An improved version of the “marching cubes” algorithm [W. Lorensen and H. Cline, Comp. Graph. 21, (1987)] for the generation of isosurfaces from 3D data fields is presented and applied to molecular surfaces. The new algorithm avoids inconsistent pattern definitions of the original one, which lead to artificial gaps. The advantage of a logarithmic interpolation procedure, in particular for data fields typically occurring in molecular science, is demonstrated. An example is the generation of molecular surfaces based upon electron density data. © 1993 John Wiley & Sons, Inc.

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Scaling properties of the surfaces of 53 proteins are studied on the basis of experimentally determined 3-D structures of these biological macromolecules. It is found that the surfaces show self similarity within a yardstick range of 1.5 A less than epsilon less than 15 A. The self similarity is measured by the fractal dimension D of the surface. Two different algorithms for the determination of the fractal dimension are applied, both based on cubic yardstick particles. One is related to the contact surface (CS), which was first introduced by Connolly (17), while the other corresponds to the solvent accessible surface (SAS) of Richards (9). The fractal dimensions of both are different. While the CS type approach leads to relatively high values of D in the range 2.5 to 2.6 the SAS approach gives fractal dimensions of D approximately 2.

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