The Carbamate Reaction of Glycylglycine, Plasma, and Tissue Extracts Evaluated by a pH Stopped Flow Apparatus*

We have used a stopped flow rapid reaction pH apparatus to investigate the carbamate equilibrium in glycylglycine solutions and in three biological tissues. human plasma. sheep muscle. and sheep brain. as well as to investigate the kinetics of carbamate formation in glycylglycine solution and in human plasma. The rapid reaction apparatus was equipped with a pH sensitive glass electrode in order to follow the time course of pH from 0.005 to 100 s after rapid mixing of a solution of amine or protein and CO,. Two phases of the pH curve were observed: a fast phase representing carbamate formation, and a slow phase due to the hydration of CO, which was uncatalyzed since a carbonic anhydrase inhibitor was added to the biological solutions. From the time course of pH change during the fast phase K,, the R-NH, ionization constant, and K,, the carbamate equilibrium constant as well as the velocity constant for the formation of carbamate, k, could be calculated from data at different pH and pC0,. The carbamate formed in glycylglycine solutions over a wide range of pH and pC0, was found consistent with the theory of carbamate formation and with published data. At ionic strength 0.16 and X” pK, is 7.67. pK, 4.58. The heat of the carbamate reaction (AH) was calculated to be -3.2 kcal/mol between 20” and :37”. K, of glycylglycine depends quantitatively on ionic strength as predicted by the Debye-Htickel theory.

The method was greatly improved by using a continuous flow rapi d reaction apparatus equipped with a CO, electrode as described by Constantine et al. (12) to follow the time course of pC0, i n the mixture (2,5,13).
where the indices refer to the situation before (pH,) and after (pH,) carbamate formation, and @-NHCOO-j is the carbamate concentration when carbamate equilibrium is reached. If, simplifying, all buffering groups except the amino groups are described as B- (unprotonated) and BH (protonated), the total concentration of protonated groups in the solution is:   ). This problem was solved by a trial and error procedure. In Fig. 6 the plot obtained from the data in Fig. 56 is shown. As predicted by Equation 10, for the data both at pH 8.0 and pH 7.5, straight lines are obtained (correlation coefficients around 0.99). The pK, and pK, values for 37" calculated from the plots in Fig. 6 are shown in the first two lines of Table I and are almost identical for the two different pH values. We conclude that these data obtained over a wide range of pH and pC0, are entirely consistent with the described theory of carbamate formation, especially with regard to the complete dissociation of carbamic acid.  is calculated from the results of Table I to be 1.95 at 20". It appears, therefore, that, in contrast to Faurholt's view, the activity of [R- NHCOO-] behaves as predicted by the Debye-Htickel theory and is affected by ionic strength like other divalent ions. The dependence of pK, upon ionic strength then may be described by: Comparison of pK, and pK, with Data in Literature-In Table II values of the thermodynamic constants pK, and pK, for glycylglycine at 20" are compiled. It can be seen that pK, as well as pK, presented here tally with the values in the literature obtained by different methods. We conclude that the described method of carbamate measurement is well suited to determine the carbamate equilibrium constant as well as the ionization constant of the amino group of glycylglycine. This seems to justify confidence that the method can be used as a reliable tool to obtain the same information on amino groups of proteins.

Carbamate Kinetics
The present method allows us to study the kinetics of carbamate formation as well as its equilibria. The kinetics of carbamate formation is described by the following equation ( is the concentration of carbamic acid. The latter is given by: The values in the first two lines are obtained from the plot in Fig. 6.  , dpH/dt as a function of pH and t can be obtained, but is of little use as it cannot be integrated analytically. Fortunately (pH -pH,sh. t) is an exponential function of time in all experiments so that a simple relationship of the form "Calculated from the constants of Table I for p = 0 using Equation 14 (pK,) and Neuberger's (20) relation (pK,).
*Obtained from titration curves corrected for ionic strength (20) and for temperature (21). cCorrected for 20" with AH = -3.2 kcal/mol, and for /1 = 0 according to Equation 14.  Fig. 76 shows that the measured kinetic curves are consistent with the theory of carbamate formation. Table III shows the velocity constants of carbamate formation obtained in this way for 37" and 20". It can be seen that the velocity constants, and the activation energy calculated from them, agree reasonably with data obtained by other authors.

Carbamate Formation in Plasma
Carbamate Equilibrium Fig. 8 shows results obtained with plasma solutions of ionic strength 0.15 at 37". Qn+/Prot, the approximate amount of H+ per protein produced by carbamate formation, is plotted uersus PH equ,lr the pH at carbamate equilibrium (see Fig. 4). QH+ was calculated from Equation 4 using the buffer factor of the plasma solution as shown in Fig. lb. The protein concentration in grams/100 ml, as obtained with the biuret method, was converted to moles/liter using the molecular weight of albumin, 69,000. Four sets of data at four different CO, partial pressures (pCO,,,, = 359, 140, 79, 38 Torr) were obtained, each set with four to seven different pH values between pH 6.9 and 8.3.
Each point in Fig. 8 represents the average of about five measurements performed at the same pH and pC0,. The relative standard deviations (variation coefficients) of the values of Qn+/Prot obtained under identical conditions averaged to 3.5%. They did not vary significantly with the size of the value of Qu+/Prot for 0.5 5 QH+/Prot 5 10. Values of Qn+/Prot obtained with plasma from fresh blood did not differ significantly from values obtained at the same pH and pCOl with plasma from outdated blood.
Groups Responsible for Plasma Carbamate-In the case of hemoglobin, the protein whose carbamate reaction has been studied most extensively, it has been assumed that only the a-amino groups of the NH, termini contribute significantly to carbamate formation at pH <8 (1,5,28). How many (u-amino groups per protein are to be expected in plasma, if an arbitrary plasma protein molecular weight of 69,000 is chosen? The number of end groups of some of the plasma proteins is known. Albumin (60% of the plasma protein) and transferrin are single polypeptide chains of 69,000 and 89,000 molecular weight, respectively. Most y-globulins and fibrinogen have 2 free NH,-terminal amino groups/molecule at molecular weights of 160,000 and 341,000, respectively (29, 30). On the basis of a molecular weight of 69,000, this leads to less than 1 tr-amino group/protein molecule. Therefore, if the assumption that only <r-amino groups form carbamate were true for plasma protein, we would expect QH+ /Prot to level off at a value < 1. Fig. 8 shows that carbamate/plasma protein does not reach a maximum around 1, but increases steeply with increasing pH. At pH 8 and pC0, ,n,x = 359 Torr, QH+ /Prot reaches a value of -10. This is clearly incompatible with the conception that only (r-amino groups form carbamate: groups in addition to the a-amino groups must participate in the carbamate formation. The groups most likely to do this are the t-amino groups of the lysine side chains.  Jensen (22) "Calculated from the rate constants at 37" and 20". b Obtained between 10" and 30". 6.10-3 The conclusion that at least two types of groups must be involved in the carbamate formation of plasma is also reached, when a plot of l/( Qn+ /Prat) uersus l/[CO,] is made of the data obtained in plasma. For sets of data at pH 7.9, 7.7, 1.5, and 7.4 (obtained by interpolation from Fig. 8) we find that, in contrast to the case of glycylglycine, there is no value of n, which yields roughly the same values of K, and K,, or positive values for both K, and K,, at al1 these pH values. This indicates that the present data are not compatible with the assumption of only one species of binding sites. We therefore made an attempt to fit constants representing two types of binding sites to the data. Equilibrium Constants K, and K, and n-If two types of groups contribute to carbamate formation, Qn+ /Prat, as can be derived from Equations 1, 2, and 9, is given by the following expression: where the indices 1 and 2 designate the two types of groups. Accordingly, the carbamate formation is described by six constants: n,, K,,, K,,, n,, K,,, K,,. Since the plot according to Equation 10 is not applicable to the case of two types of binding sites, the following procedure was used to find the best values for these constants. Numerical values for the constants were chosen arbitrarily.
For al1 data points shown in Fig The calculated values of Q,+/Prot, ij,, were then compared with the measured values, q,. It has been mentioned that the relative standard deviations were about the same for all numerical values of QH+ /Prot. Therefore, the differences q, -dt were weighted by dividing by q, (31), and the sum of squares for all data points, 4, was calculated from o=s [yq' (26) were m is the number of data points. Using the gradient technique of Fletcher and Powell (32)3 the values of the six constants were varied until the minimum for 4 was found.
The procedure was started using [CO,,,,] as an estimate of [CO,], the CO, concentration at carbamate equilibrium. After obtaining first estimates of the equilibrium constants, carbamate concentrations, [R-NHCOO-1, could be calculated from QH+/Prot. This allowed us to get new estimates of [CO,] via Equation 20. Then the entire procedure was repeated until the differences between the old and the new estimates of [CO,] were negligible ( <O.l%). In order to ensure that the constants obtained in this way reflect the true, not merely a local, minimum of 4, the initial guesses of the constants K, and K, were varied within +l order of magnitude, those of the n value within + 100%. The calculations were performed on a Siemens 4004/BS 1000 digital computer.
The constants obtained from this fit are compiied in Table  IV. They were used to calculate the curves in Fig. 8 for the respective experimental conditions of the four data sets. It can be seen that the calculated curves reasonably fit the measured data points. The overall goodness of the fit can be expressed quantitatively by R*, the fraction of variation in the dependent variable (Q"+/Prot) which is explained by variations in the independent variables ([CO,] and [H+]) (33). RZ was found to be 0.97. This high value indicates that, in spite of the diversity of the plasma proteins, plasma carbamate can be adequately described on the basis of two species of participating groups. As a measure of the reliability of the numerical values obtained for the single constants their standard errors may be taken. The latter were calculated following the procedure proposed by Tukey (34) and Dammkoehler (33) and are listed in Table IV. The values of constants shown in Table IV allow us to identify type 1 as an a-amino group since (a) a value of 7.00 for pK, lies in the range generally expected for a-amino groups (35), and (b) a value of n = 0.55 agrees with the value expected from molecular weight and subunit structure of the plasma proteins as far as they are known (see discussion in the foregoing chapter). Type 2 can be associated with e-amino groups on the basis of the high value of pK, which is reasonably close to Tanford's (35) value for the c-amino groups of albumin (9.4 after correction for 37").
A value of n = 5.9 for e-amino groups may appear low in view of the 59 t-amino groups of the albumin molecule (36). However, (a) all other plasma proteins have a markedly lower lysine content than albumin (37), and (b) only part of the e-amino groups may be accessible for carbamate formation in the pH range investigated by us. The values of pK, obtained for types 1 and 2 are both well in the range expected from the pK, values of amino acids and peptides (13,22,38).
Carbamate Dissociation Curve of Plasma--In Fig. 9 carbamate dissociation curves of human plasma at 37" calculated for a total protein concentration of 7 g/100 ml are shown. The 'We are indebted to Dr. Martin Pring, Philadelphia, for kindly providing a Fortran subroutine of the Fletcher and Powell method. The constants were obtained from a least squares fit assuming that two types of CO, binding sites, 1 and 2, occur in plasma. Given are the number of binding sites, n (based on an arbitrary molecular weight of 69,000 for plasma protein), -log 10 of the carbamate equilibrium constants, pK,, of the ionization constants of the amino groups, pK,, and the velocity constants of carbamate formation, k.. The standard errors were calculated according to Tukey (34) and Dammkoehler (33). Type 1 may be interpreted as a-NH, groups, type 2 as (-NH, groups (see text).
where prot] is the plasma protein molar concentration (molecular weight 69,000). No direct comparison of these data with Stadie and O'Brien's (39) data is possible, since their measurements were done in concentrated plasma protein solutions at 0" and at pH 9 only. It can be seen from Fig. 9 that, in the physiological range of pH and pCO,, plasma carbamate is more sensitive to changes in [H'] than in [CO,]. This stipulates an extremely small arteriovenous concentration difference of plasma carbamate: increasing the arterial pC0, of 37 Torr by 14% to its venous value of 42 Torr (40), and shifting pH from 7.46 to 7.43 (which is a 7% increase in H+ concentration), leads to a rise of carbamate concentration from 0.631 mM to 0.633 mM only. Thus, plasma carbamate does not contribute significantly to the CO, exchange in the respiratory cycle. It may play a role, however, during transient pC0, changes by virtue of the fact that its formation is 2 orders of magnitude faster than the formation of bicarbonate, which in plasma is not catalyzed by carbonic anhydrase.

Carbamate Kinetics
In order to evaluate the kinetics of carbamate formation in plasma the pH records of seven stopped flow experiments covering the pH range from 7.6 to 9.1 were analyzed. pCO,,,. was 38 Torr in all experiments. Temperature was 37", ionic strength 0.15. The first two-thirds of the fast phases of the pH records were linearized as described for glycylglycine: plotting log (pH -pH, -s,.t) uersus time straight lines with correlation coefficients >0.998 were obtained for all experimental records studied. After differentiating the regression equations obtained from these plots, for any value of pH within the linearized part of the experimental pH curve a corresponding value of dpH/dt could be calculated. The experimental pairs of pH and dpH/dt thus obtained were used for the kinetic analysis as shall be shown below.
Different Kinetics of a-and c-Amino Groups-An attempt was made to explain the carbamate kinetics in plasma with the assumption of an identical velocity constant k, for the two types of carbamate binding sites but the values obtained  Table IV. depended strongly on the pH. k, dropped from a value of 12,000 M-I s-l at pH 9 to 7,000 M-I s' at pH 7.6. This was taken as an indication that the two kinds of carbamate forming groups are not only different with respect to their pK, values, but also show a different kinetic behavior. Indeed, Chipperfield (27) has shown that the carbamate formation velocity constant of amino acids and peptides increases with the pK value of the amino group. Therefore, different velocity constants, k,, and k,,, were assigned to the two species of groups and their values were fitted to the experimental data. The fitting procedure was done in the following way. Arbitrary values of k,, and k,, were inserted into the differential equations describing the formation of carbamate by the two kinds of groups, which were formulated analogously to the kinetic equations for glycylglycine (Equations 18 to 21). These equations were integrated numerically for the conditions of each kinetic experiment using the Runge-Kutta method described by Zurmiihl (31). For identical values of pH, theoretical values of dpH/dt (c?,) obtained in the course of the integration were compared with experimental values of dpH/dt (d,) obtained from the linearized experimental record, and the sum of squares, F, was calculated for all kinetic experiments according to: where m, the number of compared values of dpH/dt, was given by the step size of the integration. This procedure did not require knowledge of the lag time. In a manner similar to that described for the carbamate equilibrium constants, the best values of k,, and k,, were determined by searching the minimum of F.
The velocity constants of carbamate formation in plasma obtained in this way are listed in Table IV together with the  equilibrium constants. The multiple correlation statistic Rz is 0.95, which indicates that the model we have employed can satisfactorily describe the kinetics of carbamate formation in plasma. This provides additional evidence that in plasma two types of groups, which are essentially homogeneous in themselves, participate in carbamate formation.
Forster et al. (2) determined an overall kinetic constant of 11,000 Mm' s-' for human hemoglobin which would compare quite well with an overall k, for plasma protein as may be seen from Table IV. The dependence of k, on pK,, expressed as Alog  kJApK,, is calculated from Table IV  We attempted to examine the question of carbamate formation in tissues by virtue of the present method. This question has been extensively discussed (41)(42)(43)(44)(45)(46)(47), mainly because of its bearing on the validity of the determination of intracellular pH from intracellular pC0, and total CO1 concentration, but never has been resolved. Fig. 10 shows the results obtained for an extract from skeletal muscle (thigh) from sheep. Measurements at two partial pressures, pC0, mix of 74 and 140 Torr, in a pH range between 6.4 and 8.3 were performed. The same pattern of pH dependence as in plasma was found: for both CO1 partial pressures, QH+ per tissue, wet weight, is less than 1 mmol/kg at pH < 7, but shows a steep increase with pH at pH > 7. At pH 8 QH+ reaches a value of about 10 mmol/kg. This pronounced increase in Q H+ in the alkaline pH range suggests that in muscle, as in plasma, a large number of e-amino groups are available for carbamate formation. Table V shows data for brain tissue of sheep. For pC0, m,x = 3.5 Torr measurements at three pH values were done. As in muscle, &a+ shows a strong dependence on pH. Assuming a value of 1.5 for y (see Equation 9). the carbamate concentrations are estimated to be 0.33 mM for muscle at pH 7.0 and pC0, = 70 Torr, and 0.08 mM for brain at 35 Torr and pH 7.0. It should be noted that not all the carbamate-forming material of the tissues may have been contained in the tissue extracts and these concentrations therefore may be somewhat underestimated. and Fearon (41) concluded that in rat muscle there is a barium-soluble noncarbonate CO, fraction of 8 mmol/kg out of 14.8 mmol/kg of total CO,. This is more than 10 times the carbamate concentration we expect from Fig. 10 for sheep muscle at an intracellular pH of 7. The data in Fig. 10 do show, however, that a carbamate concentration of 8 mmol/kg can occur in muscle, but at pH values far above the physiological range.
We suggest that the high values of noncarbonate CO, found by Conway and Fearon (41) and by Butler et al. (46) may be an artifact caused by formation of appreciable amounts of carbamate during the experimental procedure they used. In their analytical procedure, 2-g pieces of freshly excised muscle tissue are introduced into 0.2 N KOH and left there for an hour, during which period the pH in the muscle pieces increases from 7 to about 12. Several minutes are required for the average pH in the muscle to go from pH 8 to pH 9.5.' Rough calculations show that, although the pC0, of the tissue decreases with increasing pH, the intracellular carbamate concentration may easily rise to 8 mmol/kg as pH rises from 8 to 9.5, and that in this pH range only a few seconds are necessary for this amount of carbamate to be formed. Thus, we conclude that carbamate formation in the muscle exposed to KOH (rather than an  to be far less affected by a neglect of intracellular carbamate concentrations than has been postulated by Conway and Fearon (41). In brain with pH, = 7, pC0, = 35 Torr and an intracellular water content of 67% neglect of carbamate would lead to an overestimation of pH, by -0.006 pH units, in muscle this error would be -0.012 pH unit for pH, = 7, pCOl = 70 Torr and 67% water. These errors being minor in view of the many uncertainties of all methods of pH, estimation, the often made assumption (42,43,(45)(46)(47) that carbamate may be neglected in evaluating the intracellular pH by the CO, method appears to be justified.