The form birefringence of macromolecules

Abstract

Perutz has shown that the birefringence changes when the water in a haemoglobin crystal is replaced by salt solution. The effect of this substitution in the birefringenee is calculated and compared with Perutz's observations. There is agreement as to the order of magnitude of the effect, but the optical data indicated a more elongated molecule (a/b ,-~ 1.45) than that deduced from the X-ray data (a/b ,.~ 1.3). This discrepancy is not to be stressed, since the form of the molecule is not yet certain and the measurements of change in birefringence are very approximate. A further exploration of the effect may yield a useful method of estimating the form of other protein molecules. 1 In the preceding paper Perutz (1953) has measured the change in birefringence which occurs when a salt solution replaces water between the molecules of the haemoglobin crystal. The observed birefringence is considered to be due partly to an intrinsic birefringence of the molecule itself, and partly to the elongated form of large molecules of high refractive index which are immersed in a liquid of lower refractive index. Calculations of the form birefringence, and of its variation when the refractive index of the liquid is varied, are made in this note and compared with Perutz's observations. If parallel spheroids with major and minor axes a and b and dielectric constant ~9 are arranged in a regular way in a liquid of somewhat lower dielectric constant el, they are polarized to a greater extent when the electric field is parallel to the long axis than when it is parallel to a short axis. The appropriate equations are derived in § 2 of this note, where it is shown that f(e~-ex) e = ezJr 1 +(1-~~z)/sz}L ' e being the mean dielectric constant, f the fraction of the volume occupied by the spheroids, and L a de-polarizing coefficient depending on the ratio a/b. L~, the depolarizing coefficient for an electric field parallel to a, is less than L~ and L r when the spheroid is prolate. By substituting the values of L in the formula, and putting nv = e=, n~ = e~, we can evaluate the form bixefringence (n~-n~) or (n~-n=), which of course in this case is of the positive type. The observed birefringence is the resultant of the intrinsic birefringence and the form birefringence, and we cannot compare the calculated form birefringence with observation because the intrinsic birefringence is not known. We can, however, calculate the change in form birefringence A (n~-n~) when the refractive index of the liquid is varied, and compare this with Perutz's observations. The form birefringence diminishes when salt solution is substituted for water because nz, the refractive index of the liquid, approaches n2, the re-fractive index of the protein. It should vanish when n z is equal to n 2. The intrinsic birefringence remains unchanged. We have assumed a value 1.60 for n~, the refractive index of protein, based on measurements by Adair & Adair (1934) of the refractive index of protein solutions. This value may be somewhat uncertain, but a test shows that the calculated values of A(n~-n=) are affected only to a slight extent by comparatively large changes in the value assumed for n~. For instance if ne is in error by 0.05, the calculated value of A(n~-n~) would be changed by only 5?/0, which is much less than the error of the observations. A complication arises because the protein molecule is believed to be surrounded by a water layer into which the salt does not enter; the effect of this water layer is considered in the next section where it is shown that as a consequence of its presence the 'matching' refractive index is 1.53 and not 1.60. 0,t 1, 0"2 _-1 2