation. (2) Deviations of bond angles from their equilibrium values, in energy-minimized conformations, were compared with values deduced from crystals of terminally-blocked amino acids. With both the CHARMM and AMBER potentials using flexible geometry, one or more excessive deviations was observed in the C7ax local minimum.(ABSTRACT TRUNCATED AT 400 WORDS)

Method of modeling protein structure by the two-dimensional nuclear magnetic resonance spectroscopy data; application to the proteinase inhibitor BUSI IIA from bull seminal plasma

A new approach is suggested to model the spatial structure of protein molecules in solution based on combined use of the methods of theoretical conformational analysis and NMR spectroscopy data. At the first stage, special means are used to convert d connectivity information into the most probable values of dihedral angles. This allows search for possible spatial structures in the limited regions of the conformational space at further stages using the methods of the theoretical conformational analysis. The suggested approach was verified in reconstructing the spatial backbone structure of the fragment 17-57 of the proteinase inhibitor BUSI IIA from the bull seminal plasma. The structural model parameters are compared with the corresponding characteristics obtained from the X-ray analysis data for the homologic proteinase inhibitor from the Japanese quail ovomucoid. The suggested approach is shown to correctly reproduce both the general molecule topology and the conformations of individual amino acid residues.

Relative stabilities and transitions of DNA conformations in 1:1 electrolytes: a theoretical study

We use a recently developed formalism (1) to calculate the salt dependent part of the free energy determining DNA conformational stability in 1:1 electrolytes. The conformations studied are the A, B, C and alternating-B right-handed forms and the ZI, ZII left-handed forms of DNA. In the case of the B-ZI transition of d(G-C).d(G-C) helices in NaCl solution, the free energy contribution considered suffices to describe the transition in a quantitative manner. The theory also predicts the occurrence of salt-induced B-A transitions which have been recently observed with poly[d(n2 A-T)] and poly[d(G-C)]. In other cases, additional terms in the free energy balance, particularly due to hydration effects, must be at least as important as salt effects in determining conformational stability and structural transitions in solution. If diffuse ionic cloud electrostatic effects alone would dominate in all cases, the relative helical stabilities at 0.2 M monovalent salt would decrease in the order C greater than B greater than A greater than ZII greater than ZI greater than alternating-B. At high salt concentrations (2.0 M-5.0 M), the order would be alternating-B greater than ZI greater than A greater than ZII greater than B greater than C.

Conformational studies of nucleic acids: III. Empirical multiple correlation functions for nucleic acid torsion angles

There are seven significantly variable torsion angles in each monomer unit of a polynucleotide. Because of this, it is computationally infeasible to consider the energetics of all conformations available to a nucleic acid without the use of simplifications. In this paper, we develop functions suggested by and regression fit to crystallographic data which allow three of these torsion angles, alpha (O3'-P-O5'-C5'), delta (C5'-C4'-C3'-O3') and epsilon (C4'-C3'-O3'-P), to be calculated as dependent variables of those remaining. Using these functions, the seven independent torsions are reduced to four, a reduction in complexity sufficient to allow an examination of the global conformational energetics of a nucleic acid for the remaining independent torsion angles. These functions are the first to quantitatively relate a dependent nucleic acid torsion angle to several different independent angles. In all three cases the data are fit reasonably well, and in one case, alpha, the fit is exceptionally good, lending support for the suitability of the functions in conformational searches. In addition, an examination of the most significant terms in each of the correlation functions allows insight into the physical basis for the correlations.