Biomolecular force fields: where have we been, where are we now, where do we need to go and how do we get there?

In this perspective, we review the theory and methodology of the derivation of force fields (FFs), and their validity, for molecular simulations, from their inception in the second half of the twentieth century to the improved representations at the end of the century. We examine the representations of the physics embodied in various force fields, their accuracy and deficiencies. The early days in the 1950s and 60s saw FFs first introduced to analyze vibrational spectra. The advent of computers was soon followed by the first molecular mechanics machine calculations. From the very first papers it was recognized that the accuracy with which the FFs represented the physics was critical if meaningful calculated structural and thermodynamic properties were to be achieved. We discuss the rigorous methodology formulated by Lifson, and later Allinger to derive molecular FFs, not only obtain optimal parameters but also uncover deficiencies in the representation of the physics and improve the functional form to account for this physics. In this context, the known coupling between valence coordinates and the importance of coupling terms to describe the physics of this coupling is evaluated. Early simplified, truncated FFs introduced to allow simulations of macromolecular systems are reviewed and their subsequent improvement assessed. We examine in some depth: the basis of the reformulation of the H-bond to its current description; the early introduction of QM in FF development methodology to calculate partial charges and rotational barriers; the powerful and abundant information provided by crystal structure and energetic observables to derive and test all aspects of a FF including both nonbond and intramolecular functional forms; the combined use of QM, along with crystallography and lattice energy calculations to derive rotational barriers about ɸ and ψ; the development and results of methodologies to derive "QM FFs" by sampling the QM energy surface, either by calculating energies at hundreds of configurations, or by describing the energy surface by energies, first and second derivatives sampled over the surface; and the use of the latter to probe the validity of the representations of the physics, reveal flaws and assess improved functional forms. Research demonstrating significant effects of the flaws in the use of the improper torsion angle to represent out of plane deformations, and the standard Lorentz-Berthelot combining rules for nonbonded interactions, and the more accurate descriptions presented are also reviewed. Finally, we discuss the thorough studies involved in deriving the 2nd generation all-atom versions of the CHARMm, AMBER and OPLS FFs, and how the extensive set of observables used in these studies allowed, in the spirit of Lifson, a characterization of both the abilities, but more importantly the deficiencies in the diagonal 12-6-1 FFs used. The significant contribution made by the extensive set of observables compiled in these papers as a basis to test improved forms is noted. In the following paper, we discuss the progress in improving the FFs and representations of the physics that have been investigated in the years following the research described above.

Force field development phase II: Relaxation of physics-based criteria or inclusion of more rigorous physics into the representation of molecular energetics.

In the previous paper, we reviewed the origins of energy based calculations, and the early science of FF development. The initial efforts spanning the period from roughly the early 1970s to the mid to late 1990s saw the development of methodologies and philosophies of the derivation of FFs. The use of Cartesian coordinates, derivation of the H-bond potential, different functional forms including diagonal quadratic expressions, coupled valence FFs, functional form of combination rules, and out of plane angles, were all investigated in this period. The use of conformational energetics, vibrational frequencies, crystal structure and energetics, liquid properties, and ab initio data were all described to one degree or another in deriving and validating both the FF functional forms and force constants. Here we discuss the advances made since in improving the rigor and robustness of these initial FFs. The inability of the simple quadratic diagonal FF to accurately describe biomolecular energetics over a large domain of molecular structure, and intermolecular configurations, was pointed out in numerous studies. Two main approaches have been taken to overcome this problem. The first involves the introduction of error functions, either exploiting torsion terms or introducing explicit 2-D error correction grids. The results and remaining challenges of these functional forms is examined. The second approach has been to improve the representation of the physics of intra and intermolecular interactions. The latter involves including descriptions of polarizability, charge flux aka geometry dependent charges, more accurate representations of spatial electron density such as multipole moments, anisotropic nonbond potentials, nonbond and polarization flux, among others. These effects, though not as extensively studied, likely hold the key to achieving the rigorous reproduction of structural and energetic properties long sought in biomolecular simulations, and are surveyed here. In addition, the quality of training and validation observables are evaluated. The necessity of including an ample set of energetic and crystal observables is emphasized, and the inadequacy of free energy as a criterion for FF reliability discussed. Finally, in light of the results of applications of the two approaches to FF development, we propose a "recipe" of terms describing the physics of inter and intramolecular interactions whose inclusion in FFs would significantly improve our understanding of the energetics and dynamics of biomolecular systems resulting from molecular dynamics and other energy based simulations.

Quantum Derivative Fitting and Biomolecular Force Fields: Functional Form, Coupling Terms, Charge Flux, Nonbond Anharmonicity, and Individual Dihedral Potentials.

Computer simulations are increasingly prevalent, complementing experimental studies in all fields of biophysics, chemistry, and materials. Their utility, however, is critically dependent on the validity of the underlying force fields employed. In this Perspective we review the ability of quantum mechanics, and in particular analytical ab initio derivatives, to inform on the nature of intra- and intermolecular interactions. The power inherent in the exploitation of forces and second derivatives (Hessians) to derive force fields for a variety of compound types, including inorganic, organic, and biomolecules, is explored. We discuss the use of these quantities along with QM energies and geometries to determine force constants, including nonbond and electrostatic parameters, and to assess the functional form of the energy surface. The latter includes the optimal form of out-of-plane interactions and the necessity for anharmonicity, and terms to account for coupling between internals, to adequately represent the energy of intramolecular deformations. In addition, individual second derivatives of the energy with respect to selected interaction coordinates, such as interatomic distances or individual dihedral angles, have been shown to select out for the corresponding interactions, annihilating other interactions in the potential expression. Exploitation of these quantities allows one to probe the individual interaction and explore phenomena such as, for example, anisotropy of atom-atom nonbonded interactions, charge flux, or the functional form of isolated dihedral angles, e.g., a single dihedral X-C-C-Y about a tetrahedral C-C bond.

Mechanism of androgen receptor antagonism by bicalutamide in the treatment of prostate cancer.

The androgen receptor (AR) plays a key role in regulating gene expression in a variety of tissues, including the prostate. In that role, it is one of the primary targets in the development of new chemotherapeutics for treatment of prostate cancer and the target of the most widely prescribed current drug, bicalutamide (Bcu), for this disease. In view of its importance, and the absence of a crystal structure for any antagonist--AR complex, we have conducted a series of molecular dynamics-based simulations of the AR--Bcu complex and quantum mechanical (QM) calculations of Bcu, to elucidate the structural basis for antagonism of this key target. The structures that emerge show that bicalutamide antagonizes AR by accessing an additional binding pocket (B-site) adjacent to the hormone binding site (HBS), induced by displacing helix 12. This distorts the coactivator binding site and results in the inactivation of transcription. An alternative equienergetic conformational state of bicalutamide was found to bind in an expanded hormone pocket without materially perturbing either helix 12 or the coactivator binding site. Thus, both the structural basis of antagonism and the mechanism underlying agonist properties displayed by bicalutamide in different environments may be rationalized in terms of these structures. In addition, the antagonist structure and especially the induced second site (B-site) provide a structural framework for the design of novel antiandrogens.

Keeping it in the family: folding studies of related proteins.

Investigators have recently turned to studies of protein families to shed light on the mechanism of protein folding. In small proteins for which detailed analysis has been performed, recent studies show that transition-state structure is generally conserved. The number and structures of populated folding intermediates have been found to vary in homologous families of larger (greater than 100-residue) proteins, reflecting a balance of local and global interactions.

Derivation of class II force fields. VI. Carbohydrate compounds and anomeric effects.

The methodology for deriving class II force fields has been applied to acetal, hemiacetal, and carbohydrate compounds. A set of eighteen model compounds containing one or more anomeric centers was selected for generating the quantum mechanical energy surface, from which the force field was derived and the functional form assessed. The quality of the fit was tested by comparing the energy surface predicted by the force field with ab initio results. Structural, energetic, and dynamic properties (vibrational frequencies) were analyzed. In addition, alpha and beta anomeric equilibrium structures and energies of 2-methoxytetrahydropyran, 2-deoxyribose, and glucose were computed at the HF/6-31G* and higher ab initio levels. These calculations provide test data from molecules outside the training set used to derive the force field. The quantum calculations were used to assess the ability of the class II force field and two quadratic diagonal (class I) force fields, CVFF, and Homans' extension of the AMBER force field, to account for the anomeric effects on the structural and energetic properties of carbohydrate systems. These class I force fields are unable to account for observed structural and energetic trends, exhibiting deviations as large as 5 kcal/mol in relative energies. The class II force field, on the other hand, is shown to reproduce anomeric structural as well as energetic differences. An energy component analysis of this force field shows that the anomeric differences are dominated by torsional energies, although coupling terms, especially angle/torsion, also make significant contributions (roughly 1 kcal/mol in glucose). In addition, the force field accurately accounts for both anomeric and exo-anomeric energy differences in 2-methoxytetrahydropyran, and anomeric energy differences in 2-deoxyribose and glucose.

Conformational analysis of endothelin-1: effects of solvation free energy.

In order to investigate conformational preferences of the 21-residue peptide hormone endothelin-1 (ET-1), an extensive conformational search was carried out in vacuo using a combination of high temperature molecular dynamics/annealing and a Monte Carlo/minimization search in torsion angle space. Fully minimized conformations from the search were grouped into families using a clustering technique based on rms fitting over the Cartesian coordinates of the atoms of the peptide backbone of the ring region. A wide range of local energy mining were identified even though two disulfide bridges (Cys1-Cys15 and Cys3-Cys11) constrain the structure of the peptide. Low energy conformers of ET-1 as a nonionized species in vacuo are stabilized by intramolecular interaction of the ring region (residues 1-15) with the tail (residues 16-21). Strained conformations for individual residues are observed. Conformational similarity to protein loops is established by matching to protein crystal structures. In order to assess the influence of aqueous environment on conformational preference, the electrostatic contribution to the solvation energy was calculated for ET-1 as a fully ionized species (Asp8, Lys9, Glu10, Asp18, N- and C-terminus) using a continuum electrostatics model (DelPhi) for each of the conformers generated in vacuo, and the total solvation free energy was estimated by adding a hydrophobic contribution proportional to solvent accessible surface area. Solvation dramatically alters the relative energetics of ET-1 conformers from that calculated in vacuo. Conformers of ET-1 favored by the electrostatic solvation energy in water include conformers with helical secondary structure in the region of residues 9-15. Perhaps of most importance, it was demonstrated that the contribution to solvation by an individual charge depends not only on its solvent accessibility but on the proximity of other charges, i.e., it is a cooperative effect. This was shown by the calculation of electrostatic solvation energy as a function of conformation with individual charges systematically turned "on" and "off". The cooperative effect of multiple charges on solvation demonstrated in this manner calls into question models that relate solvation energy simply to solvent accessibility by atom or residue alone.

Computer simulation of the free energy of peptides with the local states method: analogues of gonadotropin releasing hormone in the random coil and stable states.

The Helmholtz free energy F (rather than the energy) is the correct criterion for stability; therefore, calculation of F is important for peptides and proteins that can populate a large number of metastable states. The local states (LS) method proposed by H. Meirovitch [(1977) Chemical Physics Letters, Vol. 45, p. 389] enables one to obtain upper and lower bounds of the conformational free energy, FB (b,l) and FA (b,l), respectively, from molecular dynamics (MD) or Monte Carlo samples. The correlation parameter b is the number of consecutive dihedral or valence angles along the chain that are taken into account explicitly. The continuum angles are approximated by a discretization parameter l; the larger are b and l, the better the approximations; while FA can be estimated efficiently, it is more difficult to estimate FB. The method is further developed here by applying it to MD trajectories of a relatively large molecule (188 atoms), the potent "Asp4-Dpr10" antagonist [cyclo(4/10)-(Ac-delta 3Pro1-D-pFPhe2-D-Trp3-Asp4-Tyr5-D-Nal6-Leu7-Arg8 -Pro9- Dpr10-NH2)] of gonadotropin releasing hormone (GnRH). The molecule was simulated in vacuo at T = 300 K in two conformational states, previously investigated [J. Rizo et al. Journal of the American Chemical Society, (1992) Vol. 114, p. 2860], which differ by the orientation of the N-terminal tail, above (tail up, TU) and below (tail down, TD) the cyclic heptapeptide ring. As in previous applications of the LS method, we have found the following: (1) While FA is a crude approximation for the correct F, results for the difference, delta FA = FA (TD)-FA (TU) converge rapidly to 5.6 (1) kcal/mole as the approximation is improved (i.e., as b and l are increased), which suggests that this is the correct value for delta F; therefore TD is more stable than TU. (The corresponding difference in entropy, T delta SA = 1.3(2) kcal/mole, is equal to the value obtained by the harmonic approximation.) (2) The lowest approximation, which has the minimal number of local states, i.e., based on b = 0 (no correlations) and l = 1 (the angle values are distributed homogeneously), also leads to the correct value of delta F, within the error bars. This is important since the lowest approximation can be applied even to large proteins. (3) The method enables one to define the entropy of a part of the molecule and thus to measure the flexibility of this part.(ABSTRACT TRUNCATED AT 400 WORDS)

Conformational analysis of a highly potent dicyclic gonadotropin-releasing hormone antagonist by nuclear magnetic resonance and molecular dynamics.

Structural analysis of constrained (monocyclic) analogues of gonadotropin-releasing hormone (GnRH) has led to the development of a model for the receptor-bound conformation of GnRH and to the design of highly potent, dicyclic GnRH antagonists. This is one of the first cases where a dicyclic backbone has been introduced into analogues of a linear peptide hormone with retention of high biological activity. Here we present a conformational analysis of dicyclo(4-10,5-8)[Ac-D-2Nal1-D-pClPhe2-D-Trp3-Asp4+ ++-Glu5-D-Arg6-Leu7-Lys8- Pro9-Dpr10]-NH2 (I), using two-dimensional nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics simulation. Compound I inhibits ovulation in the rat at a dose of 5-10 micrograms (Rivier et al. In Peptides: Chemistry, Structure ad Biology; Rivier, J. E., Marshall, G. R., Eds.; ESCOM: Leiden, The Netherlands, 1990; pp 33-37). The backbone conformation of the 4-10 cycle in this dicyclic compound is very similar to that found previously for a parent monocyclic (4-10) GnRH antagonist (Rizo et al. J. Am. Chem. Soc. 1992, 114, 2852-2859; ibid. 2860-2871), which gives strong support to the hypothesis that GnRH adopts a similar conformation upon binding to its receptor. In this conformation, residues 5-8 form a "beta-hairpin-like" structure that includes two transannular hydrogen bonds and a Type II' beta turn around residues D-Arg6-Leu7. The "tail" of the molecule formed by residues 1-3 is somewhat structured but does not populate a single major conformation. However, the orientation of the tail on the same side of the 4-10 cycle as the 5-8 bridge favors interactions between this bridge and the tail residues. These observations correlate with results obtained previously for the parent monocyclic (4-10) antagonist, and have led to the design of a series of new dicyclic GnRH antagonists with bridges between the tail residues and residues 5 or 8.

On achieving better than 1-A accuracy in a simulation of a large protein: Streptomyces griseus protease A.

Computational methods are frequently used to simulate the properties of proteins. In these studies accuracy is clearly important, and the improvement of accuracy of protein simulation methodology is one of the major challenges in the application of theoretical methods, such as molecular dynamics, to structural studies of biological molecules. Much effort is being devoted to such improvements. Here, we present an analysis of a 187-ps molecular dynamics simulation of the serine protease Streptomyces griseus protease A in its crystal environment. The reproduction of the experimental structure is considerably better than has been achieved in earlier simulations--the root mean square deviation of the simulated structure from the x-ray structure being less than 1 A, a significant step toward the goal of simulating proteins to within experimental error. The use of a longer cutoff with truncation rather than a switching function, inclusion of all crystalline water and the counterions in the crystallization medium, and use of the consistent valence force field characterize the differences in this calculation.

Synthesis and theoretical conformational studies of gonadotropin-releasing hormone analogs containing tetrahydroisoquinoline carboxylic acid.

A series of analogs of gonadotropin-releasing hormone (GnRH) containing the conformationally restrictive residue tetrahydroisoquinoline carboxylic acid (Tic) or its non-restricted parent phenylalanine were synthesized and evaluated for anti-ovulatory activity in the rat. The series, based on the potent linear parent compound Ac-DNal1-DCpa2-DPal3- Ser4-Tyr5-DPal6-Leu7-Arg8-Pro9-DAla10-NH2, included L-Tic in positions 1, 2, 3, 7 and 9, D-Tic in positions 1, 2, 3, 6 and 9, or D-Phe in positions 2 and 3 for comparison. The most potent analog in this series, with D-Tic in position 6, fully inhibited ovulation at 2.5 micrograms compared to near complete inhibition at 0.5 microgram for the parent compound. A theoretical analysis of the conformational restrictions imposed on mainchain and sidechain torsional angles by the incorporation of Tic was conducted in vacuo using molecular mechanics techniques. Using cyclo(4-10)-[Ac-delta 3Pro1,DCpa2,DTrp3,Asp4,DNal6,Dpr10]- GnRH as a template conformer for which NMR conformational data is available, it was found that the potency of the different analogs correlated with the strain energy required to deform the mainchain and backbone angles of residues to values which would be expected if Tic were present and if the analog assumed the same solution structure. In particular, the effect of DTic at position 6 is to maintain the type II' beta-turn involving residues 5-8 found in active GnRH analogs.

Theoretical studies on the dihydrofolate reductase mechanism: electronic polarization of bound substrates.

We have applied local density functional theory, an ab initio quantum mechanical method, to study the shift in the spatial electron density of the substrate dihydrofolate that accompanies binding to the enzyme dihydrofolate reductase. The results shed light on fundamental electronic effects due to the enzyme that may contribute to catalysis. In particular, the enzyme induces a long-range polarization of the substrate that perturbs its electron density distribution in a specific and selective way in the vicinity of the bond that is reduced by the enzyme. Examination of the electron density changes that occur in folate reveals that a similar effect is seen but this time specifically at the bond that is reduced in this substrate. This suggests that the polarization effect may be implicated in the reaction mechanism and may play a role in determining the sequence whereby the 7,8-bond in folate is reduced first, followed by reduction of the 5,6-bond in the resulting dihydro compound.

Influence of environment on the antifolate drug trimethoprim: energy minimization studies.

Environmental effects on trimethoprim (TMP), an inhibitor of bacterial dihydrofolate reductase (DHFR), were investigated with energy minimizations in vacuo, in the crystal, and in aqueous solution. The conformations, harmonic dynamics, and energetics of the antibacterial drug calculated in these environments were compared with each other and with those of two enzyme-bound drugs. Valence and torsion angles and their energies and overall intra- and intermolecular energies compensated one another in the minimized TMP structures. The conformations of the isolated and aqueous molecules were similar to that of TMP bound to chicken liver DHFR, while the structures from the TMP crystal and from the Escherichia coli DHFR complex were unique. Since neither the small-molecule crystal nor a local minimum of the isolated molecule gave the conformation of TMP bound to the bacterial enzyme, a combination of several experimental and theoretical techniques may be necessary to probe accessible conformations of a molecule.

The electrostatic potential of Escherichia coli dihydrofolate reductase.

Escherichia coli dihydrofolate reductase (DHFR) carries a net charge of -10 electrons yet it binds ligands with net charges of -4 (NADPH) and -2 (folate or dihydrofolate). Evaluation and analysis of the electrostatic potential of the enzyme give insight as to how this is accomplished. The results show that the enzyme is covered by an overall negative potential (as expected) except for the ligand binding sites, which are located inside "pockets" of positive potential that enable the enzyme to bind the negatively charged ligands. The electrostatic potential can be related to the asymmetric distribution of charged residues in the enzyme. The asymmetric charge distribution, along with the dielectric boundary that occurs at the solvent-protein interface, is analogous to the situation occurring in superoxide dismutase. Thus DHFR is another case where the shape of the active site focuses electric fields out into solution. The positive electrostatic potential at the entrance of the ligand binding site in E. coli DHFR is shown to be a direct consequence of the presence of three positively charged residues at positions 32, 52, and 57--residues which have also been shown recently to contribute significantly to electronic polarization of the ligand folate. The latter has been postulated to be involved in the catalytic process. A similar structural motif of three positively charged amino acids that gives rise to a positive potential at the entrance to the active site is also found in DHFR from chicken liver, and is suggested to be a common feature in DHFRs from many species. It is noted that, although the net charges of DHFRs from different species vary from +3 to -10, the enzymes are able to bind the same negatively charged ligands, and perform the same catalytic function.

Predicted three-dimensional structure of the protease inhibitor domain of the Alzheimer's disease beta-amyloid precursor.

Alzheimer's disease is characterized by the deposition of amyloid beta-protein as plaques and tangles in the brains of its victims. The amyloid precursor can be expressed with or without the inclusion of a protease inhibitor domain, the potential role of which in amyloidogenesis has prompted the generation of a model of its three-dimensional structure based on the known structure of a related inhibitor. The model structure predicts that the mutated residues are almost entirely on the surface of the inhibitor domain, while conserved residues constitute the hydrophobic core. In addition, several pairs of structurally complementary, or concerted, mutations are seen. These structural features provide strong evidence for the validity of the modeled structure, and it is suggested that the presence of complementary mutations may be used as a criterion for evaluating protein structures built by homology, in addition to the (spatial) location of the mutations. The terminal residues delimiting the domain are among those furthest from the protease binding site and are in close proximity to one another, thus suggesting the ability of the domain to function as a structural cassette within the context of a larger protein. The electrostatic potentials of the inhibitor and of the related bovine pancreatic trypsin inhibitor reveal how two inhibitors with very different net charges can bind with approximately the same binding constant to trypsin and suggest a mutation of trypsin that might selectively enhance the binding of the amyloid inhibitor domain. The model provides a structural basis for understanding the functional roles of residues in the domain and for designing simpler molecules to test as pharmacologic agents for intervention in Alzheimer's disease.

Electron redistribution on binding of a substrate to an enzyme: folate and dihydrofolate reductase.

The migration of electron density of a substrate (folate) on binding to an enzyme (dihydrofolate reductase) is studied by a quantum-mechanical method originally developed in solid state physics. A significant polarization of the substrate is induced by the enzyme, toward the transition state of the enzymatic reaction, at the same time giving rise to "electronic strain energy" in the substrate and enhanced protein-ligand interactions. The spatial arrangement of protein charges that induces the polarization is identified and found to be structurally conserved for bacterial and vertebrate dihydrofolate reductases.

Changes in the electron density of the cofactor NADPH on binding to E. coli dihydrofolate reductase.

Quantum-mechanical electron density calculations reveal that a significant polarization is induced in the cofactor NADPH (reduced nicotinamide adenine dinucleotide phosphate) on binding to the enzyme dihydrofolate reductase. The calculations indicate that electron density corresponding to approximately 0.7 electron charges is shifted within the molecule, extending over more than 20 A. Further calculations on proposed enzyme mutants show that the polarization of NADPH on binding to DHFR is, in large part, induced by a motif of three positively charged residues. This motif was also identified to be directly responsible for the positive electrostatic potential surrounding the cofactor binding site in the enzyme. The possibility of this long-range polarization of NADPH was originally proposed based on a previous study of ligand binding to DHFR where a conserved structural motif of three positively charged residues was found to play a major role in polarizing the substrate folate over its entire length of 18 A.

Molecular dynamics study of the structure and dynamics of a protein molecule in a crystalline ionic environment, Streptomyces griseus protease A.

A large-scale molecular dynamics simulation of the behavior of a serine protease (Streptomyces griseus protease A) in a crystalline environment has been performed. All atoms (including hydrogens) of two protein molecules and the surrounding solvent of crystallization, consisting of both water and salt ions, were explicitly represented, and a relatively long range of interactions (up to 15 A) were included. The simulation is the longest so far reported for a protein in such an environment (60 ps). The use of the full crystalline environment allows a direct comparison of the structure and dynamic properties of the protein and surrounding solvent to be made with the experimental X-ray structure. Here we report the comparison of the protein structures and analyze the energetics of the system, including interaction with the aqueous environment. Subsequent papers will deal with other aspects of the simulation. The overall root mean square differences between the time-averaged molecular dynamics structure and that from crystallography, for all well-ordered, non-hydrogen atoms, are 1.67 and 1.25 A for the two molecules taken as the asymmetric unit. An extensive analysis of the conformation of substructural elements and individual residues and their deviation from experiment has revealed a strong influence of the ionic medium on their behavior. Implications of the results for free energy calculations and for future directions are also discussed.

Design of biologically active, conformationally constrained GnRH antagonists.

The introduction of conformational constraints into a flexible peptide hormone can be exploited to develop models for the conformation required for receptor binding and activity. In this review, we illustrate this approach to analog design using our work on antagonists of gonadotropin-releasing hormone (GnRH). Design of a conformationally constrained, competitive antagonist of GnRH, cyclo[delta 3,4 Pro-D4ClPhe-DTrp-Ser-Tyr-DTrp-NMeLeu-Arg-Pro-bet a Ala] led to the prediction of its bioactive conformation. Template forcing experiments show that this conformation is accessible to other active GnRH analogs. Two-dimensional NMR studies verified the predicted conformation in solution. The predicted binding conformation has recently been used to design two new analogs incorporating side chain-side chain linkages suggested by the conformational model: Ac-delta 3,4Pro-D4FPhe-DTrp-Dap-Tyr-DTrp-Leu-Arg-Asp-Gly- NH2 and Ac-delta 3,4Pro-D4FPhe-DTrp-Dap-Tyr-D2Nal-Leu-Arg-Pro-Asp -NH2. These analogs were synthesized and the one predicted to be most similar to the parent conformation had equivalent potency while the second, designed to refine the conformational hypothesis, was found to exhibit enhanced potency, thus confirming the original binding conformation hypothesis. These compounds and their derivatives now provide a new class of GnRH antagonists possessing both high biological potency and limited conformational flexibility, thus making them ideal for both biophysical and structure-activity studies.

Catalysis of a rotational transition in a peptide by crystal forces.

Detailed examination of the dynamics trajectories of the isolated cyclic peptide cyclo-(Ala-Pro-D-Phe)2 and of the molecule in its crystalline environment led to the unexpected observation that the methyl groups of the alanine residues rotated more frequently during a simulation in the crystal environment than in a simulation of the isolated peptide. In effect, the crystal environment is "catalyzing" the rotational isomerization of the methyl groups. In order to understand how the crystal forces increase the rate of this rotation, and to explore any possible analogy to the inducing of strained conformations of ligands by enzymes, the barriers to rotation in the two environments were studied by using the torsion angle forcing method. The crystal forces induce a different, higher energy, conformation of the peptide than is found for the isolated molecule, and the different rates of rotation have been explained in terms of the resulting specific intramolecular interactions that, it turns out, give rise to the lower rotational barrier. Molecular dynamics simulations of the peptide were also run at higher temperatures in order to calculate the barriers to rotation through the use of Arrhenius plots. The barriers obtained in this way agree well with the barriers obtained through an adiabatic reaction path derived by rotating the methyl through the barrier while minimizing all remaining degrees of freedom. The rates of rotation calculated from these adiabatic barriers also agree well with the rates observed during the 300 K simulations.