Abstract
Recent work has enabled us to quantitate the four variables (2,3DPG concentration, pH_{i}, nonS hemoglobin composition, and O_{2} saturation) that modulate the equilibrium solubility (c_{sat}) of Hb S inside sickle erythrocytes (SS RBCs). Using measured values of mean corpuscular hemoglobin concentration (MCHC), 2,3DPG concentration, and %Hb (F+A_{2}), along with estimates of pH_{i}and the Δc_{sat} due to partial oxygenation of SS RBCs in the microcirculation, we calculated the mean polymer fraction (f_{p}) in erythrocytes from 46 SS homozygotes. Values of f_{p} derived from the conservation of mass equation ranged from 0.30 to 0.59. MCHC and %Hb F were major determinants of the magnitude of f_{p}; 2,3DPG concentration and pH_{i}also contributed, but to a lesser extent. A clinical severity score (CSS) was assigned to each patient based on mean hospitalization rate. There was a weak, but statistically significant, negative correlation between f_{p} and steady state hematocrit (P = .017), but none between f_{p} and whole blood hemoglobin concentration (P = .218). Although there was no correlation between f_{p} and mean number of hospitalization days per year, patients with the greatest number of admissions and hospitalization days were found only among those who had an f_{p} > 0.45. All five patients who died during the followup period (median, 7 years; range, 3 to 10 years) had f_{p} values ≥0.48. However, patients with few admissions, low hospitalization days, and long survivals occurred at all f_{p} levels. These results suggest that the clinical course of homozygous SS disease cannot be predicted by mean f_{p}calculations, which assume a homogeneous distribution of the five variables that modulate intraerythrocytic polymerization. A heterogeneous distribution is more likely; so the amount of polymerized Hb S could vary considerably among cell populations. Factors such as membrane abnormalities and endothelial cell interactions may also contribute to clinical severity.
THE PRIMARY CAUSE of the clinical symptomatology of sickle cell anemia is the intracellular polymerization of sickle hemoglobin (Hb S) that occurs when sickle erythrocytes (SS RBCs) are partially deoxygenated under the hypoxic conditions of the microcirculation. This, in turn, makes SS RBCs less deformable and ultimately results in the debilitating microvascular occlusions and hemolytic anemia characteristic of the disease. Recent work13 has enabled us to quantitate the four variables (2,3DPG concentration, pH_{i}, nonS hemoglobin composition, and O_{2} saturation) that modulate the equilibrium solubility (c_{sat}) of Hb S inside sickle erythrocytes (SS RBCs).
The requirements for therapeutic inhibition of Hb S gelation have been set forth by Sunshine et al,4 who showed that there is a relationship between the kinetics of polymerization (t_{d}) and the solubility (c_{sat}) under various cellular conditions. They also showed the extent by which t_{d} must be increased to provide an amelioration of homozygous sickle cell disease to the less severe clinical conditions of S/β^{+}thal, S/HPFH, and A/S trait. Although there was a strong correlation with nonHb S hemoglobin composition, there was only a weak one at constant hemoglobin concentration. A detailed analysis of the nucleationcontrolled polymerization that underlies sickling has been elucidated by these same investigators.5 6
Attempts by a variety of investigators716 to correlate hematologic parameters with the clinical severity of various sickling disorders have, for the most part, been only partially successful. Some earlier studies used only painful crises to score illness severity.1719 Others20 21 used a composite vasoocclusive severity score to assign weighted values to the presence of various vasoocclusive events in a cohort of patients. This assessment of clinical severity showed no correlation with any laboratory parameters; however, the clinical severity score (CSS) and erythrocyte adherence to endothelial cells were strongly correlated.22
Eaton et al23 showed in a series of reports that the polymer content of the sickle erythrocyte depends on hemoglobin concentration and composition,24 as well as O_{2}saturation.25 The quantitative relationships among these three cellular variables and the equilibrium aggregation of deoxyHb S may be found in Eaton and Hofrichter.5 6 Subsequently, Noguchi et al,2631 using the conservation of mass equation of Ross et al32 and the activity coefficients of Ross and Minton,33 were able to quantitate intraerythrocytic polymer fraction (f_{p}) by a theoretical analysis of Hb S solubility that accounted for these three cellular variables. A series of reports that used this framework to quantitate intracellular polymer content in various sickling syndromes,31 34 as well as in erythrocytes from individual patients,35 has shown an inverse correlation between f_{p} and whole blood hemoglobin concentration, a hematologic index of hemolytic severity. Furthermore, in the latter study,35 a visual analogue scale (VAS) was used on a cohort of 30 patients to indicate perceived disease severity. The VAS score showed significant positive correlations with the calculated values of f_{p} at both the venous pO_{2}(40 mm Hg) and P_{50}.
In addition to the three major determinants of the polymerization tendency of sickle erythrocytes cited above, we have shown that two other cellular variables (2,3diphosphoglycerate [2,3DPG] concentration and intracellular pH [pH_{i}]) exert separate, but interdependent, effects on the equilibrium solubility (c_{sat}) of unliganded Hb S.1 In a separate study, we were able to quantitate the sparing effect of nonS hemoglobins on the solubility of partially liganded Hb S in the region of pathophysiologic interest (25% to 70% saturation2). It was found that hemoglobins F and A_{2} are equipotent in their effects on c_{sat}, as are hemoglobins A and C, but to a lesser extent. Thus, all five cellular variables (2,3DPG, pH_{i}, nonS hemoglobins, O_{2} saturation, and mean corpuscular hemoglobin concentration [MCHC]) that determine the polymerization tendency of sickle erythrocytes can now be quantitated by use of the requisite experimental values.3
Our earlier study3 showed that depletion of intracellular 2,3DPG produced a consistent reduction in the sickling tendency of erythrocytes from four sickle cell anemia patients with widely differing hematologic features. Furthermore, estimates were made of the decrease in f_{p} evoked by loss of 2,3DPG by using appropriate values of the four variables that interact to affect polymerization in a 2,3DPG–dependent manner (2,3DPG concentration, pH_{i}, O_{2} saturation, and MCHC).
In the present study, we used similar laboratory data, plus those for nonS hemoglobin composition, for a cohort of 46 homozygous sickle cell anemia patients, to quantitate all five cellular variables that modulate the intracellular polymer content of SS RBCs. We then attempted to correlate the values of f_{p} so obtained with hemolytic and vasoocclusive severity for each patient.
MATERIALS AND METHODS
General methods.
Venous blood from 46 SS patients in the steady state was collected in standard heparin Vacutainer tubes and sampled within 2 hours. Informed consent was obtained before blood collection. All patients were adults, age 18 years or greater (mean age, 30.4 ± 8.9 years; range, 18 to 51 years). The male to female ratio was 0.64. No patient had undergone a blood transfusion for at least at least 3 months before blood collection. Hemoglobin concentrations were measured with Drabkin's reagent36 and used, along with the spun hematocrit, to calculate MCHC. Red blood cell adenosine triphosphate (ATP) and 2,3DPG concentrations were measured using Sigma kits (Sigma, St Louis, MO). Hemoglobins F and A_{2} were quantitated in hemolysates by alkali denaturation37 and elution from diethylaminoethyl (DEAE)cellulose columns,38 respectively. Intracellular pH (pH_{i}) was estimated by use of the factor relating pH_{i} to 2,3DPG concentration.3
Mean polymerization tendency of sickle erythrocytes from individual patients.
A quantitative approach to sickle cell disease severity must take into account the extent of polymer formation at equilibrium in the circulating erythrocytes of individual SS patients. Of the five cellular variables that determine intracellular polymer content,3 three (2,3DPG concentration, % nonS hemoglobins [F and A_{2}], and MCHC) were measured directly. Values of pH_{i} were estimated from the 2,3DPG concentration and the loss of Bohr protons due to partial ligation and depolymerization at the O_{2} tension of the microcirculation (pO_{2} = 20 mm Hg1). The O_{2}saturation corresponding to this partial pressure (≈25%) was assumed to be the same for each patient's erythrocytes. Knowledge of four of these five variables (2,3DPG concentration, pH_{i}, nonS Hb composition, and O_{2} saturation) permits one to determine c_{sat}, the equilibrium solubility of intraerythrocytic Hb S at 25% O_{2} saturation, without measuring it directly.3
One can derive increments of c_{sat} for each of these four parameters by use of various empirical relationships we deduced (ie, the interdependence of 2,3DPG concentration and pH_{i} ^{1,3} and the sparing effect of nonS hemoglobins2 24 39) and the effect of ligation on solubility deduced by others.23 Thus: c_{sat} = c_{sat} ^{o} + Δc_{sat} ^{2,3DPG} + Δc_{sat} ^{Hb(F+A2)} + Δc_{sat} ^{25%O2 satn}. The relevant c_{sat} is then obtained as the sum of the increments due to cellular modulators of solubility plus c_{sat} ^{o}, the intraerythrocytic solubility for unliganded, 2,3DPGsaturated Hb S at pH 7.41, which has a value of 18.0 g/dL (this baseline solubility was deduced in Poillon and Kim1).
For our patient with the lowest f_{p} (0.30), each of these increments can be estimated: keeping in mind that the Bohr effect for SS red blood cells is about twice that for AA red blood cells (ie, −0.99 and −0.42, respectively40) and that this translates into a loss of approximately four and two Bohr protons on complete ligation, one can estimate the pH decrement for 25% oxygenation of SS red blood cells as follows: the Bohr protons released at this saturation = 25/89 × 4H^{+}/tetramer = 1.12H^{+}/tetramer, where 89% is the O_{2}saturation at which f_{p} = 0. Then ΔpH/ΔH^{+} = −0.28 × 1.12/4 = −0.078 pH unit, where −0.28 is the pH change for release of all four Bohr protons at 89% O_{2} saturation1 and Δc_{sat}/ΔpH = 10.8 × −0.078 = −0.85 g/dL (where 10.8 g/dL is the increment in c_{sat} per pH unit1).
Effects of nonS hemoglobins (F and A_{2}) and the degree of ligation on c_{sat} are as follows: Δc_{sat}/ΔHb(F+A_{2}) = 0.334 × 18.5 = 6.18 g/dL (where 0.334 is the c_{sat} increment for 1% Hb[F+A_{2}]^{2} and 18.5 is the % Hb[F+A_{2}] for this patient; Δc_{sat}/Δ25% O_{2} saturation = 2.46 g/dL [derived from the empirical relationship between c_{sat} and O_{2} saturation deduced in Sunshine et al^{25}]). Thus, the overall solubility at 25% O_{2} saturation for Hb S in SS erythrocytes from this particular patient is: 18.0 − 0.85 + 6.18 + 2.46 = 25.8 g/dL.
The conservation of mass equation f_{p} = c_{p}(c_{t} − c_{sat})/c_{t}(c_{p} − c_{sat}) shows the relationship among three intracellular concentrations in determining the polymer content of sickle erythrocytes at any degree of oxygenation: c_{p}, the polymer concentration, 69.3 g/dL (taken from Sunshine et al24); c_{t}, the intracellular hemoglobin concentration or MCHC, which has a value of 31.8 g/dL for this particular patient; and c_{sat}, the equilibrium solubility, which has a value of 25.8 g/dL here. Substitution of these values into the conservation of mass equation gives f_{p} = 0.30.
This equation has general use for estimating the mean f_{p}for unfractionated SS erythrocytes. That is, the two variables that show the strongest correlation with f_{p} (see Results) are nonS hemoglobin composition and MCHC. Thus, one must have accurate values for these parameters to obtain a reliable estimate of f_{p}. For the other two parameters, O_{2} saturation is held constant at 25% (corresponding to a Δc_{sat} of 2.46 g/dL) and the decrement in pH evoked by 2,3DPG and H^{+}loss at 25% O_{2} saturation (−0.078 pH unit) is considered constant and corresponds to a decrement in c_{sat}of −0.85 g/dL.
Our findings that polymer fraction correlates well with both Hb F (Fig1) and MCHC (Fig 2) have been shown by us2 and by others.24 39 Although these are strong associations, the simultaneous variation in other parameters that influence f_{p} may introduce a certain amount of noise to the overall expression of polymer fraction.
Assessment of clinical severity.
Because painful crisis is the most common acute event experienced by SS patients, the number of pain episodes requiring hospitalization and administration of narcotic analgesics was used to assess clinical severity for the cohort of 46 patients who were followed for up to 10 years (1986 to 1995). The median followup time was 7 years, with a range of 3 to 10 years. The mean number of admissions and mean hospitalization days were determined retrospectively. For the purposes of this study, we assumed each hospital admission to be due to painful crisis because 87% of all hospital discharges of sickle cell patients listed sickle cell crisis as a discharge diagnosis during the followup period. A modification of the vasoocclusive severity score of Hebbel et al20 was used to assign an index of clinical severity for each patient. Our CSS was assigned solely on the basis of hospitalizations and did not include contributions from organ dysfunction due to specific vasoocclusive events. To compute the average number of hospitalizations per year, we divided the number of hospital admissions during the followup period (regardless of length of hospital stay) by the number of years of followup. Then, CSS (Table1, column 10) was assigned as follows: 15 patients with no hospitalizations or less than one per year, 0 points; those with means of 1 to 5 per year (25 patients), 1 point; 6 to 10 per year (5 patients), 2 points; more than 10 per year (1 patient), 3 points. A second clinical severity measurement was also used: the mean number of hospital days per year (Table 1, column 9), obtained by dividing total number of days each subject was an inpatient during the followup period by the number of years of followup.
Statistical methods.
Analyses of variance were performed and used unpaired Student'sttest (two tailed). To show linear relationships between f_{p} and other variables, both ordinary least squares linear regression and nonparametric tests (Spearman rank correlation) were performed. These tests then generated correlation coefficients andP values (two tailed) for the slope. Except where noted, all correlation coefficients and P values are reported for ordinary linear regression.
RESULTS
Mean values for laboratory and clinical parameters.
Because of its length, the table showing composite laboratory and clinical data for the entire cohort of 46 SS patients is not shown here in full detail. Instead, we have compiled in Table1 the mean values for three of the five cellular variables (MCHC, 2,3DPG concentration, and % Hb[F+A_{2}]) that interact to determine polymer content, as well as those for whole blood hemoglobin and ATP concentrations and for hospitalization days and clinical severity score. The mean values of hematocrit, intracellular hemoglobin concentration (MCHC), %Hb F, and %Hb A_{2} shown in Table 1(26.1 ± 4.3, 33.7 ± 1.5 g/dL, 5.5% ± 4.4%, and 3.0% ± 0.6%, respectively) are in the range found in other studies of this nature.715 Mean values for ATP and 2,3DPG concentrations are 1.4 ± 0.2 and 6.1 ± 0.8 mmol/L, respectively. These values are elevated by ≈25% relative to those for normal adult blood, as was shown in our earlier study1and by Steinberg et al.13 The mean value of hospitalization days per year was 21.8 ± 27.8 and the mean value of CSS was 0.83 ± 0.71.
Dependence of polymer fraction on Hb F concentration and MCHC.
Linear regression plots of f_{p} as a function of %Hb F and MCHC are shown in Figs 1 and2, respectively. The corresponding correlation coefficients were −0.710 and 0.677, and the slopes were significantly different from zero (P < 10^{4}) in each case. Thus, a highly significant correlation exists between intracellular polymer content and nonS hemoglobin composition, as well as intracellular hemoglobin concentration. The strong dependence of polymer fraction on Hb F concentration and MCHC is well known and has been documented by us2 and by others.24 39
By contrast, for a plot of f_{p} versus 2,3DPG concentration (data not shown), there was no association between these two variables (correlation coefficient = 0.199; P = .185).
Hemolytic and clinical severity: Is there a correlation with polymerization tendency?
An attempt was made to correlate polymer fraction f_{p} with hematocrit and whole blood hemoglobin concentration, the laboratory parameters that best reflect hemolytic severity in sickle cell anemia. The linear regression plot of f_{p} versus hematocrit (Fig 3), gave a correlation coefficient of −0.350 and a P value of .0173 for the slope, indicating a negative relationship between f_{p} and hematocrit; for the Spearman rank correlation test, the values were r = −0.403 and P = .0054. The linear regression plot of f_{p} versus whole blood hemoglobin concentration (Fig4) also showed a negative correlation coefficient of −0.198. However, the P value was .187, indicating no statistically significant association between f_{p} and hemoglobin concentration in this group of patients; nonparametric tests gave essentially the same results (r = −0.225; P = .133) indicating no statistically significant association between f_{p} and hemoglobin concentration in this group of patients.
An attempt was made to correlate f_{p} with hospitalization data as an index of clinical severity. The linear regression plot of hospitalization days/yr versus f_{p}(Fig 5) gave a correlation coefficient of 0.089 and a P value of .555 for the slope. Thus, there was no statistically significant association between these two variables. Certain trends were discernible however: (1) No patient with f_{p} less than 0.45 had a high number of mean hospitalization days per year (Fig 5), and (2) these patients also had CSS values of 0 or 1 and none had values of 2 or 3 (Fig 6). On the other hand, patients with high f_{p} did not necessarily have high hospitalization rates; instead, many had few mean hospital days (Fig 5) and low clinical severity scores (Fig 6). This suggested that a high f_{p} could be a necessary, but not sufficient condition, for high vasoocclusive severity. Other factors such as membrane abnormalities or endothelial adhesion tendency probably influence severity in patients with high f_{p}, as well.
Figure 6 shows a plot of the clinical severity score (see footnote in Table 1) versus polymer fraction. These data are not amenable to statistical analysis and are shown only to demonstrate that values of 0 and 1 for CSS encompass f_{p}values throughout the range observed (0.30 to 0.59). By contrast, there were a few patients (six in all) with CSS values of 2 or 3, and these tended to have high values of f_{p} (0.47 to 0.58).
Six of the 46 patients were lost to followup soon after the study. For the remaining 40 patients, the median followup period was 7 years (range, 3 to 10 years). Five of these patients have died of sickle cell disease complications. The polymer fractions were 0.48 in erythrocytes from three of these patients and 0.54 and 0.58 for the other two. No patient with a polymer fraction less than 0.48 died during the followup period.
DISCUSSION
The underlying pathophysiologic events in sickle cell anemia are chronic hemolysis and microvascular occlusion. The principal clinical manifestations arising from these events are anemia, acute painful crises, and organ dysfunction. The marked variability in severity of symptoms among SS patients has made it difficult to establish a meaningful clinical severity scoring system for this disease.41 Although a single measurable parameter for assessing clinical severity does not exist, a useful index that assigned weighted scores to the presence of a group of vasoocclusive events was devised by Hebbel et al20 for this purpose. Because painful episodes requiring hospitalization are the most frequent vasoocclusive event in this disease,42 we used only such hospitalization data to assign a clinical severity score for each patient evaluated and did not assess the contribution of organ damage to the clinical picture.
We have been able to quantitate the interaction among the five cellular variables (2,3DPG concentration, pH_{i}, nonS hemoglobin composition, O_{2} saturation, and MCHC) that modulate the polymerization tendency of sickle erythrocytes (Table 1) in a cohort of homozygous SS patients (n = 46). There was an excellent correlation between the calculated values of f_{p} and two parameters: %Hb F and MCHC (Figs 1 and 2). Thus, these independent cellular variables influence polymerization tendency in a strong and predictable fashion: that is, f_{p} varies inversely with Hb F concentration and directly with MCHC. We next attempted to correlate the calculated values of f_{p} for these patients with indices of hemolytic and clinical severity. Linear regression plots of f_{p} versus hematocrit (Fig 3), whole blood hemoglobin concentration (Fig 4), and hospitalization days/yr (Fig 5) were made. An inverse correlation was found between f_{p} and hematocrit, which would be expected if low values of f_{p} were associated with lower hemolytic rates and vice versa. The correlation between f_{p} and whole blood hemoglobin concentration was not significant (Fig 4). These results are discrepant with those of Keidan et al,35 who showed a strong negative correlation between f_{p} and hemoglobin concentration. Although we can offer no explanation for this anomaly, it may be due to variation in the number of patients evaluated (this study, n = 46; Keidan et al, n = 30).
The correlation between f_{p} and vasoocclusive severity measured by hospitalization data, however, was not good. Whereas f_{p} > 0.45 appeared to be necessary for a severe clinical course and perhaps also for short survival, many SS patients with high f_{p} had a mild clinical course. The only other study in which a correlation between f_{p} and clinical severity for a cohort of homozygous SS patients was attempted is that of Keidan et al35 in which laboratory and clinical parameters for 30 patients were evaluated. In this case, the solubility of mixtures of Hb S with nonS hemoglobins, as a function of O_{2} saturation, was estimated by use of theoretical assumptions regarding the thermodynamics of gelation.28 30 34 Keidan et al35 calculated values of f_{p} at pO_{2}= 0 (0% saturation) and pO_{2} = 40 mm Hg (corresponding to the oxygen saturation of the venous circulation); these values correlated well (P < .05) with a visual analogue scale used by each patient to indicate perceived disease severity. A strong inverse correlation (P < .01) was also found between f_{p} at pO_{2} = 40 mm Hg and whole blood hemoglobin concentration, suggesting that polymerization tendency at the venous pO_{2} is a determinant of the hemolytic rate in individuals homozygous for Hb S.
We can offer several reasons for the disparity between our findings and those of Keidan et al.35 First, our calculations of f_{p} used measured values of the cellular variables that modulate the solubility of partially liganded Hb S (2,3DPG concentration, nonS hemoglobin composition, and MCHC). It is the interplay of these variables, along with pH_{i} and O_{2} affinity, that determine c_{sat}, the solubility of monomeric Hb S inside the partially oxygenated sickle erythrocyte. Second, our patient population was skewed toward individuals with the greatest disease severity, as our clinic tends to attract such patients. Third, different criteria were used to assess disease severity.
Because the microvascular occlusion that underlies the pathophysiology of sickle cell anemia is polymerizationdependent, the polymer fraction of erythrocytes from individual patients should correlate with disease severity. Our results seem to indicate, however, that the clinical course of homozygous SS disease in individual patients cannot be predicted exclusively by f_{p}, which assumes a homogeneous distribution of the five cellular variables that modulate intraerythrocytic polymerization. This suggests that the assumption of a uniform distribution in the cell population of the variables that modulate polymer formation (intracellular hemoglobin concentration, 2,3DPG concentration, pH_{i}, nonS hemoglobin composition, and O_{2} saturation) may not be valid.26 27
Because polymerization is far from equilibrium in the majority of cells in circulating erythrocytes,43 44 a quantitative approach to disease severity would require a kinetic analysis and knowledge of the distribution of delay times (t_{d}) for intracellular polymerization, which has not yet been done. However, the wellknown supersaturation relationship45 relates t_{d} to c_{i} and c_{sat} [(1/t_{d} = γ•(c_{i}/c_{sat})^{n}, where γ is a kinetic constant and n has values of 30 to 40] so that kinetic parameters should correlate with equilibrium parameters. Distributions of f_{p} at equilibrium would also be helpful, but such data are not available. One is left, then, with the measurement of whole cell average parameters (ie, pH_{i}, 2,3DPG concentration, nonS hemoglobin composition, and MCHC).
It has been amply demonstrated46 47 that the red blood cell population in sickle cell anemia is not homogeneous,43 44but contains cells of widely varying Hb F content, 2,3DPG, and total hemoglobin concentration (MCHC). Thus, the amount of polymerized Hb S varies considerably among the cell population, and our calculated values of f_{p} represent only a weightmean average. Accordingly, the red blood cell heterogeneity in individual patients implies that some cells are much higher in MCHC than others; some are devoid of Hb F, while others are rich in it; and cells show considerable variability in 2,3DPG concentration and O_{2}saturation. The net result is that f_{p} varies considerably and the mean f_{p} for all cells does not provide a reliable yardstick to measure disease severity.
Footnotes

Address reprint requests to Oswaldo Castro, MD, Center for Sickle Cell Disease, Howard University, 2121 Georgia Ave, Washington, DC 20059.

The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. section 1734 solely to indicate this fact.
 Submitted November 6, 1996.
 Accepted October 20, 1997.
 Copyright © 1998 American Society of Hematology