EXCHANGE OF SUBSTANCES THROUGH CAPILLARY WALLS 



973 



20,000 



- 25,000 



l-- 30,000 



- 60,000 



fig. 3.2. First derivative of protein osmotic pressure-con- 

 centration curve to show deviation from van't Hoff's law. At 

 infinite dilution the mean number average molecular weight of 

 plasma proteins is almost 100,000 but in normal plasma their 

 osmotic behavior corresponds to an ideal solute of mol wt 

 37,000. 



If c is expressed in g per 100 ml, RT in liter-atmos- 

 pheres, and IT in atmospheres, then 



Mol Wght. = 10c RT/II (3.2) 



The potential application of equation 3.2 to the 

 determination of molecular weights led protein 

 chemists to investigate in detail the theory and 

 technique of osmotic measurements. As early as 

 1905, Reid (293) used Starling's technique to esti- 

 mate the molecular weight of hemoglobin. Subse- 

 quent studies by S0rensen (342), Adair (1, 2), and 

 others showed that protein osmotic pressure is de- 

 pendent upon ionic strength, net charge, and other 

 factors not included in van't Hoff's limiting law for 

 ideal solutions. Deviations from the limiting law 

 increase rapidly as a function of protein concentration 

 (figs. 3.1 and 3.2) and estimates of molecular weight 

 can only be made on the basis of extrapolation to 

 zero concentration. The chief technical difficulty con- 

 fronting early workers was the long period required 

 to reach equilibrium across artificial membranes. 

 In order to avoid bacterial degradation of protein 

 it was necessary to carry out measurements at low 

 temperature; days or even weeks were required for 

 each determination. Nevertheless, the first satis- 

 factory estimates of the molecular weights of serum 

 albumin (3), ovalbumin (342), and hemoglobin (2) 

 were obtained by this method. 



Advances in the technique of osmometry have 

 reduced considerably the time required for the 

 equilibration process. 



Equilibration across a semipermeable membrane, following 

 a step change in either hydrostatic or osmotic pressure, pro- 

 ceeds exponentially with a time constant equal to the product 

 of membrane resistance and volume distensibility 



% Equilibrium = IOo[l-exp-f-j^ — — -. J (3.3) 



ffi p fn' 



where r m is membrane resistance to solvent flow and v py v m 

 are the volume distensibilities of the pressure measuring device 

 and membrane, respectively. The resistance (r m ) of membranes 

 capable of restraining the passage of serum albumin is seldom 

 less than io 1 mm Hg per ml per hour per cm 2 membrane. 

 The essential factor limiting the rate of approach to equilibrium 

 is therefore the volume of fluid which must pass through the 

 membrane in order to actuate the pressure detector and 

 satisfy the volume-pressure characteristics of the membrane. 

 For example, a typical osmometer with a membrane surface 

 area of 10 cm 2 must have a total volume distensibility of less 

 than 3 X io~ 4 ml per mm Hg in order to achieve 95 per cent 

 equilibrium in 1 hour (equation 3.3). 



In 1936 Hepp (151) described an osmometer in which 

 distensibility of the membrane (»,„) was made extremely small, 

 the chief volume displacement being confined to slight changes 

 in fluid level of the capillary tube manometer used to detect 

 pressure balance. Equilibration time was reduced to about 2 

 hours. Osmometers of the Hepp type have been widely used 

 by subsequent investigators and the osmotic pressure-concen- 

 tration curves shown in figure 3.1 are based on data obtained 

 with this instrument. A recent description of the construction 

 and use of Hepp osmometers has been published by Meschia 

 (248). Further reduction in volume displacement can be ob- 

 tained through the use of sensitive, recording pressure trans- 

 ducers having volume distensibilities less than io~ 6 ml per mm 

 Hg. With the aid of such transducers it is theoretically possible 

 to achieve 95 per cent equilibration across available protein- 

 impermeable membranes in less than 1 min. Recording os- 

 mometers of this type, having time constants of less than 5 

 min, have been in use in the authors' laboratory for several 

 years (277, 280I. Similar instruments, suitable for the rapid 

 estimation of protein osmotic pressure in o. 1 ml plasma, have 

 recently been described by Hansen (142). 



B. Protein Osmotic Pressure of Human Plasma 



Osmotic pressure-concentration curves for normal 

 human plasma, serum albumin, and two globulin 

 components of plasma are shown in figure 3.1. 

 The curves were obtained at physiological pH and 

 ionic strength, but the original measurements have 

 been corrected to 37 C. Experimental points, taken 

 from Oncley et al. (268), are shown for 7-globulin 

 in order to indicate the magnitude of experimental 

 error when a pure component is measured. The 

 smooth curves for albumin, whole plasma, and 

 ft-globulin are based on data in references (268, 

 270, 312, 313, 343)- Normal human plasma has a 



