Investigation of the Three-Dimensional Macromolecular Structures J´ an Buˇ sa a,b,c , Jozef Dˇ zurina a,b , Edik Hayryan a,b,c , J´ an Plavka a,b , Imrich Pokorn´ y a,b , Jaroslav Skˇ riv´ anek a,b,c , Shura Hayryan c , Chin-Kun Hu c , Ming-Chya Wu c a Technical University in Koˇ sice, Slovak Republic b Laboratory of Information Technologies, JINR c Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan Solvent environment plays a crucial role on the structure and function of biological macromolecules, such as DNA, RNA and proteins. Exact determination of direct inter- actions between the macromolecules and the solvent molecules still remains a very hard mathematical and computational problem. For this reason different kinds of approxima- tions are usually done which allow description of these extremely complicated interactions through physically averaged macroscopic parameters. Such effective parameters include, for example, solvent accessible area of the solute molecule (in the calculation of thermo- dynamic properties and three-dimensional structure of macromolecules) and the so called excluded volume (see Figure 1). Computation of these parameters requires evaluation of complicated algorithms. For this reason, any effort to development an effective analytical methods is always welcome. Figure 1: A molecular surface Lee and Richards [4], and Chothia [5], introduced a solvent-accessible surface. The accessible surface is traced out by the probe sphere center as it rolls over the protein. It is a kind of expanded van der Waals surface. The molecular surface was first computed by Greer and Bush [8], Richmond [10] has defined the solvent-excluded volume to mean the volume contained within the solvent accessible surface, i.e. the volume which is inacces- sible to the centers of solvent particles. That is the union of the expanded atom spheres. The excluded volume is an important quantity in the theory of gases and liquids [9]. The exploration of molecular volume and surface is essential for the understanding of drug ac- tion since short range dispersion forces play a major role in the binding of drug molecules to receptors (http://server.ccl.net/cca/documents/molecular-modeling). The problem of the computation of volume and the surface area of the union of overlap- ping spheres has been the subject of methods both numerical (Rowlinson [3]; Pavani and 238