Prediction of thermodynamic instabilities of protein solutions from simple protein–protein interactions Tommaso D’Agostino a , José Ramón Solana b , Antonio Emanuele a,⇑ a Dipartimento di Fisica e Chimica, Università di Palermo, Via Archirafi 36, 90123 Palermo, Italy b Departamento de Física Aplicada, Universidad de Cantabria, 39005 Santander, Spain article info Article history: Received 15 October 2012 In final form 31 January 2013 Available online 14 February 2013 Keywords: Liquid–liquid demixing Square well potential Protein solution Spinodal line Solvent mediated protein–protein interaction Entropy driven phase transition abstract Statistical thermodynamics of protein solutions is often studied in terms of simple, microscopic models of particles interacting via pairwise potentials. Such modelling can reproduce the short range structure of protein solutions at equilibrium and predict thermodynamics instabilities of these systems. We introduce a square well model of effective protein–protein interaction that embeds the solvent’s action. We modify an existing model [45] by considering a well depth having an explicit dependence on temperature, i.e. an explicit free energy character, thus encompassing the statistically relevant configurations of solvent mol- ecules around proteins. We choose protein solutions exhibiting demixing upon temperature decrease (lysozyme, enthalpy driven) and upon temperature increase (haemoglobin, entropy driven). We obtain satisfactory fits of spinodal curves for both the two proteins without adding any mean field term, thus extending the validity of the original model. Our results underline the solvent role in modulating or stretching the interaction potential. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction An aqueous solution of a single protein species is a highly com- plex system. The basis of such complexity is the large number of microscopic configurations thermally available to each solute (pro- tein) molecule alone and the even larger number of microscopic configurations available to liquid water alone [1]. When solutes are in solution, configurations of solute and solvent are modified by interactions among solutes and liquid water with corresponding entropy and enthalpy costs (or gains) of those modifications. These costs are highly nonadditive [1] and, in consequence, the observed effects can be exquisitely specific. On the grounds of such complex- ities, it is not a surprise if entropy plays a crucial role in the inter- action of proteins with other proteins and solutes. This consideration makes the free energy of the entire system the appropriate quantity describing the thermodynamic behaviour of protein solutions, and not the simple energy landscape coming from energies of intra- and inter-protein interactions microscopi- cally described by local pair potentials. Studying statistical thermodynamics of protein solutions is a necessary task for understanding the macroscopic phenomena occurring in them, such as phase separation and formation of crys- tals [2–4] and aggregates. Besides, it is of high relevance for under- standing mechanisms of protein activity [5]. These studies are also very important for nanophysics, clinical sciences, biotechnologies and food technologies, as well as for fundamental physics [6–18]. In addition, an accurate microscopic description of protein–protein and protein–solvent interactions can also be used to predict micro- scopic structural details of protein solutions. The theoretical description of the thermodynamic and struc- tural properties of protein solutions requires the accurate knowl- edge of the protein–protein interactions combined with appropriate statistical mechanical methods. This is a formidable challenge because of the complexity of the interaction themselves. As an example of such complexity we only mention the relevance of the solvent mediated protein–protein interactions included in the so called hydrophobic effect [19]. Some success has been achieved with the use of simple, short-ranged, potential models in combination with statistical mechanics theories, an approach that has proved to be useful to reproduce some of the properties of colloidal suspensions. Phase transitions, as well as other macro- scopic phenomena, are on the contrary intrinsic long range effects of the microscopic interactions [19], and thus short-ranged interac- tions are hardly appropriate to describe the experimental data. Nevertheless, it is possible to describe correctly liquid–liquid phase transition by using a short range interaction potential and the modified Mean Spherical Approximation (mMSA) 1 [20]. Often, sim- 0301-0104/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.chemphys.2013.01.041 ⇑ Corresponding author. E-mail address: antonio.emanuele@unipa.it (A. Emanuele). 1 This feature is explained by noticing that the use of mMSA brings a mean field character to the model and thus accounts for averaged long range effects; conversely, short range properties of those solution are not correctly predicted by using mMSA. Chemical Physics 424 (2013) 50–55 Contents lists available at SciVerse ScienceDirect Chemical Physics journal homepage: www.elsevier.com/locate/chemphys