Akbar Nayeem

Heisenberg spin exchange and molecular diffusion in liquid crystals

Heisenberg spin exchange (HE) studies of translational diffusion of the nitroxide radicals PD‐tempone and P probe in two liquid crystalline solvents 6OCB–8OCB and 4O,6 are described. It is shown that while PD‐tempone undergoes strong exchange in the two solvents, the more anisotropic P‐probe exhibits a tendency toward weak exchange which becomes more prominent in the low temperature mesophases. The molecular diffusion rates measured from our HE studies are compared with rates measured over larger distances using electron‐spin resonance (ESR) imaging methods; we find that, in similar thermotropic liquid crystals, the former are somewhat faster. Also, while diffusion rates for PD‐tempone (using HE) in the ordered phases of 6OCB–8OCB are consistent with a single activation energy, those in 4O,6 show variations; suggesting that probe expulsion from core to chain regions in the former most likely occurs prior to SA formation, whereas in the latter it occurs in the SA phase. The absence of discontinuities in ou...

From secondary structure to three-dimensional structure: Improved dihedral angle probability distribution function for use with energy searches for native structures of polypeptides and proteins

An improved scheme to help in the prediction of protein structure is presented. This procedure generates improved starting conformations of a protein suitable for energy minimization. Trivariate gaussian distribution functions for the π, ψ, and χ1 dihedral angles have been derived, using conformational data from high resolution protein structures selected from the Protein Data Bank (PDB). These trivariate probability functions generate initial values for the π, ψ, and χ1 dihedral angles which reflect the experimental values found in the PDB. These starting structures speed the search of the conformational space by focusing the search mainly in the regions of native proteins. The efficiency of the new trivariate probability distributions is demonstrated by comparing the results for the α‐class polypeptide fragment, the mutant Antennapedia (C39 → S) homeodomain (2HOA), with those from two reference probability functions. The first reference probability function is a uniform or flat probability function and the second is a bivariate probability function for π and ψ. The trivariate gaussian probability functions are shown to search the conformational space more efficiently than the other two probability functions. The trivariate gaussian probability functions are also tested on the binding domain of Streptococcal protein G (2GB1), an α/β class protein. Since presently available energy functions are not accurate enough to identify the most native‐like energy‐minimized structures, three selection criteria were used to identify a native‐like structure with a 1.90‐Å rmsd from the NMR structure as the best structure for the Antennapedia fragment. Each individual selection criterion (ECEPP/3 energy, ECEPP/3 energy‐plus‐free energy of hydration, or a knowledge‐based mean field method) was unable to identify a native‐like structure, but simultaneous application of more than one selection criterion resulted in a successful identification of a native‐like structure for the Antennapedia fragment. In addition to these tests, structure predictions are made for the Antennapedia polypeptide, using a Pattern Recognition‐based Importance‐Sampling Minimization (PRISM) procedure to predict the backbone conformational state of the mutant Antennapedia homeodomain. The ten most probable backbone conformational state predictions were used with the trivariate and bivariate gaussian dihedral angle probability distributions to generate starting structures (i.e., dihedral angles) suitable for energy minimization. The final energy‐minimized structures show that neither the trivariate nor the bivariate gaussian probability distributions are able to overcome the inaccuracies in the backbone conformational state predictions to produce a native‐like structure. Until highly accurate predictions of the backbone conformational states become available, application of these dihedral angle probability distributions must be limited to problems, such as homology modeling, in which only a limited portion of the backbone (e.g., surface loops) must be explored.

A statistical analysis of side-chain conformations in proteins: Comparison with ECEPP predictions

A comparison of the statistical distributions of side-chain conformations of 17 amino acids (Gly, Ala, and Pro excluded), observed in 63 nonhomologous globular proteins (covering 10,832 residues), is made with similar distributions calculated from the low-energy conformational states for the same amino acids (blocked with acetyl and N-methylamide groups at the N- and C-termini, respectively) obtained by Vásquezet al. [(1983),Macromolecules16, 1043–1049 using the ECEPP/2 force field. Those residues (i) with linear side chains (Arg, Lys, Met, Cys, Ser), or those that are unbranched through theγ-carbon atom (Glu, Gln) show good agreement, whereas (ii) those with side chains that are branched at Cβ or Cγ show poor agreement with ECEPP calculations. A possible explanation for this is shown to be the greater tendency for side-chain atoms in class (ii) to interact with the backbone and/or adjacent side chains. Accordingly, ECEPP/3 calculations, carried out after elongating the backbone chain of the model peptide unit (by adding three Ala residues on each side of the central residue, and then blocking the termini as before), result in distributions that are often closer to the observed side-chain distributions. The implications of these results for the relative importance of short-range versus long-range interactions in determining protein structure are discussed.

Critical fluctuations and molecular dynamics at liquid‐crystalline phase transitions. II. Electron spin resonance experiments

Electron spin resonance (ESR) relaxation studies at nematic–isotropic (N–I), and nematic–smectic‐A (N–SA ) phase transitions in two liquid crystals, 4O,6 and 6OCB–8OCB, using the three spin probes, PD‐tempone, MOTA, and P are described. In general, one finds that (i) at the N–I transition, as TNI is approached, the linewidths diverge with a critical exponent of 1/2; (ii) at the N–SA transition, the linewidths diverge with a 1/3 power law as the transition is approached from the nematic side. The nature of the critical divergences in the relaxation parameters is interpreted and analyzed in terms of fluctuations in the nematic and smectic order parameters at the respective transitions and the coupling of the orientational dynamics of the probe to these modes. Good quantitative agreement with theory for the N–I transition required the inclusion of the effects of asymmetric probe ordering. The theory developed in detail in paper I is applied to interpret the results at the N–SA transition. This theory is exte...

ESR and Molecular Motions in Liquid Crystals: Motional Narrowing

Theoretical and experimental aspects of spin relaxation in liquid crystals are considered here, with primary emphasis on the motional narrowing regime. ESR studies of translational motion in mesophases are also described.

ESR Studies of Molecular Dynamics at Phase Transitions in Liquid Crystals

Order parameter fluctuations at mesomorphic phase transitions modulate the molecular dynamics of spin probes, thereby affecting spin relaxation. The anomalous relaxation rates at the phase transitions (T*) often diverge as |T - T*| γ, where γ is a critical exponent, and has been noted to be universal. For N-I transitions, γ = -½, and for SA−N transitions, γ = −1/3. Theoretical models are discussed that provide a unified framework for rationalising the experimental results.

ESR and Slow Motions in Liquid Crystals

The theory of slow motional ESR is outlined, with applications to nitroxide spectra in liquid crystals. The computer algorithms for implementing the theory based on the stochastic Liouville equation are also discussed.

ESR And Liquid Crystals: Statistical Mechanics and Generalised Smoluchowski Equations

A general overview of molecular dynamics in liquid crystals is presented, which will serve as the basis for our discussion of ESR experiments.

THERMODYNAMICS OF LIQUID CRYSTALS AND THE RELATION TO MOLECULAR DYNAMICS: ESR STUDIES

Molecular theories, derived from ESR studies of molecular dynamics, that provide a basis for understanding the stability of phases of thermotropic and lyotropic liquid crystals, are discussed.