COVOL: An Interactive Program for Evaluating Second Virial Coefficients from the Triaxial Shape or Dimensions of Rigid Macromolecules

Abstract

An interactive program is described for calculating the second virial coefficient contribution to the thermodynamic nonideality of solutions of rigid macromolecules based on their triaxial dimensions. The FORTRAN-77 program, available in precompiled form for the PC, is based on theory for the covolume of triaxial ellipsoid particles [Rallison, J. M., and S.E Harding. (1985). J. Colloid Interface Sci. 103:284-289]. This covolume has the potential to provide a magnitude for the second virial coefficient of macromolecules bearing no net charge. Allowance for a charge-charge contribution is made via an expression based on Debye-Hückel theory and uniform distribution of the net charge over the surface of a sphere with dimensions governed by the Stokes radius of the macromolecule. Ovalbumin, ribonuclease A, and hemoglobin are used as model systems to illustrate application of the COVOL routine.

Insight into protein–protein interactions from analytical ultracentrifugation

“…A way of dealing with this problem was introduced in 1999 using a procedure known as COVOL [9,10]. It is based on earlier theory [11] allowing the calculation of the exclusion volume contribution to the second thermodynamic virial coefficient B ex .…”

“…The example shown in Figure 2 [14] is again for a heterologous dimerization between molecules of similar molecular mass, in this case involving two proteins involved in molecular recognition at the cell surface: CD2 (M = 28.3 kDa) and CD48 (M = 28.7 kDa). A value for the second virial coefficient (B 11 ) based on the dimensions from X-ray crystallography of 85 Å (1 Å = 0.1 nm)× 23 Å × 25 Å for CD2 and 94 Å × 49 Å × 67 Å for CD48 and the application of the software COVOL [9,10] (http://www.nottingham. ac.uk/ncmh/software) yielded an average B 11 = 1.8 × 10 −4 ml · mol · g −2 and hence knowing this, from the experimental data, a value for K d of ∼(1.0 ± 0.3) × 10 −4 M was estimated, in good agreement with an estimate of ∼(7.5 ± 1.5) × 10 −5 M from surface plasmon resonance.…”

Concentration dependence of translational diffusion coefficients for globular proteins

“…54 The experimental results have therefore been subjected to linear regression analysis according to eqn (6) with two assigned values of k D to obtain D 0 and hence their bestt description in terms of that model: k D ¼ +4.20 mL g À1 for eqn (14) is considerably smaller than the experimental uncertainty inherent in its measurement, the consideration of D to be a concentrationindependent parameter for this system is justied.…”

Individual Second Virial Coefficient Determination of Monomer and Oligomers in Heat-Stressed Protein Samples Using Size-Exclusion Chromatography-Light Scattering

“…The B 22,HS for the monomer, dimer, trimer, and tetramer were calculated as 1.94 × 10 −5 , 9.76 × 10 −6 , 6.49 × 10 −6 , and 4.87 × 10 −6 , respectively. These values were calculated using the formula B HS = uN A /(2MW 2 ), as described by Harding et al 37 Here, u is the excluded volume, N A is the Avogadro's num- Figure 9. Determination of the ratio of the apparent second viral coefficient B 22 and the hard sphere repulsion contribution to the second virial coefficient B ex for monomer (black columns), dimer (grey columns), trimer (black and white striped columns), and tetramer (white columns) of (a) protein X and (b) protein Z. ber, and MW is the molecular weight of the species (150 kDa for a monomer).…”