Adsorption thermodynamics of two-domain antifreeze proteins: theory and Monte Carlo simulations

In this paper we develop the statistical thermodynamics of two-domain antifreeze proteins adsorbed on ice. We use a coarse-grained model and a lattice network in order to represent the protein and ice, respectively. The theory is obtained by combining the exact analytical expression for the partition function of non-interacting linear k-mers adsorbed in one dimension, and its extension to higher dimensions. The total and partial adsorption isotherms, and the coverage and temperature dependence of the Helmholtz free energy and configurational entropy are given. The formalism reproduces the classical Langmuir equation, leads to the exact statistical thermodynamics of molecules adsorbed in one dimension, and provides a close approximation for two-dimensional systems. Comparisons with analytical data obtained using the modified Langmuir model (MLM) and Monte Carlo simulations in the grand canonical ensemble were performed in order to test the validity of the theoretical predictions. In the MC calculations, the different mechanisms proposed in the literature to describe the adsorption of two-domain antifreeze proteins on ice were analyzed. Indistinguishable results were obtained in all cases, which verifies the thermodynamic equivalence of these mechanisms and allows the choice of the most suitable mechanism for theoretical studies of equilibrium properties. Even though a good qualitative agreement is obtained between MLM and MC data, it is found that the new theoretical framework offers a more accurate description of the phenomenon of adsorption of two-domain antifreeze proteins.