Conformational Distribution Function of a Disaccharide in a Liquid Crystalline Phase Determined Using NMR Spectroscopy Baltzar Stevensson, § Clas Landersjo ¨ , ‡ Go ¨ ran Widmalm, ‡ and Arnold Maliniak* ,§ DiVision of Physical Chemistry and Department of Organic Chemistry, Arrhenius Laboratory, Stockholm UniVersity, S-106 91 Stockholm, Sweden Received January 30, 2002 Proteins, nucleic acids, and carbohydrates all show conforma- tional flexibility, but the extent is dependent on the structure and their environment. The motion in saccharides, in particular at the glycosidic linkage, defined by torsion angles φ and ψ is of importance for molecular properties and biological function. Thus, the approximation of a single molecular structure is certainly an oversimplified picture. To obtain complete information about the molecular structure we desire to determine the conformational distribution function, P(φ,ψ). Analysis of molecular conformations has for a considerable time relied on either the nuclear Overhauser effect (NOE), spin-spin (J) couplings, or a combination of these two. Recently, the application of dilute liquid crystalline phases (bicelles) as solvents enabled a slight net orientation of nonspherical “solute” molecules and therefore determination of through-space magnetic dipole- dipole (DD) interactions. These provide a powerful tool for molecular structure analysis of saccharides in ordered phases. 1-4 The DD interactions depend on the spin-spin distances and on the orientations of the internuclear vectors with respect to the external magnetic field. This means that the dipolar coupling is a valuable probe of long-range order and molecular structure. To extract useful information from the experimental DD couplings in a flexible molecule, we need a theoretical tool to be used in the analyses. Several such approaches have been considered for the interpretation of dipolar couplings. The simplest possible model assumes that only a small set of minimum-energy structures is populated. More realistic models allow for continuous bond rotations. Two approaches that have been frequently used for interpretations of dipolar couplings in bulk liquid crystals are: (i) the additive potential model (AP) 5 and (ii) the maximum entropy method (ME). 6 Both methods have been successfully applied in experimental and computational studies of the orientational order and molecular conformations in mesogenic molecules. 7-9 The models suffer, however, from serious limitations: the AP method requires an a priori knowledge of the functional form of the torsional potential, relevant for the investigated molecular fragment. The ME approach though, gives the flattest possible distribution consistent with the experimental data set, which results in an incorrect description of systems with low orientational order. 6,9 These two limitations have an obvious relevance for investigations of saccha- rides in dilute liquid crystals: we do not have the torsional potential function for the glycosidic linkage, and the orientational order is indeed very low. Here we present a novel approach for construction of the conformational distribution function P(φ,ψ) from the NMR pa- rameters. The procedure, which is valid in the low-order limit, was constructed as a combination of the AP and ME approaches, subsequently referred to as the APME method. In particular, the intraresidue dipolar couplings were used to determine the orienta- tional order, while the conformational distribution function P(φ,ψ) was constructed from the interresidue DD- and J couplings, together with NOEs. We apply our analysis to R-L-Rhap-(1f2)-R-L-Rhap- OMe, shown in Figure 1, which is a model for part of the O-antigen repeating unit of the lipopolysaccharide from pathogenic Shigella flexneri bacteria. The saccharide exhibits motion over the glycosidic linkage as established from a preliminary analysis of intraring dipolar coup- lings using the generalized degree of order (GDO) approach. 1,10 The GDOs in the two rigid rings differ by a factor of 1.2 (ϑ R ) 0.0059 and ϑ R′ ) 0.0072), whereas identical values are expected for rigidly connected fragments. The general expression for conformation dependent dipolar couplings, D ij (φ,ψ) can be written (in Hz) as: 5 where a,b ) (x,y,z) refers to an arbitrary coordinate frame fixed in one of the two rigid units, l ) R,R′, and θ ij a is the conformation- dependent angle between the internuclear vector and the a-axis. Similarly, the conformation-dependent elements of the order matrix are denoted S ab l (φ,ψ). The analysis of intraring couplings is in principle simple, because we do not need to explicitly consider the φ,ψ dependence. The interpretation of interresidue couplings, however, requires an expression for a molecular ordering matrix where both fragments contribute. To obtain S ab l (φ,ψ), we consider the AP 5 model where the singlet orientational distribution function (ODF), P(,γ,φ,ψ), is related to the potential of mean torque. Note that the angles  and γ define molecular orientation in the director frame. This potential is determined by the expansion coefficients, ǫ ab l , which depend on the orientational order and the segmental (R,R′) anisotropic interactions. In the limit of low-molecular order, the ODF can be Taylor-expanded and truncated after the second term. This results in the following expression for the order parameter: where µ,ν ) (x,y,z) in the frame of R′, ǫ ab l is defined in units of RT, and T aµ is an element of the φ,ψ-dependent transformation matrix that relates coordinate systems fixed in rings R and R′. An equivalent relationship is obtained for S ab R′ (φ,ψ) by interchanging the indices R and R′. Note that two important assumptions have * To whom correspondence should be addressed. E-mail: arnold.maliniak@ physc.su.se. § Division of Physical Chemistry. ‡ Department of Organic Chemistry. D ij (φ,ψ) ) µ 0 16π 2 γ i γ j p r ij 3 (φ,ψ) ∑ a,b cos θ ij a cos θ ij b S ab l (φ,ψ) (1) S ab R (φ,ψ) ) 1 5RT (ǫ ab R + ∑ µ,ν T aµ (φ,ψ)ǫ µν R′ T bν (φ,ψ)) (2) Published on Web 05/07/2002 5946 9 J. AM. CHEM. SOC. 2002, 124, 5946-5947 10.1021/ja025751a CCC: $22.00 © 2002 American Chemical Society