Quantitative estimation of urate transport in nephrons in relation to urinary excretion employing benzbromarone-loading urate clearance tests in cases of hyperuricemia.

BACKGROUND: A four-component system for urate transport in nephrons has been proposed and widely investigated by various investigators studying the mechanisms underlying urinary urate excretion. However, quantitative determinations of urate transport have not been clearly elucidated yet.
METHODS: The equation C(ua) = {C(cr)(1 - R(1)) + TSR}(1 - R(2)) was designed to approximate mathematically urate transport in nephrons, where R(1) = urate reabsorption ratio; R(2) = urate postsecretory reabsorption ratio; TSR = tubular secretion rate; C(ua) = urate clearance, and C(cr) = creatinine clearance. To investigate relationships between the three unknown variables (R(1), R(2), and TSR), this equation was expressed as contour lines of one unknown on a graph of the other two unknowns. Points at regular intervals on each contour line for the equation were projected onto a coordinate axis and the high-density regions corresponding to high-density intervals of a coordinate were investigated for three graph types. For benzbromarone (BBR)-loading C(ua) tests, C(ua) was determined before and after oral administration of 100 mg of BBR and C(ua)BBR(∞) was calculated from the ratio of C(ua)BBR(100)/C(ua).
RESULTS: Before BBR administration, points satisfying the equation on the contour line for R(1) = 0.99 were highly dense in the region R(2) = 0.87-0.92 on all three graphs, corresponding to a TSR of 40-60 ml/min in hyperuricemia cases (HU). After BBR administration, the dense region was shifted in the direction of reductions in both R(1) and R(2), but TSR was unchanged. Under the condition that R(1) = 1 and R(2) = 0, urate tubular secretion (UTS) was considered equivalent to calculated urinary urate excretion (U(ex)) in a model of intratubular urate flow with excess BBR; C(ua)BBR(∞) = TSR was deduced from the equation at R(1) = 1 and R(2) = 0. In addition, TSR of the point under the condition that R(1) = 1 and R(2) = 0 on the graph agreed with TSR for the dense region at excess BBR. TSR was thus considered approximately equivalent to C(ua)BBR(∞), which could be determined from a BBR-loading C(ua) test. Approximate values for urate glomerular filtration, urate reabsorption, UTS, urate postsecretory reabsorption (UR(2)), and U(ex) were calculated as 9,610; 9,510; 4,490; 4,150, and 440 μg/min for HU and 6,890; 6,820; 4,060; 3,610, and 520 μg/min for normal controls (NC), respectively. The most marked change in HU was the decrease in TSR (32.0%) compared to that in NC, but UTS did not decrease. Calculated intratubular urate contents were reduced more by higher UR(2) in HU than in NC. This enhanced difference resulted in a 15.4% decrease in U(ex) for HU.
CONCLUSION: Increased UR(2) may represent the main cause of urate underexcretion in HU.

Introduction

Urinary urate is excreted via a complicated combination of urate transport in nephrons [1, 2, 3]. Earlier studies on urate transport in nephrons, including micropuncture, microinjection, and microperfusion experiments, have indicated that urate is filtered freely at the glomerulus [4, 5, 6], and intratubular urate contents are adjusted following bidirectional urate transport, including reabsorptions and secretion [1, 2, 7]. To analyze the mechanisms underlying urinary urate excretion, a four-component system has been investigated and endorsed by various investigators [1, 5, 8, 9, 10, 11]. According to that system, most of the urate filtered through the glomerulus [urate glomerular filtration (UGF)] is considered to be reabsorbed [(urate reabsorption (UR1)] at proximal sites of the tubules, and residual urate contents in intratubular fluid are supplemented by urate tubular secretion (UTS) [12, 13]. Considerable amounts of secreted urate are thought to be reabsorbed in urate postsecretory reabsorption (UR2) [9, 14, 15]. Quantitative analysis of the amount of each fraction, i.e. UGF, UR1, UTS, and UR2, as well as calculated urinary urate excretion (Uex), has been performed using probenecid and pyrazinamide, and ratios of each fraction have been estimated as approximately 99, 50, 40, and 10% of UGF, respectively [1, 2, 16]. To analyze the amount of each kind of transport, probenecid has been used as a reabsorption inhibitor and pyrazinamide as a secretion inhibitor. However, the latter has also been reported as a reabsorption accelerator rather than as an inhibitor [17, 18, 19]. Contributions of each type of transport have thus to be clearly elucidated in quantitative analyses.

Benzbromarone (BBR) has recently been reported as a major and strong inhibitor of urate transport into epithelial cells of nephrons by strongly inhibiting the URAT1 urate transporter [20]. In addition, findings that BBR does not exert uricosuric effects in patients with hypouricemia caused by damage to URAT1 [21] suggest that the inhibitory effects of BBR are specific to URAT1. Using these characteristics of BBR, we attempted to quantitatively estimate urate transport in nephrons in relation to urinary urate excretion employing the equation Cua = {Ccr(1 − R1) + TSR}(1 − R2) [16], where Cua, R1, R2, and TSR are urate clearance, urate reabsorption ratio, urate postsecretory reabsorption ratio, and tubular secretion rate, respectively, without inhibiting urate secretion using pyrazinamide. In parallel with recent progress in urate transporter investigations [20, 22, 23, 24], studies on total amounts of urate transport as a summation of the actions of these transporters will also be important for understanding the mechanisms of urinary urate excretion in human subjects, particularly in patients with hyperuricemia (HU).

Materials and Methods

Subjects comprised 20 male gouty patients with HU (age range, 22–62 years) showing serum urate concentration (Sua; >7.0 mg/dl), together with 10 male volunteers as normal controls (NC; age range, 21–44 years). Administration of all medication affecting Sua, such as BBR, probenecid, allopurinol, diuretics, losartan, fenofibrate, and nucleoside derivatives, was discontinued for at least 2 weeks prior to experiments. All patients provided written informed consent. For BBR-loading Cua tests, a single dose of 100 mg of BBR was administered orally and urine fractions were collected 60 to 0 min before and 180 to 240 min after BBR administration [16]. Blood samples were collected 30 min before and 210 min after BBR administration. Urate and creatinine concentrations in urine fractions and blood samples were determined using a multichannel autoanalyzer (type 7180; Hitachi, Tokyo) that employed automation of uricase peroxidase and creatininase peroxidase procedures, respectively. Cua and Ccr were calculated as reported previously [16, 25, 26] before and after BBR administration, and are expressed assuming a standard body surface area of 1.73 m2.

Quantitative Expression of Urate Transport in Nephrons Using an Equation

The equation Uex = {Ccr·Sua(1 − R1) + UTS}(1 − R2) was designed to calculate urate transport by secretion and reabsorption in relation to urinary urate excretion based on a four-component system [16]. Since UTS could be expressed as TSR Sua, because UTS has been shown to be influenced by urate concentration in the circulating blood in the kidney in microinjection and microperfusion experiments [27], we obtained

For calculating urate transport using this equation, the following assumptions were set after referring to previous reports of experimental data:

(1) urate passed through the glomerular membrane without any loss or retention [4, 5, 6];

(2) 99% of UGF was reabsorbed at proximal sites of tubules when BBR was not administered [1, 2];

(3) BBR strongly inhibited reabsorptions [20, 21] (R1 and R2), but did neither inhibit TSR nor Ccr in the BBR-loading Cua test;

(4) urate concentration in tubular secretion fluid was proportional to Sua[27], and

(5) levels of UR2 were proportional to intratubular urate contents.

Estimation of CuaBBR(∞)

Effects of oral doses of BBR on the Cua curve determined by the Cua test [16] were simulated using the exponential equation y = b − c · e−ax, where y is Cua, × is BBR dose, and a, b, and c are constants [16]. Constants a, b, and c were calculated by applying the least-square method as 0.0090, 45.6, and 40.5 for HU and 0.0081, 80.1, and 70.2 for NC, respectively. The ratio of CuaBBR(100)/CuaBBR(∞) on the curve was calculated as 0.639 for HU and 0.610 for NC, where CuaBBR(100) is Cua after administration of 100 mg BBR. Accordingly, CuaBBR(∞) could be calculated as CuaBBR(100)/0.639 for HU and CuaBBR(100)/0.610 for NC [16].

Results

Graphic analysis of the relationship between R1, R2, and TSR was performed in the equation,

The equation was plotted as contour lines for one of the three unknowns (R1, R2, or TSR) on graphs with the other two unknowns as variables. Any number of contour lines and points satisfying the equation could be plotted, but the points at regular intervals on contour curves were particularly dense with respect to a coordinate within a certain region. The scale of the coordinates for this dense region and the values of the contour line could indicate closer relationships between R1, R2, and TSR.

Without BBR Administration

R-versus-TSR Graph. Using equation 1, contour lines of R2 versus TSR with respect to several values of R1 were plotted. Coordinates of TSR were limited to <200 ml/min, since higher values would not be encountered under usual conditions. The contour lines of the equation lay within the graph area for R1 = 0–1.0. R1 was assumed to be 0.99 without BBR administration; the R2 values on the contour line for R1 = 0.99 ranged from 0 to nearly 1.0, and the range for the dense region was from R2 = 0.87 to nearly 1.0 in HU. The corresponding TSR range for the dense region was >40 ml/min (fig. 1).

Fig. 1

Investigation of condensed site of location of points corresponding to the equation Cua = {Ccr (1 − R1) + TSR}(1 − R2) as a contour line of R1 on R2 versus TSR plot as variables in HU. Area A = Without BBR; areas B/C = excess BBR; point D = tentatively under the condition of R1 = 1 and R2 = 0. Cua values of 4.9 ml/min at BBR(–) and 52.6 ml/min at excess of BBR, respectively.

R-versus-TSR Graph. Using equation 1, contour lines of R1 versus TSR with respect to several values of R2 were plotted. Almost all points in the graph area could be reached by a contour line, except a small area above the R2 = 0 contour line. On the line R1 = 0.99, corresponding to the condition without BBR administration, all TSR values in the range >5 ml/min could be reached. However, contour lines were dense in the range of R2 = 0–0.92 in HU. The corresponding TSR range for this dense area was 5–60 ml/min (fig. 2).

Fig. 2

Investigation of condensed site of location of points corresponding to the equation Cua = {Ccr (1 − R1) + TSR}(1 − R2) as a contour line of R2 on R1 versus TSR plot as variables in HU. Area A = Without BBR; areas B/C = excess BBR; point D = tentatively under the condition of R1 = 1 and R2 = 0. Cua values of 4.9 ml/min at BBR(–) and 52.6 ml/min at excess of BBR, respectively.

R-versus-R Graph. Using equation 1, contour lines of R1 versus R2 with respect to several values of TSR were also plotted. All points above the TSR = 0 contour line could be reached. For R1 = 0.99, this included the full range of R2, but contour lines with respect to TSR were particularly dense in the narrow range R2 = 0.87 to nearly 1.0 in HU. The corresponding TSR values of the contour lines through this R2 range were from 40 to 200 ml/min (fig. 3).

Fig. 3

Investigation of condensed site of location of points corresponding to the equation Cua = {Ccr (1 − R1) + TSR}(1 − R2) as a contour line of TSR on R1 versus R2 plot as variables in HU. Area A = Without BBR; areas B/C = excess BBR; point D = tentatively under the condition of R1 = 1 and R2 = 0. Cua values of 4.9 ml/min at BBR(–) and 52.6 ml/min at excess of BBR, respectively.

In the above three graphic analyses of the relationships between R1, R2, and TSR, while BBR was not administered, the common location of the dense R2 range on the R1 = 0.99 line showed good agreement in the R2-versus-TSR and R1-versus-R2 graphs. The range was R2 = 0.87 to nearly 1.0. However, contour lines were not dense in the R1-versus-TSR graph with respect to TSR, so that density in the R2 direction was decreasing in inverse proportion to increasing TSR volume. Dense regions with respect to projection onto a coordinate axis of regular intervals of points on each contour line must be for all three graphic analyses, thus involving all three unknowns; that is, it is not sufficient that points be dense for some coordinate in two of the graphs but not in the third. Only within the narrow region R2 = 0.87–0.92 on the line R1 = 0.99 are the points dense in all three graphic analyses. The corresponding TSR range was 40–60 ml/min. In this region, solutions to equation 1 are most dense with respect to all three unknowns. This region was thus considered the most probable location for points corresponding to the equation in HU (area A on each graph, fig. 1, 2, 3).

Graphic analyses were undertaken in the same manner in NC. The most probable regions for R1, R2, and TSR were calculated as 0.99, 0.86–0.88, and 70–90 ml/min, respectively.

After BBR Administration

With BBR administration, R1 and R2 were reduced, but TSR was unchanged, as inhibitory actions of BBR are considered specific to URAT1 [20, 28]. In addition, Ccr in the glomerulus, which corresponds to TSR in tubules, was also unchanged during BBR-loading Cua tests. Accordingly, contour lines were shifted parallel to the R1 and R2 axes on the graphs, but were not moved along the TSR axis. When BBR doses were increased, Cua was also increased in a dose-dependent manner [16]. At excess of BBR, equation 1 could be rewritten as follows:

Shift of the site of dense points on contour lines of equation 1 from BBR = 0 to excess BBR was investigated on the three graphs in the same manner as cases without BBR.

R-versus-TSR Graph. Contour lines of R1 were shifted parallel to the R2 axis and intervals widened. Area A was also shifted parallel to the R2 axis and could reach area B (between the contour lines for R1 = 0 and R1 = 0.99 with BBR). The corresponding R2 was from 0 to 0.68. Kramp and Lenoir [29] performed micropuncture and microperfusion experiments showing that in BBR-pretreated rats, the inhibition rate of UR1 at proximal sites of tubules was faster and higher compared to distal sites. Referring to these data, the range of area B could be further reduced. Furthermore, the rate of inhibition of UR1 at excess BBR might not be complete due to the existence of other kinds of urate transporters [22, 30] that might be less inhibited by BBR than URAT1 [20, 21]. The region in which points at regular intervals on contour lines of equation 2 projected onto a coordinate axis were most dense could thus be speculated to lie probably closer between R1 = 0.2 and R1 = 0.5 with excess BBR, so the corresponding R2 was calculated from equation 2 as 0.44–0.64 and the corresponding TSR was 40–60 ml/min in HU (area C, fig. 1).

R-versus-TSR Graph. The contour lines of R2 shifted parallel to the R1 axis and intervals widened. Area A also shifted parallel to the R1 axis and reached area C (between R1 = 0.2 and R1 = 0.5 with BBR), as speculated above. The corresponding R2 and TSR values were 0.54–0.59 and 40–60 ml/min, respectively, in HU (fig. 2).

R-versus-R Graph. Contour lines of TSR were moved with respect to both the R1 and R2 axes, and became more diagonal and intervals widened, as before. Area A was also shifted diagonally and reached area C, as speculated above. The corresponding R2 and TSR values were 0.44–0.64 and 40–60 ml/min, respectively, in HU (fig. 3).

These findings on analysis at excess BBR suggest that solutions to equation 2 were most dense in area C, where R1, R2, and TSR were estimated to be 0.2–0.5, 0.54–0.59, and 40–60 ml/min in HU and 0.2–0.5, 0.48–0.54, and 70–90 ml/min in NC, respectively.

Relationship between TSR and CBBR(∞)

A point corresponding to the condition of R1 = 1 and R2 = 0 at excess BBR was introduced on the three graphs and shown as point D (double circles in fig. 1, 2, 3, respectively), where the situation of urate transport could be explained, so that UGF was completely reabsorbed and UTS did not receive any reabsorption in the intratubular urate flow model [16]. If UuaBBR(∞) were determined under this condition, then UuaBBR(∞) would correspond to UTS, so CuaBBR(∞) would correspond to TSR. Point D and area C, where points corresponding to equation 2 were dense, were separated from each other on the graphs, but both showed relationships between R1, R2, and TSR under the same condition of CuaBBR(∞) with excess of BBR. TSR could thus be deduced from CuaBBR(∞) at R1 = 1 and R2 = 0 in equation 2. The three graphs showed that TSR of point D was in the same range as TSR of area C, namely 40–60 ml/min. TSR was thus considered approximately equivalent to CuaBBR(∞). TSR of point D was also equivalent to that of area A. Using CuaBBR(100), an approximation of TSR was obtained from equation 2 as follows:

Accordingly, R2 could be calculated from equation 2 as follows:

Equations for estimating urate transport and urinary urate excretion are summarized in table 1.

Table 1

Equations for approximating urate transport and urinary urate excretion without BBR administration

Equation	Unit
Cua = {Ccr (LR1) + TSR}(1-R2)
CuaBBR(∞) = CuaBBR(100)/α	ml/min
TSR= CuaBBR(100)/α − 0.01·Ccr	ml/min
R2 = 1 − Cua·α/CuaBBR(100)	(ratio)
UGF = Sua·Ccr	μg/min
UTS = TSR·Sua	μg/min
UR2= (0.01 UGF + UTS)·R2	μg/min
Uex = 0.01 UGF + UTS – UR2	μg/min

See text for abbreviations, α was replaced by 0.610 and 0.639 for NC and HU, respectively.

Inhibition of R1 and R2 by BBR

When BBR was administered, the region of highly dense points of equation 1 was considered to be shifted from area A to area B, and more probably to area C at excess BBR on the graphs. R1 in area B could be distributed within R1 = 0–0.99 and that in area C could be reduced to R1 = 0.2–0.5, as speculated above in each stage of BBR dose. The range of R2 in area C could be calculated from equation 1 at each BBR dose using the corresponding Cua (fig. 4). Estimates of R2, shown by the middle point of area C, remained in the upper region of the R2 range and gradually decreased with increasing BBR doses. With excess BBR, R2 reached around 0.58. Area C could be selected in a narrow range, as the contour lines were crowded in the upper region of area B. The corresponding mean R1 in area C decreased rapidly to an area between R1 = 0.3 and R1 = 0.4 at 25 mg of BBR, which was continued until excess of BBR. Marked differences between inhibition patterns of R1 and R2 by single administration of BBR represented an interesting finding.

Fig. 4

Inhibition of R1 and R2 by BBR. Area A = Without BBR; area B = ranging between R1 = 0 and R = 0.99 at BBR(+); area C = ranging between R1 = 0.5 and R = 0.2 at BBR(+). R2 and corresponding R1 were calculated from equation 1. From mean of R2 in area C, R1 in area C was also calculated using the equation and was expressed using scale of R2.

Estimated Urate Transport Amounts in Nephrons and Urinary Excretion in HU

Urate transport amounts in approximation of UGF, UR1, UTS, UR2, and Uex were calculated using the equations in table 1 and are shown in table 2. Ratios of each transport to UGF in HU and NC were comparable to those reported previously [1, 2], and ratios of UTS, UR2, and Uex to UGF in HU were significantly lower than those in NC (fig. 5).

Table 2

Urate transport in nephrons and urinary excretion in hyperuricemia

	BBR-loading Cua tests						Approximate urate transport in nephrons					Uex
	Sua	Uua	Cua	Ccr	R	CuaBBR	UGF	UTS	TSR	UR2	R2
HU (n = 20)
Mean	87.7	6.00	4.90	109.2	4.57	33.7	9,610	4,490	51.6	4,150	0.905	440
SD	10.4	1.57	1.13	14.5	1.25	7.5	2,110	990	11.6	940	0.022	110
SE	2.3	0.35	0.25	3.2	0.28	1.7	470	220	2.6	210	0.005	25
NC (n = 10)
Mean	53.4	7.66	9.80	129.6	7.60	47.1	6,890	4,060	75.9	3,610	0.872	520
SD	6.5	0.95	1.13	10.0	1.06	5.7	700	710	9.3	660	0.015	80
SE	2.0	0.30	0.36	3.2	0.33	1.8	220	220	3.0	210	0.005	25
p value							<0.0001	0.055	<0.0001	0.009	<0.0001	0.0002

CuaBBR = Cua after administration of 100 mg of BBR. Sua: μg/ml; Uua: μg/kg/min; Cua: ml/min/1.73 m2; UGF, UTS: μg/min; TSR: ml/min/1.73 m2; UR2, Uex: μg/min.

Fig. 5

Comparison of urate transport and intratubular urate contents between HU and NC. UGF: μg/min, and UR1, UTS, UR2, and Uex: μg/min.

Comparing urate transport and intratubular urate contents in nephrons between HU and NC, UGF was significantly higher in HU (39.5%) than in NC, but the difference in intratubular urate contents was minimal at the UR1 stage. TSR in HU was significantly lower (32.0%) compared to that in NC, but UTS in HU was slightly higher (10.6%) than that in NC, and intratubular urate contents in HU were also slightly higher than those in NC at the UTS stage (11.1%). UR2 in HU was significantly higher (15.0%) than that in NC. Since UR2 corresponded to approximately 90% of intratubular urate contents at the stage, residual intratubular urate contents were greatly influenced by the small difference in UR2 between HU and NC. Intratubular urate contents in HU had been higher than those in NC from the stage of UGF to UTS, even with large variations present, but urate contents showed an inverse relationship at the UR2 stage. Subsequently, Uex in HU was 15.4% lower than that in NC, suggesting that higher UR2 in HU than in NC represents the crucial factor for reducing Uex, rather than significantly higher UGF in HU compared to that in NC (fig. 5). R2 in HU was only 3.8% higher than that in NC, but intratubular urate contents were supposed to be elevated by increased UTS and were enlarged to 15.4% at the UR2 stage, suggesting that elevation of intratubular urate contents by addition of increased UTS in HU resulted in enhancement of increased UR2 and subsequently induced enhancement of the rate of urate underexcretion (15.4%) in HU.

Discussion

In this study, quantitative estimations of urate transport and intratubular urate contents in nephrons were investigated in relation to urinary urate excretion based on the four-component system by designing the equation Cua = {Ccr(1 − R1) + TSR}(1 − R2), using assumptions introduced by previous reports of experimental data. High-density regions with respect to the projection onto a coordinate axis of points at regular intervals on contour lines of this equation were analyzed on graphs plotted for two of three unknowns (R1, R2, and TSR) as variables, with the remaining unknown used to determine the contour line, so that densities and locations of these points on the contour lines of the equation could indicate the relationships of the three unknowns. R1 was assumed to be 0.99 before BBR administration and the R2 values of points satisfying the equation were highly dense in a narrow R2 range, which was regarded as the probable value of R2. With BBR administration, contour lines were shifted parallel to the R1 or R2 axes, but not to the TSR axis. CuaBBR(∞) was considered equivalent to TSR from the intratubular urate flow model in the nephron, as well as from deduction of the relationship that CuaBBR(∞) = TSR from equation 2 under condition of R1 = 1 and R2 = 0. TSR could thus be estimated by BBR-loading Cua tests. Urate transport coefficients estimated by calculations in our laboratory were comparable to previously reported data [1, 2].

R2 was slightly higher in HU than in NC (3.8%). This difference was enhanced to 15.0% at the UR2 stage by increases in UTS, resulting in a 15.4% decrease in Uex for HU compared to that for NC. If significant decreases in TSR in HU were unaccompanied by hyperuricemia, Uex in HU would be further decreased. As an example, if Sua in HU was 5.3 mg/dl (the same as Sua in NC), UGF, UTS, UR2, and Uex in HU could be calculated as 5,780; 2,730; 2,520, and 270 μg/min, respectively, and the decrease in Uex in HU would be markedly higher than that in NC. Since significant decreases in TSR among HU were observed widely in frequency and highly in grade from the early stage of gouty patients and TSR was placed in the upper reaches of intratubular urate flow in nephrons compared to UR2, hyperuricemia was suggested to originate with an initial decrease in TSR, producing urate underexcretion and subsequently resulting in urate retention and hyperuricemia. Accordingly, decreased TSR would be a fundamental phenomenon for HU, and hyperuricemia could be considered as a reasonable reaction toward recovering from the decrease of Uex in HU. Actually, the decreased Uex that might be induced by decreased TSR was well compensated by hyperuricemia (table 2).

Analyzing the relationships between R1, R2, and TSR in equation 1, regular points satisfying the equation on the contour line of R1 = 0.99 were more dense in a certain small R2 range that could be understood more easily when projected onto the R2 axis. The dense region was considered to represent a region in which solutions to the equation were most dense, so solutions were located in this region most frequently in the sense of a probability distribution. Similar reasoning could be used to consider the common R2 values appearing in all three graphic analyses as the most dense region with respect to R1, R2, and TSR. This region is the most frequent in terms of probability. In other regions, the probability was reduced because of low density. Since dense areas in the graphs could select a narrow range of R2 and TSR, we considered these to be the areas where the equation best approximated the relationship between the three unknowns.

In an analysis of the high-density region corresponding to the equation after BBR administration, area C was designated as meeting the condition that R1 was lower than R2 on BBR inhibition, referring to Kramp's experiments. The data satisfying this condition also coincided with histochemical findings reported by Enomoto et al. [20], and Enomoto and Endou [28], who reported that URAT1 was more frequently located in proximal sites than in distal sites of tubular epithelial cells. Other kinds of experiments in cultured cells have suggested that the inhibition rate of UR1 at BBR-saturated concentrations was around 55% [30]. Inhibition of UR1 might not reach the level of complete inhibition even with excess BBR due to the potential presence of transporters other than URAT1 [20, 22] despite the higher affinity of this transporter for BBR. The high-density region corresponding to the equation was thus considered to be concentrated in area C. The large distance between area C and point D was not reduced at excess BBR, mainly due to the low grade of inhibition on R2, reflecting the paucity of URAT1 transporters at distal sites in tubules [20].

Equation 1 was designed for investigation of relationships between R1, R2, and TSR, but Uua determined by Cua tests and Uex calculated by the equation showed a highly significant correlation (r = 0.85, p < 0.0001; fig. 6), suggesting that designing equation 1 under our assumptions and using the following calculations could be considered suitable.

Fig. 6

Correlation between urinary urate excretion and Uex. ● = HU; ▿ = NC.

Equation 1 was considered under the assumption that UGF, UR1, UTS and UR2 were sequential, but some investigators have suggested that reabsorption and secretion could occur simultaneously in the same segment of the proximal tubule [31, 32, 33]. In that case, the following equation could be constructed using the same assumptions applied to equation 1 in the intratubular urate flow model [16].

where summation of ΔUTS(1 − R2) was assumed to reach UTS1 to obtain experimental data that Uua = 6.00 and 7.66 for HU and NC, respectively, by BBR-loading Cua tests (table 2), then

After substituting experimental data of table 2 for Cua, Ccr, and CuaBBR(∞), graphic analysis of equation 3 was performed in the same manner as in the case of the equation 1, estimating R1, R2, and TSR1 as 0.99, 0.91–0.94 and 40–60 ml/min for HU and 0.99, 0.87–0.90 and 70–90 ml/min for NC, respectively (fig. 7, 8). These findings indicate that the urate transport coefficients are almost the same as in equation 1. Both analyses thus reached the same conclusion that increased postsecretory reabsorption may represent the main cause of urate underexcretion in HU.

Fig. 7

Investigation of condensed site of locations of points corresponding to the equation Cua = Ccr(1 − R1) + TSR1(1 − R2) as a contour line of R1 on R2 versus TSR1 plot as variables in HU in the same manner as the equation Cua = {Ccr(1 − R1) + TSR}(1 − R2) in figure 1. Area A = Without BBR; areas B/C = excess BBR; point D = tentatively under the condition of R1 = 1 and R2 = 0. Cua values were 4.9 ml/min at BBR(–) and 52.6 ml/min at excess of BBR, respectively.

Fig. 8

Investigation of condensed site of location of points corresponding to the equation Cua = Ccr(1 − R1) + TSR1(1 − R2) as a contour line of R2 on R1 versus TSR1 plot as variables in HU in the same manner as Cua = {Ccr(1 − R1) + TSR}(1 − R2) in figure 2. Area A = Without BBR; areas B/C = excess BBR; point D = tentatively under the condition of R1 = 1 and R2 = 0. Cua values were 4.9 ml/min at BBR(–) and 52.6 ml/min at excess of BBR, respectively.

Some investigators [34] have reported that secretion might be overestimated in the four-component theory. However, according to our analyses, the possibility seems relatively unlikely because few corresponding points for both equation 1 and equation 3 were located both in low TSR regions and in low R2 regions on the graphs.

Studies on quantitative estimation of urate transport in the nephron could result in a more precise understanding of the pathophysiology of urate transport and intratubular flow of urate contents in HU. For example, instead of a significant decrease in TSR among HU compared to that in NC, UTS among HU was higher than that in NC, as the low TSR was compensated by high Sua in HU. The increase in UTS enhanced increases in UR2, which subsequently enhanced decreases in Uex for HU.

Since cases of hyperuricemia show a large degree of variability in the level of Sua and amount of Uua, as well as in qualities such as overproduction and underexcretion [25, 26, 35], analyses and investigations of greater numbers of HU are needed. Such investigations are currently underway in our laboratory. Estimation of R1, R2, and TSR and inhibition by BBR might yield more information and shed light on the mechanisms underlying urate underexcretion, which would also facilitate an understanding of the pathophysiology of urate underexcretion among individual HU in medical practice.

Conclusion

To estimate urate transport contents in nephrons, the equation Cua = {Ccr(1 − R1) + TSR}(1 − R2) was designed and high-density regions with respect to the projection onto a coordinate axis of points at regular intervals on contour lines of this equation were investigated on graphs for two of three unknowns (R1, R2, and TSR). TSR was found to approximately correspond to CuaBBR(∞), which could be determined by the BBR-loading Cua test. UGF, UR1, UTS, UR2, and Uex were approximated as 9,610; 9,510; 4,490; 4,150, and 440 μg/min in HU and 6,890; 6,820; 4,060; 3,610, and 520 μg/min in NC, respectively. Decreased TSR in HU was suspected as a fundamental change in terms of a high incidence of low TSR cases and high rate of decrease in TSR, as well as the pathophysiology of urate underexcretion. Increased UR2 was considered to be the main cause of urate underexcretion in HU.