A linear-scaling semiempirical method, LocalSCF, has been proposed for the quantum-chemical calculations of ultralarge molecular systems by treating the large-scale molecular task as a variational problem. The method resolves the self-consistent field task through the finite atomic expansion of weakly nonorthogonal localized molecular orbitals. The inverse overlap matrix arising from the nonorthogonality of the localized orbitals is approximated by preserving the first-order perturbation term and applying the second-order correction by means of a penalty function. This allows for the separation of the orbital expansion procedure from the self-consistent field optimization of linear coefficients, thereby maintaining the localized molecular orbital size unchanged during the refinement of linear coefficients. Orbital normalization is preserved analytically by the variation of virtual degrees of freedom, which are orthogonal to the initial orbitals. Optimization of linear coefficients of localized orbitals is performed by a gradient procedure. The computer program running on a commodity personal computer was applied to the GroEL-GroES chaperonin complex containing 119,273 atoms.

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A brief survey of the state of the art in methods of calculations of protein-ligand interaction energies in docking complexes is presented. A new computational technique is proposed that allows one to fundamentally improve the performance of large scale serial calculations of docking complexes using the AM1/PM3 semiempirical methods. The technique explicitly al lows for a specific feature of docking problems, viz., the need for calculating numerous ligand complexes with a specified protein whose noninteracting part remains "frozen" during computa tions. The interaction energies calculated using the new method differ only slightly from the results of complete АМ1 calculations and the performance attained is high enough to solve practical drug design problems.Key words: large scale calculations of docking complexes, fast quantum chemical calcula tions, semiempirical methods.The determination of activity of relatively small ligand molecules (prototypes of active principles of drugs) in the interaction with large protein molecules is a key problem in biochemistry. Knowledge of energies of the interaction of a protein with ligands for very large ligand collections is of crucial importance for efficient targeted drug design. Meanwhile, the design of pharmaceuticals including high ly specific and even individually "tuned" ones (in the fu ture) belongs to scientific challenges of crucial importance.It is appropriate to begin large scale preliminary screening of ligands to choose best candidates from the standpoint of ligand-protein interactions with theo retical studies using computer simulation followed by more expensive and long term experiments with the ligands chosen.The increasing use of computer assisted docking* is due to important role of this technique for novel drug de sign technologies. The demand of rapidly developing phar maceutical industry for less expensive drug design, which becomes increasingly more complicated 1 against the back ground of exponentially increasing computer performance, makes the docking (or, more generally, computer assisted * From this point on we use the term "docking" in a broad sense including the determination of ligand arrangement in the protein cavity and the energy of the protein-ligand interaction.

A new fast computational method for mass calculations of docking complexes by the AM1/PM3 semiempirical methods is proposed. The computation time is shortened by at least an order of magnitude compared to alternative schemes of quantum chemical calculations. The root mean square deviation of the AM1 calculated energies of formation of complexes from the results obtained by conventional diagonalization procedure is at most 0.4 kcal mol -1 .Relationships between the biological activity and theoretical estimates of protein-ligand interaction ener gies can be used for prediction of activity, in particu lar, for solving topical tasks in drug design (see, e.g., Refs 1 and 2).Quantum chemical methods seem to be the most promising and versatile tool of estimation of proteinligand interaction energies and elucidaton of the geom etry and electronic structure of protein-ligand complexes. However, such methods can hardly be used for mass cal culations of practically interesting docking complexes comprised of a few thousand atoms each because of very high computational cost of the calculations of large mo lecular systems. 3,4Recently, a number of specific semiempirical 5,6 and ab initio 7,8 quantum chemical methods and programs for calculations of very large biomolecules were developed. Improved performance is, in particular, achieved by using quite rough approximations, which include fragmenta tion of molecules into small fragments, closure of the broken bonds, and mutual influence of the fragments in the framework of the additive scheme. 7,8 However, even in this case the performance is too low to carry out mass calculations of docking complexes. The quantum mechanical/molecular mechanics (QM/MM) methods 2,9-11 are used if only a small fragment of a complex requires the full QM treatment; the remaining part of the complex is calculated by the MM methods. As a result, the prob