Extracting Ramachandran torsional angle distributions from 2D NMR data using Tikhonov regularization /

Solid state nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for studying structural and dynamical properties of disordered and partially ordered materials, such as glasses, polymers, liquid crystals, and biological materials. In particular, twodimensional( 2D) NMR methods such as ^^C-^^C correlation spectroscopy under the magicangle- spinning (MAS) conditions have been used to measure structural constraints on the secondary structure of proteins and polypeptides. Amyloid fibrils implicated in a broad class of diseases such as Alzheimer's are known to contain a particular repeating structural motif, called a /5-sheet. However, the details of such structures are poorly understood, primarily because the structural constraints extracted from the 2D NMR data in the form of the so-called Ramachandran (backbone torsion) angle distributions, g{^,'4)), are strongly model-dependent. Inverse theory methods are used to extract Ramachandran angle distributions from a set of 2D MAS and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) data. This is a vastly underdetermined problem, and the stability of the inverse mapping is problematic. Tikhonov regularization is a well-known method of improving the stability of the inverse; in this work it is extended to use a new regularization functional based on the Laplacian rather than on the norm of the function itself. In this way, one makes use of the inherently two-dimensional nature of the underlying Ramachandran maps. In addition, a modification of the existing numerical procedure is performed, as appropriate for an underdetermined inverse problem. Stability of the algorithm with respect to the signal-to-noise (S/N) ratio is examined using a simulated data set. The results show excellent convergence to the true angle distribution function g{(j),ii) for the S/N ratio above 100.

Effect of the position of the double-bond in monounsaturated phospholipids on the dynamics of model membranes

Therllloelynalllics of lllodel 11lel1ll)rane systeills containing 1110nollnsaturatecl I)lloSI)holil) ids is strongly infllienced l)y the I)osition of the C==C dOlll)le })ond in tIle acyl chain. The telllI)eratllres of both chain-nlelting (TM) and La -+ HI! (TH) I)hase traIlsitions are lowered by IIp to 20°C when C==C is Inoved froln positions 6 or 11 to I)osition 9 in an 18-carl)on chain. This work is an attellll)t to ellicidate the uIlderlying Illoleclilar Illechanisllls reSI)Onsi])le for tllese draillatic tllerillodynaillic changes. Mixtllres of di-18: 1 l)hoSI)hatidylethanolanline with C==C at l)ositioIlS 6, 9, 11 were llsed, witll a sI1lall aI1lOlint of I)erdellterated tetradecanol, known to })e a gooel rel)Orter of the cllain Illoleclilar order. SI)ectral second 11I0I1lents were llsed to Illonitor tIle La -+ HII I)hase transition, which was fOllnd to ])e ])road (2-6°C), with a slight llysteresis on heatiIlg/cooling. The orientational order I)rofiles were nleasllred 1lSiIlg 2H Illiclear Illagnetic resonance and changes in these order I)rofiles between La aIld HII I)hases silow l)oth a local increase in order in the vicinity of the C==C bonds and an o\Terall decrease ill the average orientational order of the chain as a whole. These Sll])tle changes recluire })oth high-fidelity SI)ectrosCol)y and a careflll data analysis that takes into aCCOllnt the effects due to l)artiall1lagnetically-indllced orientational ordering of the l)ilayers. In tIle COIltext of SOllle recently rel)Orted cross-relaxation 11leaSlirenlents in Silllilar l)llOSI)llolil)iels, 0111' reslilts sllggest that large-anll)litllde conforlllational changes in the interior of tIle I110del 111eI11])ranes I)lay a 1110re significant role than I)reviollsly thOllght.

The finite bandwidth model for spin fluctuations in Pd

The frequency dependence of the electron-spin fluctuation spectrum, P(Q), is calculated in the finite bandwidth model. We find that for Pd, which has a nearly full d-band, the magnitude, the range, and the peak frequency of P(Q) are greatly reduced from those in the standard spin fluctuation theory. The electron self-energy due to spin fluctuations is calculated within the finite bandwidth model. Vertex corrections are examined, and we find that Migdal's theorem is valid for spin fluctuations in the nearly full band. The conductance of a normal metal-insulator-normal metal tunnel junction is examined when spin fluctuations are present in one electrode. We find that for the nearly full band, the momentum independent self-energy due to spin fluctuations enters the expression for the tunneling conductance with approximately the same weight as the self-energy due to phonons. The effect of spin fluctuations on the tunneling conductance is slight within the finite bandwidth model for Pd. The effect of spin fluctuations on the tunneling conductance of a metal with a less full d-band than Pd may be more pronounced. However, in this case the tunneling conductance is not simply proportional to the self-energy.