Role of solvent accessible surface area in the conformational equilibrium of n-butane in liquids Angelo Riccio a , Giuseppe Graziano b,⇑ a Dipartimento di Scienze Applicate, Università di Napoli ‘Parthenope’, Centro Direzionale Isola C4, 80143 Napoli, Italy b Dipartimento di Scienze Biologiche ed Ambientali, Università del Sannio, Via Port’Arsa 11, 82100 Benevento, Italy article info Article history: Received 13 November 2010 In final form 11 December 2010 Available online 15 December 2010 abstract Explicit computer simulations have unequivocally demonstrated that water significantly affects the con- formational equilibrium of n-butane, favouring the gauche conformation with respect to the trans confor- mation. In this Letter, it is shown that a theoretical approach, grounded on the basic notion that the fundamental difference among the various n-butane conformations is the solvent-excluded volume they produce, is able to quantitatively reproduce the dependence of the conformational Gibbs energy upon the dihedral angle in both water and carbon tetrachloride. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Hydrophobic interactions are widely considered to play the fun- damental role in driving the folding of globular proteins in water, governing the equilibrium among the various conformational states of the polypeptide chain [1–3]. It would be useful to shed light on the mechanism of hydrophobic interactions by studying an idealized case in which other effects are not operative. The simplest nonpolar chain molecule, possessing solely one conforma- tional degree of freedom, the u dihedral angle, is that of n-butane. It was expected and it has been verified, by means of both theoret- ical approaches and computer simulations, that water significantly affects the conformational equilibrium of n-butane, leading to an increase in the population of the gauche conformation at the ex- pense of that of the trans conformation [4–13]. In addition, it has been calculated that a qualitatively similar effect is operative in carbon tetrachloride [8]. This means that the topic has been inves- tigated in detail and the dependence of DG on the u dihedral angle is qualitatively well established. We would like to provide a simple theoretical approach grounded on the basic notion that the fundamental difference among the various n-butane conforma- tions is the solvent-excluded volume they produce [14], as origi- nally pointed out by Ben-Naim [15]. Liquids are a condensed state of matter and a suitable cavity has to be created into them in order to insert a solute molecule. Even though cavity creation may appear as a conceptual/theoret- ical process, it plays a central role in solvation thermodynamics [1–3,14]. In particular, the creation of a cavity in a solvent, at constant temperature, pressure and number of particles, produces a solvent-excluded volume because, in order to have the cavity van der Waals volume empty, the centre of solvent molecules cannot penetrate the shell region between the van der Waals sur- face of the cavity and the solvent accessible surface of the cavity itself [14]. This shell region, regardless of its shape, is correctly described and measured by the solvent accessible surface area [16] of the cavity, SASA c . Cavities suitable to host the different conformations of n-butane have practically the same van der Waals volume, but different SASA c and so they produce different solvent-excluded volumes (see Figures 1a and b). A decrease in solvent-excluded volume translates into a gain of configura- tional/translational entropy of solvent molecules (i.e., there is an increase in the available configurational space), that favours the more compact molecular conformations of the solute [14,17] (i.e., gauche versus trans in the case of n-butane; folded versus unfolded conformations in the case of globular proteins). On this basis, we would like to show that the effect of water on the conformational equilibrium of n-butane can be rational- ized at a molecular level, and there is no need to invoke the reorganization of water–water H-bonds around the nonpolar n-butane molecule. 2. Theoretical approach The Gibbs energy change governing the conformational equilib- rium of n-butane in water and in carbon tetrachloride is directly and exactly linked to the difference in Ben-Naim standard Gibbs energy of solvation [12] among the different conformations: DG ð uÞ¼ DG Å ðuiÞ  DG Å ðujÞ ð1Þ where u i is the dihedral angle value corresponding to the ith conformation, and u j is the dihedral angle value corresponding to the jth conformation; the superscript filled circle indicates the Ben-Naim standard Gibbs energy of solvation, referring to the 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.12.042 ⇑ Corresponding author. Fax: +39 0824 23013. E-mail address: graziano@unisannio.it (G. Graziano). Chemical Physics Letters 502 (2011) 180–183 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett