## Abstract

The colloid or protein osmotic pressure (Π) is a function of protein molarity (linear) and of Donnan and other effects. Albumin is the major osmotic protein, but also globulins influence Π. Equations based on concentrations of albumin and nonalbumin (globulin concentration + fibrinogen concentration) protein approximate Π better than albumin alone. Globulins have a wide range of molecular weights, and a 1956 diagram indicated that Π of globulin fractions decreased in the order α_{1}-, α_{2}-, β-, and γ-globulin. The molecular weight of the serum protein fractions had been extrapolated, so van't Hoff's law and nonlinear regression analysis of the curves permitted expression of the diagram as an equation: , where Π_{s,Ott,2°C,cmH2O} is Π of serum at 2°C (in cmH_{2}O) computed from the 1956 diagram, C_{tot} is the concentration (g/l) of total protein in serum, and *x*_{alb}, *x*_{α1}, *x*_{α2}, *x*_{β}, and *x*_{γ} are the fractions of albumin, α_{1}-, α_{2}-, β-, and γ-globulin, respectively. At one and the same concentration of fractions, Π_{“Ott”} decreases in the order α_{1}-globulin, albumin, α_{2}-globulin, β-globulin, and γ-globulin.

- protein osmotic pressure
- serum protein fractions
- electrophoresis

early formulas for approximating protein osmotic pressure (Π) of serum (Π_{s}) from concentrations of albumin (C_{alb}) and globulin (C_{glob}) (7) were replaced in the 1960s by equations that reflected van't Hoff and Donnan parts of Π (5). Two equations based on concentration of total protein (C_{tot}) and C_{alb} (C_{tot} - C_{alb} = C_{glob} + C_{fibr}, where C_{fibr} is concentration of fibrinogen) were compared (2), but a diagram revealed a most obvious fact, Π of C_{glob} depends on the molecular weight (MW) of the molecules (1). The late Arthur C. Guyton published a diagram (4) on Π of electrophoretic serum protein fractions traced (1) to Ott (6). The diagram initiated this attempt to express Ott's (6) curves as equations.

## METHODS

The Π depends on protein molality or molarity, ions attracted (Donnan effect) by charged protein (3-5), pH, and apparently protein interactions (5).

The number of protein solutes in serum is low, so molarity (concentration/MW; concentration in g/l solution) has been used to calculate the coefficient of the linear part of Π from van't Hoff's law, Π = RT (concentration/MW), where R is the gas constant and T is the temperature in K (3). Ott determined Π of electrophoretic serum fractions at 2°C, and from van't Hoff's law extrapolated the average MW of albumin (69,000) and of α_{1}- (45,000), α_{2}- (115,000), β-(125,000), and γ-globulin (145,000) fractions (6). These MWs were used here to calculate coefficients of the five linear van't Hoff terms in the equation (see results, Fig. 1).

Donnan effects become progressively more significant the higher the C_{tot} (3-6). Coefficients for (virial) second-power terms that made curves approach 10 points on each of Ott's five curves (6) were calculated by nonlinear regression using Nelder and Mead's simplex procedure (http://www.library.cornell.edu/nr/bookcdpf.html). Third-power terms did not improve the fit.

## RESULTS

The result is in which Π_{s,“Ott”,2°C,cmH2O} is computed Π of serum at 2°C (in cmH_{2}O); and *x*_{α1}, *x*_{alb,} *x*_{α2}, *x*_{β}, and *x*_{γ} are the fractions (α_{1}-globulin concentration/C_{tot}, etc.) of α_{1}-, albumin, α_{2}-, β-, and γ-globulins, respectively. The parts of the equation are arranged on top of each other and here in order of decreasing coefficients, which reflect increase of protein fraction MW (see methods). The computed equation multiplies Π_{“Ott”,2°C} by 310/275 to give Π_{“Ott”} at 37°C.

Figure 1 was computed by Π_{“Ott”,2°C}. The figure differs slightly from Ott's diagram (6) and from Guyton's version (Ref. 4, Fig. 30-9) of it. The scale is close to Guyton's scale (units differ) and permits detection of differences with the help of a transparent copy of either diagram.

Computed Π_{“Ott”,2°C} was compared at 10 g/l steps of fraction concentration (C_{fraction}) with caliper readings from Ott's (6) and from Guyton's (4) diagrams. At 50-80 g/l, Π_{“Ott”} often differed from Ott readings by 1 cmH_{2}O and once (α_{1}-globulin concentration, 80 g/l) by 2 cmH_{2}O. Readings from Guyton's version were almost consistently slightly lower than computed Π_{“Ott”} and readings from Ott's curves.

Table 1 illustrates theoretical relationships between Π_{“Ott”} and C_{fraction}, shows Π_{“Ott”} at one average clinical distribution of fractions, and exemplifies change of the pressure at increase of C_{glob} followed by decrease of C_{alb}.

## DISCUSSION

Fibrinogen has a higher MW than IgG and should influence Π less than γ-globulin, but, as part of plasma total protein, C_{fibr} contributes to Π of other proteins (Fig. 1). The error induced by relying on serum instead of plasma should, however, with few exceptions, be smaller than that caused by omission of the effect of low-MW globulin fractions.

Does Π_{“Ott”} reflect Ott's (6) diagram adequately? At C_{fraction} >55 g/l, Ott's curves for α_{1}-globulin and albumin seem straight, in contrast to the curves in Guyton's modified (how?) version (4) of Ott's diagram. If Ott's curves were drawn by hand, it may be difficult to find equations that fit them exactly. The difference between Π_{“Ott”} of serum fractions and readings from Ott's (6) diagram was small. Computed Π_{“Ott”} may agree fairly well with Ott's data.

Ott's maximum ±6.7% difference between calculated and measured Π was reduced to ±4.5% after exclusion of analbuminemic and nephrotic sera (6). At strong increase of high (α_{2}-and β-lipoproteins, IgM) or low (monoclonal Ig heavy chains) MW globulins, the equation over- and underestimates, respectively, measured Π (6, 7). If Ott's data are checked, it may be worthwhile to pay attention to the influence of acidosis (5) on fraction Π.

Colloid osmometry has little place in clinical routine. The fact that C_{alb} is the main determinant of Π_{s} in health may have led to the view (textbooks of clinical chemistry) that C_{alb} reflects change of Π_{s} in disease. Because of the second-power terms, increase of C_{glob} (any globulin) increases the osmotic effect of C_{alb} by increasing C_{tot} (Fig. 1). In this respect, equations based on C_{tot} and C_{alb} (2) are correct. Neither approach indicates that C_{alb} may be low, despite (because of?) high Π_{s}: both ignore the effect of low-MW globulins (Table 1).

Clinical errors could be avoided by computing Π_{s,“Ott”} at fractionation of serum, a routine investigation. I restrict myself to a few examples of possible implications of Π_{s,“Ott”}.

Filtration of fluid from plasma driven by capillary pressure (Pc) minus tissue pressure (Pti; Pc - Pti = ΔP) is rather effectively opposed by Π_{s} minus tissue Π (ΔΠ) at capillary endothelial small pores, and increase of Π_{s} tends to increase the volume of plasma (3-5). In acute phase reactions, Π_{s,“Ott”} increases because many reactants are α_{1}- and α_{2}-globulins (1). The present author is less competent than Guyton's (4) followers to evaluate the influence of increase of plasma volume on cardiac output, etc.

In humans, C_{alb} and concentration of γ-globulin correlate with their catabolism (3, 7), which takes place outside plasma, and high Π_{s} is believed to downregulate hepatic albumin synthesis (3). Increase of C_{glob} may be followed by decrease of C_{alb} in states (3) generally associated with acute phase reactions, but Π_{s} was calculated by an equation based on C_{tot} and C_{alb} (3). Might Π_{s,“Ott”} (Table 1) add theoretical credibility to findings that indicate autoregulation of Π_{s} also by plasma protein extravasation and catabolism and prove helpful in making decisions about colloid substitution therapy?

The findings in humans could be explained by the fact that there are, in addition to small endothelial pores, very sparse pores so large that they permit passage of most plasma proteins (2, 7) and in which flow is opposed very weakly by ΔΠ. Increase of Π_{s} and Pc (isogravimetry) and reabsorption by ΔΠ of low-protein fluid through small pores have been suggested to enhance large-pore protein convection (Ref. 3 in Ref. 2). In this or other experimental studies on protein transfer familiar to me, little attention is paid to change of Pc at capillary pulsation of maximal vasodilatation (4), and tissue Π and protein catabolism. I have come across no attempts to copy, in intact laboratory animals, human diseases (1, 2) preceded by increase of γ-globulin concentration and associated with increase of α-globulin concentration and decrease of C_{alb}.

What is relevant may be change of Π_{s} from the individual's average in health. In Ott's clinical series, a Π_{52°C} > 40 cmH_{2}O was, however, high (6). Methods for determination of protein are changing, but the changes of C_{fraction} in Table 1 are small compared with many met in clinical work. The clinical value of Π_{“Ott”} remains to be established.

## Acknowledgments

The author is no longer affiliated with institutions listed and is presently retired.

I am grateful to Jarmo Hallikainen for calculating the coefficients of the second-power terms, to Mikael Lampinen for adapting the equation to Excel, to Veikko Näntö, Martti Lalla, and Georg Hintze for constructive criticism, and to Sune Backlund for checking the principles of calculation of Π and for brushing up a dilettante's physical wording. The computed equation (Excel) can be sent to others by E-mail.

## Footnotes

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- Copyright © 2004 the American Physiological Society