A Simulated Annealing Algorithm for Geometrical
Assessment of Macromolecular Hydrophobic Interaction
Tomoko Hara

Carlos Adriel Del Carpio

hara@translell.eco.tut.ac.jp

carlos@translell.eco.tut.ac.jp

Laboratory for Informatics & AI in Molecular and Biological Sciences
Department of Ecological Engineering. Toyohashi University of TechnologyTempaku, Toyohashi 441-8580, Japan

1 Introduction
Macromolecular interaction is critical to many biological and biochemical processes and phenomena
in living systems. Its assessment would lead to a deeper understanding of many relevant phenomena
at the molecular level such as molecular and cellular recognition, signal transmission, and many otherprocesses in life systems, as well as in drug and protein engineering.
It is widely recognized that one of the primary organizing principles in structural biochemistry andbiology is the so called hydrophobic e ect. The hydrophobic e ect is the tendency of apolar molecularspecies to associate spontaneously in aqueous solutions. The hydrophobic e ect at the molecular level
involves contact interactions among apolar groups which are stabilized by entropic e ects originatedin the solvent.
In the present work we approach the problem rstly from a geometrical point of view. This consistsin the evaluation of the changes in solvent accessible surface area (SASA) of proteins or any othermacromolecules at interaction with other molecular species. We propose a methodology to assesshydrophobic interaction as a function of the decrement of SASA and the optimal accommodation of
the interacting surfaces of macromolecules so as to maximize this decrement.
Finally we apply our methodology and attempt to assess the best con gurations at interaction ofmacromolecular complexes in aqueous solutions.

2 Methodology
Estimation of interaction energies of solutes based on the solvent accessible surface area combinedwith experimental data was attempted by Eisenberg et al. [1]. In general, and in Eisenberg's modelin particular, the interaction energy among molecules in solution is composed by four terms: vander Waals interactions (repulsion term) Evdw , the cavity formation energy or void term Ecav , theelectrostatic interaction Ecoulomb , and the hydrophobic interaction Eh ; i.e.:
Einteraction = Evdw + Ecav + Ecoulomb + EhThe electrostatic term can be computed by the classical Coulomb law (0 por apolar or neutral
solutes), the vdW interaction is well characterized, while the cavity formation energy is that arrivingfrom the exclusion of solvent molecules initially attached to the interacting molecules.
Here we concentrate on the hydrophobic interaction energy which can be expressed as:
Eh =X  SASA
mi=1i

380i

From this equation it is evident that the interaction energy will be proportional to the SASA of
the macromolecular system. Thus it can be hypothesized that a decrement in the overall SASA of thesystem will lead to a more stable con guration.
Assuming small changes on the cavity formation and van der Waals energies, we have implemented
a simulated annealing algorithm to search the con gurational space at interaction of two (or more)
molecular systems. The degrees of freedom for non exible systems are ve (positioning the center ofmass of one of the molecules at the origin of coordinates, the other molecule position is de ned by thethree relative coordinates of position respect to the rst molecule, and the two of rotation around its
own axis), as shown in Fig. 1.

3 Results and DiscussionFig. 2 illustrates the change in SASA with the con guration adopted at interaction by a bi-molecularsystem. The complex is composed of a peptide compose of 98 atoms and the other of 23 atoms. SASA
is computed using the Richmond algorithm [2] and the temperature of the annealing processes wasinitially set to 0.5.
As predicted, a geometrical accommodation of both molecules so as to reduce the overall SASA as
well as void formation in the contact surfaces is evident.
Further development of the present system will lead to the characterization of the potential ofmean force (PMF) for di erent systems.

Figure 1: Freedom degrees fora system composed of 2 biomolecules.

Figure 2: Variation of SASA for a systemof 2 molecules.

References[1] Eisenberg, D. and McLachlan, A.D., Solvation energy in protein folding and binding, NATURE,
319:199{203, 1986.
[2] Richmond, T.J., Solvent Accessible Surface Area and Excluded Volume in Proteins, J. Mol. Biol.,
178:63{89, 1984.

381