CRANKITE: A fast polypeptide backbone conformation sampler

Background

CRANKITE is a suite of programs for simulating backbone conformations of polypeptides and proteins. The core of the suite is an efficient Metropolis Monte Carlo sampler of backbone conformations in continuous three-dimensional space in atomic details.

Methods

In contrast to other programs relying on local Metropolis moves in the space of dihedral angles, our sampler utilizes local crankshaft rotations of rigid peptide bonds in Cartesian space.

Results

The sampler allows fast simulation and analysis of secondary structure formation and conformational changes for proteins of average length.     

Comparison of a Monte Carlo Strategy with a Combined DG/MDSA Method for Structure Determination of Bicyclic Peptides

The MC simulation program MOCCA and the combined methods of Distance Geometry and Molecular Dynamics are utilised for structural studies of four isomers of the bee venom toxin apamin. For the MC strategy the conformational space is reduced to torsional degrees of freedom. The study compares the efficiency of both simulation strategies for structure determination of bicyclic peptides and examines the limits of the Monte Carlo method. MOCCA shows a lower efficiency as compared to the combined methods of Distance Geometry and Molecular Dynamics for the structure determination of the bicyclic isomers of apamin.Electronic Supplementary Material available.     

Monte Carlo simulations of a polymer chain conformation. The effectiveness of local moves algorithms and estimation of entropy

A linear chain on a simple cubic lattice was simulated by the Metropolis Monte Carlo method using a combination of local and non-local chain modifications. Kink-jump, crankshaft, reptation and end-segment moves were used for local changes of the chain conformation, while for non-local chain rearrangements the "cut-and-paste" algorithm was employed. The statistics of local micromodifications was examined. An approximate method for estimating the conformational entropy of a polymer chain, based on the efficiency of the kink-jump motion respecting chain continuity and excluded volume constraints, was proposed. The method was tested by calculating the conformational entropy of the undisturbed chain, the chain under tension and in different solvent conditions (athermal, theta and poor) and also of the chain confined in a slit. The results of these test calculations are qualitatively consistent with expectations. Moreover, the obtained values of the conformational entropy of self avoiding chain with ends fixed over different separations, agree very well with the available literature data.

Conformational dynamics of subtilisin-chymotrypsin inhibitor 2 complex by coarse-grained simulations

An off-lattice dynamic Monte Carlo (MC) method is used to investigate the conformational dynamics of chymotrypsin inhibitor 2 (CI2) and subtilisin in both free and complex forms over two time windows, referring to short and long time scales. The conformational dynamics of backbone bonds analysed from several independent trajectories reveal that: Both the inhibitor and the enzyme are restricted in their bond rotations, excluding a few bonds, upon binding; the effect being greatest for the loop regions, and for the inhibitor. A cooperativity in the near-neighbor bond rotations are observed on both time scales, whereas the cooperative rotations of the bonds far along the sequence appear only in the long time window, and the latter time window is where most of the interactions between the inhibitor and the enzyme are observed. Upon binding, the cooperatively rotating parts of the inhibitor and the enzyme are readjusted compared to their free forms, and new correlations appear. The binding loop, although it is the closest contact region, is not the only part of the inhibitor involved in the interactions with the enzyme. Loops 3 and 8 and the helices F and G in bound enzyme and the binding loop of the inhibitor contribute at the most to the collective motions of whole structure on the slow time scale and are apparently important for enzyme-inhibitor interactions and function. The results in general provide evidence for the contribution of the loops with cooperative motions to the extensive communication network of the complex.     

Conformational Dynamics of Subtilisin-Chymotrypsin Inhibitor 2 Complex by Coarse-Grained Simulations

Abstract

An off-lattice dynamic Monte Carlo (MC) method is used to investigate the conformational dynamics of chymotrypsin inhibitor 2 (CI2) and subtilisin in both free and complex forms over two time windows, referring to short and long time scales. The conformational dynamics of backbone bonds analysed from several independent trajectories reveal that: Both the inhibitor and the enzyme are restricted in their bond rotations, excluding a few bonds, upon binding; the effect being greatest for the loop regions, and for the inhibitor. A cooperativity in the near-neighbor bond rotations are observed on both time scales, whereas the cooperative rotations of the bonds far along the sequence appear only in the long time window, and the latter time window is where most of the interactions between the inhibitor and the enzyme are observed. Upon binding, the cooperatively rotating parts of the inhibitor and the enzyme are readjusted compared to their free forms, and new correlations appear. The binding loop, although it is the closest contact region, is not the only part of the inhibitor involved in the interactions with the enzyme. Loops 3 and 8 and the helices F and G in bound enzyme and the binding loop of the inhibitor contribute at the most to the collective motions of whole structure on the slow time scale and are apparently important for enzyme-inhibitor interactions and function. The results in general provide evidence for the contribution of the loops with cooperative motions to the extensive communication network of the complex.     

The Conformational Ensembles of α-Synuclein and Tau: Combining Single-Molecule FRET and Simulations

Intrinsically disordered proteins (IDPs) are increasingly recognized for their important roles in a range of biological contexts, both in normal physiological function and in a variety of devastating human diseases. However, their structural characterization by traditional biophysical methods, for the purposes of understanding their function and dysfunction, has proved challenging. Here, we investigate the model IDPs α-Synuclein (αS) and tau, that are involved in major neurodegenerative conditions including Parkinson’s and Alzheimer’s diseases, using excluded volume Monte Carlo simulations constrained by pairwise distance distributions from single-molecule fluorescence measurements. Using this, to our knowledge, novel approach we find that a relatively small number of intermolecular distance constraints are sufficient to accurately determine the dimensions and polymer conformational statistics of αS and tau in solution. Moreover, this method can detect local changes in αS and tau conformations that correlate with enhanced aggregation. Constrained Monte Carlo simulations produce ensembles that are in excellent agreement both with experimental measurements on αS and tau and with all-atom, explicit solvent molecular dynamics simulations of αS, with much lower configurational sampling requirements and computational expense.Abbreviations used: AAMD, all-atom molecular dynamics; ECMC, experimentally constrained Monte Carlo; ET_eff, energy transfer efficiency; (sm)FRET, (single molecule) Förster resonance energy transfer; IDP, intrinsically disordered protein; LJ, Lennard-Jones; MC, Monte Carlo; MD, molecular dynamics; PRE, paramagnetic relaxation enhancement; SAX(N)S, small-angle x-ray (neutron) scattering; UMC, unconstrained Monte Carlo     

Conformational dynamics of chymotrypsin inhibitor 2 by coarse-grained simulations

A coarse-grained dynamic Monte Carlo (MC) simulation method is used to investigate the conformational dynamics of chymotrypsin inhibitor 2 (CI2). Each residue is represented therein by two interaction sites, one at the alpha-carbon and the other on the amino acid side-chain. The energy and geometry parameters extracted from databank structures are used. The calculated rms fluctuations of alpha-carbon atoms are in good agreement with crystallographic temperature factors. The two regions of the protein that pack against each other to form the main hydrophobic core exhibit negatively correlated fluctuations. The conformational dynamics could efficiently be probed by the time-delayed orientational and conformational correlation functions of the virtual bonds: the active site loop, excluding the active site bond, the turn region, and the N-terminal of the alpha-helix are relatively more mobile regions of the structure. A correlation is observed between the hydrogen/deuterium (H/D) exchange behavior and the long-time orientational and conformational autocorrelation function values for CI2. A cooperativity in the rotations of the bonds near in sequence is observed at all time windows, whereas the cooperative rotations of the bonds far along the sequence appear at long time windows; these correlations contribute to the stability of the secondary structures and the tertiary structure, respectively.     

Efficient deformation algorithm for plasmid DNA simulations

Background

Plasmid DNA molecules are closed circular molecules that are widely used in life sciences, particularly in gene therapy research. Monte Carlo methods have been used for several years to simulate the conformational behavior of DNA molecules. In each iteration these simulation methods randomly generate a new trial conformation, which is either accepted or rejected according to a criterion based on energy calculations and stochastic rules. These simulation trials are generated using a method based on crankshaft motion that, apart from some slight improvements, has remained the same for many years.

Results

In this paper, we present a new algorithm for the deformation of plasmid DNA molecules for Monte Carlo simulations. The move underlying our algorithm preserves the size and connectivity of straight-line segments of the plasmid DNA skeleton. We also present the results of three experiments comparing our deformation move with the standard and biased crankshaft moves in terms of acceptance ratio of the trials, energy and temperature evolution, and average displacement of the molecule. Our algorithm can also be used as a generic geometric algorithm for the deformation of regular polygons or polylines that preserves the connections and lengths of their segments.

Conclusion

Compared with both crankshaft moves, our move generates simulation trials with higher acceptance ratios and smoother deformations, making it suitable for real-time visualization of plasmid DNA coiling. For that purpose, we have adopted a DNA assembly algorithm that uses nucleotides as building blocks.     

A model for protein-DNA interaction dynamics

We map a simplified version of the protein-DNA interaction problem into an Ising-model in a random magnetic field. The model includes a "head" which moves along the chain while interacting with the underlying spins. The head moves by using the statistical fluctuations of base openings. A Monte Carlo (MC) simulation of this model reveals the possibility of biased diffusion in one direction, followed by sequence identification and binding. The model provides some insight into the mechanisms used by some repressor proteins to diffuse and bind to specific DNA-binding sites.     

Monte Carlo replica‐exchange based ensemble docking of protein conformations

A replica‐exchange Monte Carlo (REMC) ensemble docking approach has been developed that allows efficient exploration of protein–protein docking geometries. In addition to Monte Carlo steps in translation and orientation of binding partners, possible conformational changes upon binding are included based on Monte Carlo selection of protein conformations stored as ordered pregenerated conformational ensembles. The conformational ensembles of each binding partner protein were generated by three different approaches starting from the unbound partner protein structure with a range spanning a root mean square deviation of 1–2.5 Å with respect to the unbound structure. Because MC sampling is performed to select appropriate partner conformations on the fly the approach is not limited by the number of conformations in the ensemble compared to ensemble docking of each conformer pair in ensemble cross docking. Although only a fraction of generated conformers was in closer agreement with the bound structure the REMC ensemble docking approach achieved improved docking results compared to REMC docking with only the unbound partner structures or using docking energy minimization methods. The approach has significant potential for further improvement in combination with more realistic structural ensembles and better docking scoring functions. Proteins 2017; 85:924–937. © 2016 Wiley Periodicals, Inc.     

Maximum entropy approach to the determination of solution conformation of flexible polypeptides by global conformational analysis and NMR spectroscopy – Application to DNS1-c-[d-A2bu2, Trp4,Leu5]- enkephalin and DNS1-c-[d-A2bu2, Trp4, d-Leu5]enkephalin

A method is proposed to determine the conformational equilibrium of flexible polypeptides in solution, using the data provided by NMR spectroscopy and theoretical conformational calculations. The algorithm consists of the following three steps: (i) search of the conformational space in order to find conformations with reasonably low energy; (ii) simulation of the NOE spectrum and vicinal coupling constants for each of the low energy conformations; and (iii) determining the statistical weights of the conformations, by means of the maximum-entropy method, in order to obtain the best fit of the averaged NOE intensities and coupling constants to the experimental quantities. The method has been applied to two cyclic enkephalin analogs: DNS¹-c-[d-A₂bu²,Trp⁴,Leu⁵]enkephalin (ENKL) and DNS¹-c-[d-A₂bu²,Trp⁴,d-Leu⁵]enkephalin (ENKD). NMR measurements were carried out in deuterated dimethyl sulfoxide. Two techniques were used in conformational search: the electrostatically driven Monte Carlo method (EDMC), which results in extensive search of the conformational space, but gives only energy minima, and the molecular dynamics method (MD), which results in a more accurate, but also more confined search. In the case of EDMC calculations, conformational energy was evaluated using the ECEPP/3 force field augmented with the SRFOPT solvation-shell model, while in the case of MD the AMBER force field was used with explicit solvent molecules. Both searches and subsequent fitting of conformational weights to NMR data resulted in similar conformations of the cyclic part of the peptides studied. For both ENKL and ENKD a common feature of the low-energy solution conformations is the presence of a type II or type IV -turn at residues 3 and 4; the ECEPP/3 force field also gives a remarkable content of type III -turn. These -turns are tighter in the case of ENKL, which is reflected in different distributions of the d-A₂bu(NH)...d-A₂bu(CO) and d-A₂bu(NH)...Gly³(CO) hydrogen-bonding distances, indicating that the d-A₂bu(NH) amide proton is more shielded from the solvent than in the case of ENKD. This finding conforms with the results of temperature coefficient data of the d-A₂bu(NH) proton. It has also been found that direct (MD) or Boltzmann (EDMC) averages of the observables do not exactly conform with the measured values, even when explicit solvent molecules are included. This suggests that improving force-field parameters might be necessary in order to obtain reliable conformational ensembles in computer simulations, without the aid of experimental data.     

Picosecond dynamics in haemoglobin from different species: A quasielastic neutron scattering study

Background

Dynamics in haemoglobin from platypus (Ornithorhynchus anatinus), chicken (Gallus gallus domesticus) and saltwater crocodile (Crocodylus porosus) were measured to investigate response of conformational motions on the picosecond time scale to naturally occurring variations in the amino acid sequence of structurally identical proteins.

Methods

Protein dynamics was measured using incoherent quasielastic neutron scattering. The quasielastic broadening was interpreted first with a simple single Lorentzian approach and then by using the Kneller–Volino Brownian dynamics model.

Results

Mean square displacements of conformational motions, diffusion coefficients of internal dynamics and residence times for jump-diffusion between sites and corresponding effective force constants (resilience) and activation energies were determined from the data.

Conclusions

Modifications of the physicochemical properties caused by mutations of the amino acids were found to have a significant impact on protein dynamics. Activation energies of local side chain dynamics were found to be similar between the different proteins being close to the energy, which is required for the rupture of single hydrogen bond in a protein.

General significance

The measured dynamic quantities showed significant and systematic variations between the investigated species, suggesting that they are the signature of an evolutionary adaptation process stimulated by the different physiological environments of the respective protein.     

Challenges in structure prediction of oligomeric proteins at the united-residue level: searching the multiple-chain energy landscape with CSA and CFMC

A revised version of the Conformational Space Annealing (CSA) global optimization method is developed, with three separate measures of structural similarity, in order to overcome the inability of a single distance measure to evaluate multiple-chain protein structures adequately. A second search method, Conformational Family Monte Carlo (CFMC), involving genetic-type moves, Monte Carlo-with-minimization perturbations, and explicit clustering of the population into conformational families, is adapted to treat multiple-chain proteins. These two methods are applied to two oligomeric proteins, the retro-GCN4 leucine zipper and the synthetic domain-swapped dimer. CFMC proves superior to CSA in its search for low-energy representatives of its conformational families, but both methods encounter difficulty in finding the native packing arrangements in the absence of native-like symmetry constraints, even when native monomers are present in the population.     

Gibbs-Ensemble Molecular Dynamics: Liquid-Gas Equilibria for Lennard-Jones Spheres and n-Hexane

Abstract

We present a novel method to simulate phase equilibria in atomic and molecular systems. The method is a Molecular Dynamics version of the Gibbs-Ensemble Monte Carlo technique, which has been developed some years ago for the direct simulation of phase equilibria in fluid systems. The idea is to have two separate simulation boxes, which can exchange particles (or molecules) in a thermodynamically consistent fashion. Here we pres the derivation of the generalized equations of motion and discuss the relation of the resulting trajectory averages to the relevant ensemble. We test this Gibbs-Ensemble Molecular Dynamics algorithm by applying it to an atomic and a molecular system, i.e. to the liquid-gas coexistence in a Lennard-Jones fluid and in n-hexane. In both cases our results are in good accord with previous mean field and Gibbs-Ensemble Monte Carlo results as well as with the experimental data in the case of hexane. We also show that our Gibbs-Ensemble Molecular Dynamics algorithm like other Molecular Dynamics techniques can be used to study the dynamics of the system. Self-diffusion coefficients calculated with this method are in agreement with the result of conventional constant temperature Molecular Dynamics.     

Hamiltonian Monte Carlo methods for efficient parameter estimation in steady state dynamical systems

Background

Parameter estimation for differential equation models of intracellular processes is a highly relevant bu challenging task. The available experimental data do not usually contain enough information to identify all parameters uniquely, resulting in ill-posed estimation problems with often highly correlated parameters. Sampling-based Bayesian statistical approaches are appropriate for tackling this problem. The samples are typically generated via Markov chain Monte Carlo, however such methods are computationally expensive and their convergence may be slow, especially if there are strong correlations between parameters. Monte Carlo methods based on Euclidean or Riemannian Hamiltonian dynamics have been shown to outperform other samplers by making proposal moves that take the local sensitivities of the system’s states into account and accepting these moves with high probability. However, the high computational cost involved with calculating the Hamiltonian trajectories prevents their widespread use for all but the smallest differential equation models. The further development of efficient sampling algorithms is therefore an important step towards improving the statistical analysis of predictive models of intracellular processes.

Results

We show how state of the art Hamiltonian Monte Carlo methods may be significantly improved for steady state dynamical models. We present a novel approach for efficiently calculating the required geometric quantities by tracking steady states across the Hamiltonian trajectories using a Newton-Raphson method and employing local sensitivity information. Using our approach, we compare both Euclidean and Riemannian versions of Hamiltonian Monte Carlo on three models for intracellular processes with real data and demonstrate at least an order of magnitude improvement in the effective sampling speed. We further demonstrate the wider applicability of our approach to other gradient based MCMC methods, such as those based on Langevin diffusions.

Conclusion

Our approach is strictly benefitial in all test cases. The Matlab sources implementing our MCMC methodology is available from https://github.com/a-kramer/ode_rmhmc.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-253) contains supplementary material, which is available to authorized users.     

Conformational properties of glucose-based disaccharides investigated using molecular dynamics simulations with local elevation umbrella sampling

Explicit-solvent molecular dynamics (MD) simulations of the 11 glucose-based disaccharides in water at 300 K and 1 bar are reported. The simulations were carried out with the GROMOS 45A4 force-field and the sampling along the glycosidic dihedral angles ? and ψ was artificially enhanced using the local elevation umbrella sampling (LEUS) method. The trajectories are analyzed in terms of free-energy maps, stable and metastable conformational states (relative free energies and estimated transition timescales), intramolecular H-bonds, single molecule configurational entropies, and agreement with experimental data. All disaccharides considered are found to be characterized either by a single stable (overwhelmingly populated) state ((1→n)-linked disaccharides with n = 1, 2, 3, or 4) or by two stable (comparably populated and differing in the third glycosidic dihedral angle ; gg or gt) states with a low interconversion barrier ((1→6)-linked disaccharides). Metastable (anti-? or anti-ψ) states are also identified with relative free energies in the range of 8-22 kJ mol⁻¹. The 11 compounds can be classified into four families: (i) the α(1→1)α-linked disaccharide trehalose (axial-axial linkage) presents no metastable state, the lowest configurational entropy, and no intramolecular H-bonds; (ii) the four α(1→n)-linked disaccharides (n = 1, 2, 3, or 4; axial-equatorial linkage) present one metastable (anti-ψ) state, an intermediate configurational entropy, and two alternative intramolecular H-bonds; (iii) the four β(1→n)-linked disaccharides (n = 1, 2, 3, or 4; equatorial-equatorial linkage) present two metastable (anti-? and anti-ψ) states, an intermediate configurational entropy, and one intramolecular H-bond; (iv) the two (1→6)-linked disaccharides (additional glycosidic dihedral angle) present no (isomaltose) or a pair of (gentiobiose) metastable (anti-?) states, the highest configurational entropy, and no intramolecular H-bonds. The observed conformational preferences appear to be dictated by four main driving forces (ring conformational preferences, exo-anomeric effect, steric constraints, and possible presence of a third glycosidic dihedral angle), leaving a secondary role to intramolecular H-bonding and specific solvation effects. In spite of the weak conformational driving force attributed to solvent-exposed H-bonds in water (highly polar protic solvent), intramolecular H-bonds may still have a significant influence on the physico-chemical properties of the disaccharide by decreasing its hydrophilicity. Along with previous work, the results also complete the suggestion of a spectrum of approximate transition timescales for carbohydrates up to the disaccharide level, namely: ∼30 ps (hydroxyl groups), ∼1 ns (free lactol group, free hydroxymethyl groups, glycosidic dihedral angle in (1→6)-linked disaccharides), ∼10 ns to 2 μs (ring conformation, glycosidic dihedral angles ? and ψ). The calculated average values of the glycosidic torsional angles agree well with the available experimental data, providing validation for the force-field and simulation methodology employed.     

HYPER: A hierarchical algorithm for automatic determination of protein dihedral-angle constraints and stereospecific CβH2 resonance assignments from NMR data

A new computer program, HYPER, has been developed for automated analysis of protein dihedral angle values and CH₂ stereospecific assignments from NMR data. HYPER uses a hierarchical grid-search algorithm to determine allowed values of , , and ₁ dihedral angles and CH₂ stereospecific assignments based on a set of NMR-derived distance and/or scalar-coupling constraints. Dihedral-angle constraints are valuable for restricting conformational space and improving convergence in three-dimensional structure calculations. HYPER computes the set of , , and ₁dihedral angles and CH₂ stereospecific assignments that are consistent with up to nine intraresidue and sequential distance bounds, two pairs of relative distance bounds, thirteen homo- and heteronuclear scalar coupling bounds, and two pairs of relative scalar coupling constant bounds. The program is designed to be very flexible, and provides for simple user modification of Karplus equations and standard polypeptide geometries, allowing it to accommodate recent and future improved calibrations of Karplus curves. The C code has been optimized to execute rapidly (0.3–1.5 CPU-sec residue^–1 using a 5° grid) on Silicon Graphics R8000, R10000 and Intel Pentium CPUs, making it useful for interactive evaluation of inconsistent experimental constraints. The HYPER program has been tested for internal consistency and reliability using both simulated and real protein NMR data sets.     

Prediction of Conformational Free Energy Differences of Solutes in Solution∶ An MC-MST Study

This study reports an extension of the MC-MST method to explore the conformational space of molecules in condensed phases. The MC-MST method combines a Monte Carlo (MC) Metropolis algorithm to sample the conformational space with the semiclassical version of the Miertus-Scrocco-Tomasi (MST) continuum model to treat solvation effects. The extension of the MC-MST method to describe the solvent-induced changes in the conformational space is examined for 1,2-dichloroethane and the two tautomers of neutral histamine. The results allow us to discuss the capabilities of the MC-MST method to reproduce the conformational preferences of molecules in solution.     

Examination of structural characteristics of the potent oxytocin antagonists [dPen1,Pen6]-OT and [dPen1,Pen6, 5-tBuPro7]-OT by NMR, Raman, CD spectroscopy and molecular modeling.

The synthesis and biological evaluation of penicillamine(6)-5-tert-butylproline(7)-oxytocin analogs and comparison with their proline(7)-oxytocin counterparts has led to the discovery of two potent oxytocin (OT) antagonists: [dPen(1),Pen(6)]-oxytocin (1, pA(2) = 8.22, EC(50) = 6.0 nM) and [dPen(1),Pen(6),5-tBuPro(7)]-oxytocin (2, pA(2) = 8.19, EC(50) = 6.5 nM). In an attempt to understand the conformational requirements for their biological activity, spectroscopic analyses of 1 and 2 were performed using (1)H NMR, laser Raman and CD techniques. In H(2)O, oxytocin analogs 1 and 2 exhibited cis-isomer populations of 7% and 35%, respectively. Measurement of the amide proton temperature coefficients revealed solvent shielded hydrogens for Gln(4) and Pen(6) in the major trans-conformer of 1 as well as for Gln(4) in the minor cis-conformer of 2. Few long-distance NOEs were observed, suggesting conformational averaging for analogs 1 and 2 in water; moreover, a lower barrier (16.6 +/- 0.2 kcal/mol) for isomerization of the amide N-terminal to 5-tBuPro(7) relative to OT was calculated from measuring the coalescence temperature of the Gly(9) backbone NH signals in the NMR spectra of 2. Observed bands in the Raman spectra of 1 and 2 correspond to C(beta)-S-S-C(beta) dihedral angles of +110-115 degrees and +/-90 degrees , respectively. In water, acetonitrile and methanol, the CD spectra for 1 exhibited a positive maximum around 236-239 nm; in trifluoroethanol, the spectra shifted and a negative maximum was observed at 240 nm. The CD spectra of 2 were unaffected by solvent changes and exhibited a negative maximum at 236-239 nm. The CD and Raman data both suggested that a conformation having a right-handed screw sense about the disulfide and a chi(CS-SC) dihedral angle value close to 115 degrees was favored for analog 1 in water, methanol and acetonitrile, but not trifluoroethanol, where a +/-90 degrees angle was favored. Analog 2 was more resilient to conformational change about the disulfide, and adopted a preferred disulfide geometry corresponding to a +/-90 degrees chi(CS-SC) dihedral angle. Monte Carlo conformational analysis of analogs 1 and 2 using distance restraints derived from NMR spectroscopy revealed two prominent conformational minima for analog 1 with disulfide geometries around +114 degrees and +116 degrees . Similar analysis of analog 2 revealed one conformational minimum with a disulfide geometry around +104 degrees . In sum, the conformation about the disulfide in [dPen(1),Pen(6)]-OT (1) was shown to be contingent on environment and in TFE, adopted a geometry similar to that of [dPen(1),Pen(6),5-tBuPro(7)]-OT (2) which appeared to be stabilized by hydrophobic interactions between the 5-tBuPro(7) (5R)-tert-butyl group, the Leu(8) isopropyl sidechain and the Pen(6)beta-methyl substituents. In light of the conformational rigidity of 2 about the disulfide bond, and the similar geometry adopted by 1 in TFE, a S-S dihedral angle close to +110 degrees may be a prerequisite for their binding at the receptor.