Adsorption of three-domain antifreeze proteins on ice: a study using LGMMAS theory and Monte Carlo simulations

Abstract

In the present work, the adsorption of three-domain antifreeze proteins on ice is studied by combining a statistical thermodynamics based theory and Monte Carlo simulations. The three-domain protein is modeled by a trimer, and the ice surface is represented by a lattice of adsorption sites. The statistical theory, obtained from the exact partition function of non-interacting trimers adsorbed in one dimension and its extension to two dimensions, includes the configuration of the molecule in the adsorbed state, and allows the existence of multiple adsorption states for the protein. We called this theory "lattice-gas model of molecules with multiple adsorption states" (LGMMAS). The main thermodynamics functions (partial and total adsorption isotherms, Helmholtz free energy and configurational entropy) are obtained by solving a non-linear system of j equations, where j is the total number of possible adsorption states of the protein. The theoretical results are contrasted with Monte Carlo simulations, and a modified Langmuir model (MLM) where the arrangement of the adsorption sites in space is immaterial. The formalism introduced here provides exact results in one-dimensional lattices, and offers a very accurate description in two dimensions (2D). In addition, the scheme is capable of predicting the proportion between coverage degrees corresponding to different conformations in the same energetic state. In contrast, the MLM does not distinguish between different adsorption states, and shows severe discrepancies with the 2D simulation results. These findings indicate that the adsorbate structure and the lattice geometry play fundamental roles in determining the statistics of multistate adsorbed molecules, and consequently, must be included in the theory.

Thermal hysteresis activity of antifreeze proteins: A model based on fractional statistics theory of adsorption

“…The study in Refs. [22][23][24] confirmed also the importance of the size and structure of the protein in determining its activity. These findings are consistent with previous results addressing the effect of impurities on the growth of crystals from aqueous solutions [25].…”

“…A similar effect was reported by DeLuca et al [13], who reported that an increment in the AFP activity is observed when the type III AFP is linked to other proteins and thus its size is increased. From a theoretical point of view, several models have been proposed relating thermal hysteresis activity with the portion of ice surface occupied by AFPs [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. These approaches stimulate the researchers to develop more refined theoretical solutions for the adsorption thermodynamics of complex adsorbates (in this case, proteins of different sizes and shapes).…”

“…Each AFP molecule was modeled as a linear chain of n beads (domains) joined by flexible linkers, able to adsorb in different configurations or adsorption states. This new scheme, denoted as lattice-gas model of molecules with multiple adsorption states, has demonstrated to be a more accurate approach to characterize the adsorption process of two- [23] and three-domain [24] AFPs. The study in Refs.…”

Crystal Growth from Aqueous Solution in the Presence of Structured Impurities

“…However, further comprehensive analysis of other interest systems through the proposed formalism appears necessary to discern its applicability, reliability, and accuracy. Along this line, future efforts will be devoted to the study of crystal growth in the presence of n -domains antifreeze proteins. − Previous investigations in these systems point out that the structure of the adsorbate and the geometry of the lattice play essential roles in determining the thermodynamic properties of the adsorbed proteins.…”