… must be analytically calculated. In this article, we describe a new method for calculating
both the surface area and the gradient exactly and efficiently. We use the intersection of Ž . …

… of the gradients of the accessible surface area. Here we describe the procedure for calculating
… We did more accurate testings by calculating the areas of individual atoms as well as the …

… to efficiently compute accurate volumes and surface areas of … to accumulate volumes and
their gradients on the tree data … , yields accurate analytic volumes and surface areas.64 The …

… All surface area and curvature calculations are analytic and … of a macromolecule, calculations
of its surface area are both … of surface tension and the right hand side is the gradient of …

… rapid and accurate method for calculating the accessible surface area. … J~ for one
energy function evaluation plus one gradient … for macromolecules, models based on solvent-accessible …

… molecules and their gradients with respect to their atomic … unfolded conformations of
macromolecules of any chemical … in evolution of exact analytical methods calculating atomic SASA.…

… reasonably accurate approach for calculating conformational … of atoms of macromolecules
are not accessible to solvent. To … In this work, the final rms gradients are all smaller than 1.0 � …

… All gradient elution runs were carried out with linear gradients. … For different packings as
in the present study where surface area and pore size are varied but surface chemistry is held …

… , an exact analytical function for accessible surface area or equivalently the surface area
exterior … The accessible surface areas and gradients for each atom of the protein oxy-myoglobin …

… and analysis. Furthermore, we outline methods leading to the formation of orthogonal gradients…
two being the procedure by which macromolecules are attached to the surface (cf. Fig. 1). …