Chemical evidence for the tradeoff-in-the-nephron hypothesis to explain secondary hyperparathyroidism.

BACKGROUND: Secondary hyperparathyroidism (SHPT) complicates advanced chronic kidney disease (CKD) and causes skeletal and other morbidity. In animal models of CKD, SHPT was prevented and reversed by reduction of dietary phosphate in proportion to GFR, but the phenomena underlying these observations are not understood. The tradeoff-in-the-nephron hypothesis states that as GFR falls, the phosphate concentration in the distal convoluted tubule ([P]DCT]) rises, reduces the ionized calcium concentration in that segment ([Ca++]DCT), and thereby induces increased secretion of parathyroid hormone (PTH) to maintain normal calcium reabsorption. In patients with CKD, we previously documented correlations between [PTH] and phosphate excreted per volume of filtrate (EP/Ccr), a surrogate for [P]DCT. In the present investigation, we estimated [P]DCT from physiologic considerations and measurements of phosphaturia, and sought evidence for a specific chemical phenomenon by which increased [P]DCT could lower [Ca++]DCT and raise [PTH]. METHODS AND
FINDINGS: We studied 28 patients ("CKD") with eGFR of 14-49 mL/min/1.73m2 (mean 29.9 ± 9.5) and 27 controls ("CTRL") with eGFR > 60 mL/min/1.73m2 (mean 86.2 ± 10.2). In each subject, total [Ca]DCT and [P]DCT were deduced from relevant laboratory data. The Joint Expert Speciation System (JESS) was used to calculate [Ca++]DCT and concentrations of related chemical species under the assumption that a solid phase of amorphous calcium phosphate (Ca3(PO4)2 (am., s.)) could precipitate. Regressions of [PTH] on eGFR, [P]DCT, and [Ca++]DCT were then examined. At filtrate pH of 6.8 and 7.0, [P]DCT was found to be the sole determinant of [Ca++]DCT, and precipitation of Ca3(PO4)2 (am., s.) appeared to mediate this result. At pH 6.6, total [Ca]DCT was the principal determinant of [Ca++]DCT, [P]DCT was a minor determinant, and precipitation of Ca3(PO4)2 (am., s.) was predicted in no CKD and five CTRL. In CKD, at all three pH values, [PTH] varied directly with [P]DCT and inversely with [Ca++]DCT, and a reduced [Ca++]DCT was identified at which [PTH] rose unequivocally. Relationships of [PTH] to [Ca++]DCT and to eGFR resembled each other closely.
CONCLUSIONS: As [P]DCT increases, chemical speciation calculations predict reduction of [Ca++]DCT through precipitation of Ca3(PO4)2 (am., s.). [PTH] appears to rise unequivocally if [Ca++]DCT falls sufficiently. These results support the tradeoff-in-the-nephron hypothesis, and they explain why proportional phosphate restriction prevented and reversed SHPT in experimental CKD. Whether equally stringent treatment can be as efficacious in humans warrants investigation.

Introduction

The parathyroid hormone concentration ([PTH]) rises as the glomerular filtration rate (GFR) falls in patients with chronic kidney disease (CKD) [1]. This phenomenon, secondary hyperparathyroidism (SHPT), causes skeletal morbidity and may contribute to other uremic manifestations [2-4]. PTH also raises concentrations of fibroblast growth factor 23, which may exert its own toxic effects [5-7].

During the past 50 years, seven theories have been advanced to explain the pathogenesis of SHPT [8]. The most recent of these, the tradeoff-in-the-nephron hypothesis, attributes SHPT to an increased phosphate concentration in the distal convoluted tubule ([P]DCT), where PTH regulates reabsorption of ionized Ca (Ca++) [8-11]. According to this hypothesis, high [P]DCT reduces [Ca++]DCT, and [PTH] rises to maintain Ca++ reabsorption at a rate compatible with normocalcemia [8,12,13]. The hypothesis integrates the micropuncture observation that [P]DCT rose in animals with CKD fed a standard diet [9], and explains why dietary restriction or intestinal binding of phosphate prevented, mitigated, or reversed SHPT in animals and humans [14-22]. The term “tradeoff-in-the-nephron” invites a comparison to the original tradeoff hypothesis, which attributed SHPT to an interaction between phosphate and Ca++ in plasma [23].

If creatinine clearance (Ccr) is accepted as a surrogate for GFR, the ratio of the phosphorus excretion rate (EP) to Ccr quantifies the amount of P excreted per volume of filtrate. Moreover, EP/Ccr is proportional to [P]DCT if fractional delivery of filtrate to the DCT is assigned a constant value [8,12,13,24,25]. In a cohort of 30 patients with stages G3 or G4 CKD, significant correlations between [PTH] and EP/Ccr were demonstrated under multiple conditions, but a chemical mechanism to explain these correlations was not investigated [24].

The Joint Expert Speciation System (JESS) employs a compilation of thousands of equilibria to predict concentrations of ions and other chemical entities under defined conditions [26,27]. In the present study, we deduced concentrations of Ca and P in the DCT ([Ca]DCT and [P]DCT) from laboratory measurements and physiologic considerations, and posited evidence-based assumptions concerning other constituents in that segment. With this information, JESS was used to calculate [Ca++]DCT under various modeling scenarios, of which the most germane proved to be ones that excluded or included possible precipitation of amorphous calcium phosphate (Ca3(PO4)2 (am., s.)). Regressions of [PTH] on [Ca++]DCT were then performed at pH 6.6, 6.8, and 7.0, which are representative values over the documented pH range in the DCT [28]. If precipitation of amorphous calcium phosphate (Ca3(PO4)2 (am., s.)) occurred as filtrate reached saturation with this solid, total [P]DCT reduced [Ca++]DCT in advanced CKD to values associated with increased [PTH]. Relationships of [PTH] to [Ca++]DCT and to eGFR were virtually identical.

Methods

Subjects and laboratory determinations

Between 2010 and 2013, data were collected from 28 control subjects with estimated GFR (eGFR) > 60 mL/min/1.73m2 and 30 patients with eGFR 14–49 mL/min/1.73m2. GFR was estimated with the 4-variable MDRD formula. All participants were normocalcemic (8.5–10.2 mg/dL in our hospital laboratory). Two patients with CKD were excluded from the present study, one because the serum ultrafilterable calcium concentration ([Cauf]s) was reported to be lower than the ionized calcium concentration ([Ca++]s)–a physiologic impossibility–and one because the association of [PTH] of 169 pg/mL with [Ca++]s of 1.35 mM implied autonomy of PTH secretion. A control subject who failed to collect a 24-hour urine specimen was also excluded. The study sample in the present report therefore includes 28 patients with CKD (denoted as “CKD”) and 27 control subjects (denoted as “CTRL”). CKD and CTRL were not matched for age, race, or gender.

The data considered herein were obtained before experimental interventions were initiated [12,13,24,25]. Aliquots of urine, serum, and plasma were obtained at a clinic visit occurring between 8:00 and 10:00 a.m. Subjects performed a urine collection during the 24 hours preceding the visit and were instructed to take no medicines or food after midnight of their appointment day. Serum (s) and urine (u) concentrations of creatinine, calcium, and phosphorus were measured by autoanalyzer. [Ca++]s, [Cauf]s, and plasma [PTH]1–84 ([PTH]) were measured as previously described [12].

Estimation of total phosphate and calcium concentrations in the DCT

Phosphate and calcium exist in filtrate of the DCT as either free ions (PO43– and Ca++) or chemical species derived from the ions by formation reactions. Most derived species, such as H2PO4–, HPO4 =, and CaHPO40, exist in solution (i.e., are dissolved), but solid phases such as brushite and amorphous calcium phosphate may precipitate if their solubility product constants are exceeded. The extent of formation of any chemical species, including precipitates, can be calculated from the total concentrations [P]DCT and [Ca]DCT using thermodynamic relationships and equilibrium constants described in the chemical literature. However, it is necessary in such calculations to stipulate a priori which if any precipitates may be formed. Such stipulations are based on certain empirical rules of thumb, particularly Ostwald’s Rule of Stages, as described below.

Total [P]DCT and [Ca]DCT were estimated in this work under the following assumptions: the rate of phosphate delivery to the DCT equals the excretion rate of phosphorus (EP) [29]; the rate of calcium delivery to this segment is 10% of the filtration rate of calcium, or 0.1(eGFR)[Cauf]s [30]; and fractional delivery of filtrate (FDf) to the DCT is 0.2 in controls and 0.35 in subjects with CKD [31-33]. Accordingly, total [Ca]DCT was computed as 0.1(eGFR)[Cauf]s/(0.35)eGFR in CKD and as 0.1[(eGFR)[Cauf]s/(0.2)eGFR in CTRL. Similarly, total [P]DCT was calculated as (24h EP)/0.35(eGFR) in CKD and as (24h EP)/0.2(eGFR) in CTRL. Equations for total [Ca]DCT and [P]DCT thus simplified to 0.1[Cauf]s/FDf and (24h EP)/{FDf(eGFR)}, respectively.

Estimation of other total concentrations in the DCT

Filtrate pH and total concentrations in the DCT of sodium, potassium, magnesium, chloride, urate, sulfate, citrate, oxalate, bicarbonate, creatinine, and urea were estimated by appropriate combinations of the following: ultrafilterable concentrations in serum; estimated GFR (eGFR); published micropuncture data [28,30-38]; studies of urine dilution with water loading [39]; excretion rates of anions not reabsorbed or secreted in the distal nephron [40-45]; and assumptions concerning FDf at normal and reduced GFR [31-33]. The concentration of ammonium in the DCT was assumed to be negligible. Details concerning assignment of concentrations, including pH, are provided in Supporting Information.

Determination of [Ca++]DCT using JESS

From estimated total concentrations and relevant equilibria, routine chemical speciation models were constructed to solve mass balance equations for each applicable DCT component. The calculated ionic strength of DCT filtrate allowed the ionic activity quotients of all chemical reactions to be inferred. For each possible solid phase, the saturation index (SI) was calculated as IAP/Ksp, where IAP is the ion activity product and Ksp is the solubility product constant [27]. If logSI is < 0, it follows that SI is < 1 and the compound in question is fully dissolved at equilibrium. If logSI is ≥ 0, it follows that SI is ≥ 1 and filtrate is saturated or supersaturated with the solid.

In the present work, possible solid phases in the DCT included brushite (CaHPO4.2H2O) and Ca3(PO4)2, (am., s.), but the former was dismissed because logSIbrushite was uniformly negative in both groups and all scenarios. In contrast, at pH 6.8, logSICa3(PO4)2 (am., s.) exceeded zero in approximately half of CKD and a majority of CTRL when precipitation of this solid was not assumed. Ostwald’s rule of stages suggests that in a fluid supersaturated with multiple solids, the one with logSI closest to 0 is likely to precipitate first [27,46]. In the present study, JESS analyses indicated that this solid phase was Ca3(PO4)2 (am., s.) in the DCT of both CKD and CTRL. Two additional modeling scenarios, one with and one without precipitation of Ca3(PO4)2 (am., s.), were therefore investigated. When precipitation was assumed in states of saturation or supersaturation, consequences were examined at pH 6.6, 6.8, and 7.0. In each scenario, [Ca++]DCT, [CaHPO40]DCT, [Cacit–]DCT, [Caox0]DCT, [CaHCO3+]DCT, and [CaSO40]DCT were calculated as concentrations of the most likely pertinent species of dissolved calcium.

Statistical analysis

The ultimate goals of the present study were to identify a chemical phenomenon by which increased [P]DCT could reduce [Ca++]DCT in CKD; to ascertain whether [PTH] would vary significantly with [Ca++]DCT if that reduction occurred; and to consider the possibility that [PTH] was related to eGFR because it was related to [Ca++]DCT. Table 1 summarizes the sequence of questions addressed and the examinations conducted to pursue these goals.

Table 1

Rationale for inquiries into the tradeoff-in-the-nephron hypothesis.

QUESTIONS	RELEVANT EXAMINATIONS
Were [PTH], total [P]DCT, and total [Ca]DCT related to eGFR?	Regressions of [P]DCT and [Ca]DCT on eGFR, and of [PTH] on 100/eGFR (Fig 1)
Was [PTH] related to total [P]DCT and total [Ca]DCT?	Regressions of [PTH] on [P]DCT and [Ca]DCT (Fig 1)
Did pH affect precipitation of Ca3(PO4)2 (am., s.) in the DCT?	Box-and-whisker plots of logSICa3(PO4)2 at pH 6.6, 6.8, and 7.0 (Fig 2); plot of logSICa3(PO4)2 against pH at fixed [P]DCT and [Ca]DCT (S1 Fig)
Was [Ca++]DCT related to total [P]DCT? To total [Ca]DCT?	Regressions of [Ca++]DCT on [P]DCT and [Ca]DCT at pH 6.6, 6.8, and 7.0 (Figs 3, 4, S2 and S3)
If [Ca++]DCT was related to [P]DCT, did precipitation of Ca3(PO4)2 (am., s.) mediate that relationship?	Linkage of precipitation of Ca3(PO4)2 (am., s.) (Fig 2) to regressions of [Ca++]DCT on [P]DCT (Figs 3, 4, S2 and S3)
Was [Ca++]DCT related to [CaHPO40)DCT?	Plots of [Ca++]DCT against [CaHPO40]DCT at pH 6.6, 6.8, and 7.0 (S4 and S5 Figs)
Did anions other than phosphate affect [Ca++]DCT?	Plots of [Ca++]DCT against [Cacit+]DCT, [Caox0]DCT, [CaHCO3+]DCT and [CaSO40]DCT at pH 6.8 (S5 Fig)
Was [PTH] related to [Ca++]DCT?	Regressions of [PTH] on [Ca++]DCT (Figs 3, 4, S2 and S3)
Did the relationship of [PTH] to [Ca++]DCT explain the relationship of [PTH] to eGFR?	Comparison of regressions of log[PTH] on log[Ca++]DCT and log[PTH] on log(eGFR) after standardization of logarithmic values (Fig 5)

In each subset of subjects, mean values were determined for parameters not affected by pH or precipitation of Ca3(PO4)2 (am., s.), including eGFR, [PTH], 24h EP, 24h ECa, [P]s, [Ca++]s, [Cauf]s, [P]DCT, and [Ca]DCT. For each of these parameters, normality of distribution was examined with plots and with the Shapiro-Wilk test. When distributions were judged to be normal, differences between means were assessed with t-tests for unpaired values (unequal variances assumed). When distributions were skewed, differences between medians were assessed with the Mann Whitney U test. Results were considered to be statistically significant at p < 0.05.

The hypothesis investigated in the present study was that [Ca++]DCT induced by [P]DCT determines [PTH] in stages G3 and G4 CKD. For comparative purposes, we examined least-squares regressions of total [P]DCT and total [Ca]DCT on eGFR, and regressions of [PTH] on total [P]DCT, total [Ca]DCT, and eGFR (Fig 1). None of these regressions was affected by pH or the state of precipitation of Ca3(PO4)2 (am., s.).

Fig 1

Linear regressions unaffected by pH or precipitation of Ca3(PO4)2 (am., s.).

Since JESS identified Ca3(PO4)2 (am., s.) as the Ca species most likely to precipitate in the DCT, we examined the maximum, minimum, median, mean, and 25th to 75th percentiles of logSICa3(PO4)2 (am., s.) at pH 6.8 with precipitation excluded, and at pH 6.6, 6.8, or 7.0 with precipitation assumed if logSICa3(PO4)2 (am., s.) equaled or exceeded zero (Fig 2).

Fig 2

Dependence of logSICa3(PO4)2 (am., s.) on pH in the DCT.

Factors determining [Ca++]DCT (“determinants”) were sought with least-squares regressions of [Ca++]DCT on total [P]DCT and total [Ca]DCT. The tradeoff-in-the-nephron hypothesis was tested with regressions of [PTH] on [Ca++]DCT at pH 6.6, 6.8, and 7.0, assuming precipitation of Ca3(PO4)2 (am., s.) if logSI was ≥ 0 (Figs 3,4, S2 and S3). In combined CKD and CTRL, inverse curvilinear relationships between [PTH] and either eGFR or [Ca++]DCT were assessed as power functions in the form y = kx + c, where y = [PTH] and x = eGFR (Fig 1) or [Ca++]DCT (Figs 3 and 4). Relationships between [PTH] and both eGFR and [Ca++]DCT were then investigated by log-log transformation of these variables and subsequent standardization of logarithmic values (Fig 5).

Fig 3

Regressions assuming pH 6.8 and precipitation of Ca3(PO4)2 (am., s.).

Fig 4

Regressions assuming pH 7.0 and precipitation of Ca3(PO4)2 (am., s.).

Fig 5

Regressions of [PTH] on eGFR and [Ca++]DCT after log-transformation of variables and standardization of logarithmic values.

To investigate the possibility that CaHPO40 was a mediator of the effect of total [P]DCT on [Ca++]DCT, we produced scatterplots of [CaHPO40]DCT against total [P]DCT, and of [Ca++]DCT against [CaHPO40]DCT, at pH 6.6, 6.8, and 7.0 (S4 Fig). To determine whether other Ca species had affected [Ca++]DCT, we examined regressions of [Ca++]DCT on [Cacit–]DCT, [Caox0]DCT, [CaHCO3+]DCT, and [CaSO40]DCT, assuming pH 6.8 and precipitation of Ca3(PO4)2 (am., s.) if logSI was ≥ 0 (S5 Fig).

Although we assumed in the present work that fractional delivery of calcium to the DCT (FDCa) was 0.1 in both CKD and CTRL, we also considered the possibility that in CKD, a higher FDCa might increase the effect of total [Ca]DCT on [Ca++]DCT. To investigate that possibility, we performed regressions of [Ca++]DCT on total [Ca]DCT, [Ca++]DCT on [P]DCT, and [PTH] on [Ca++]DCT at FDCa 0.15 and 0.2 and pH 6.6, 6.8, and 7.0 (S6 and S7 Figs).

Statistical analyses were carried out with Microsoft Excel and R version 4.0.3 (R Core Team, 2020) [47].

Clinical research policies

The research project that provided the data reported herein [12,13] was approved and periodically reviewed by the Institutional Review Board (IRB) of the Stratton Veterans’ Affairs Medical Center, Albany, NY, USA. The project was conducted with adherence to the Declaration of Helsinki, and written informed consent was obtained from all participants. Data employed in the present study were obtained from tests on urine, serum and plasma obtained at an IRB-approved research clinic visit. IRB oversight over access to all data was in place.

Results

We present our results in accordance with the order of questions posed in Table 1. Table 2 compares means of variables that were not affected by filtrate pH or precipitation of Ca3(PO4)2 (am., s.) in the DCT.

Table 2

Parameters unaffected by pH or precipitation of Ca3(PO4)2 (am., s.) in the DCT.

Parameter	Subjects with CKD(n = 28)	Control subjects(n = 27)	p
eGFR, mL/min/1.73m2	29.9 (9.5)	86.2 (10.2)	< 0.001
[PTH], pg/mL	82.9 (47.6)	29.0 (12.4)	< 0.001
[Ca++]s, mol/L x 103	1.24 (0.05)	1.26 (0.03)	0.1
[Cauf]s, mol/L x 103	1.34 (0.05)	1.34 (0.06)	0.9
[P]s, mol/L x 103	1.15 (0.24)	1.11 (0.20)	0.7
EP, mol/24h x 102	2.60 (0.83)	2.66 (1.03)	0.8
ECa, mol/24h x 103	1.05 (0.74)	3.31 (1.84)	< 0.001
Total [Ca]DCT, mol/L x 104	3.82 (0.14)	6.71 (0.31)	< 0.001
Total [P]DCT, mol/L x 103	1.89 (0.75)	1.07 (0.38)	< 0.001

aValues are mean (SD).

[Ca++]s, [Cauf]s, [P]s, and 24-hour EP were not different in CKD and CTRL. In CKD, eGFR was lower, [PTH] higher, 24h ECa lower, total [Ca]DCT lower, and total [P]DCT higher than in CTRL.

Fig 1 depicts regressions that were not affected by filtrate pH or precipitation of Ca3(PO4)2 (am., s.).

Fig 1A shows that total [P]DCT varied inversely with eGFR in CKD but not CTRL, and total [Ca]DCT was unrelated to eGFR in each group. [PTH] rose with [P]DCT in CKD but not CTRL (Fig 1B); in contrast, [PTH] was inversely related to [Ca]DCT in CTRL but not CKD (Fig 1C).

Fig 1D shows that [PTH] varied inversely with eGFR in CKD and directly with eGFR in CTRL. However, a scatterplot of [PTH] (y) against eGFR (x) in the combined groups appeared to depict a hyperbola described in part by the formula xy = k (Fig 1D). Accordingly, a least-squares regression of [PTH] (y) on 100/eGFR (100/x) displayed a linear relationship (Fig 1E). The associated equation was then modified to express [PTH] (y) as a power function of eGFR (x) in the form y = kx + c. The hyperbola described by the function is included in Fig 1F.

Fig 2 depicts the median, mean, 25th-75th percentile range, and upper and lower limits of logSICa3(PO4)2 (am., s.) in CKD and CTRL under four combinations of conditions. LogSICa3(PO4)2 (am., s.) was 0 at saturation and > 0 at supersaturation. In Fig 2A, pH was 6.8 and precipitation was considered not to occur; in Fig 2B–2D, at pH 6.6, 6.8, and 7.0, precipitation was assumed to occur when DCT filtrate was saturated or supersaturated with Ca3(PO4)2 (am., s.).

JESS predicted that with no precipitation, the DCT would be saturated or supersaturated with this compound at pH 6.8 in half of CKD and a majority of CTRL (Fig 2A). In contrast, at pH 6.6, saturation with Ca3(PO4)2 (am., s.) was predicted in no subjects with CKD and in five CTRL (Fig 2B). At pH 6.8, saturation with and consequent precipitation of Ca3(PO4)2 (am., s.) were predicted in the top two quartiles of CKD and in all but four CTRL (Fig 2C). At pH 7.0, precipitation was predicted in all but four CKD and in all CTRL (Fig 2D). If [Ca]DCT and [P]DCT were fixed hypothetically at 0.5 mM and 1.5 mM respectively, saturation with Ca3(PO4)2 (am., s.) occurred at pH 6.73 (see S1 Fig and related discussion in SI).

Under conditions in which precipitation of Ca3(PO4)2 (am., s.) did not occur (Fig 2A and 2B), linear regressions showed that total [Ca]DCT was a major and [P]DCT was a minor determinant of [Ca++]DCT (see S2 and S3 Figs and related discussion in SI). In contrast, when precipitation was assumed to occur in states of supersaturation (Fig 2C and 2D), regressions showed that [P]DCT was the sole determinant of [Ca++]DCT (Figs 3A, 3B, 4A and 4B).

At pH 6.8, [PTH] varied inversely with [Ca++]DCT in CKD but not CTRL, and began to rise unequivocally in CKD at [Ca++]DCT of approximately 2.8 x 10−4 mol/L (Fig 3C). In the combined groups, a scatterplot of [PTH] (y) against [Ca++]DCT (x) appeared to depict a hyperbola described in part by the formula xy = k (Fig 3C). A significant least-squares regression of [PTH] (y) on 10/[Ca++]DCT (10/x) was accordingly documented (Fig 3D), and the associated linear equation was modified to express [PTH] (y) as a power function of [Ca++]DCT (x) in the form y = kx + c. The hyperbola described by the function is included in Fig 3E.

At pH 7.0, results resembled and accentuated those obtained at pH 6.8. [Ca++]DCT was again entirely dependent on [P]DCT in both groups, but relationships were curvilinear rather than linear (Fig 4A). [Ca++]DCT remained independent of total [Ca]DCT (Fig 4B). [PTH] rose as [Ca++]DCT fell in CKD but not CTRL, and the trajectory of [PTH] became more positive at [Ca++]DCT of approximately 2.0 mol/L x 10−4 (Fig 4C). Again, a scatterplot of [PTH] against [Ca++]DCT in both groups appeared to depict a hyperbola described in part by the equation xy = k (Fig 4C). A significant linear regression of [PTH] (y) on 10/[Ca++]DCT (x) was accordingly demonstrated (Fig 4D), and the associated equation was modified to express [PTH] (y) as a power function of [Ca++]DCT (x) in the form y = kx + c. The hyperbola described by the function is included in Fig 4E.

Because relationships of [PTH] to eGFR and to [Ca++]DCT were visually similar (Figs 1F, 3E, and 4E), we performed an additional test of the hypothesis that the first relationship resulted from the second. Whereas (kx + c) is not amenable to log transformation, the general formula y = kx–a simpler power function of x–transforms to the linear equation logy = logk + n(logx).

Fig 5 presents results of this modification for y = [PTH] and x = eGFR or [Ca++]DCT at pH 6.8 or 7.0.

Fig 5A, 5C, and 5E show that at either pH value, log transformations yielded significant linear regressions of log[PTH] on both log(eGFR) and log([Ca++]DCT x 104). These results indicate that in addition to the hyperbolic formulas in Figs 1F, 3E, and 4E, power functions of the form y = kxn related [PTH] (y) to both eGFR and [Ca++]DCT (x) in combined CKD and CTRL. In Fig 5B, 5D, and 5F, each value of log[PTH], log(eGFR) and log([Ca++]DCT x 104) was assigned a z-score. After this standardization procedure, slopes of lines relating log[PTH] to either log(eGFR) or log([Ca++]DCT x 104) were virtually identical, as is indicated by the extreme overlap in confidence intervals.

Other issues are examined in Supporting Information. Although precipitation of Ca3(PO4)2 (am., s.) was assumed in most scenarios, we also considered the possibility that formation of CaHPO40 might cause a reduction of [Ca++]DCT and an elevation of [PTH] as [P]DCT rose (S4 Fig). In CKD and CTRL, [CaHPO40]DCT increased with total [P]DCT at pH 6.6, 6.8, and 7.0 (S4A and S4B Fig). [Ca++]DCT fell as [CaHPO40]DCT rose, but at a given [CaHPO40]DCT, [Ca++]DCT varied markedly with pH and therefore did not appear to be controlled by [CaHPO40]DCT per se (S4C and S4D Fig). The small calculated formation of CaHPO40 as a percentage of total calcium argues strongly against a role for this species in determination of [Ca++]DCT.

Assuming pH 6.8 and precipitation of Ca3(PO4)2 (am., s.), we examined regressions of [Ca++]DCT on concentrations of Cacit−and other Ca complexes to ascertain whether these compounds could reduce [Ca++]DCT and raise [PTH] secondarily. [Ca++]DCT varied inversely with [CaHPO40]DCT, presumably because of the relationship of [CaHPO4]DCT to [P]DCT (S4 Fig), and directly with concentrations of all other complexes (S5 Fig). Citrate, oxalate, bicarbonate, and sulfate did not reduce [Ca++]DCT significantly.

In principle, fractional delivery of filtered calcium to the DCT (FDCa) could have been higher in CKD than the assigned value, 0.1, with the result that total [Ca]DCT exerted an effect on [Ca++]DCT that was not evident at FDCa 0.1. We therefore examined regressions of [Ca++]DCT on total [Ca]DCT, [Ca++]DCT on total [P]DCT, and [PTH] on [Ca++]DCT at FDCa 0.15 or 0.2. At pH 6.6, 6.8, and 7.0, logSICa3(PO4)2 (am., s.) was essentially zero in all subjects at both FDCa values (data not shown), and therefore indicated universal precipitation of Ca3(PO4)2 (am., s.) at the increased values of FDCa. At pH 6.6, a previously significant relationship of [Ca++]DCT to total [Ca]DCT disappeared (S3B Fig), and a strong relationship of [Ca++]DCT to total [P]DCT emerged (S6 and S7 Figs). At pH 6.8 and 7.0, [Ca++]DCT remained independent of [Ca]DCT and exclusively dependent on [P]DCT (S6 and S7 Figs). Regressions of [PTH] on [Ca++]DCT were significant at both values of FDCa and all three pH values; R2 for these regressions was similar to values obtained at FDCa 0.1 (Figs 3 and 4).

Discussion

Background and summary of principal findings

In stages G3 and G4 CKD, one of the cardinal features of SHPT is persistence of normal [Ca++]s and [Cauf]s until CKD is far advanced [12]. If Ccr is assumed to approximate GFR, [Cauf]s equals ECa/Ccr + TRCa/Ccr, i.e., the summed amounts of Ca excreted and reabsorbed per volume of filtrate [12,48]. Since flux of Ca into plasma determines and equals ECa, the ratio ECa/Ccr, calculated as [Ca]u[cr]p/[cr]u, quantifies the contribution of net influx from all sources to [Cauf]s [48]. TRCa/Ccr, the difference between [Cauf]s and ECa/Ccr, describes the simultaneous contribution of tubular Ca reabsorption. Ordinarily, influx provides 1–2% and reabsorption 98–99% of the flux maintaining normal [Cauf]s [12].

PTH regulates reabsorption of the 10% of filtered Ca that reaches the DCT by controlling expression of the apical calcium channel transient receptor potential vanilloid 5 (TRPV5), the intracellular transporter calbindin-D28K, and the basolateral extrusion proteins sodium-calcium exchanger 1 (NCX1) and plasma membrane calcium ATPase 1b (PMCA1b) [10,11,30]. In primary hyperparathyroidism (PHPT), elevated [PTH] causes hypercalcemia by increasing TRCa/Ccr [12,49]; in SHPT, comparable or higher [PTH] is associated with and presumably required to achieve normal TRCa/Ccr and normocalcemia [12]. This presumption is consistent with the observation that cinacalcet, a calcimimetic that suppresses synthesis and secretion of PTH, reduced tubular Ca reabsorption and caused hypocalcemia as it lowered [PTH] in CKD stages G3 and G4 [50].

The tradeoff-in-the-nephron hypothesis states that as GFR falls, [Ca++]DCT also falls in response to increased total [P]DCT; if [P]DCT reduces [Ca++]DCT sufficiently, [PTH] rises to preserve Ca reabsorption and maintain normocalcemia [8]. Whereas the hypothesis was previously supported by significant relationships of [PTH] to EP/Ccr, a surrogate for [P]DCT [12,13,24,25], the present study showed additionally that [Ca++]DCT is related to total [P]DCT in CKD and CTRL (Figs 3A and 4A). If precipitation of amorphous Ca3(PO4)2 is posited in states of supersaturation, the results imply that in CKD, [PTH] increases as [P]DCT rises and [Ca++]DCT falls. At FDCa 0.1 and pH 6.8 or 7.0, the upward trajectory of [PTH] is accentuated at a sufficiently reduced [Ca++]DCT (Figs 3E and 4E). A critical observation is that in combined CKD and CTRL, curvilinear relationships of [PTH] to [Ca++]DCT and to eGFR are essentially identical after log-transformation of variables and standardization of logarithmic values (Fig 5).

Estimation of total [Ca]DCT and [P]DCT

Our estimations of total [Ca]DCT and [P]DCT are based on published physiologic observations and measurements of [Cauf]s, eGFR, and 24-hour EP. Given that micropuncture studies of normal rodents showed fractional Ca delivery to the DCT of 10% [30], we calculated total [Ca]DCT as the rate of Ca delivery divided by the rate of filtrate delivery to the DCT, or (0.1)eGFR[Cauf]s/{FDf(eGFR)}, where FDf = fractional delivery of filtrate to that segment. This formula simplified to total [Ca]DCT = (0.1)[Cauf]p/FDf. We assumed FDf of 0.2 in CTRL and 0.35 in CKD [31-33]; since [Cauf]s was not different in CKD and CTRL, FDf was solely responsible for differences in total [Ca]DCT in the two groups. In CKD, higher FDf lowered total [Ca]DCT; this consequence could possibly have obscured an effect of higher FDCa on [Ca++]DCT, but when FDCa was increased to 0.15 or 0.2, [Ca++]DCT remained independent of total [Ca]DCT, and total [P]DCT continued to be the sole determinant of [Ca++]DCT (S6 and S7 Figs).

Diurnal variation in [P]s necessitated a different line of reasoning to estimate total [P]DCT [51]. Because EP approximates the rate at which phosphate is delivered to the DCT [29], we inferred, in accordance with classic micropuncture observations [9], that normal phosphate influx from the gut raises [P]DCT as GFR falls. We also recognized that a correlation between [PTH] and [P]DCT would explain why limiting intestinal phosphate influx has consistently prevented, mitigated, or reversed SHPT in animal and human studies [8,14-22].

Determinants of [Ca++]DCT

According to JESS calculations, the principal determinant of [Ca++]DCT depended on whether precipitation of Ca3(PO4)2 (am., s.) occurred in the DCT. When no precipitation, FDCa 0.1, and pH 6.8 were assumed (S2 Fig), total [Ca]DCT was found to be the major factor and total [P]DCT a minor factor determining [Ca++]DCT in CKD and CTRL. At pH 6.6, mean logSICa3(PO4)2 (am., s.) was substantially negative, the DCT was not saturated with this solid (with five exceptions in CTRL), and relationships of [Ca++]DCT to [Ca]DCT and [P]DCT resembled those predicted in the absence of precipitation at pH 6.8 (S2 and S3 Figs). When precipitation, FDCa 0.1, and pH 6.8 or 7.0 were assumed, supersaturation of the DCT with Ca3(PO4)2 (am., s.) was more prevalent, and [P]DCT emerged as the sole determinant of [Ca++]DCT (Figs 3 and 4). When precipitation and FDCa 0.15 or 0.20 were assumed, supersaturation with Ca3(PO4)2 (am., s.) was universal at pH 6.6, 6.8, and 7.0, and [Ca++]DCT was determined exclusively by [P]DCT (S6 and S7 Figs). We therefore conclude that the effect of [P]DCT on [Ca++]DCT is dominant when precipitation of Ca3(PO4)2 (am., s.) occurs and negligible when precipitation does not occur. By inference, tradeoff-in-the-nephron is not applicable when FDCa is ≤ 0.1 and pH is ≤ 6.6 simultaneously, but it is applicable under the more likely conditions that either pH is ≥ 6.7 (S1 Fig), or FDCa is ≥ 0.1 (S6 and S7 Figs), or both are true. In all scenarios, we presume that the solid phase of Ca3(PO4)2 (am., s.) may dissolve downstream in a more acidic milieu [52].

If precipitation of Ca3(PO4)2 (am., s.) was not assumed, [CaHPO40]DCT became the only plausible phosphate-containing determinant of [Ca++]DCT, but JESS calculations rendered this scenario unlikely; [Ca++]DCT was consistently predicted to be an order of magnitude higher than [CaHPO40]DCT, and [Ca++]DCT varied substantially with pH at a given [CaHPO40]DCT (S4 Fig). We conclude that CaHPO40 did not mediate the effect of [P]DCT on [Ca++]DCT.

We also investigated the effect of anions other than phosphate on [Ca++]DCT. Regressions of [Ca++]DCT on [Cacit–]DCT, [Caox0]DCT, [CaHCO3+]DCT, and [CaSO40]DCT were performed to ascertain whether these compounds had reduced [Ca++]DCT, but [Ca++]DCT and concentrations of each complex varied in the same direction (S5 Fig). These results support the inference that precipitation of amorphous Ca3(PO4)2 determined [Ca++]DCT, and [Ca++]DCT determined complex concentrations other than [CaHPO40]DCT. Low relative concentrations of these complexes preclude the possibility that [Ca++]DCT was suppressed by substances such as citrate or oxalate.

Regressions of [PTH] on total [P]DCT, [Ca++]DCT, and eGFR

[PTH] rose with total [P]DCT in CKD (Fig 1B). Although [Ca++]DCT was inversely related to [P]DCT in CKD and CTRL, reductions in [Ca++]DCT were apparently sufficient to raise [PTH] in CKD only. When precipitation of Ca3(PO4)2 (am., s.) was excluded from consideration or appeared not to have occurred, total [Ca]DCT was the primary determinant of [Ca++]DCT, and substantial elevations of [PTH] were predicted over a narrow range of [Ca++]DCT (S2 and S3 Figs). When precipitation of Ca3(PO4)2 (am., s.) occurred at pH 6.8 or 7.0, [P]DCT was the sole determinant of [Ca++]DCT; [PTH] increased to abnormal levels over a wider and more plausible range of [Ca++]DCT, and a continuous hyperbolic relationship between [PTH] and [Ca++]DCT emerged if CKD and CTRL were considered together (Figs 3 and 4). After log-log transformation of variables and standardization of logarithmic values, relationships of [PTH] to eGFR and to [Ca++]DCT were found to be virtually identical (Fig 5).

At pH values typical of the DCT [28], we infer that increased [P]DCT mediates a decline in [Ca++]DCT through precipitation of Ca3(PO4)2 (am., s.). If [Ca++]DCT is sufficiently reduced, [PTH] rises to maintain normal Ca++ reabsorption. The similarity of relationships of [PTH] to [Ca++]DCT and [PTH] to eGFR suggests that the first relationship causes the second (Figs 1F, 3E, 4E, and 5).

Strengths and limitations of the present study

In the present study, we employed laboratory data and evidence-based physiologic assumptions to estimate total [P]DCT and [Ca]DCT [29, 30], and we drew on published information to assign concentrations to other constituents of DCT filtrate [31-45]. JESS calculations using representative values of [P]DCT and [Ca]DCT predicted precipitation of Ca3(PO4)2 (am., s.) at pH ≥ 6.73 (S1 Fig); similarly, calculations based on measured values showed that at pH ≥ 6.8, [P]DCT determined [Ca++]DCT by inducing precipitation of Ca3(PO4)2 (am., s.). [PTH] rose in curvilinear fashion as eGFR and [Ca++]DCT fell (Figs 1F, 3E, and 4E); moreover, after log-transformation of variables and standardization of logarithmic values, lines relating [PTH] to eGFR and [PTH] to [Ca++]DCT had virtually identical slopes. A strength of our study is the coincidence of robust methodology with chemical evidence that in CKD, phosphate raises [PTH] by reducing [Ca++]DCT. The effect of [P]DCT on [Ca++]DCT is consistent at FDCa 0.1, 0.15, and 0.2, and it explains why cinacalcet reduced Ca reabsorption and caused hypocalcemia in CKD stages G3 and G4 [50].

Although our observations support the tradeoff-in-the-nephron hypothesis, it is reasonable to question why R2 values for some pertinent regressions are not higher. Several explanations present themselves. First, precipitation that reduces [Ca++]DCT occurs only when the DCT is supersaturated with Ca3(PO4)2 (am., s.). Since supersaturation was not universal in CKD at FDCa of 0.1 (Fig 2C and 2D), [P]DCT affected [Ca++]DCT differently in individual subjects. A related consideration is that uromodulin, a protein secreted by the thick ascending limb of Henle’s loop, prevents aggregation of calcium phosphate crystals and may therefore have interfered with precipitation of Ca3(PO4)2 in the DCT (am., s.) [53].

A second potential limitation is that loop diuretic therapy could have contributed to SHPT in CKD [54]. However, patients were instructed to abstain from food or medicines for at least eight hours before plasma was obtained to measure [PTH], and 24-hour ECa was reduced in proportion to eGFR in CKD (Table 1). We suspect that the contribution of loop diuresis to SHPT was minimal.

A third limitation is that we associated [PTH] at a single moment with calculations of [P]DCT and [Ca++]DCT from 24-hour data. Since [P]DCT varies through the day with consumption of food and changes in phosphate reabsorption [51], it is unlikely that our calculated concentrations were identical to those present in the fasting state when blood was sampled for PTH assays. Given that the half-life of PTH is a few minutes [55], we presume that [PTH] was more closely related to a contemporaneous than to an average [P]DCT.

Additional limitations arise from assumptions that FDf to the DCT was fixed at 0.2 in CTRL and 0.35 in CKD, and filtrate pH was uniformly 6.6, 6.8, or 7.0. Errors were also inherent in estimations of GFR and determinations of 24-hour ECa and EP. Single-nephron GFR varies in animal models of CKD [9], and it is unclear how this variability affected our data. Although equilibrium constants, especially solubility products of solid phases, are somewhat uncertain, we doubt that these uncertainties undermine our results.

Summary and conclusions

We describe an examination of the tradeoff-in-the-nephron hypothesis with the Joint Expert Speciation System. At pH values typical of the DCT, we present evidence that [P]DCT determines [Ca++]DCT by inducing precipitation of Ca3(PO4)2 (am., s.). Although this phenomenon occurs in both CKD and CTRL, [Ca++]DCT appears to fall sufficiently to raise [PTH] in CKD only. Whether they are defined by the equation y = kx + c or the simpler power function y = kx, relationships of [PTH] to [Ca++]DCT and [PTH] to eGFR are so similar that the former seems likely to cause the latter. Our observations strongly suggest that the tradeoff-in-the-nephron hypothesis explains SHPT in stages G3 and G4 CKD. They also suggest that humans with SHPT may be treated successfully by reducing phosphate influx in proportion to the reduction in GFR.

Plot of logSI(Ca3PO42) (am.,s.) vs. pH.

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Regressions assuming pH 6.8 and no precipitation of Ca3(PO4)2 (am., s.).

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Regressions assuming pH 6.6 and precipitation of Ca3(PO4)2 (am., s.).

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Relationship of [Ca++]DCT to [CaHPO40]DCT at pH 6.6, 6.8, and 7.0.

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Effect of Ca-anion complexes on [Ca++]DCT.

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Regressions at FDCa to DCT of 0.15 and pH of 6.6 (a-c), 6.8 (d-f), and 7.0 (g-i).

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Regressions at FDCa of 0.2 and pH of 6.6 (a-c), 6.8 (d-f), and 7.0 (g-i).

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Assumed anion excretion rates at normal and reduced GFR.

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Estiimated total concentrations in the DCT.

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Supplemental information.

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Raw data.

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