Barriers to Forced Transitions in Polysaccharides Patrick O’Donoghue and Zaida Ann Luthey-Schulten* Department of Chemistry, UniVersity of Illinois at Urbana-Champaign,Urbana, Illinois 61801 ReceiVed: July 12, 2000; In Final Form: August 31, 2000 Recent atomic force microscopy (AFM) experiments have measured the elastic properties of polysaccharides. The results of these experiments suggest that their elastic responses can be understood in terms of the conformational transitions of the monomeric units. In amylose, the unbranched form of starch found in plants, forced extensions by AFM have lead to the conclusion that the basic elastic unit, an R-D-glucopyranose ring, extends by a chair-to-boat conformational transition. Forced extensions on cellulose, the main component in plants, Archea (in a modified form), and Eubacteria cell walls, showed no elongation of the monomeric unit, -D-glucopyranose. In this study, we used ab initio HF/6-31G* calculations to investigate a series of boat conformations and a twist-boat conformation, which are likely candidates for the elongated structures seen in AFM experiments. Using a linear transit method, we constructed conformational pathways in the form of potential curves which start from the ground-state chair conformation and end at one of these boat or twist- boat structures. For the amylose monomer, we examined three conformational transitions, including two distinct boat forms and a twist-boat form. The results match those reported in the AFM experiments. For the cellulose monomer, we show that only forced compressions are possible whereas extensions are forbidden. The compression has a barrier height of ∼13 kcal mol -1 . First-passage times are determined for each transition and used to understand the effect of the applied force on the time scales of these ring conformational transitions. Introduction The elastic properties of polysaccharides have been studied in a series of recent AFM experiments. 1-6 The results of these experiments suggest that the elastic properties can be understood in terms of the chair-to-boat conformational transition of the monomeric units. More specifically, Marszalek et al. 2 have made the interesting argument that the number of conformational transitions measured in the force extension curves can be correlated with the number of glycosidic linkages in the axial orientation. The glycosidic oxygens in amylose are situated axially (O 1a ) and equatorially (O 4e ), and in cellulose, both are equatorially oriented (see Figures 1a-3a). 7,8 According to the force extension curves measured by the Fernandez group, 2 cellulose is completely rigid, and amylose undergoes a single conformational transition. The extensions are in agreement with the elongation of the O 1 O 4 vector that would occur in the transition from the most stable chair form of the pyranose ring, 4 C 1 , to the boat or twist-boat conformation, and the elastic properties are eliminated upon the chemical opening of the ring. The results from similar experiments on a series of other polysaccharides agreed with the predicted number of transitions. These predictions were based on a rather simple mechanical model of the pyranose ring and its response to the AFM forces. The authors argue that the stretching forces applied to axial glycosidic oxygens produce a torque about the C 2 O 5 virtual axis that promotes a transition to the boat conformation, whereas forces applied to equatorial oxygens have a significantly smaller torque. This type of transition, described in ref 2 and hereinafter referred to as model 1, produces a particular boat endpoint when applied to R-D-glucose and is best described by a change of the C 1 -C 2 -C 3 -C 4 ring dihedral angle. Although the Fernandez group assumes that a model 1 transition occurs in amylose during the AFM experiments, the experimental results are not clear about the conformation of the elongated pyranose. On the basis of our calculations, other boat conformations of compa- rable energies may indeed exhibit similar elongations. Reaching any of these other conformations requires a somewhat more general interpretation of the force interaction with the molecule. In this study, we consider two such additional endpoints. The first is a boat conformation, referred to as model 2, and the second is a twist-boat conformation, referred to as model 3. The model 2 and model 3 transitions are most clearly detected as changes in the C 5 -O 5 -C 1 -C 2 and C 1 -C 2 -C 3 -C 4 ring dihedral angles, respectively. -D-Glucose, the cellulose mono- mer, undergoes a compressive transition similar to that of model 1 and is described by a change in the C 1 -C 2 -C 3 -C 4 dihedral angle. The specifics of these force interaction models are discussed below. Although any ring dihedral angle may be used to monitor the chair-to-boat transition, these particular angles are the most convenient for viewing and presenting the molecules, and they simplify the first-passage time calculations that are typically carried out to link the potential of mean force to AFM observations. 9 We would also like to point out that we have not used the Cremer-Pople puckering coordinates. These parameters are normally used to describe the pseudorotational motions of ring molecules and are useful in characterizing the entire conformational energy surface. 10 In our treatment, we are looking at the limited chair-to-boat (or twist-boat) transition, where only one of the three puckering coordinates changes significantly. Also, the ring dihedral angles are a more “intui- tive” choice for the purposes of this study, as they may be easily correlated to changes in the length of the O 1 O 4 vector measured in AFM experiments. In this study, we also determine the energetic barriers of the transitions and characterize the boat conformers that could be * Corresponding author. Fax: (217) 244-3186. E-mail: zan@uiuc.edu. 10398 J. Phys. Chem. B 2000, 104, 10398-10405 10.1021/jp002478v CCC: $19.00 © 2000 American Chemical Society Published on Web 10/19/2000