GAFLEX: A Hybrid GA Engine
for Mapping the Con guration Hyper-Spaceof Organic Compounds in Solution
Carlos A. Del Carpio

carlos@translell.eco.tut.ac.jp

Laboratory for Informatics & AI in Moleclular and Biological Sciences
Department of Ecological Engineering, Toyohashi University of Technology
Tempaku, Toyohashi 441-8580, Japan

1 Introduction
Biological activity of drugs and other organic compounds is determined by their solubilities in wateror any other solvent or solution. Several methodologies to compute the solubilities of organic compounds have been devised, however most of them are bound to aqueous solutions, and many times themethodology works for a limited number of compounds. Furthermore, those methodologies state very
little or nothing on the structure that the compound adopts in solution, and to the date comparisonsof the structural characteristics of a molecule in solution as referred to those in the gas phase havebeen rarely reported.
In the present work we present a new and general approach for the prediction of the most stable
three dimensional structure of an organic compound in water which may be extended to any polar or
apolar solvent. From this structure (in fact, several structures), thermodynamical properties of theorganic molecules as well as solubilities and bio-activities in solution can be derived.

2 Methodology
The methodology proposed here to predict the conformation of organic compounds in solution consistsin: (a) a heuristic algorithm to search the conformation space of the solute, and (b) the developmentof the solvent e ect module. The conformational search is performed by a genetic algorithm (GA)engine [1], suitable for nding minima in complicated multidimensional surfaces. The evolutionary
engine operates on rotable bonds of the molecule as well as on ring vertices and edges, ipping andapping them. These perturbations are performed as part of the GA mutation operation.
The intramolecular force eld on which the GA operates consists of a bond and angle stretching
function, a torsional energy function, van der Waals interactions, and electrostatic interactions among
the atoms constituting the solute. The GA here is hybridized with a Newton-Raphson optimization
procedure to re ne the energy minimization.
On the other hand, the solvent e ect module expresses the constraints that the solvent imposes tothe solute in solution. The module takes into account the energy due to the cavity formation of thesolute in solution [2], the van der Waals interaction between the solute atoms and the surrounding solvent molecules, and the solvent-solute electrostatic interaction. The solvent is treated as a continuum,
and the scale particle theory is used to express the thermodynamics of cavity formation. Electrostaticinteractions are expressed by means of the generalized Born equation [3], while van der Waals interactions are computed by an empirical model based on the calculation of the solvent accessible surface
area. GAFLEX (the acronym for Genetic Algorithms for molecular FLEXibility analysis) incorporates
372

all these functions, and comparisons of geometrical characteristics in gas and solution can be carriedout for any organic molecule.

3 Results and Discussion
GAFLEX was applied to the prediction of the con guration in solution of several types of organic
compounds. Fig. 1, shows the relation between experimental and the GAFLEX computed values ofsolvation energies for di erent kinds of compounds. The correlation is very high, although still someparameterization has to performed in order to handle several other kinds of small organic molecules.
Correlation of the solvation energies with any of the di erent solubilities scales may also allow theprediction of the solubility of a compound. Here we have introduced a new force eld based on SASA tocompute the 3D structures of small organic compounds in solution. The GA operating on the variable
elements of the structure allows the mapping of the con guration hyper-space of the molecule, making
possible the prediction of the most stable conformation in solution. Further development of the system
may allow prediction of the 3D of molecules in several other solvents.

Figure 1: Calculated and experimental solvation energies for several types of organic compounds.

References[1] Del Carpio, C.A. and Gogonea, V., Modelling Proteins Conformation in Solution. Part I: A Parallel GA Engine for Protein Conformational Space Mapping, Genome Informatics 1996, Universal
Academy Press, 108{109, 1996.
[2] Ben Naim, A. and Marcus, Y., Solvation Thermodynamics of Nonionic Solutes, J. Them. Phys.,
81:2016, 1984.
[3] Still W.C., Tempczyk, A. and Hawley, R.C., and Hendrickson, T., Semianalytical Treatment ofSolvation for Molecular Mechanics and Dynamics, J. Am. Chem. Soc., 112:6127{6129, 1990.
373