976 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION II 



80i- mm Hg 



Approximate 

 hydrostatic 

 pressure in 

 glomerular 

 capillaries 



FILTRATION FRACTION 

 04 0.5 0.6 



0.7 



fig. 3.4. Illustrating the significance of protein osmotic 

 pressure for glomerular filtration. The rapid increase of protein 

 osmotic pressure as a function of concentration places an upper 

 limit to the filtration fraction of the kidney. 



30 ml per 100 ml, results in an increase of 18 mm Hg 

 in the osmotic restoring force, resisting further fluid 

 loss. If the plasma proteins behaved as ideal solutes, 

 however, the restoring force would be only 6 mm Hg. 

 Conversely, dilution of the plasma results in a greater 

 reduction of osmotic pressure than would obtain if 

 the proteins behaved as ideal solutes. These considera- 

 tions are of special importance normally in connection 

 with glomerular filtration where a relatively large 

 fraction of plasma fluid may be filtered. Figure 3.4 

 shows protein osmotic pressures in efferent glomerular 

 blood as a function of filtration fraction. It is clear 

 that the steep rise of protein osmotic pressure is an 

 important factor limiting filtration rate. For example, 

 a filtration fraction of 0.45 is the highest possible 

 value consistent with a normal plasma protein con- 

 centration (ca. 7%) and a normal hydrostatic pres- 

 sure (ca. 70 mm Hg) in the glomerular capillaries. It 

 is probable also that the high protein osmotic pressure 

 in efferent glomerular blood plays a major role in 

 providing the force for transcapillary absorption ol 

 fluid in the peritubular circulation. 



E. Physicochemical Aspects of Protein Osmotic Pressure- 

 In the preceding paragraphs we have emphasized 

 the functional significance of the large deviations from 

 van't Hoff's law which characterize osmotic behavior 

 of plasma proteins. It therefore seems appropriate to 

 discuss briefly the physical forces which contribute 

 to nonlinear osmotic behavior of this type. 



The disproportionate increase in osmotic pressure 

 as a function of protein concentration (figs. 3.1 and 



3.2) can be explained in part by net charges on the 

 protein molecules which cause unequal distribution of 

 electrolytes across the semipermeable membrane 

 (Donnan effect). Combination of van't Hoff's limiting 

 law (equation 3.1 ) with the ionic distribution required 

 by Donnan equilibrium for univalent ions yields the 

 following: relation. 



17 -- RT(c + yS^cT+Tmf -2mJ (3. 7) 



where c = protein concentration, moles per liter; 

 Z = net charge 2 on the protein, and m s = the con- 

 centration of salt solution with which the protein is 

 equilibrated. A simple derivation of equation 3.7 

 may be found in reference (156). A more convenient 

 form of equation 3.7 may be obtained from expansion 

 of the second term by means of the binomial theorem. 

 Thus, 



■y/z*C Z ' + 4m f - i. 



Z*C* 



/V 



s 4m c 64m? 



(3.8) 



The third term of the series is negligible except at 

 very low salt concentrations. Substituting the first 

 two terms of the series in equation 3.7 we obtain the 

 form derived by Scatchard et al. (3 1 3) 



n* rt(c + 



4m/ 



(3.9) 



Equation 3.7 or 3.9 describes qualitatively some of the 

 observed changes in osmotic pressure as a function of 

 protein concentration, charge, and salt concentration. 

 Thus osmotic pressure is increased when the salt con- 

 centration (m s ) is reduced or if the charge (c) is in- 

 creased in either direction from the true isoelectric 

 point. For a limited range of conditions, equation 

 3.7 or 3.9 predicts quantitatively the observed osmotic 

 pressure-concentration curves. 



For example, when albumin is equilibrated against 

 .15 m NaCl (m, = .15) at pH 7.4 the charge, z, is 

 — 1 7, whence 



n -" RT (c + 



17' 



cV 



(3.10) 

 4x.l5 ' 



Taking 69,000 as the molecular weight of albumin and 

 expressing c in g per 100 ml this becomes 



77-- 2.8c + I9c z (3.11) 



Equation 3.1 1 is almost identical with the first two 



2 Net charge, z, is defined as the algebraic sum of all charges 

 on the ionizable constituents of the protein molecule plus 

 those charges which result from binding of ions by the protein. 

 In the case of serum albumin at pH 7.4 in .15 m NaCl at 25 C 

 the net charge estimated from the titration curve is —17, made 

 up of approximately 100 negative and 83 positive charges on 

 the protein. In addition 9 or 10 chloride ions are bound to each 

 molecule (86). 



