Thermodynamics of L-valine and L-2-aminobutyric acid

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Joshua L Price and Dr. Earl M Woolley, Chemistry and Biochemistry

Understanding the thermodynamics of protein hydration is critical to elucidating protein structure and function in aqueous solution. Because they are derivative properties, apparent molar volume Vφ and apparent molar heat capacity Cp,φ are particularly useful in describing solution thermodynamics. It is difficult, however, to resolve the apparent molar volume or apparent molar heat capacity of a large protein into individual contributions from specific amino acid residues and functional groups. Small model compounds like the amino acids can provide useful estimates of these individual contributions. While the apparent molar properties of many amino acids have been studied recently, there is a need for more precise data over a wider range of temperature and concentration.

We have measured the Vφ and Cp,φ of aqueous solutions of L-valine and L-2-aminobutyric acid in protonated, deprotonated and zwitterionic forms from 5 to 125 ºC, at concentrations from 0.015 to 0.5 mol· kg-1, and at the pressure 3.5 bars. All solutions and subsequent dilutions were prepared by mass with distilled, deionized, autoclaved, degassed water and with crystalline forms of either L-valine or L-2-aminobutyric acid. Solutions of protonated and deprotonated forms of L-valine and L-2-aminobutyric acid were prepared by titration of the crystalline amino acid with standardized HCl(aq) and NaOH(aq), respectively, followed by dilution with water to the desired concentration. Zwitterionic solutions were prepared by dilution of the crystalline amino acid with water.

Solution densities were measured with a vibrating-tube densimeter and specific heat capacities were measured with a fixed-cell, power-compensation, differential output, temperature- scanning calorimeter. Vφ and Cp,φ were calculated from experimentally observed solution densities ρs and specific heat capacities cp,s, and the precisely known density ρw and specific heat capacity cp,w of water(1) as reported previously.(2,3)

Observed Vφ and Cp,φ results for protonated, zwitterionic, and deprotonated forms of L-valine and L-2-aminobutyric acid have been fit by a weighted least squares regression to three dimensional (T, m, Vφ) and (T, m, Cp,φ) surfaces, respectively, which are defined by regression equations and parameters that will be reported in a forthcoming communication.(4)

Amino acids are multifunctional compounds. While L-valine and L-2-aminobutyric acid do not have ionizable side chains, their amine and carboxylic acid groups are ionizable and can each undergo proton dissociation reactions, given in equations (3) and (4):

Screen Shot 2014-01-31 at 4.08.22 PM

where R is –CH(CH3)2 for L-valine and –CH2CH3 for L-2-aminobutyric acid. Not shown are the corresponding hydrolysis reactions.

Simple equilibrium calculations demonstrate that while the zwitterionic solutions do not dissociate or hydrolyze significantly, the solutions titrated with HCl(aq) and NaOH(aq) are in fact mixtures of protonated and zwitterionic, and deprotonated forms of the amino acid, and either HCl(aq) or NaOH(aq). Consequently, our observed Vφ and Cp,φ for these solutions are the volumes and heat capacities of mixtures, not single species. There is also an excess heat capacity associated with chemical relaxation during the calorimeter experiments.

Young’s rule allows us to calculate the contribution of each species in a mixture from the observed Vφ and Cp,φ of the mixture, and to correct for chemical relaxation.(5,6) This is possible with an estimate of the equilibrium constants of the reactions given in equations (3) and (4) and the corresponding hydrolysis reactions as functions of temperature and concentration. However, most sources in the literature report only these equilibrium constants at the standard state and over an extremely limited range of temperature.

Given an initial estimate of the regression equations and parameters for the actual Cp,φ of the protonated and deprotonated amino acids, and the regression equation and parameters for the zwitterionic amino acid, and for NaCl(aq), HCl(aq), NaOH(aq), and water(7, 8), we can calculate the change in apparent molar heat capacity ΔrCp,m for the two proton dissociation reactions given in equations (3) and (4) as functions of temperature and concentration. The change in enthalpy ΔrHm, the change in entropy ΔrSm, and the equilibrium molality quotient Qa for these reactions can then be calculated by analytical integration of our ΔrCp,m results over temperature.

The Qa results can be used determine the extent to which protonated and deprotonated forms of the amino acid dissociate or hydrolyze in the experimental solutions, and Young’s Rule can be used to obtain a new estimate of the Cp,φ for the protonated and deprotonated amino acids, which can be used to calculate new Qa results. This process can be iterated until the results stop changing. Once the Qa results have converged, they can be used to calculate Vφ for the protonated and deprotonated amino acids and ΔrVm for the two proton dissociation reactions. Regression equations and parameters for Vφ and Cp,φ of protonated and deprotonated forms of the amino acids, and figures of Vφ and Cp,φ , ΔrVm, ΔrCp,m, ΔrHm, ΔrSm, and Qa will be reported in a forthcoming paper.

References

  1. Hill, P. G.; J. Phys. Chem. 1990, 19, 1233-1274.
  2. Ballerat-Busserolles, K.; Ford, T. D.; Call, T. G.; Woolley, E. M. J. Chem. Thermodynamics 1999, 31, 741-762.
  3. Woolley, E. M. J. Chem. Thermodynamics 1997, 29, 1377-1385.
  4. Price, J. L.; Merkley, E. D.; Sorenson, E. C.; Woolley, E. M. Work in progress.
  5. Young, T. F.; Smith, M. B. J. Phys. Chem. 1954, 58, 716.
  6. Collins, C.; Tobin, J.; Shvedov, D.; Palepu, R.; Tremaine, P. R. Can. J. Chem. 2000, 78, 151- 165.
  7. Archer, D. G. J. Phys. Chem. Ref. Data 1992, 21, 793-829.
  8. Patterson, B. A., Call, T. G.; Jardine, J. J.; Origlia-Luster, M. L.; Woolley, E. M. J. Chem. Thermodynamics 2001, 33, 1237-1262.