## Isothermal Immersion Calorimetry

This involves measuring the heat effects evolved on contacting a certain amount of a solid with a solvent volume. Heat effects determined at a given

From: Methods in Biotechnology, Vol. 15: Enzymes in Nonaqueous Solvents: Methods and Protocols Edited by: E. N. Vulfson, P. J. Halling, and H. L. Holland © Humana Press Inc., Totowa, NJ

temperature and pressure correspond to the change of the enthalpy on formation of the heterogeneous system. Correct analysis of calorimetric data requires defining a system under study. We consider the case when (1) initially both protein sample and organic solvent may contain water, (2) protein immersed in a water-organic mixture forms a two-phase system including the protein phase and liquid solution, (3) the protein phase may contain both water and organic component, and (4) there is no significant dissolution of a protein in the liquid phase. Then, integral change of the enthalpy AH corresponding to introducing some amount of protein in a water-organic mixture is given by

AH=[HwMw + HS mSmS] final liquid + Hp MP + HW MW + H + Ms] final solid

- Hw mW + HS + mS] initial liquid + [HP mP + HW mW ] initial solid (1)

where Hp, HW, and HS are the partial enthalpies of the protein, water, and organic components, respectively; mP, mW, and mS are mass amounts of the protein, water, and organic components, respectively; phases (liquid or solid) and states (final or initial) are specified by subscripts. The amounts of water (mW) and of the solvent component (mf) transferred from the liquid phase to the protein phase during suspending the protein sample (i.e., sorbed) are defined as mW = [mW, initial-mW, final] liquid = [mW final - mW, initial] solid (2)

mS = [ms, initial-ms, final] liquid = [ms final - mS, initial] solid = ms, final solid (3)

By introducing the quantities of transferred amounts into Eq. 1, the final expression (Eq. 4) is obtained as:

AH = [mw, initial liquid [HW, final liquid - ^W, initial liquid ] mW [HW final solid^ HW, final liquid]

+ mW, initial solid [HW, final solid - HW, initial solid] + mP [HP, final - HP, in_itial] (4)

+ mS [HS,final solution - HS, final liquid] + mS, initial liquid [HS, final liquid - HS, initial liquid]

Equation 4 accounts for protein interactions in the solid state, the transfer of water and of the solvent from the external liquid phase into the protein solid phase, and the dilution/concentration effects in both phases. When the solidliquid ratio is small enough, the partial enthalpies of water and organic component in the external liquid phase are not changed during sample immersion. An expression useful for experimental application is given by

AH = mW_[HW, final so^id - [HW, final liqrnd] + mW, initial_solid [HW, final solid - [HW, initial solid]

+ [HP, final - HP, initial] + mSS' [HS, final solid - [HS, final liquid] (5)

where AH, and m^, mW, initial solid, and mSr are related now to the unit mass amount of protein.

Detailed thermodynamic analysis based on Eq. 5 would involve the evaluation of partial enthalpy changes of components in both phases. This analysis needs information concerning the composition of coexisting surface and/or bulk phases. However, useful conclusions may be obtained also when less information is available.

Obtained in the absence of water, the AH values demonstrate immediately the energetics of protein-organic solvent interactions. Depending on the specific mechanism, these enthalpy changes may be considered as wetting heats (if solvent molecules solvate the surface of the protein sample) or swelling heats (if the solvent molecules penetrate into the protein bulk).

In the majority of practical cases, both the protein sample and the solvent contain water. In order to distinguish between protein-water interactions (adsorption/desorption, water-stripping effect of organic solvent) and protein-organic solvent interactions, calorimetric data should be compared with water-sorption data obtained independently.

The water amount bound to proteins in organic solvents may be determined using Karl Fischer titration from the change of water concentration in the external phase (2-5). Further, the measured AH values should be plotted against the water amount mW removed by the protein sample from the external solution. Nonzero AH values obtained at zero water amounts mW will indicate the protein-organic solvent interactions. In fact, any changes of the partial enthalpies for protein, water, and solvent in the protein phase at a fixed water amount have to be related with the solvent uptake (i.e., with protein-solvent interactions). Additional information concerning the energetics of the protein system may be extracted from examining the shape of the obtained dependence. The most significant case is a linear dependence between AH and mW. In this case, the differential change AH of the enthalpy corresponding to the water sorption (dAH/ dm%)T,p is easily obtained from the constant slope of this dependence. As follows from Eq. 5 and properties of partial functions [i.e., the generalized Gibbs-Duhem equation (6)], this differential change AH corresponds to

[HW,final solid - Hw,final liquid] + (dmWdmW) T,p [HS,final solid - HS, final liquid], where

(dmf/dmW) T,p shows the relation between sorption of water and organic component by the protein sorbent. The linear dependence between AH and mtrsuggests also that the water partial enthalpy in the solid protein phase is not dependent on the sorbed amount of water. Then, the intercept of the linear AH

versus m% dependence is [Hp, final - HP, initial] + m'I [HS, final solid - ^ final liquid].

As estimated for a fixed water amount on the protein, this intercept demonstrates the effect of the organic component penetration into the protein phase. The following analysis of calorimetric data may include (1) examining the solvent nature effect on the differential sorption enthalpy of water, (2) inspecting the solvent nature effect on the enthalpy term related to the protein-solvent interactions, and (3) modeling the water concentration (activity) effect on the AH values in different solvents. All together, it may give insight to the energetic quantities characterizing protein-water and protein-solvent interactions (see Note 1).

Discussions of the theoretical background for adsorption thermodynamics and immersion calorimetry may be found in refs. 7-9. Experimental illustrations for immersion calorimetry of solid proteins in organic solvents are presented in refs. 10-14 providing a basis for given protocols.