A computer program for evaluating the hydrodynamic parameters of a macromolecule in solution for any given value of its axial dimensions.

A FORTRAN IV algorithm is given for determining the hydrodynamic parameters of a macromolecule in solution for any specified value ofthe two axial ratios (a/b, D/c) ofthe equivalent triaxial ellipsoid model of semi-axes a > b > c for its gross conformafion. Ellipsoid model Axial ratios Elliptic integrals Myoglobin I . I N T R O D U C T I O N The ellipsoid of revolution (i.e. an ellipsoid with two equal axes) has up to now been the most popular model for the gross conformation of biological macromolecules in solution. This has been until recently the most general model available for which it is possible to predict from a macromolecule's known hydrodynamic properties the shape in terms of its axial ratio without assumptions concerning hydrodynamic volume. Although prediction of the two axial ratios from knowledge of the hydrodynamic parameters of the more general tri-axial ellipsoid presents great problems Il] the converse is not so difficult: it is relatively easy to predict the hydrodynamic parameters corresponding to a given value of the axial ratios. This would have immediate application in, lor example, predicting the properties of proteins whose dimensions are known from crystallographic studies. This paper presents a program which calculates the hydrodynamic parameters for specified values of the two axial ratios (alb, blc) of a general ellipsoid, where c, b, c are the threesemi -axesanda>b>c.Foranob la tee l l ipso ido f revo lu t iona:bandforapro la te ellipsoid b : c. 2 . T H E H Y D R O D Y N A M I C S H A P E P A R A M E T E R S These can be divided into three basic classes: (i) The viscosity increment v. This is based on the effect of the dissolved macromolecule on the bulk motion of the fluid when a shear gradient is applied. (ii) The translational frictional ratio flf". This concerns the resistance to motion of a macromolecule through its solution when some form of external force (e.g. centrifugal field, diffusion gradient) is applied. (ii i) The rotational frictional ratios (/(, (i: a, b, c;"o" refers to the corresponding coefficient for a hydrated sphere of the same volume) concerns the disorientating effect on the macromolecule by the local Brownian motion of the surrounding solvent molecules. Related to these are three dielectric dispersion relaxation rattos pJp"corresponding to rotation ofa *This work was completed whilst the author was at the Department of Biochemistry, Leicester University, England.