Abstract
The activity coefficient is largely considered an empirical parameter that was traditionally introduced to correct the non-ideality observed in thermodynamic systems such as osmotic pressure. Here, the activity coefficient of free-solvent is related to physically realistic parameters and a mathematical expression is developed to directly predict the activity coefficients of free-solvent, for aqueous protein solutions up to near-saturation concentrations. The model is based on the free-solvent model, which has previously been shown to provide excellent prediction of the osmotic pressure of concentrated and crowded globular proteins in aqueous solutions up to near-saturation concentrations. Thus, this model uses only the independently determined, physically realizable quantities: mole fraction, solvent accessible surface area, and ion binding, in its prediction. Predictions are presented for the activity coefficients of free-solvent for near-saturated protein solutions containing either bovine serum albumin or hemoglobin. As a verification step, the predictability of the model for the activity coefficient of sucrose solutions was evaluated. The predicted activity coefficients of free-solvent are compared to the calculated activity coefficients of free-solvent based on osmotic pressure data. It is observed that the predicted activity coefficients are increasingly dependent on the solute-solvent parameters as the protein concentration increases to near-saturation concentrations.
Highlights
Many cells contain macromolecular crowded protein environments, and the crowded environment is an essential component of cells [1,2]
The activity coefficients of free-solvent were predicted based on protein-solvent interactions (Eqn 12) and compared to the activity coefficients of free-solvent calculated using osmotic pressure data (Eqn 5) for two proteins: bovine serum albumin (BSA) in 0.15 M NaCl, 25uC at pH 4.5, 5.4, and 7.4 and sheep hemoglobin (Hb) in 0.1 M KCl, 0uC, pH 7.43
The calculated activity coefficients of free-solvent were computed at each protein concentration by solving Eqn 5, with cI1~1, using the osmotic pressure data by Vilker et al [13] for the concentrated BSA solutions (0.15 M NaCl at 25uC, pH 4.5, 5.4, and 7.4), to the osmotic pressure data by Adair, published by Dick [14], for concentrated Hb in 0.1 M KCl, 0uC, pH 7.43, and to the osmotic pressure by Frazer and Myrick [10] for concentrated sucrose solutions
Summary
Many cells contain macromolecular crowded protein environments (mixed proteins with total concentrations between 50 – 400 g/L), and the crowded environment is an essential component of cells [1,2]. Crowded protein environments are abundant and naturally occurring, many studies focus on single protein solutions for studying and understanding the effect(s) of crowded environments. To correct for the deviations from ideal models in crowded environments, an activity coefficient is introduced which accounts for the various interactions responsible for observations. The free-solvent model, introduced by van Laar [4] and developed by Yousef et al [5,6,7,8,9] as be shown to give excellent predictability of the osmotic pressure of single and binary protein solutions up to near saturation. The free-solvent model is used to directly couple the activity coefficient of free-solvent to these parameters, providing, for the first time, a fundamental basis for the concentration dependency of the solution activity coefficients
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