A comparison of optimal and suboptimal RNA secondary structures predicted by free energy minimization with structures determined by phylogenetic comparison.

This article describes the latest version of an RNA folding algorithm that predicts both optimal and suboptimal solutions based on free energy minimization. A number of RNA's with known structures deduced from comparative sequence analysis are folded to test program performance. The group of solutions obtained for each molecule is analysed to determine how many of the known helixes occur in the optimal solution and in the best suboptimal solution. In most cases, a structure about 80% correct is found with a free energy within 2% of the predicted lowest free energy structure.     

Accurate NMR structures through minimization of an extended hybrid energy

The use of generous distance bounds has been the hallmark of NMR structure determination. However, bounds necessitate the estimation of data quality before the calculation, reduce the information content, introduce human bias, and allow for major errors in the structures. Here, we propose a new rapid structure calculation scheme based on Bayesian analysis. The minimization of an extended energy function, including a new type of distance restraint and a term depending on the data quality, results in an estimation of the data quality in addition to coordinates. This allows for the determination of the optimal weight on the experimental information. The resulting structures are of better quality and closer to the X-ray crystal structure of the same molecule. With the new calculation approach, the analysis of discrepancies from the target distances becomes meaningful. The strategy may be useful in other applications-for example, in homology modeling.     

Dynamics of phosphatidylcholine-cholesterol mixed model membranes in the liquid crystalline state.

The effects of cholesterol on the dynamics of cholestane spin probe (CSL) in various phosphatidylcholine-cholesterol mixed model membranes are examined. The lateral diffusion, D of CSL in DMPC/POPC/cholesterol ternary mixtures, is measured utilizing an improved dynamic imaging electron spin resonance method. It shows a factor of two decrease at 10 mol % and 25 degrees C, whereas it shows only a 40% decrease at 50 mol % and 50 degrees C. A comparison with results in POPC/cholesterol mixtures, which show a stronger effect of cholesterol on D, indicates that acyl chain unsaturation leads to stronger self association of cholesterol in PC model membranes. An S2CSL dependence of the activation energy for D, has been confirmed for the DMPC/POPC/cholesterol mixtures. Here SCSL is the order parameter for CSL. A similar correlation of R perpendicular, the perpendicular component of the rotational diffusion coefficient, with SCSL, which is true for all three mixtures (DMPC/cholesterol, POPC/cholesterol, and DMPC/POPC/cholesterol) we have studied, is also found. These are associated with the effects of enhanced local ordering on the free volume needed for translation and reorientation. Such correlations of dynamic properties D and R perpendicular with the thermodynamic quantity S, as well as the consistent interpretations of the effect of acyl chain unsaturation on the dynamics in terms of the activity coefficients, strongly emphasize the interrelation between the dynamic structure and the thermodynamics of the PC/cholesterol mixtures.     

Configurations of fatty acyl chains in egg phosphatidylcholine-cholesterol mixed bilayers

Based on the structural properties of cholesterol and egg phosphatidylcholine, and on the assumption that the van der Waals' type attactive interaction between the steroid nucleus and the fatty acyl chains provides a stabilizing force for the cholesterol-egg phosphatidylcholine complex, some specific orientation and configurations of the fatty acyl chains around the steroid nucleus in the interacting system are proposed in terms of an optimal packing. The proposed model suggests that the saturated chains are largely facing the flattened (α) surface of the steroid nucleus of cholesterol, while the unsaturated chains can interact with both the α and β surfaces of the steroid nucleus. It is also suggested that the angular methyl groups on the β surface of the steroid nucleus lock the unsaturated fatty acyl chain in a relatively immobile configuration. Experimental evidence which provides support for the proposed stereochemical model is presented.     

Conformational characteristics of mixed sugar puckered deoxytetranucleoside triphosphate d-GpCpGpC from energy minimization studies

As a continuation of our theoretical studies on nucleic acid subunit systems, in this article we consider the case of the tetranucleoside d-GpCpGpC, the minimally ideal representative unit for analyzing the relative stabilities of different forms of homo- and mixed helical conformation of polynucleotides. The four sugar rings are kept so as to generate B-genus, B+A genus and Z-genus conformations. Twenty five helical conformational states which resulted from judicious mixing of A-, B-, C-, W-, and Z-, states locally are subjected to energy minimization permitting the 19 dihedral angles to vary simultaneously. Conformational states corresponding to regular helical forms and mixed helical forms, when analyzed provide valuable information as to the local conformational flexibility and transitions available to polynucleotides.     

Thermodynamics of phosphatidylcholine-cholesterol mixed model membranes in the liquid crystalline state studied by the orientational order parameter.

It is shown that good estimates of the activity of cholesterol in phosphatidylcholine-cholesterol mixed model membranes are obtained by examining the orientational order parameter S of cholestane spin probe (CSL) that is obtained from electron spin resonance by spectral simulation. By introducing thermodynamic stability conditions of liquid mixtures, the variation of activity (or S) as a function of cholesterol mole fraction is utilized to predict the concentration at which the phase separation occurs. These results for DMPC and cholesterol binary mixtures agree very well with those of Tempo-partitioning experiments. The comparison of activity coefficients and the phase boundary in DMPC/cholesterol mixtures with those of POPC/cholesterol mixtures suggests that acyl chain unsaturation leads to poorer mixing of cholesterol in phosphatidylcholine model membranes at higher temperatures (i.e., greater than 35 degrees C). In ternary solutions of DMPC, POPC, and cholesterol, it is found that cholesterol shows less deviation from ideality than in either of the two binary mixtures, and this implies that the phase separation occurs at higher cholesterol concentration than in either of the two binary mixtures. The present analysis suggests that there may not be a critical point in DMPC/cholesterol mixtures, even though phase separation does occur.     

Conformational characteristics of mixed sugar puckered deoxydinucleoside triphosphate units d-pCpGp and d-pGpCp from energy minimization studies

The deoxydinucleoside triphosphate units d-pCpGp and d-pGpCp were subjected to a rigorous theoretical investigation with a view to describing their distinctive conformational characteristics. For each unit 216 probable three-dimensional forms defined by the backbone-base dihedral angles and sugar pucker modes were considered for conformational energy minimization process and scrutinized with reference to properties, such as base-stacking, hydrogen-bonding, internal flexibility and base sequence-phosphate influence. The P-O bond torsions and the phosphate groups were treated with special attention. The results reveal a number of preferred conformational states other than the known helical forms, such as, A-, B-, C-, Z-, and Watson-Crick conformation. Many interesting one-step (change in only one of the dihedral angles or sugar puckers) conformational transitions which involve just about a kcal/mol of energy came to light. The two base sequences CG and GC were noted to differ strikingly in many of their conformational characteristics.     

The solubilisation of some steroids by phosphatidylcholine and phosphatidylcholine-cholesterol vesicles.

The solubility of the three steroid hormones, progesterone, testosterone, and estradiol-17 beta in water and phosphatidylcholine vesicles was measured after shaking and ultrasonication. All three steroids have low water solubility, which increases considerably at sonication for testosterone and estradiol-17 beta. The phosphatidylcholine vesicles have a very small solubilising capacity for the steroids; about 20 mumol/mol. This increases at sonication for estradiol-17 beta and decreases for testosterone. The capacity for progesterone is almost unaltered. The incorporation of cholesterol in the vesicles decreased the solubilisation capacity for testosterone and estradiol-17 beta but increased that for progesterone of shaked preparations. For the sonicated systems the cholesterol decreased the solubilising capacity for estradiol-17 beta but increased that for testosterone. The solubilisation experiments indicate that the steroid hormones are solubilised in the hydrocarbon part of the phosphatidylcholine bilayer and also 13CNMR results support this conclusion.     

Multibilayer structure of dimyristoylphosphatidylcholine dihydrate as determined by energy minimization

Complete energy minimization was carried out on the multibilayer crystal structure of 1,2-dimyristoyl-sn-glycero-3-phosphocholine dihydrate (DMPC.2H2O), starting from the X-ray structure determination reported by Pearson and Pascher (1979) Nature 281, 499-501. The asymmetric unit contains two nonidentical DMPC molecules and four water molecules. Minimization removed the acyl chain disorder present in the X-ray structure and caused the carbon planes of the acyl chains to become mutually parallel. Two energy-minimized structures (structures I and II) were found which mainly differed in the hydrogen-bonding arrangement of the waters of hydration. In structure I as in the X-ray structure, one of the water molecules forms a hydrogen-bonded bridge between successive bilayers; but in structure II, all hydrogen bonds are satisfied on the same bilayer. Structure II corresponds to the global energy minimum and is also a suitable structure for single bilayers. The lattice constants and cell volume of the minimized structures are close to the experimental values. The electrostatic force between DMPC bilayers is attractive. The mean hydration energy of the water is -14.2 kcal/mol, which is 2.5 kcal/mol lower than the binding energy of ice.     

The T<-->R structural transition of insulin; pathways suggested by targeted energy minimization.

The transition of insulin between its crystallographically defined states T and R is connected with considerable change even of backbone structure: the N-terminal B chain (residues B1-B8) refolds from extended conformation in T into helical in R, and vice versa. Although hitherto observed only in hexamers the transition of the monomer was adequate for developing and testing the method of 'targeted energy minimization' (TEM), capable of coping with conformational changes of such extent at moderate computational expenditure. The simulation is performed in a predetermined number of steps consisting of two atomic displacements each, one by force in the direction of the target structure, the second by energy minimization releasing the constraint caused in the first. The transition pathway is represented by the string of energy minimized transient structures. Due to the directedness of the algorithm the simulated pathway for R-->T is not the reversal of that for T-->R. It is, therefore, not pretended that the minimum energy pathway was identified. In the T-->R direction the N-terminal B chain first swivels while remaining largely stretched and then winds up extending the pre-existing helix B9-B19. The A chain advances into the space abandoned and withdraws from it in the R-->T simulation. In the latter the extended helix first kinks at B8/B9, and then the B1-B8 segment is unwound and stretched. The helical H-bonds of that segment are formed late in T-->R and are maintained during almost half of R-->T. The AN helix is less stable and more involved in the transitions than helix AC.(ABSTRACT TRUNCATED AT 250 WORDS)     

Thermodynamics and dynamics of phosphatidylcholine-cholesterol mixed model membranes in the liquid crystalline state: effects of water.

A method for obtaining the thermodynamic activity of each membrane component in phosphatidylcholine (PC)/cholesterol mixtures, that is based upon ESR spin labeling is examined. The thermodynamic activity coefficients, gamma PC and gamma chol, for the PC and cholesterol, respectively, are obtained from the measured orientational order parameters, SPC and S(chol), as a function of cholesterol content for a spin-labeled PC and the sterol-type cholestane spin probe (CSL), respectively, and the effects of water concentration are also considered. At water content of 24 weight%, the thermodynamics of DMPC/cholesterol/water mixtures in the liquid-crystalline state may be treated as a two-component solution ignoring the water, but at lower water content the role of water is important, especially at lower cholesterol concentrations. At lower water content (17 wt%), gamma chol decreases with increasing cholesterol content which implies aggregation. However, at higher water content (24 wt%), gamma chol is found initially to increase as a function of cholesterol content before decreasing at higher cholesterol content. This implies a favorable accommodation for the cholesterol in the membrane at high water and low cholesterol content. Good thermodynamic consistency according to the Gibbs-Duhem equation was obtained for gamma PC and gamma chol at 24 wt% water. The availability of gamma chol (and gamma PC) as a function of cholesterol concentration permits the estimate of the boundary for phase separation. The rotational diffusion coefficients of the labeled PC and of CSL were also obtained from the ESR spectra. A previously proposed universal relation for the perpendicular component of the rotational diffusion tensor, R perpendicular, for CSL in PC/cholesterol mixtures (i.e., R perpendicular = R0 perpendicular exp(-AS2chol/RT)) is confirmed. A change in composition of cholesterol or of water for DMPC/cholesterol/water mixtures affects R perpendicular only through the dependence of S(chol) on the composition. In particular, the amount of water affects the membrane fluidity, monitored by R perpendicular for CSL, solely by the structural changes it induces in the membrane for the compositions studied. Rotational diffusion for the labeled PC is found to be more complex, most likely due to the combined action of the internal modes of motion of the flexible chain and of the overall molecular reorientation.     

Conformational studies of cyclic peptide structures in solution from 1H-Nmr data by distance geometry calculation and restrained energy minimization

The three-dimensional structure of a cyclic bouvardin analogue, cyclo (-Pro-MeTyr-Ala-MeTyr-MeTyr-D-Ala-) has been determined by distance geometry calculation and restrained energy minimization from nmr data. The preparation of the input for the distance geometry calculations, the modification of the amino acid library, and the analysis of the structures were done with the aid of a recently developed software package, GEOM. A great variety of different initial structures were explored to check the uniqueness of the determined solution structure. Calculations with 500 different initial structures and two different strategies led to a uniquely determined backbone conformation with a root mean square deviations value of 0.4 A. The backbone structure consists of two beta-turns, a beta-II turn at Pro1-MeTyr2, and a beta-VI turn at MeTyr4-MeTyr5. The efficiency of the two calculation strategies were compared in order to propose an optimal means for performing distance geometry calculations with cyclic structures.     

PMR studies of phosphatidylcholine-cholesterol vesicles interacting with lucensomycin.

Spin-lattice relaxation times (T1) were measured above the phase transition temperature on sonicated vesicles of egg- or dipalmitoyl-phosphatidylcholine containing cholesterol and/or the polyenic antibiotic, lucensomycin. T1 values of only the terminal methyl groups of the fatty acyl chains were significantly reduced by cholesterol. Lucensomycin caused, more markedly in cholesterol-containing vesicles, a selective reduction of the T1 values of the N-methyl groups. An even more conspicuous decrease, occurring only in cholesterol-containing vesicles, was observed for the transverse relaxation times (T2) of the N-methyl signals upon addition of lucensomycin. The polyene failed to remove the well-known broadening effect of cholesterol on phosphatidylcholine methylene signals. These results indicate that as lucensomycin binds to cholesterol-containing membranes, there is a detectable perturbation of the dynamic structure of the N-methyl groups with an increase in the degree of motional anisotropy. But the non-polar region of the bilayer seems not significantly perturbed by the polyene.     

Fold helical proteins by energy minimization in dihedral space and a DFIRE-based statistical energy function

Statistical energy functions are discrete (or stepwise) energy functions that lack van der Waals repulsion. As a result, they are often applied directly to a given structure (native or decoy) without further energy minimization being performed to the structure. However, the full benefit (or hidden defect) of an energy function cannot be revealed without energy minimization. This paper tests a recently developed, all-atom statistical energy function by energy minimization with a fixed secondary helical structure in dihedral space. This is accomplished by combining the statistical energy function based on a distance-scaled finite ideal-gas reference (DFIRE) state with a simple repulsive interaction and an improper torsion energy function. The energy function was used to minimize 2000 random initial structures of 41 small and medium-sized helical proteins in a dihedral space with a fixed helical region. Results indicate that near-native structures for most studied proteins can be obtained by minimization alone. The average minimum root-mean-squared distance (rmsd) from the native structure for all 41 proteins is 4.1 A. The energy function (together with a simple clustering of similar structures) also makes a reasonable selection of near-native structures from minimized structures. The average rmsd value and the average rank for the best structure in the top five is 6.8 A and 2.4, respectively. The accuracy of the structures sampled and the structure selections can be improved significantly with the removal of flexible terminal regions in rmsd calculations and in minimization and with the increase in the number of minimizations. The minimized structures form an excellent decoy set for testing other energy functions because most structures are well-packed with minimum hard-core overlaps with correct hydrophobic/hydrophilic partitioning. They are available online at http://theory.med.buffalo.edu.     

Inverted micellar structures in bilayer membranes. Formation rates and half-lives.

Two sorts of inverted micellar structures have previously been proposed to explain morphological and 31P-NMR observations of bilayer systems. These structures only form in systems with components that can adopt the inverse hexagonal (HII) phase. LIP (lipidic particles) are intrabilayer structures, whereas IMI (inverted micellar intermediates) are structures that form between apposed bilayers. Here, we calculate the formation rates and half-lives of these structures to determine which (or if either) of these proposed structures is a likely explanation of the data. Calculations for the egg phosphatidylethanolamine and the Ca+-cardiolipin systems show that IMI form orders of magnitude faster than LIP, which should form slowly, if at all. This result is probably true in general, and indicates that "lipidic particle" electron micrograph images probably represent interbilayer structures, as some have previously proposed. It is shown here that IMI are likely intermediates in the lamellar----HII phase transitions and in the process of membrane fusion in some systems. The calculated formation rates, half-lives, and vesicle-vesicle fusion rates are in agreement with this observation.     

Tertiary structure prediction of mixed α/β proteins via energy minimization

We describe an improved algorithm for protein structure prediction, assuming that the location of secondary structural elements is known, with particular focus on prediction for proteins containing β-strands. Hydrogen bonding terms are incorporated into the potential function, supplementing our previously developed residue-residue potential which is based on a combination of database statistics and an excluded volume term. Two small mixed α/β proteins, 1-CTF and BPTI, are studied. In order to obtain native-like structures, it is necessary to allow the β-strands in BPTI to distort substantially from an ideal geometry, and an automated algorithm to carry this out efficiently is presented. Simulated annealing Monte Carlo methods, which contain a genetic algorithm component as well, are used to produce an ensemble of low-energy structures. For both proteins, a cluster of structures with low RMS deviation from the native structure is generated and the energetic ranking of this cluster is in the top 2 or 3 clusters obtained from simulations. These results are encouraging with regard to the possibility of constructing a robust procedure for tertiary folding which is applicable to β-strand containing proteins. Proteins 33:240–252, 1998. © 1998 Wiley-Liss, Inc.     

Microimmiscibility and three-dimensional dynamic structures of phosphatidylcholine-cholesterol membranes: translational diffusion of a copper complex in the membrane

Saturated and unsaturated phosphatidylcholine (PC)-cholesterol membranes have been studied, with a special attention paid to fluid-phase immiscibility in cis-unsaturated phosphatidylcholine (PC)-cholesterol membranes as previously proposed and to the three-dimensional structure of the membrane. The investigation was carried out with dual probes: a membrane-soluble, square-planar copper complex, (3-ethoxy-2-oxobutyraldehyde bis(N4,N4-dimethylthiosemicarbazonato]copper(II) (CuKTSM2), and one of several nitroxide radical lipid-type spin-labels. Bimolecular collision rates between metal ion and spin-label were determined by measuring the nitroxide spin-lattice relaxation times (T1's) in the presence and absence of CuKTSM2 by use of saturation-recovery ESR techniques, and from these measured rates, translational diffusion coefficients of CuKTSM2 were estimated. Profiles of the collision rate across the membrane bilayer were obtained with Tempocholine phosphatidic acid ester, 5-doxylstearic acid, 16-doxylstearic acid, and cholesterol-type spin-labels as a function of cholesterol mole fraction, length and unsaturation of acyl chains, and temperature. In the liquid-crystalline phase of saturated PC membranes, incorporation of cholesterol decreases the collision rate at all depths in the membrane, and the effect of cholesterol is smallest in the middle of the bilayer. In trans-unsaturated PC membranes, a cholesterol-induced decrease of the collision rate was also observed, except in the head-group regions. In cis-unsaturated PC membranes, virtually no effect of cholesterol was observed on the collision rate, either with phospholipid-type spin-labels or with cholesterol-type spin-labels. This result is in clear contrast with our previous observation, in which the effect of cholesterol in cis-unsaturated PC membranes is small on the alkyl-chain motion of phospholipid-type spin-labels but large on the wobbling rotational diffusion of cholesterol-type spin-labels [Pasenkiewicz-Gierula, M., Subczynski, W. K., & Kusumi, A. (1990) Biochemistry 29, 4059-4069]. A model is proposed to explain these results in which the fluid-phase immiscibility is prevalent in cis-unsaturated PC-cholesterol membranes, but where cholesterol-rich (cholesterol oligomeric) domains are small (several lipids) and/or of short lifetime (10(-9) s to less than 10(-7) s). It is suggested that this microimmiscibility arises from the structural nonconformability between the rigid cholesterol ring structure and the rigid bend at the cis double bonds in PC alkyl chains.(ABSTRACT TRUNCATED AT 400 WORDS)     

Necessary conditions for avoiding incorrect polypeptide folds in conformational search by energy minimization

Low energy conformations have been generated for melittin, pancreatic polypeptide, and ribonuclease S-peptide, both in the vicinity of x-ray structures by energy refinement and by an unconstrained search over the entire conformational space. Since the structural polymorphism of these medium-sized peptides in crystal and solution is moderate, comparing the calculated conformations to x-ray and nmr data provides information on local and global behavior of potential functions. Local analysis includes standardization calculations, which show that models with standard geometry can approximate good resolution x-ray data with less than 0.5 Å rms deviation (RMSD). However, the atomic coordinates are shifted up to 2 Å RMSD by local energy minimization, and thus 2 Å is generally the smallest RMSD value one can target in a conformational search using the same energy evaluation models. The unconstrained search was performed by a buildup-type method based on dynamic programming. To accelerate the generation of structures in the conformational search, we used the ECEPP potential, defined in terms of standard polypeptide geometry. A number of low energy conformations were further refined by relaxing the assumption of standard bond lengths and bond angles through the use of the CHARMM potential, and the hydrophobic folding energies of Eisenberg and McLachlan were calculated. Each conformation is described in terms of the RMSD from the native, hydrogen-bonding structure, solvent-acessible surface area, and the ratio of surfaces corresponding to nonpolar and polar residues. The unconstrained search finds conformations that are different from the native, sometimes substantially, and in addition, have lower conformational energies than the native. The origin of deviations is different for each of the three peptides, but in all examples the refined x-ray structures have lower energies than the calculated incorrect folds when (1) the assumption of standard bond lengths and bond angles is relaxed; (2) a small and constant effective dielectric permittivity (ε < 10) is used; and (3) the hydrophobic folding energy is incorporated into the potential. © 1993 John Wiley & Sons, Inc.