Protocols for housing and handling of mice were approved by the Institutional Animal Care and Use Committee at Case Western Reserve University.

The compositions of solutions are shown in Table 1. For the CA assay, we combined solution A with solution B in the SF device to obtain the initial OOE solution (“Mix”) in the reaction cell. To achieve the desired pH, we titrated solutions with NaOH or HCl either at room temperature (RT, for RBC washing solution) or at 10°C (for pH calibration solution and OOE A and B solutions). pH measurements were recorded on a portable pH meter (model A121 Orion Star, Thermo Scientific, Beverly, MA) fitted with a pH electrode (Ross Sure-Flow combination pH Electrode, Thermo Scientific) at RT or at 10°C. For all work at 10°C—both pH titration of solutions and the actual experiments—we used a refrigerated, constant-temperature, shaker water bath (model RWB 3220, Thermo Fisher Scientific Inc., Asheville, NC) and several Telesystem magnetic stirrers (Thermo Fisher Scientific). Beakers containing the pH calibration buffers (pH at 6, 8, and 10, Fisher Scientific, Fair Lawn, NJ), the solutions to be titrated, and the pH electrode in its storage solution (Beckman Coulter, Inc. Brea, CA) were equilibrated, as appropriate, at either RT or 10°C. Osmolality was measured using a vapor pressure osmometer (Vapro 5520; Wescor, Inc., Logan, UT), and adjusted upward if necessary by the addition of NaCl.

For some experiments, we obtained purified bCAII, isolated from erythrocytes (C2522, Sigma-Aldrich, St. Louis, MO), and resuspended it in 0.2% bovine serum albumin at a concentration of 1 mg/mL. We added varying amounts of bCAII to establish concentrations from 0.5 to 8 μg/mL in solution A (Table 1). Rapid mixing with solution B (containing 2 μM pyranine) at 10°C in the SF reaction cell initiates the reactions HCO3−+H+→H2CO3→CO2+H2O and HCO3−+H+→CACO2+H2O, causing pH to rise exponentially. Under stopped-flow conditions, we exploited the fluorescence of pyranine to monitor this pH trajectory as described above. In other experiments, instead of adding bCAII to solution A, we added murine RBC lysate (described below), murine RBCs (described below), or mixtures of the two. In some of the lysate and RBC experiments, we instead exploited the absorbance of phenol red.

Regardless of the dye used, we fitted the pH time course with the equation

where t is time, A is the final (equilibrated) value of pH, B is the pH range, and k_ΔpH is the rate constant of the pH relaxation. We obtained A, B, and k_ΔpH using a non-linear least-squares method.

Prior to blood collection, a 1-mL syringe and attached 23-gauge needle were rinsed with 0.1% sodium heparin (H4784, Sigma-Aldrich). Adult C57/BL6 wild type (WT) mice (8–16 weeks old) were sacrificed by cervical dislocation and blood was immediately collected by the cardiac-puncture method (Parasuraman et al., 2010) using the aforementioned syringe and needle. The blood was transferred to a 1.5-mL tube, centrifuged in a Beckman Microfuge 16 Microcentrifuge (Beckman, Brea, CA) at 600 × g for 10 min and the resulting supernatant #0 and buffy coat were removed. To remove residual extracellular Hb, the pelleted RBCs were resuspended (“resuspended RBCs”) in RBC washing solution (Table 1) to a ~5–10% hematocrit (Hct), and centrifuged at 600 × g for 5 min. The supernatant from this centrifugation is supernatant #1. This process was repeated 3×, with an estimation of percent hemolysis (see below) performed at each step. After these four washes, RBCs were resuspended in RBC washing solution to a final Hct of 25–30%, and maintained for up to ~5 h on ice for experiments performed that day.

We computed the Hb concentration, [Hb], using a novel least-square's approach, based on Beer's law. It is well-known that pure Hb has an absorbance at 650 nm (A₆₅₀) of ~0 (Philo et al., 1981; Barlow et al., 1992; Hernández et al., 2009), and we found that A₆₅₀ is likewise ~0 in RBC hemolysates (data not shown; preparation described in next section). When we compared absorbance spectra of ostensibly intact RBCs with those of RBC lysates of equal [Hb] value, we found that they were virtually identical except that the spectra for ostensibly intact RBCs were displaced upward by almost exactly A₆₅₀ (not shown). Therefore, to compute [Hb]—regardless of whether we were dealing with samples of ostensibly intact RBCs or RBC lysate—we determined A₅₆₀, A₅₇₆, and A₆₅₀ on a Beckman Coulter 730 Life Science UV/Vis Spectrophotometer (Beckman, Brea, CA), using the following equation (see following section for derivation):

where l is the pathlength of 1 cm, the molar extinction coefficient for oxy-hemoglobin at 560 nm (ε₅₆₀) is 32,613.2 cm⁻¹ M⁻¹, and ε₅₇₆ is 55,540 cm⁻¹ M⁻¹ (Prahl, 1998).

After the initial centrifugation of whole blood, we estimated percent hemolysis after determining [Hb] in (a) the blood plasma (i.e., supernatant #0; see definition, above), and (b) in the pelleted RBCs after their resuspension in RBC washing solution, using the equation:

where V is volume. In Figure 5A, the resulting value is plotted as “Number of washes of RBCs” = 0.

After each step i of RBC washing, we estimated %H hemolysis by determining [Hb] in the supernatant #i and the resuspended RBCs:

where V is volume. In Figure 5A, the resulting values are plotted as “Number of washes of RBCs” = 1, 2, 3, and 4. Because a tiny fraction of RBCs may hemolyzed with each wash, the preceding equation may slightly underestimate the true %H.

According to the Beer-Lambert law, the hemoglobin concentration is [Hb] = A_λ/ℓε_λ, where A_λ is absorbance at wavelength λ, ℓ is pathlength (cm), and ε_λ is the molar extinction coefficient (cm⁻¹ M⁻¹).

To determine the concentration (C) from the following equation:

we used a least-squares method. To avoid inaccuracies caused by dividing by ε, which varies substantially, consider

If we denote

then

In the present study, we obtain three absorbance values—A₅₆₀ (560 nm is a local valley for oxygenated Hb), A₅₇₆ (576 nm is a local peak), and A₆₅₀ (650 nm is O₂ independent)—from which we derive A₁ = A₅₆₀ − A₆₅₀ and A₂ = A₅₇₆ − A₆₅₀. Because each derived A-value has a corresponding ε-value, we have two data points (A₁, ε₁) and (A₂, ε₂). The objective of the least-squares method is to find the best-fit value of C that minimizes the value of the following function:

This minimum occurs when

which occurs when

Thus, the concentration (C) is:

An RBC lysate was produced by osmotic lysis of 20 μL of freshly prepared, packed mouse RBCs (see above) in Milli-Q H₂O (Milli-Q® Integral Water Purification System, EMD Millipore Corporation, Billerica, MA) of ~1:8 dilution, followed by centrifugation at 15000 × g for 5 min in a Beckman Microfuge 16 at RT. The supernatant (cleared of cellular debris) then was removed and the hemolysate was transferred to a clean 1.5 mL tube for a spectroscopic determination of [Hb] as described above.

We achieved simulated degrees of hemolysis (Table 2, column 1), ranging from 0% (an apparent value) to 100% (an actual value) by combining different proportions of (a) freshly prepared, ostensibly intact RBCs (Table 2, column 2) and (b) a lysate (representing 100% lysis; Table 2, column 3), while maintaining the total [Hb] at 2.5 μM in the SF reaction cell.

We report results as mean ± SD. We analyze data using two-tailed unpaired student's t-test or two-tailed paired student's t-test, considering P < 0.05 as significant. In Figure 5A, we also applied the Holm-Bonferroni correction for the 10 comparisons and using α = 0.05 (Holm, 1979).

First, we test our CA assay on purified bCAII, over a range of [bCAII] values. The pyranine dye is in the syringe opposite to the one containing bCAII (Table 1). With no added CA (0 μg/ml), pH rises very slowly, reaching ~7.50 in ~200 s (Figure 2A, lowest curve). As we increase the bCAII concentration in the SF reaction cell (i.e., [bCAII]_RxCell = 0.25, 0.5, 1, 2, and 4 μg/ml), the equilibration speeds greatly. Figure 2B shows the same data as in Figure 2A, but over the first 5 s. For each [bCAII] in Figures 2A,B —and many other similar experiments—we calculate the rate constant of the pH relaxation, using a least-squares approach to fit an exponential curve to each set of (pH, t) coordinates that describes the exponential increase in pH over time. Figure 2C summarizes the dependence of the rate constant k_ΔpH on [bCAII] at 10°C, and shows that graded increases in [bCAII] cause k_ΔpH to rise linearly. The y-intercept of the line of best fit, 0.0185 s⁻¹, is the rate constant of the uncatalyzed chemical reactions that occur during the pH relaxation. The slope of the line, 0.8143 (s⁻¹)/(μg/ml), is a measure of the specific activity of the bCAII.

Next, we studied the effect of CA blocker acetazolamide (ACZ) on bCAII enzymatic activity, adding ACZ to the syringe opposite to the one containing bCAII (Table 1) to achieve a [ACZ]_RxCell in the reaction cell of 10 μM. Figures 2D,E, as expected, show that ACZ virtually collapses all the pH relaxations for the bCAII experiments (0.25–4 μg/ml) onto the curve describing no added bCAII. The summary in Figure 2F shows that, over the entire range of [bCAII] values, ACZ reduces k_ΔpH to nearly the uncatalyzed value.

Second, we extend our work to murine RBC lysates to determine if our CA assay can quantitate hemolysis. The pyranine dye is in the syringe opposite to the one containing RBC lysate (Table 1). Figures 3A,B shows six pH trajectories, similar to those in Figures 2A,B except that here (Figures 3A,B) we replace bCAII with lysate from WT mouse RBCs. A percent lysate (%L) of 100% refers to hemolysate containing 2.5 μM Hb (i.e., Hct ≅0.15%) in the SF reaction cell; a %L of 50% refers to half this concentration of hemolysate (diluted in saline), and so on. In the absence of RBC lysate (i.e., %L = 0% in Figures 3A,B), pH rises from ~7.25 to reach ~7.50 at a low rate that is similar to what we saw above in Figures 2A,B. Here in Figures 3A,B, we see that increasing %L greatly speeds the equilibration of pH. Figure 3C summarizes the best-fit k_ΔpH data from a total of nine mice. As expected, k_ΔpH has a linear dependence on %L, and the y-intercept of ~0.0183 s⁻¹ is nearly identical to the corresponding value in Figure 2C.

Figure 3D through F show that ACZ, at a [ACZ]_RxCell of 5 μM, almost completely eliminates the CA activity of the hemolysate.

In a third set of experiments, we test our CA assay by creating a solution A (Table 1) in which we combine, in different proportions: (a) freshly prepared, ostensibly “intact” RBCs (5 μM Hb, or ~0.3% Hct) with (b) a lysate from an equivalent mass of RBCs (5 μM Hb). Thus, in the SF reaction cell, after mixing with solution B, all solution A combinations generate a Hb concentration ([Hb]_RxCell)—representing the sum of Hb both inside and outside the RBCs—of 2.5 μM. Thus, this approach simulates ostensible degrees of hemolysis between 0 and 100%, inclusive. Note that the total CA activity in the reaction cell—representing the sum of CAs both inside and outside the RBCs—is also constant across all RBC/lysate mixtures. The pyranine dye is in syringe B, opposite to the one containing the RBC/lysate mixture (Table 1). Figures 4A,B show six pH trajectories obtained on blood from one mouse, and indicate that the greater the ratio of simulated RBC hemolysis the faster the equilibration of extracellular pH (pH_o).

Note that an ostensibly 0% hemolysis (lowest pH records in Figures 4A,B) produces an equilibration that is considerably faster than the truly uncatalyzed pH trajectories (i.e., the lowest pH records) in Figures 2A,B, 3A,B. Thus, ostensibly 100% intact RBCs must, in fact, be partially hemolyzed in the SF reaction cell. Figure 4C summarizes the best-fit k_ΔpH data from a total of nine mice—the same nine mice as in Figure 3C. The k_ΔpH vs. percent hemolysis relationship is linear, as in Figures 2C, 3C. However, in Figure 4C, the y-intercept—the k_ΔpH of ostensibly 100% intact RBCs from WT mice—is ~0.0820 s⁻¹. This value is more than 4-fold higher than the corresponding k_ΔpH in Figures 2C, 3C, confirming the partial lysis of these cells in the SF reaction cell.

Figures 4D,E show that ACZ, added to the syringe opposite to the one containing the RBC/lysate to achieve a [ACZ]_RxCell of 5 μM, almost completely eliminates the CA activity of the mixtures, across the entire range of simulated ostensible hemolysis. Figure 4F shows that, for all mixtures, ACZ reduces k_ΔpH to nearly the uncatalyzed value. The y-intercept in Figure 4F, which represents the near-fully uncatalyzed state, is only ~21% of the value observed in Figure 4C. Because the pyranine dye and the ACZ first make contact with the RBC/lysate in the SF reaction cell, the dye presumably reports—and the ACZ presumably slows—only the pH equilibration in the extracellular space, and not inside intact RBCs. Thus, the y-intercept in Figure 4C (which represents k_ΔpH for the uncatalyzed reaction + CA from lysed RBCs) and the y-intercept in Figure 3C (which represents k_ΔpH for the uncatalyzed reaction only) provide the information needed to compute hemolysis in the SF cell.

In a fourth set of experiments, we collect fresh whole blood from nice mice—the same nice mice as in Figures 3C, 4C—and obtain an initial hemolysis of 2.36 ± 1.04% before any washing (Figure 5A, number of washes = 0). We then wash the RBCs four times in RBC washing solution (Table 1), obtaining the percent hemolysis after each step. After the fourth wash, we arrive at a hemolysis of 0.37% ± 0.21% (which is significantly >0; P = 0.00013) before putting the RBCs into the SF device (Figure 5A). Our %H-value of 0.37%, which may slightly underestimate the true value as noted in Section Materials and Methods, is similar to the level of 0.5% reported by Itada and Forster in their ¹⁸O study (Itada and Forster, 1977).

Figures 5B–D show our approach for determining RBC hemolysis in the SF reaction cell. We first determine the relationship between k_ΔpH and the percent actual hemolysis in an experiment like that in Figure 3C, in which we combine RBC lysate with saline in various proportions. The ascending light blue line in Figure 5B is the idealized result of such an experiment, and leads to two of the three rate constants needed for the calculation of %H. The brown circle at 0% actual hemolysis (i.e., 100% pure saline), represents the uncatalyzed rate constant (k_uncat) as the overall reaction HCO3- + H⁺ → CO₂ + H₂O approaches equilibrium under the conditions of our experiments. The red circle at 100% actual hemolysis (i.e., 100% RBC lysate), represents the rate constant (k_{RBC, Lysate}) of the overall dehydration reaction, both uncatalyzed and catalyzed by the all of the CA released from our sample of RBC lysate (i.e., the [CA] corresponding to an [Hb] of ~2.5 μM). The difference between k_{RBC, Lysate} (horizontal red dashed line) and k_uncat (horizontal brown dashed line) represents the rate constant (k_{cat, max}) of that portion of the overall reaction catalyzed by all the CA present in our sample of RBCs.

The ascending dashed magenta line in Figure 5C is the idealized result of an experiment like that in Figure 4C, in which we combine ostensibly intact RBCs with pure RBC lysate in various proportions. Figure 5C leads to the third rate constant needed for the calculation of percent hemolysis. The green circle at 0% apparent hemolysis (i.e., 100% ostensibly intact RBCs), represents the rate constant (k_{RBC, OstInt}) of the overall dehydration reaction, both uncatalyzed and catalyzed by the CA released from the small fraction of RBCs that—unbeknownst to us—are hemolyzed at the time the material is inside the SF reaction cell. The difference between k_{RBC, OstInt} (horizontal green dashed line) and k_uncat (horizontal brown dashed line) represents the rate constant (k_{cat, min}) of the portion of the overall reaction catalyzed by that small amount of CA released from ostensibly intact RBCs.

Finally, in Figure 5D—a superimposition of Figures 5A,B, we see the graphical approach for computing the percent actual hemolysis in the SF reaction cell. Starting from the blue circle on the y-axis, we move to the right (blue arrow) until we reach the origin of the magenta dashed line, and then move downward (blue arrow) to read the percent actual hemolysis off the light blue x-axis. Mathematically, this value is simply k_{cat, min}/k_{cat, max}. Using the approach in Figures 5B–D, we calculate that, even if we start with washed RBCs that are only ~0.37% hemolyzed before they enter the SF device (see above), the total hemolysis is 4.93% ± 1.67% (SD) in the SF reaction cell at the end of the experiment (Figure 5E). Thus, the process of performing the SF experiment—loading the RBC mixture into the SF syringes, the flow down the tubing, and the rapid mixing in the SF reaction cell—increases hemolysis.

Lastly, we evaluate an alternative approach in which we replace stopped-flow fluorescence spectroscopy (using the dye pyranine) with stopped-flow absorbance spectroscopy (using the dye phenol red). We compare the CA-assay results—fluorescence vs. absorbance—for hemolysis on blood from three mice. As summarized in Figure 6, we find that the estimate of % hemolysis using the fluorescence approach with pyranine is indistinguishable from that that using the absorbance approach with phenol red.

In the present paper, we describe a simple and rapid assay—based upon the release of CA from RBCs—for determining the degree of hemolysis of RBCs in a SF reaction cell. Moreover, the assay occurs over a time frame and under conditions that are very similar to those of other parallel experiments that generate SF data that are sensitive to percent hemolysis. These other parallel experiments include not only measurements of Hb-O₂ saturation, but also other assays in which the release of a material (e.g., a pH-sensitive dye) previously inside the cell would confound the measurement. Our search of the literature does not identify previous methods for assessing %H in a SF reaction cell. Others have used the time course of light transmittance (a measure of light scattering) to assess relative hemolysis in assays of the osmotic fragility of RBCs (Didelon et al., 2000; Paździor et al., 2003; Górnicki, 2008). In this earlier approach, one can monitor slowly developing (over tens of seconds) changes in transmittance due to progressive hemolysis, but cannot assign a value to hemolysis per se.

In the present study, we obtain a single value of hemolysis measured over several tens of seconds, but cannot directly address the time course of hemolysis per se. However, because the time courses of pH in Figures 4A,B are exponential beginning no later than ~0.3 s after the stoppage of flow, we can conclude that the hemolysis was virtually complete by this time. In other words, the degree of hemolysis that we measure (right bar Figure 5E) presumably reflects the aggregate hemolysis that occurs to some extent in the preparation of the blood (left bar Figure 5E) but mainly in the syringes, tubing, and the first moments in the reaction cell of the SF device.

Others have previously assessed CA activity using pH-based SF approaches (Gibbons and Edsall, 1963, 1964; Ho and Sturtevant, 1963; Kernohan, 1964, 1965; Khalifah, 1971; Wistrand et al., 1975; Pocker and Bjorkquist, 1977; Crandall and O'Brasky, 1978; DeGrado et al., 1982; Sanyal et al., 1982; Baird et al., 1997; Shingles and Moroney, 1997; Wang et al., 2010) with tissue homogenates or cell-free enzyme preparations. The ionic conditions in these earlier studies would have been inappropriate for living cells. By definition, these earlier studies involved monitoring pH as the solution in the SF reaction cell transitioned from an OOE state toward an equilibrium state. However, fundamental differences between our approach and those of others are that the present assay provides:

Solutions A and B of moderate and defined pH-values. Regarding the previous SF studies of CA activity, only one (Shingles and Moroney, 1997) reports SF time courses of pH per se, and only one (Shingles and Moroney, 1997) provides sufficient detail (including pH-values of both solution A and solution B) to permit replication of the work. In our assay, both solution A (pH 7.03) and solution B (pH 8.41) have relatively moderate pH-values, thereby ensuring that the RBCs are under near-physiological electrolyte conditions throughout the assay. Even though the CA enzyme or RBCs are in the near-neutral solution A in our assay, it is important that solution B not have an extreme p-value. Earlier OOE work (Zhao et al., 1995) provided evidence of transient microdomains upon mixing of solutions A and B (i.e., the enzyme or cells in solution A could come into direct contact with relatively undiluted solution B). In principle, we could have designed a solution B with a lower pH. A consequence (all else being equal) would have been a smaller ΔpH during the relaxation phase of the experiment. However, the signal-to-noise resolution of our assays was sufficiently high that we could have still obtained reliable k_ΔpH data, even with a smaller ΔpH.

Although the assay in the present study is based on the reaction HCO3−+H+→CACO2+H2O (equivalent to the dehydration of H₂CO₃) and thus produces a pH increase, we could have constructed solutions A and B so that, upon solution mixing in the reaction cell, the OOE state would have led to the opposite reactions (equivalent to the hydration of CO₂) and thus a pH decrease.

Transport events across the RBC membrane can be extremely fast. In the present study, we chose 10°C to match the temperature in parallel work on O₂ fluxes. This temperature, although considerably less than typical physiological temperatures of mammals, is nevertheless higher than those used by other investigators in RBC-transport studies, where it is customary to lower RBC temperatures to 5°C or even 0°C (Kimzey and Willis, 1971; Lowe and Walmsley, 1986; Jensen et al., 2001; Jennings, 2005).

The 14 mammalian α CAs (Sly and Hu, 1995; Purkerson and Schwartz, 2007; Supuran, 2016) are zinc-containing metalloenzymes that are expressed in virtually every cell of the body. They are broadly divided into four subgroups: the cytosolic [a] CA I, II, III, VII, and VIII; [b] the mitochondrial CA V; [c] the secreted CA VI; and [d] the membrane-bound CAs IV, IX, XII, and XIV (Sly and Hu, 1995; Parkkila et al., 1996; Karhumaa et al., 2000; Kummola et al., 2005; Scheibe et al., 2006). A proteomics study identified CA I, II, and III in RBC cytoplasm (Kakhniashvili et al., 2004). In human erythrocytes, CA II is a high-activity isozyme; CA I contributes only half of the total CA activity although it is almost six times as abundant as CA II (Khalifah, 1971; Dodgson et al., 1988; Sly and Hu, 1995). CA III—the activity of which is reported to be only 0.03–1% that of CA II (Sly and Hu, 1995; Purkerson and Schwartz, 2007)—is expressed mainly in skeletal muscle and adipose tissue, but at lower levels in other tissues, including RBCs (Sly and Hu, 1995; Kakhniashvili et al., 2004; Pasini et al., 2006; Goodman et al., 2007). Within the RBC, these CA enzymes are critically important for converting metabolically produced CO2 to HCO3−(CO2+H2O→CAHCO3−+H+) while the RBC is in systemic capillaries, and then—after the RBC has transited to the lung—for reconverting the HCO3− to  CO2(HCO3−+H+→CACO2+H2O) in the pulmonary capillaries for elimination in the exhaled air.

Although a mass-spectrometry analysis study reveals no evidence of membrane-associated CAs in RBCs (Low et al., 2002), immunological and kinetic evidence points to a tiny amount of CA IV, presumably on the outer surface, that could contribute 0.2% of total CA activity (Wistrand et al., 1999). If this CA IV estimate for RBCs is correct, then 0.2/4.93% ≅ 4% of the estimated %H of 4.93% (Figure 5E) in the SF reaction cell could reflect the presence of extracellular-facing CA IV rather than hemolysis per se (i.e., we may slightly overestimate the degree of hemolysis).

The following analyses of our data provide evidence that our CA assay behaves in a stable and precise way:

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.