Biotransport - Principles of Biomedical Engineering - page 37

Table 2.2 Physical Parameters for Common Biological Molecules

MW (Daltons) Diameter (Å)

D at 37°C [m 2 /s]

∞

Urea 60.1 5.69 1.81 × 10 −9

Creatinine 113.1 7.19 1.29 × 10 −9

Glucose 180.16 8.52 9.55 × 10 −10

Vitamin B 12 1355.42 16.63 3.79 × 10 −10

Epidermal growth factor (EGF) 6,600 37 (at 34°C) 1.67 × 10 −10 (at 34°C)

Nerve growth factor (NGF) 26,500 49 (at 34°C) 1.27 × 10 −10 (at 34°C)

Bovine serum albumin 69,000 65 6.7 × 10 −11

Source: [2-4].

is the density of the solute and typically varies between 1.265-1.539 g/cm 3
for globular proteins. Equations (2.9) and (2.10) estimate free diffusivity of solutes
in a homogeneous medium. However, the presence of other molecules affects the
diffusivity constant. To account for some of the alterations, free solution diffusivity
is related to the diffusivity constant in Fick's first law by

where ρ

Dk ∞ =

AB D

where k D is called a hindrance coefficient for diffusion. In the absence of specific
interactions such as adsorption and electrical effects, k D for spherical solutes in
membranes with cylindrical pores is a function of the ratio of the solute radius to
the membrane pore radius. However, the temperature dependence of the diffusion
coefficient of a spherical molecule is not linear. The temperature dependence of dif-
fusivity constant also arises from the viscosity changes.

EXAMPLE 2.6

A main protein component in serum is 4.5g per 100 mL of albumin (MW = 75,000; diam-
eter = 70Å). Calculate the diffusion coefficient of component at 37°C in water.

Solution: To solve for the diffusion coefficients:

m = viscosity of water at 37°C = 0.76 cP = 0.76 * 10 − 3 Ns/m 2

N A = 6*1,023 K/J

r = 70Å = 70*10 − 10 m

RT 8.3143 J/mol.K * 310 K

D

= =

∞

6 rN 6 * 70 * 10

− 10

m * 0.76 * 10

− 3

Ns/m * 6 * 10

2 23

molecules/mol πμ π

A

= 8.54*10 − 11 m 2 /s = 8.54*10 − 7 cm 2 /s

The experimentally reported D ∞ value (Table 2.2) is slightly less than this value.