Stereochemistry of nucleic acids and polynucleotides. VI. Minimum energy conformations of dimethyl phosphate

As part of a study on the conformation of polynucleotides and nucleic acids the preferred conformations of the model conpound dimethyl phosphate are worked out using potential energy functions. In calculating the total potential energy associated with the conformation, nonbonded, torsional, and electrostatic terms have been considered. The variation of the total conformational energy is represented as a function of two torsion angles ? and ψ which are the rotations about the two phosphoester bonds. The most stable conformations are found to be the gauche–gauche conformations about these bonds. The conformations observed for phosphodiesters in the solid state and in the proposed structures of polynucleotides and nucleic acids cluster around the minimum. Also, regions of minimum energy correspond well with the typical allowed regions of a representative dinucleotide.     

Minimum energy conformations of DNA dimeric subunits: Potential energy calculations for dGpdC,dApdA, dCpdC,dGpdG, and dTpdT

Minimum energy conformations have been calculated for the deoxydinucleoside phosphates dGpdC, dApdA, dCpdC, dGpdG, and dTpdT. In these potential energy calculations the eight diheldral angles and the sugar pucker were flexible parameters. A substantial survey of conformation space was made in which all staggred combination ofthe dihedral angles ω′,ω, and ψ, in conjuction with C(2′)-endo puker, were used as starting conformers for the energy minimization. The most important conformations in the C(3′)-endo-puckering domain have ψ = g⁺; ω′,ω = g^?,g^?(A-form),g⁺, g⁺, and g^?,t. With C(2′)-endo-type puker the most important conformations have ψ = g⁺; ω′,ω =g^_,g^_(B-form) and g⁺,t; and ψ =t; ω′,ω =g^_,t(Watson-Crick from) and t,g⁺ (skewed). Stacked bases are a persistent feature of the low-energy conformations, the g⁺ conformer being an exception. Freeing the suger puker allowed this conformation to become low energy, with C(3′)-exo puker. It also caused other low-energy forms, such and the Waston-Crick conformation, to become more favourable. Conformation flexibility in the sugar puker and in ψ, as well as the ω′,ω angle pair, is indicated for the dimeric subunits of DNA.     

Calculated minimum energy conformations of nonactin

Nonactin is a cyclic actinomycete metabolite which has been implicated as an ion carrier in the passive transport of potassium across certain biological membranes. In order to discover the conformations of the molecule which are involved in its biochemical function, computer calculations were initiated to derive the energetically favored conformations of the nonactin ring. By assuming that all the relevant three-dimensional conformations of nonactin have the same symmetry property as that suggested by the chemical structure of the molecule (S₄) it was possible to generate a representative sample of all sterically allowed conformations of nonactin. The energies of these conformations were calculated by taking into account the nonbonded interactions among the 116 atoms of the molecule and the torsional potential energy of the 20 rotatable backbone bonds of the ring. The initial results reported in this paper indicate that even in the absence of potassium ion the nonactin ring folds into the same compact tennis-ball seam-like conformation that was found by an X-ray crystallographic investigation of the nonactin/KNCS complex.     

Free energy of imperfect nucleic acid helices. II. Small hairpin loops

Physical studies of enzymically synthesized oligonucleotides of defined sequence are used to evaluate quantitatively the stability of small RNA hairpin loops and helices. The series (Ap)₄G(pC) _N(pU)₄, N = 4, 5 or 6, exists as monomolecular hairpin helices when N ≥ 5, and as imperfect dimer helices when N ≤ 4. In this size range, hairpin loops become more favorable (less destabilizing thermodynamically) as they increase in size from 3 to 4 to 5 unbonded nucleotides. Very small hairpin loops are particularly destabilizing; molecules whose base sequence would imply a hairpin loop of three nucleotides will generally exist with a loop of five, including a broken terminal base pair.Thermodynamic parameters for base pair and loop formation are calculated by a method which makes unnecessary the use of measured enthalpies of polynucleotide melting. Literature data on oligonucleotide double helices yield estimates of the free energy contribution from each of the six types of stacking interactions between three possible neighboring base pairs. The advantage of this approach is that the properties of oligonucleotides are used in predicting the stability of small RNA helices, avoiding the long extrapolation from the properties of high polymers.We provide Tables of temperature-dependent free energies that allow one to predict the stability and thermal transition temperature of many simple RNA secondary structures (applicable to ~1 m-Na⁺ concentration). As an example, we apply the rules to an isolated fragment of tRNA^Ser (yeast) (Coutts, 1971), whose properties were not used in calculating the free-energy parameters. The experimental melting temperature of 88 °C is predicted with an error margin of 5 deg. C.     

Geometry of proline-containing alpha-helices in proteins.

Crystal structure analysis of proline-containing alpha-helices in proteins has been carried out. High resolution crystal structures were selected from the Protein Data Bank. Apart from the standard internal parameters, some parameters which are specifically related to the bend in the helix due to proline have been developed and analyzed. Finally the position and nature of these helices and their interactions with the rest of the protein have been analyzed.     

Excited states and energy transfer among DNA bases in double helices.

The study of excited states and energy transfer in DNA double helices has recently gained new interest connected to the development of computational techniques and that of femtosecond spectroscopy. The present article points out contentious questions regarding the nature of the excited states and the occurrence of energy transfer and shows how they are currently approached. Using as example the polymer poly(dA) . poly(dT), composed of about 2000 adenine-thymine pairs, a model is proposed on the basis of time-resolved measurements (fluorescence decays, fluorescence anisotropy decays and fluorescence spectra, obtained with femtosecond resolution), associated to steady-state spectra. According to this qualitative model, excitation at 267 nm populates excited states that are delocalized over a few bases (excitons). Ultrafast internal conversion directs the excited state population to the lower part of the exciton band giving rise to fluorescence. Questions needing further investigations, both theoretical and experimental, are underlined with particular emphasis on delicate points related to the complexity and the plasticity of these systems.     

Calculating the free energy of association of transmembrane helices

A large number of experimental studies have been devoted to quantifying the interaction between transmembrane (TM) helices in detergent micelles and, more recently, in bilayers. Theoretical calculation of association free energy of TM helices would be useful for predicting the propensity of given sequences to oligomerize and for understanding the difference between association in micelles and in bilayers. In this article, the theoretical foundation for calculating the standard association free energy of TM helices is laid out and is applied to glycophorin A in both micelles and bilayers. The standard association free energy is decomposed into the effective energy, translational, rotational, and conformational entropy terms. The effective energy of association is obtained by molecular dynamics simulations in an implicit membrane model. The translational and rotational entropy of association is calculated from the probability distribution of the translational and rotational degrees of freedom obtained from the molecular dynamics simulations. The side-chain conformational entropy of association is estimated from the probability distribution obtained by rigid rotation of all side-chain dihedral angles. The calculated standard association free energy of glycophorin A in N-dodecylphosphocholine micelles is in good agreement with the experimental value. The translational entropy cost is larger, whereas the rotational entropy cost is smaller in bilayers than in micelles. The standard association free energy in 1,2-dimyristoyl-sn-glycero-3-phosphocholine bilayers is calculated to be approximately 1.3 kcal/mol more favorable than in N-dodecylphosphocholine micelles, consistent with available experimental data.     

The dynamics,structure, and conformational free energy of proline-containing antifreeze glycoprotein

Recent NMR studies of the solution structure of the 14-amino acid antifreeze glycoprotein AFGP-8 have concluded that the molecule lacks long-range order. The implication that an apparently unstructured molecule can still have a very precise function as a freezing inhibitor seems startling at first consideration. To gain insight into the nature of conformations and motions in AFGP-8, we have undertaken molecular dynamics simulations augmented with free energy calculations using a continuum solvation model. Starting from 10 different NMR structures, 20 ns of dynamics of AFGP were explored. The dynamics show that AFGP structure is composed of four segments, joined by very flexible pivots positioned at alanine 5, 8, and 11. The dynamics also show that the presence of prolines in this small AFGP structure facilitates the adoption of the poly-proline II structure as its overall conformation, although AFGP does adopt other conformations during the course of dynamics as well. The free energies calculated using a continuum solvation model show that the lowest free energy conformations, while being energetically equal, are drastically different in conformations. In other words, this AFGP molecule has many structurally distinct and energetically equal minima in its energy landscape. In addition, conformational, energetic, and hydrogen bond analyses suggest that the intramolecular hydrogen bonds between the N-acetyl group and the protein backbone are an important integral part of the overall stability of the AFGP molecule. The relevance of these findings to the mechanism of freezing inhibition is discussed.     

Free energy of imperfect nucleic acid helices. 3. Small internal loops resulting from mismatches

Physical studies of enzymioally synthesized oligoribonucleotides of defined sequence are used to evaluate quantitatively the destabilizing influence of mismatched bases in a double helix. The series (A-)₄G(-C)_n(-U)₄, N = 1 to 6, exist as imperfect dimer helices when N is equal to or less than 4, and as monomolecular hairpin helices when N is 5 and 6. Internal loops become progressively more destabilizing as their size increases from 2 to 4 to 6 nucleotides resulting from 1, 2 and 3 consecutive mismatched base pairs. However, the stability of a helix will generally be greater if a given number of mismatched pairs occur consecutively rather than in isolation from one another.These data may be used for improved calculations of stability of RNA secondary structure, to estimate the frequency of structural fluctuations in a double helix and to assess the stability of modified polynucleotide helices. An unmodified double helix of one million randomly arranged base pairs should contain on the time average approximately 10 G.C and 500 A.U pairs in non-hydrogen bonded, unstacked conformations at 25 °C. Our estimate of the effect of mismatching on T_m values of high polymers is less precise because of the long temperature extrapolation required. However, we estimate that DNA or RNA treated with mutagens which interrupt up to 20% of the nucleotide pairs will show a drop of about 1.2 deg. C in melting temperature with each unit per cent of modification.     

Determining minimum energy conformations of polypeptides by dynamic programming

A combinatorial optimization approach is used for solving the multiple-minima problem when determining the low-energy conformations of short polypeptides. Each residue is represented by a finite number of discrete states corresponding to single residue local minima of the energy function. These precomputed values constitute a search table and define the conformational space for discrete minimization by a generalized dynamic programming algorithm that significantly limits the number of intermediate conformations to be generated during the search. Since dynamic programming involves stagewise decisions, it results in buildup-type procedures implemented in two different forms. The first procedure predicts a number of conformations by a completely discrete search and these are subsequently refined by local minimization. The second involves limited continuous local minimization within the combinatorial algorithm, generally restricted to two dihedral angles in a buildup step. Both procedures are tested on 17 short peptides previously studied by other global minimization methods but involving the same potential energy function. The discrete method is extremely fast, but proves to be successful only in 14 of the 17 test problems. The version with limited local minimization finds, however, conformations in all the 17 examples that are close to the ones previously presented in the literature or have lower energies. In addition, results are almost independent of the cutoff energy, the most important parameter governing the search. Although the limited local minimization increases the number of energy evaluations, the method still offers substantial advantages in speed.     

Resistance of proline-containing peptides to ruminal degradation in vitro.

Mixed ruminal bacteria utilized an enzymatic digest of casein at a rate faster than that for an enzymatic digest of gelatin, but neither amino acid source was completely utilized even when the incubation period was as long as 96 h. Since the reaction of ninhydrin with the residual nonammonia, nonprotein nitrogen was more than twofold stronger when the samples were hydrolyzed with 6 N HCl, it appeared that much of the residual nitrogen was from peptides. Approximately 66% of the nonammonia, nonprotein, ninhydrin-reactive material could not be recovered as amino acids, but there was a significant decrease in total amino acid nitrogen when the samples were pretreated with a C18 Sep-Pak column to remove peptides. The resistant peptides had an abundance of proline, and subsequent incubations showed that synthetic dipeptides which contained proline were hydrolyzed slowly. Lysine appears to be the amino acid which is most apt to limit ruminant production. Dipeptides containing proline and lysine were hydrolyzed at least fivefold slower than lysine-alanine. Methionine, another potentially limiting amino acid, was also degraded at a slower (2.5-fold) rate when it was present as part of a proline dipeptide.     

Global minimum energy conformations of thyrotropin releasing hormone analogs by simulated annealing. II

Lowest conformational energy structures of seventeen thyrotropin releasing hormone analogs have been studied by simulated annealing. A surprising conformational similarity was observed for the peptide backbone. The possible role of each substituent in its biological activity is inferred. A composite hydrogen-bonding environment is proposed for the TRH with respect to receptor binding.     

Resistance of proline-containing peptides to ruminal degradation in vitro.

Mixed ruminal bacteria utilized an enzymatic digest of casein at a rate faster than that for an enzymatic digest of gelatin, but neither amino acid source was completely utilized even when the incubation period was as long as 96 h. Since the reaction of ninhydrin with the residual nonammonia, nonprotein nitrogen was more than twofold stronger when the samples were hydrolyzed with 6 N HCl, it appeared that much of the residual nitrogen was from peptides. Approximately 66% of the nonammonia, nonprotein, ninhydrin-reactive material could not be recovered as amino acids, but there was a significant decrease in total amino acid nitrogen when the samples were pretreated with a C18 Sep-Pak column to remove peptides. The resistant peptides had an abundance of proline, and subsequent incubations showed that synthetic dipeptides which contained proline were hydrolyzed slowly. Lysine appears to be the amino acid which is most apt to limit ruminant production. Dipeptides containing proline and lysine were hydrolyzed at least fivefold slower than lysine-alanine. Methionine, another potentially limiting amino acid, was also degraded at a slower (2.5-fold) rate when it was present as part of a proline dipeptide.     

Peptide helices with pendant cycloalkane rings. Characterization of conformations of 1-aminocyclooctane-1-carboxylic acid (Ac8c) residues in peptides.

A pentapeptide, Boc-Leu-Ac8c-Ala-Leu-Ac8c-OMe 1, an octapeptide, Boc-Leu-Ac8c-Ala-Leu-Ac8c-Ala-Leu-Ac8c-OMe 2 and a tripeptide, Boc-Aib-Ac8c-Aib-OMe 3 containing the 1-aminocyclooctane-1-carboxylic acid residue (Ac8c) were synthesized and conformationally characterized by x-ray diffraction studies in the crystal state. Peptides 1 and 2 were also studied by NMR in CDC13 solution. Peptide 1 adopts a purely 3(10)-helical conformation in crystals, stabilized by three intramolecular 1 <-- 4 hydrogen bonds. Peptide 2 in crystals is largely 3(10)-helical with distortion in the backbone at the N-terminus by the insertion of a water molecule between Ac8c (2) CO and Ala (6) NH groups. Peptide 3 forms a C10-ring structure, i.e. a type III (III') beta- turn conformation stabilized by an intramolecular 1 <-- 4 hydrogen bond. Five cyclooctane rings assume boat-chair conformations, whereas the sixth [Ac8c(8) in 2] is appreciably distorted, resembling a chiral intermediate in the pseudorotational pathway from the boat-chair to the twisted boat-chair conformation. Internal bond angles of the cyclooctane rings are appreciably distorted from the tetrahedral value, a characteristic feature of the cyclooctane ring. Peptide 1 crystallized in the space group P212121 with a = 11.900(4) A, b = 18.728(6) A, c = 20.471(3) A and Z = 4. The final R1 and wR2 values are 0.0753 and 0.2107, respectively, for 3901 observed reflections [Fo > or = 3 sigma (Fo)]. Peptide 2 crystallized in space group P21 with a = 12.961(5) A, b = 17.710(10) A, c = 15.101(7) A, beta = 108.45(4) degrees and Z = 2. The final R1 and wR2 values are 0.0906 and 0.1832, respectively, for 2743 observed reflections [Fo > or = 3sigma (Fo)]. 1H-NMR studies on both the peptides strongly suggest the persistence of 3(10)-helical conformations in solution. Peptide 3 crystallized in the space group P21/n, with a = 10.018(1) A, b = 20.725(1) A, c = 12.915(1) A and Z = 4. The final R1 and wR2 values are 0.0411 and 0.1105, respectively, for 3634 observed reflections [Fo > or = 4sigma (Fo)].     

Normal-mode-analysis-monitored energy minimization procedure for generating small-molecule bound conformations

The energy minimization of a small molecule alone does not automatically stop at a local minimum of the potential energy surface of the molecule if the minimum is shallow, thus leading to folding of the molecule and consequently hampering the generation of the bound conformation of a guest in the absence of its host. This questions the practicality of virtual screening methods that use conformations at local minima of their potential energy surfaces (local minimum conformations) as potential bound conformations. Here we report a normal-mode-analysis-monitored energy minimization (NEM) procedure that generates local minimum conformations as potential bound conformations. Of 22 selected guest-host complex crystal structures with guest structures possessing up to four rotatable bonds, all complexes were reproduced, with guest mass-weighted root mean square deviations of <1.0 A, through docking with the NEM-generated guest local minimum conformations. An analysis of the potential energies of these local minimum conformations showed that 22 (100%), 18 (82%), 16 (73%), and 12 (55%) of the 22 guest bound conformations in the crystal structures had conformational strain energies of less than or equal to 3.8, 2.0, 0.6, and 0.0 kcal/mol, respectively. These results suggest that (1) the NEM procedure can generate small-molecule bound conformations, and (2) guests adopt low-strain-energy conformations for complexation, thus supporting the virtual screening methods that use local minimum conformations.     

A theoretical estimate of the energy barriers between stable conformations of the proline dimer.

Semi-empirical energy calculations for an internal Pro-Pro dimer are presented that take into account the nature of the flexibility of the proline ring due to its puckering. Calculations show that three stable conformations are available for the dimer: the cis (ω = 0°, ψ = 160°); the trans (ω = 180°, ψ = 160°, also referred to as trans′); and the cis′ (ω = 180°, ψ = ?40°) conformations. The best conformational pathways between these stable conformations are determined. Calculations also show that the barrier for cis′–trans′ conversion is of the same order of magnitude as that for cis–trans conversion.