BIOLOGY. Thomas E. Creighton. European Molecular Biology Laboratory. London, England. Copyright O 1999 by John Wiley & Sons, Inc. ISBN 0-471-15302-8.
ENCYCTOPEDIA OF
MOLECULAR BIOLOGY ThomasE. Creighton EuropeanMolecular Biology Laboratory London, England
CopyrightO 1999 by John Wiley & Sons,Inc. ISBN 0-471-15302-8
A Wiley-lntersciencePublication
fohn Wiley & Sons,Inc. New York/ Chichester / Weinheim/ Brisbane / Singapore / Toronto
DIFFUSION S. E. HARDING Diffusion is the movement of molecules ir.irhin a iiquid driven by therrnal fluctuations. It is import,ant for most biologicai processes; indeed, the diffusion together of trvo reactants can be the limiting factor for man_vprocesses.s,hen the reacrron is said to be diffusion-controlled. There are t\\'o tlpes of diffusional rnolion: (I\ transl.cLttonal diffusion, where a molecule n-rovesrts relative position ri.ithin a three-dimensional svstem,fand (2 ro tat tonaL d.iffu.stor,-.v,here a molecuie spins or rotates about one or nore of irs axes. The rates at rvhich molecules undergo bolh trpes of diffusion are measured b,v their respectir.e drffusion coefficients. D. and D.. The SI lrnit for D, is the ''Fick or mr/s. but for hisrorical and other reasons, biologists lend to use the cgs (Centigrade_ g r a m - s e c o n d ) s y s t e m u n i t o f c m : / s . T h e s e m e a s u r e n e n L sc a n grve important information about the sizes, structures, and physical properties of the moleclries. At room tempL.rature and in dilute solution, a small prolein of molecular rveight approximatelv 20,000 will have D, of about 10 6 cm2z,s.a larse v i r u s b e t w e e n 1 0 - 7 t o 1 0 - 6 c m z , t s ;a b a c t e r i a l s p o . e a b o u t 10-s cm2,/s.Some representative values are given in Table l. T R A N S L A T I O N A LD I F F U S T O N The translational diffusion coefficient, D,, describes the tendency of a molecule to move (transiational motion) under the influence ofeither (1) a concentration gradient or (2) Brownian motion. The movement of molecules in a gradient in which their concentration varies, dc/dr, where c is the concentration (in grams per milliliter) at each point r, is given by Fick's f irst law: (1) J -- -D,(dc/dx) where J is the mass of particles crossing a 1-cm2 cross section per second. The same D, characterizes the Brownian diffusion of the molecule:
(xz;;l: zD4
(2)
DIFFUSTON Table 1. Translational Diffusion Coefficients rameters of Some Morecules, Macromorecules lar Assemblies
Substance Water Sucrose Ribonuclease Ovalbumin Fibrinogen Dynein' Turnip yellow mosaic virus
Nlolecuiar Weight
18 342 13,700 45,000 330,000 2.5x 106 5.7 x 106
Ijt
x D;0.*, cmTs
230 46.0 111 . 7.8 2.0 1.1* 1
/
pa_
and Derived and Biomorecu-
tn8 ,
the variation in the height of the boundary, specii.icaliy, max.rmum valte of d.c/dr, with time, f : / a \2
f
t;l
I
rH, A
/
a
193 27.5 107 10(
152
_4rD,t
(5)
whereA is the area under the curve o{ dc / d.xversus -r. A plot of (A/ H)2 versus time will yield D, from the slope; an example is grven in Figure 1. Equation 5 assumes that there is no loss of material from the boundary, that is, that the area A remains constant. 1.his assumption is reasonable for homogeneous protein preparatrons but may not be valid for polydisperse materiais such as mucus glycoproteins and polysaccharides. These methods have aiso generally been superseded by dynamic light scattering. Nevertheless, the classical measurements are preferable with nonglobular macromolecules, with asymmetric shapes.
0.8B 3.64 5.18 202 36.7 28.9
'.{lthough
the molecuiar weight ofdynein is smaller than that ofturnip yellorv mosarc vrrus. its diffusion coefficient is smaller because it is more asymmetric. Values of Dj0.,. and molecular weight M" for dynein are also strongly dependent on salt concentration.
rvhere / is the tin.re and (x2) is the average of the square of the distance the particle has moved. The value of D, depends not only on the intrinsic size and shape of the molecule but also on the viscosity anci temperature of the medium in whrch ir is suspended. The value ofDl must therefore be norn-ralizedto standard conditions, the standar.cl conditions normall,v used are those of water at 20.0.C. The D, corresponding to these conciitions is normally clesignated D.rr,". It can be caiculated from the vaiue actuall-v measured rrt atbsoiute temperature T and in buffer,,b.'. D7;,, rvith tl_re e
