Computer Physics Communications 147 (2002) 307–312 www.elsevier.com/locate/cpc Thermodynamics of proteins: Fast folders and sharp transitions Audun Bakk a , Paul G. Dommersnes a , Alex Hansen a,∗ , Johan S. Høye a , Kim Sneppen a , Mogens H. Jensen b a Department of Physics, Norwegian University of Science and Technology, NTNU, NO-7491 Trondheim, Norway b Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark Abstract Several small globular proteins exhibit a simple two-state folding process (sharp transition). The rather short folding times of proteins (fast folders) indicate that folding is guided through some sequence of contact bindings. We discuss the possibility for reconciling a two-state folding event with a sequential folding process, i.e. a folding pathway in a schematic model of protein folding. We show that both single and multiple folding pathways can lead to an apparent two-state folding from a thermodynamic point of view. We also discuss water interactions in protein folding, leading to cold and warm destabilization of the protein.  2002 Published by Elsevier Science B.V. PACS: 87.14.Ec; 05.70.Ce; 87.15.Aa Keywords: Protein folding; Thermodynamics; Folding pathway; van’t Hoff enthalpy relation 1. Introduction Proteins appear to fold into a unique native confor- mation, in spite of an “astronomical” number of al- ternative configurations. This apparent paradox, usu- ally attributed to Levinthal [1], is further sharpened in view of the fact that there is experimental evidence that the folding transition behaves nearly like a two-state system for many single domain proteins [2,3]. This means that for these proteins the transition from dena- tured (unfolded) to native (folded) state occurs rather directly without observed intermediates. One might think that such a two-state behavior excludes the pos- sibility of guiding the protein to the native state. The purpose of the present work is to quantify the degree of * Corresponding author. E-mail address: alexh@phys.ntnu.no (A. Hansen). guiding that is compatible with the observed two-state folding process. The van’t Hoff enthalpy relation relates the latent heat (Q) of a smoothed-out first order phase transition, taking place at T c , to the height of the heat capacity peak C [4] Q 2 = αk B T 2 c C, (1) where α is a dimensionless proportionality factor and k B is the Boltzmann constant. A small α indicates a sharp transition. The T c is defined as the temperature where the protein has equal free energies in the native state and in the denatured state. When the transition is two-state it is known that α = 4 [4] and when the transition has intermediates then α> 4 [5]. For the small single domain proteins ribonuclease, lysozyme, chymotrypsin, cytochrome c, and myoglobin Privalov and Khechinashvili [4] 0010-4655/02/$ – see front matter  2002 Published by Elsevier Science B.V. PII:S0010-4655(02)00293-X