Tamás Beke

Toward a rational design of β-peptide structures

Intrinsic conformational characteristics of β‐peptides built up from simple achiral and chiral β‐amino acid residues (i.e., HCO‐β‐Ala‐NH2, HCO‐β‐Abu‐NH2) were studied using quantum chemical calculations and 1H‐NMR spectroscopy. A conformer‐based systematic and uniform nomenclature was introduced to differentiate conformers. Geometry optimizations were performed on all homoconformers of both HCO‐(β‐Ala)k‐NH2 and HCO‐(β‐Abu)k‐NH2 (1 ≤ k ≤ 6) model systems at the RHF/3‐21G and RHF/6‐311++G(d, p) levels of theory. To test for accuracy and precision, additional computations were carried out at several levels of theory [e.g., RHF/6‐31G(d), and B3LYP/6‐311++G(d, p)]. To display the folding preference, the relative stability of selected conformers as function of the length of the polypeptide chain was determined. Ab initio population distribution of hexapeptides and the conformational ensemble of synthetic models composed of β‐Ala and β‐Abu studied using 1H‐NMR in different solvents were compared at a range of temperatures. Helical preference induced by various steric effects of nonpolar side chains was tested using higher level ab initio methods for well‐known model systems such as: HCO‐(β‐HVal‐β‐HAla‐β‐HLeu)2‐NH2, HCO‐(ACHC)6‐NH2, HCO‐(trans‐ACPC)6‐NH2, and HCO‐(cis‐ACPC)6‐NH2. The relative stabilities determined by theoretical methods agreed well with most experimental data, supporting the theory that the local conformational preference influenced by steric effects is a key determining factor of the global fold both in solution and in the gas phase.

On the flexibility of β‐peptides

The full conformational space was explored for an achiral and two chiral β‐peptide models: namely For‐β‐Ala‐NH2, For‐β‐Abu‐NH2, and For‐β‐Aib‐NH2. Stability and conformational properties of all three model systems were computed at different levels of theory: RHF/3‐21G, B3LYP/6‐311++G(d,p)//RHF/3‐21G, B3LYP/6‐311++G(d,p), MP2//B3LYP/6‐311++G(d,p), CCSD//B3LYP/6‐311++G(d,p), and CCSD(T)//B3LYP/6‐311++G(d,p). In addition, ab initio E = E(φ, μ, ψ) potential energy hypersurfaces of all three models were determined, and their topologies were analyzed to determine the inherent flexibility properties of these β‐peptide models. Fewer points were found and assigned than expected on the basis of Multidimensional Conformational Analysis (MDCA). Furthermore, it has been demonstrated, that the four‐dimensional surface, E = E(φ, μ, ψ), can be reduced into a three‐dimensional one: E = E[φ, f(φ), ψ]. This reduction of dimensionality of freedom of motion suggests that β‐peptides are less flexible than one would have thought. This agrees with experimental data published on the conformational properties of peptides composed of β‐amino acid residues.

A theoretical comparison of self-assembling α- and β-peptide nanostructures: Toward design of β-barrel frameworks

Self-assembling peptide-based nanotubes are among the most investigated bioactive compounds as a result of their numerous potential applications as novel biomaterials. To support rational bottom-up design of such artificial nanosystems, here we investigate structural and energetic properties of various sheet-derived nanotubes. We carried out high level quantum chemical calculations on large models, composed of up to 32 amino acids, and characterized structures from extended beta-sheets to the molecular framework of beta-barrel proteins. Surprisingly, enzyme-resistant nonnatural beta-peptides have an affinity to form nanotubes that is remarkably higher than that of natural alpha-peptides. We analyzed the stability of both systems depending on (i) parallel or antiparallel orientation, (ii) the number of peptide strands, and (iii) the formed hydrogen bond pattern. Applicability is outlined by investigating guest molecules in the tubes. It is hoped that the structural and energetic data presented here will be effectively used in the design of novel peptide nanosystems.

Extended Apolar β-Peptide Foldamers: The Role of Axis Chirality on β-Peptide Sheet Stability

This study is on structure and stability of sheetlike conformers of beta-peptides; never seen new foldamers are reported here for the first time. Single- and double-stranded structures are analyzed, and the seeds of large beta-layers and biocompatible nanomaterials are described here. Both the monomeric, HCO-[NH-CH(2)-CH(2)CO](n)-NH(2), and dimeric forms, [HCO-(beta-Ala)(n)-NH(2)](2) n = 3 and 4, of oligo-beta-alanine supramolecular complexes are evaluated by using an adequate level of theory M052X/6-31G(d) for peptides of this size. Polymers composed of backbone foldamers with the central mu torsion angle set to an anti orientation were all probed. Sheet structures built up of strands with carbonyl groups monotonically facing the same spatial direction, polar strands, were previously assigned and synthesized ( Seebach , D. Chem. Biodiversity 2004 , 1 , 1111 - 1239 ). Now we are presenting a novel beta-peptide sheet structure of alternating carbonyl group orientations, called as apolar strands. These novel secondary structural elements of beta-peptides are structural analogs of beta-pleated sheets of proteins. Interestingly enough, the latter type of apolar strands are foreseen as very stable supramolecular complexes and are more firm by approximately 10 kcal.mol(-1) than the aforementioned polar strands. Furthermore, apolar strands lack the inherent twisting of beta-layers, present in polar strands resulting in the tubular shape. Once the effect of substitution of Hbeta1 and/or Hbeta2 atoms are revealed on foldamer stability, short peptide sequence could be designed and synthesized. These new, conformationally optimized beta-sheetlike nanostructures of increased stability with little or no twisting could be used as enzymatically resistant ( Frackenpohl , J. , Arvidsson , P. I. , Schreiber , J. V. , and Seebach , D. ChemBioChem 2001 , 2 , 445 - 455 ) biomaterials. These newly designed models systems could enlarge the arsenal of durable polyesters of similar chemical constitution (e.g., -[O-CH(CH(3))-CH(2)CO](n)- and -[O-CH(COOH)-CH(2)CO](n)-) already used as artificial heart valves, for example.

Combined NMR three‐bond scalar coupling measurements and QM calculations to calculate OH‐rotamer equilibrium of polyalcohols

A combined but independently applied NMR and QM procedure has been used to investigate the conformational properties of the exchangeable hydroxyl protons of polyalcohols. In this study, to demonstrate the applicability of such a strategy, we investigated a simple monosaccharide, i.e. α‐ and β‐anomers of a D‐glucopyranoside derivative. The redundant set of experimental vicinal homonuclear and heteronuclear scalar couplings involving the OH‐protons obtained for both anomers of our model compound were simultaneously analyzed to yield the preferred OH‐rotamer populations and moreover to parametrize a new Karplus‐type equation for 3JC(i−1)OH(i) coupling. The populations of the lowest energy conformers and the conformational‐averaged coupling constants were independently calculated using the QM approach in both vacuum and chloroform. The similarity of the estimated rotamer populations obtained by two very different techniques and the similarity of the experimental and calculated coupling constants suggest that these approaches can be used in conjunction and in a fully integrated way to determine a more accurate atomic level description of molecular conformers.

Peptide models XXXIV. Side-chain conformational potential energy surfaces associated with all major backbone folds of neutral tautomers of N- and C-protected l-histidine. An ab initio study on ethylimidazole and N-formyl-l-histidinamide

Abstract Both tautomers of N -formyl- l -histidinamide and ethylimidazole were subjected to conformational analysis at the ab initio RHF/6-31G(d) level of theory. Side-chain potential energy surfaces (PES) were calculated for the nine typical backbone conformations predicted by Multidimensional Conformational Analysis. The side-chain torsions of N -formyl- l -histidinamide ( χ 1 and χ 2 ) were characterized with respect to the shapes of the PES. All envisaged minima were fully optimized. For each conformer of N -formyl- l -histidinamide stabilization energy was calculated and compared to values determined for other amino acid residues.

Determining suitable lego-structures to estimate stability of larger peptide nanostructures using computational methods

Nanofibers, nanofilms and nanotubes constructed of one to four strands of oligo-alpha- and oligo-beta-peptides were obtained by using carefully selected building units. Lego-type approaches based on thermoneutral isodesmic reactions can be used to reconstruct the total energies of both linear and tubular periodic nanostructures with acceptable accuracy. Total energies of several different nanostructures were accurately determined with errors typically falling in the subchemical range. Thus, attention will be focused on the description of suitable isodesmic reactions that have enabled the determination of the total energy of polypeptides and therefore offer a very fast, efficient and accurate method to obtain energetic information on large and even very large nanosystems.

On the flexibility of ?-peptides

The full conformational space was explored for an achiral and two chiral β‐peptide models: namely For‐β‐Ala‐NH2, For‐β‐Abu‐NH2, and For‐β‐Aib‐NH2. Stability and conformational properties of all three model systems were computed at different levels of theory: RHF/3‐21G, B3LYP/6‐311++G(d,p)//RHF/3‐21G, B3LYP/6‐311++G(d,p), MP2//B3LYP/6‐311++G(d,p), CCSD//B3LYP/6‐311++G(d,p), and CCSD(T)//B3LYP/6‐311++G(d,p). In addition, ab initio E = E(φ, μ, ψ) potential energy hypersurfaces of all three models were determined, and their topologies were analyzed to determine the inherent flexibility properties of these β‐peptide models. Fewer points were found and assigned than expected on the basis of Multidimensional Conformational Analysis (MDCA). Furthermore, it has been demonstrated, that the four‐dimensional surface, E = E(φ, μ, ψ), can be reduced into a three‐dimensional one: E = E[φ, f(φ), ψ]. This reduction of dimensionality of freedom of motion suggests that β‐peptides are less flexible than one would have thought. This agrees with experimental data published on the conformational properties of peptides composed of β‐amino acid residues.

On the flexibility of beta-peptides.

The full conformational space was explored for an achiral and two chiral β‐peptide models: namely For‐β‐Ala‐NH2, For‐β‐Abu‐NH2, and For‐β‐Aib‐NH2. Stability and conformational properties of all three model systems were computed at different levels of theory: RHF/3‐21G, B3LYP/6‐311++G(d,p)//RHF/3‐21G, B3LYP/6‐311++G(d,p), MP2//B3LYP/6‐311++G(d,p), CCSD//B3LYP/6‐311++G(d,p), and CCSD(T)//B3LYP/6‐311++G(d,p). In addition, ab initio E = E(φ, μ, ψ) potential energy hypersurfaces of all three models were determined, and their topologies were analyzed to determine the inherent flexibility properties of these β‐peptide models. Fewer points were found and assigned than expected on the basis of Multidimensional Conformational Analysis (MDCA). Furthermore, it has been demonstrated, that the four‐dimensional surface, E = E(φ, μ, ψ), can be reduced into a three‐dimensional one: E = E[φ, f(φ), ψ]. This reduction of dimensionality of freedom of motion suggests that β‐peptides are less flexible than one would have thought. This agrees with experimental data published on the conformational properties of peptides composed of β‐amino acid residues.