e. Eq. (21)) have been observed to accurately predict non-ideal solution behavior in multi-solute solutions using only single-solute data, it would be useful to compare the accuracy of the predictions of these three models in as many multi-solute solutions of cryobiological interest as possible. Such information could be used to help choose the optimal model for working with a given solution system of interest. Limited comparisons between these solution theories SGI-1776 in vitro have been made in the past [3], [14], [21] and [55],

but these have been restricted to only a few of the multi-solute systems for which data are available in the literature, and none have directly compared the molality- and mole fraction-based forms of the multi-solute osmotic virial equation. There has yet to be a comprehensive quantitative study comparing the abilities of all three of these models to predict non-ideal multi-solute solution behavior for the range of available cryobiologically-relevant multi-solute data in which the predictions of all three models are based on a single consistent set of binary solution data. Such a study is the ultimate goal of this work; however, there are some issues that must first be addressed. Solute-specific coefficients are available in the literature for a variety of solutes http://www.selleckchem.com/products/MDV3100.html for both the multi-solute osmotic virial equation [55] and the freezing point summation model [38] and [75]. However, the binary solution

data sets used to curve-fit for these coefficients are not consistent—i.e. different data sets were used to obtain the

osmotic virial coefficients than were used to obtain the freezing point summation coefficients, and, in fact, only half of the solutes which have had osmotic virial coefficients determined have had freezing point summation coefficients determined. As such, before comparing the predictions made by the three non-ideal models being studied here, solute-specific coefficients will need to be curve-fit for each model for all solutes Sclareol of interest using a single consistent collection of binary solution data sets. Additionally, it should be noted that the mole fraction-based osmotic virial coefficients previously presented by Prickett et al. [55] were not curve-fit using Eq. (8) to convert between osmolality and osmole fraction; rather, the following conversion equation was used equation(27) π̃=M1x1π. Eq. (27) arises from an a priori assumption that is true only under very specific conditions, namely, an ideal dilute solution if the relationship between osmole fraction and chemical potential is defined as in this paper and in reference [14] (the relationship is not given in reference [55]). Since the conversion between osmolality and osmole fraction is useful only in non-ideal circumstances and we have carefully defined all of the surrounding relationships in this work, we suggest that Eq. (27) not be used. Accordingly, we have herein used Eq.