Homeostasis of β₂-microglobulin in diabetics and non-diabetics with modest cadmium intoxication

Study design

This investigation employed a case-control design. A purposive sampling technique was used to recruit type 2 diabetics and controls in equal numbers. Recruitments occurred during annual checkups at a local health center in Pakpoon Municipality, Nakhon Si Thammarat Province, Thailand. Diabetics and controls were matched for age, gender, and locality, and all subjects were at least 40 years old.

Exclusion criteria were non-resident status, current pregnancy and/or breastfeeding, and hospital records or a physician’s diagnosis of an advanced chronic disease, including heart disease, stroke, and cancer. Control subjects were in good general health and met all exclusion criteria. Sociodemographic data, educational attainment, occupation, health status, family history of diabetes, and smoking status were ascertained by structured interview questionnaires. After exclusion of outliers and subjects with missing data, 65 diabetics and 72 controls were included for analysis.

Diabetes was defined as fasting plasma glucose [Glc]_p levels ≥ 126 mg/dL or a physician’s diagnosis. Some patients with DM took metformin. Special diets were not employed in diabetics or controls. Reported use of dietary supplements was 3% among controls and 7% among diabetics^[28].

Technical considerations

Participants were asked to fast overnight, and collection of blood and urine samples was carried out at the Pakpoon health center on the morning of the following day. For the glucose assay, blood samples were collected in tubes containing fluoride that inhibited glycolysis. Blood samples for Cd analysis were collected in separate tubes containing ethylenediamine tetra-acetic acid (EDTA) as an anticoagulant. To prevent the degradation of β₂M in acidic conditions, an alkaline (NaOH) solution was added to adjust the pH of urine samples to > 6 before their storage. Blood and urine samples were kept on ice and transported within one hour to the laboratory of Walailak University, where samples of plasma and serum were prepared. Aliquots of urine, whole blood, serum, and plasma were stored at -80 °C for later analysis.

The plasma glucose assay was based on the oxidase-peroxidase method (Glu Colorimetric Assay Kit, Elabscience, Houston, TX, USA)^[29]. Assays of creatinine in urine and plasma were based on Jaffe’s alkaline picrate method, as described previously^[30]. The human beta-2 microglobulin/β₂M ELISA pair set (Sino Biological Inc., Wayne, PA, USA) was employed to determine serum and urine concentrations of β₂M ([β₂M]_s and [β₂M]_u), with a lower limit of detection of 3.13 pg/mL. We assumed that [β₂M]_s and the plasma concentration ([β₂M]_p) were equal.

Urinary and whole blood Cd concentrations ([Cd]_u, [Cd]_b) were determined with GBC System 5000 graphite furnace atomic absorption spectrometry (AAS) (GBC Scientific Equipment, Hampshire, IL, USA)^[31]. Standards with As, Be, Cd, Cr (VI), Hg, Ni, Pb, Se, and Tl were used to calibrate the instrument (Merck KGaA, Darmstadt, Germany). Reference urine metal levels 1, 2, and 3 (Lyphocheck, Bio-Rad, Hercules, CA, USA) were used for quality control, analytical accuracy, and precision assurance. When [Cd]_u and [Cd]_b were less than their detection limit of 0.1 µg/L, the concentration assigned was the detection limit value divided by the square root of 2^[32].

Normalization of cadmium and β₂m excretion rates

Excretion of substance x (E_x) was normalized to creatinine clearance (C_cr) with the formula E_x/C_cr = [x]_u[cr]_p/[cr]_u, where x = Cd or β₂M, [x]_u = urine concentration of x (mass/volume), [cr]_p = plasma creatinine concentration (mg/dL), and [cr]_u = urine creatinine concentration (mg/dL). E_x/C_cr expresses the amount of x excreted per volume of glomerular filtrate^[8]. Normalization to C_cr simultaneously corrects for urine dilution and functional nephron mass. E_x/C_cr is not affected by muscle mass.

Estimated glomerular filtration rate

Estimated GFR (eGFR) was ascertained with Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations published in 2009^[33]. CKD stages 1, 2, 3, 4, and 5 corresponded to eGFR of 90-119, 60-89, 30-59, 15-29, and < 15 mL/min/1.73 m², respectively.

Derivation of a conceptual framework for analysis of β₂M homeostasis

Assume that:

      (a) I_β2M = influx of β₂M into plasma from nucleated cells;

      (b) GSC_β2M = glomerular sieving coefficient of β₂M = 1 (i.e., all β₂M in filtered plasma enters filtrate)^[11,12];

      (c) F_β2M = rate of filtration (and subsequent renal disposition) of β₂M;

      (d) Plasma is in equilibrium with respect to β₂M (I_β2M = F_β2M).

It follows that:

      (1) I_β2M = F_β2M = GFR[β₂M]_p, where [β₂M]_p is the plasma concentration of the protein.

Dividing by GFR and rearranging,

      (2) [β₂M]_p = I_β2M/GFR = F_β2M/GFR.

Since filtered β₂M is either excreted or reabsorbed and degraded,

      (3) F_β2M = GFR[β₂M]_p = E_β2M + TD_β2M,

where = E_β2M and TD_β2M are rates of excretion and tubular degradation of β₂M, respectively. Dividing by GFR,

      (4) [β₂M]_p (mass/vol of plasma) = E_β2M/GFR + TD_β2M/GFR (both ratios in units of mass/vol of filtrate).

Substitution of creatinine clearance (C_cr) for GFR in equation 4 permits estimation of E_β2M/GFR and TD_β2M/GFR from measurements in simultaneous aliquots of serum and urine. Thus,

      E_β2M/C_cr = [β₂M]_uV_u/[cr]_uV_u/[cr]_p; after simplification,

      E_β2M/C_cr = [β₂M]_u[cr]_p/[cr]_u. It follows that

      (5) [β₂M]_p = E_β2M/C_cr + TD_β2M/C_cr = [β₂M]_u[cr]_p/[cr]_u + TD_β2M/C_cr, and

      (6) TD_β2M/C_cr = [β₂M]_p - E_β2M/C_cr = [β₂M]_p - [β₂M]_u[cr]_p/[cr]_u.

As functions of both I_β2M and GFR (equation 2), [β₂M]_p and TD_β2M/C_cr are quite variable, and a less confounded parameter of tubular β₂M handling is needed. FrTD_β2M, the fraction of filtered β₂M that is degraded by tubules, is calculated as follows:

      (7) FrTD_β2M = TD_β2M/F_β2M = TD_β2M/[β₂M]_pC_cr = (TD_β2M/C_cr)/[β₂M]_p.

In subjects with severe Cd intoxication, FrTD_β2M may be substantially reduced^[34].

The conventional parameter for assessing degradation of β₂M is [β₂M]_u/[cr]_u, which is a function of E_β2M. However, because TD_β2M/C_cr and [β₂M]_p are highly variable, relationships between FrTD_β2M and E_β2M or E_β2M/C_cr cannot be precise. Since filtered β₂M is either excreted or reabsorbed and degraded,

      F_β2M = E_β2M + TD_β2M, and

      (8) E_β2M = F_β2M - TD_β2M

      = F_β2M - (FrTD_β2M)(F_β2M)

      = (1 - FrTD_β2M)(F_β2M).

E_β2M is ultimately a function of both FrTD_β2M and F_β2M (I_β2M), and a single value of E_β2M is compatible with multiple combinations of these parameters. The argument does not change if equations (8) above are divided by C_cr. Since F_β2M/C_cr = [β₂M]_s (equation 2),

      (9) E_β2M/C_cr = [β₂M]_s - TD_β2M/C_cr

      = [β₂M]_s - (FrTD_β2M)[β₂M]_s

      = (1 - FrTD_β2M)[β₂M]_s.

E_β2M/C_cr is therefore a function of FrTD_β2M and [β₂M]_s, and a single value of E_β2M/C_cr is compatible with multiple combinations of FrTD_β2M and [β₂M]_s.

Calculations

E_Cd/C_cr, F_β2M, E_β2M/C_cr, TD_β2M/C_cr, and FrTD_β2M were calculated in accordance with equations 1-9. For calculation of F_β2M (equation 1), eGFR in mL/min/1.73m² was multiplied by 1.44 to yield eGFR in L/d. For calculation of TD_β2M/C_cr (equation 5), E_β2M/C_cr in g/L of filtrate was multiplied by 10^-3 to yield E_β2M/C_cr in mg/L of filtrate, the unit of TD_β2M/C_cr.

Statistical analyses

Data in Table 2 (characteristics of diabetics and controls) were analyzed with IBM SPSS Statistics 21 (IBM Inc., New York, NY, USA). Conformity of continuous variables to a normal distribution was assessed by the one-sample Kolmogorov-Smirnov test. Logarithmic transformation was applied to E_Cd/E_cr and E_Cd/C_cr, which showed right-skewed distributions. Estimated GFR values, which showed a left-skewed distribution, were analyzed without transformation. The Mann-Whitney U test was used to assess differences between DM and CTRL. Pearson’s chi-squared test was used to determine differences in percentages and prevalences of female gender, smoking, and eGFR < 60 mL/min/1.73 m². A multiple linear regression model was used to assess contributions of demographic parameters to variability of FrTD_β2M. Correlation matrices were generated from regression analyses of all homeostatic relationships examined in the present study. Correlations involving F_β2M, FrTD_β2M, and E_β2M/C_cr were organized by gender and presence or absence of diabetes. The resulting table is presented in the Supplementary Materials. Statistical significance was indicated by P-values ≤ 0.05.

We used Microsoft Excel to examine a simple linear regression (SLR) of eGFR on E_Cd/C_cr and SLRs of F_β2M, [β₂M]_p, FrTD_β2M, TD_β2M/C_cr, and E_β2M/C_cr on determinants suggested by equations 1-9. When SLRs revealed associations of a parameter with multiple potential determinants, we performed multilinear regressions (MLRs) to identify confounders and mutually independent relationships.

Participants

Characteristics of cases (DM) and controls (CTRL) are compared in Table 2. Values of E_Cd/E_cr and E_Cd/C_cr were generally lower than in our previous assessments of other populations^[7,35], and values of E_Cd/E_cr were substantially lower than in Japanese subjects from polluted and non-polluted areas who were studied in the 1990s^[34]. Mean age was slightly higher in CTRL, and body mass index (BMI) and fasting plasma glucose were higher in DM. Differences between groups in the following parameters were not statistically significant: [cr]_s, [cr]_u, eGFR, % eGFR < 60 mL/min/1.73m², [Cd]_u, [Cd]_b, and E_Cd/C_cr. [β₂M]_s, F_β2M, E_β2M/C_cr, and TD_β2M/C_cr were higher in DM, and FrTD_β2M was slightly higher in CTRL. All differences in homeostatic parameters were significant at P < 0.001.

Regression of eGFR on E_Cd/C_cr

Figure 1 depicts SLRs of eGFR on E_Cd/C_cr in DM and CTRL. The figure shows that eGFR was weakly and inversely related to E_Cd/C_cr in CTRL and unrelated to E_Cd/C_cr in DM. In both groups, the entire range of eGFR was evident at minimal values of E_Cd/C_cr. In six subjects with E_Cd/C_cr > 0.05 µg/L of filtrate, all values of eGFR were ≤ 80 mL/min/1.73m². In CTRL, the modest inverse relationship of eGFR to E_Cd/C_cr was created by points from relatively few subjects. We do not know why DM was not similarly affected.

Figure 1. Linear regressions of eGFR on E_Cd/C_cr. Scatter diagrams present data from diabetics (DM, blue) and non-diabetic controls (CTRL, orange). An inverse relationship is evident in CTRL. No relationship is evident in DM. Cd: Cadmium; cr: creatinine; eGFR: estimated glomerular filtration rate; E_Cd/C_cr: amount of Cd excreted per volume of glomerular filtrate; DM: group with diabetes mellitus; CTRL: control group without diabetes.

Regressions of F_β2M on its determinants

Equation 1 states in part that I_β2M equals F_β2M. The implied assumption is that in free-living subjects, plasma is in equilibrium with respect to β₂M, as it is for other substances^[36,37]. Stated differently, I_β2M, the rate at which β₂M enters plasma, equals F_β2M, the rate at which kidneys dispose of the protein. The remainder of equation 1 states that F_β2M (I_β2M) equals eGFR[β₂M]_s. If I_β2M varies during the day, we infer that [β₂M]_s varies promptly in response because eGFR is stable. Consequently, F_β2M approximates I_β2M from moment to moment and can therefore be employed as an ascertainable surrogate for I_β2M in linear regressions.

The graphs in Figure 2 show that in our study sample, F_β2M varied over its range, 100 to 2,000 mg/d, by a factor of 20. At the same time, except for a few low outliers, eGFR varied over its range, 55 to 110 mL/min/1.73m², by a factor of 2 [Figure 2C]. Because Cd inflicts injury on multiple cell types^[38], we speculated that I_β2M might correlate with E_Cd/C_cr, a crude measure of the body burden of Cd, but the SLR of F_β2M on E_Cd/C_cr was not significant in DM or CTRL [Figure 2A]. F_β2M, the product of eGFR and [β₂M]_s (equation 1), was closely related to [β₂M]_s in both groups, directly but marginally related to eGFR in CTRL, and unrelated to eGFR in DM [Figure 2B and C, Table 3]. In CTRL, an MLR showed that significant associations persisted between F_β2M and both [β₂M]_s and eGFR [Table 4]. Differences between groups in relationships of F_β2M to eGFR may have resulted from the greater range of and wider variation around the mean of F_β2M in DM. The key takeaway from Figure 2 is that [β₂M]_s, a by-product of I_β2M (equation 2), was the principal determinant of F_β2M in both groups.

Figure 2. Linear regressions of F_β2M on potential determinants. Scatter diagrams present data from diabetics (DM, blue) and non-diabetic controls (CTRL, orange). The graphs plot F_β2M against (A) E_Cd/C_cr, (B) [β₂M]_s, and (C) eGFR. No relationships are evident in (A). Strong direct relationships are evident in both groups in (B). In (C), a direct relationship is evident in CTRL, but no relationship is evident in DM. Cd: Cadmium; cr: creatinine; β₂M: β₂-microglobulin; F_β2M: rate of glomerular filtration of β₂M; DM: group with diabetes mellitus; CTRL: control group without diabetes; E_Cd/C_cr: amount of Cd excreted per volume of glomerular filtrate; [β₂M]_s: serum concentration of β₂M; eGFR: estimated glomerular filtration rate.

Regressions of [β₂M]_s on its determinants

If I_β2M = F_β2M = eGFR[β₂M]_p (equation 1), then [β₂M]_p = I_β2M/eGFR = F_β2M/eGFR (equation 2). In the present study, [β₂M]_s, like F_β2M, was not related to E_Cd/C_cr in DM and CTRL [Figure 3A]_, but it was closely and directly related to F_β2M in both groups [Figure 3B]. This observation is expected because an SLR of F_β2M on [β₂M]_s was highly significant [Figure 2B]. We include Figure 3B because F_β2M = I_β2M, and the high R² values indicate that I_β2M was the principal determinant of [β₂M]_s in our subjects. [β₂M]_s was inversely but marginally related to eGFR in DM and unrelated to eGFR in CTRL. In both groups, the disproportionate influence of I_β2M on [β₂M]_s probably resulted from the fact that F_β2M (I_β2M) varied over its range by a factor of approximately 20; in contrast, eGFR varied by a factor of 2, with a few outliers at the low end of the range [Figure 3B and C].

Figure 3. Linear regressions of [β₂M]_s on potential determinants. Scatter diagrams present data from diabetics (DM, blue) and non-diabetic controls (CTRL, orange). The graphs plot [β₂M]_s against (A) E_Cd/C_cr, (B) F_β2M, and (C) eGFR. No relationships are evident in (A). Strong direct relationships are evident in both groups in (B). In (C), a weak inverse relationship is evident in DM, and no relationship is evident in CTRL. Cd: Cadmium; cr: creatinine; β₂M: β₂-microglobulin; [β₂M]_s: serum concentration of β₂M; DM: group with diabetes mellitus; CTRL: control group without diabetes; E_Cd/C_cr: amount of Cd excreted per volume of glomerular filtrate; F_β2M: rate of glomerular filtration of β₂M; eGFR: estimated glomerular filtration rate.

Increased [β₂M]_s in diabetics may be of more than academic interest. In an analysis of data from the Third National Health and Nutrition Examination Survey (NHANES III), Cheung et al found in diabetics > 20 years old that [β₂M]_s was independently predictive of all-cause and diabetes-related mortality^[39]. Survival curves of subjects in the highest, intermediate, and lowest tertiles of [β₂M]_s showed markedly different life expectancies over almost 20 years. The authors argued that these differences might have resulted from pro-inflammatory and amyloidogenic properties of β₂M and from cytotoxicity of advanced glycation end products of the protein. In addition to mortality, the severity of diabetes-related morbidities has also been associated with increased [β₂M]_s^[40].

In the present study, one easily overlooked finding emerges from Figures 2 and 3. In CTRL, [β₂M]_s remained stable as F_β2M rose proportionately with eGFR [Figure 3C]. We therefore infer that high GFR increased and low GFR decreased I_β2M, and Figure 2C supports that inference. In DM, the slope of the line relating F_β2M to eGFR was positive, but the regression was not significant [Figure 2C]; [β₂M]_s fell as eGFR rose, and the SLR just missed statistical significance [Figure 3C].

Regressions of FrTD_β2M on its determinants

FrTD_β2M is the ratio of the rate of degradation to the rate of filtration of β₂M; thus, FrTD_β2M = TD_β2M/F_β2M. If the numerator and denominator of this ratio are divided by C_cr, FrTD_β2M = (TD_β2M/C_cr)/[β₂M]_s (equation 7).

In Figure 4, all graphs show that the range of FrTD_β2M was 0.991 to 1 in DM and 0.996 to 1 in CTRL. These observations are consistent with the slightly lower mean FrTD_β2M in DM [Table 2]. FrTD_β2M was inversely but weakly related to E_Cd/C_cr in both groups [Figure 4A]. R² values indicate that in DM and CTRL, variation in E_Cd/C_cr accounted for 11% and 5.8% of variation in FrTD_β2M; in both groups, high and low values of FrTD_β2M were found in subjects with negligible Cd excretion, and statistically significant associations were created by relatively few points. Figure 4A suggests that in a minority of both groups, Cd impaired proximal tubular degradation of β₂M. However, it is also true that the 13 lowest values of FrTD_β2M were seen in diabetics, and only four of them exhibited exceptional Cd excretion. We infer that an unidentified effect of diabetes compromised tubular processing of β₂M in some subjects.

Figure 4. Linear regressions of FrTD_β2M on potential determinants. Scatter diagrams present data from diabetics (DM, blue) and non-diabetic controls (CTRL, orange). The graphs plot FrTD_β2M against (A) E_Cd/C_cr, (B) F_β2M, (C) [β₂M]_s, (D) TD_β2M/C_cr, and (E) eGFR. Inverse relationships are evident in both groups in (A). In (B), a weak direct relationship is evident in DM, and no relationship is evident in CTRL. That pattern is repeated in (C) and (D). Direct relationships are evident in both groups in (E). Cd: Cadmium; cr: creatinine; β₂M: β₂-microglobulin; FrTD_β2M: fractional tubular degradation of filtered β₂M; DM: group with diabetes mellitus; CTRL: control group without diabetes; E_Cd/C_cr: amount of Cd excreted per volume of glomerular filtrate; F_β2M: rate of glomerular filtration of β₂M; [β₂M]_s: serum concentration of β₂M; TD_β2M/C_cr: amount of β₂M undergoing tubular degradation per volume of glomerular filtrate; eGFR: estimated glomerular filtration rate.

FrTD_β2M varied directly with F_β2M, [β₂M]_s, and TD_β2M/C_cr in DM but was not significantly related to these parameters in CTRL [Figure 4B-D]. The SLRs in CTRL make mathematical sense because the numerator and denominator of FrTD_β2M, TD_β2M/C_cr, and [β₂M]_s were virtually identical throughout their ranges, and F_β2M was primarily a function of [β₂M]_s. A small cluster of diabetics with simultaneous reductions of FrTD_β2M, TD_β2M/C_cr, and [β₂M]_s accounted for the inter-group differences in Figs 4B-D, but we have no explanation for the cluster. Again, we infer that an unidentified effect of diabetes compromised tubular processing of β₂M in some subjects.

FrTD_β2M varied directly and significantly with eGFR in DM and CTRL [Figure 4E]; in other words, FrTD_β2M was lowest at low eGFR and highest at high eGFR in both groups. In SLRs, high E_Cd/C_cr, low eGFR, and DM appeared to reduce FrTD_β2M [Figure 4]; the effects of Cd and DM were sporadic, and the effect of eGFR was somewhat more uniform [Figure 4A and E]. In DM, an MLR showed persistent associations of FrTD_β2M with E_Cd/C_cr, F_β2M, [β₂M]_s, and eGFR; in CTRL, an MLR showed continued association of FrTD_β2M with eGFR but not with E_Cd/C_cr [Table 4]. Thus, in CTRL, a relationship between eGFR and E_Cd/C_cr [Figure 1] explained the significant regression of FrTD_β2M on E_Cd/C_cr. In DM, E_Cd/C_cr persisted as an independent determinant of FrTD_β2M because Cd caused a miniscule but statistically significant reduction in FrTD_β2M in a few subjects [Figure 4A]. [β₂M]_s and its two determinants, I_β2M (F_β2M) and eGFR, retained independent effects on FrTD_β2M in DM [Table 4].

The relationships between FrTD_β2M and eGFR in the two groups were unexpected. Because TD_β2M/C_cr = [β₂M]_p - E_β2M /C_cr, and FrTD_β2M = ([β₂M]_p - E_β2M /C_cr)/[β₂M]_p, [β₂M]_p exerts almost identical influence on the numerator and denominator of the ratio. Since [β₂M]_p = I_β2M/GFR, the effect of GFR on FrTD_β2M is also equally distributed. We must therefore conclude that rising eGFR increased and falling eGFR reduced FrTD_β2M for reasons that were not revealed by the present analysis.

The relatively low values of R² for MLRs in Figure 4 suggest that in both DM and CTRL, most of the variation of FrTD_β2M was driven by unidentified factors [Table 4]. Although this variation was discernible, we reiterate that it occurred within tenths of a percentage point in our sample. A multiple regression model in which age, body mass index, smoking, and gender were included provided no additional insight into determinants of FrTD_β2M (data not shown).

Regressions of TD_β2M/C_cr on its determinants

TD_β2M/C_cr quantifies the amount of β₂M reabsorbed and degraded by proximal tubules per volume of filtrate. In theory, if a maximum capacity for β₂M reabsorption exists, TD_β2M/C_cr reaches a plateau at sufficiently increased F_β2M (I_β2M), and E_β2M/C_cr rises thereafter in parallel with F_β2M. If a tubular maximum does not exist, or if it exceeds all F_β2M, then TD_β2M/C_cr consistently rises in parallel with F_β2M.

Because Cd injures proximal tubular cells, we speculated that TD_β2M/C_cr might reach a plateau in sufficiently intoxicated subjects. However, Figure 5A demonstrates that TD_β2M/C_cr was unrelated to E_Cd/C_cr in DM and CTRL. In both groups, the highest and lowest values of TD_β2M/C_cr were seen at the lowest values of E_Cd/C_cr, and intermediate values of TD_β2M/C_cr were seen at the highest values of E_Cd/C_cr. TD_β2M/C_cr rose linearly with F_β2M and did not reach a plateau [Figure 5B]. TD_β2M/C_cr was virtually identical to [β₂M]_s at all values of [β₂M]_s [Figure 5C]; this finding resulted from the calculation of TD_β2M/C_cr as [β₂M]_s - E_β2M/C_cr (equation 5), and from the fact that E_β2M/C_cr was 0.01 to 0.001 of [β₂M]_s in all subjects.

Figure 5. Linear regressions of TD_β2M/C_cr on potential determinants. Scatter diagrams present data from diabetics (DM, blue) and non-diabetic controls (CTRL, orange). The graphs plot TD_β2M/C_cr against (A) E_Cd/C_cr, (B) F_β2M, (C) [β₂M]_s, (D) FrTD_β2M, and (E) eGFR. No relationships are evident in (A). Strong direct relationships are evident in both groups in (B) and (C). In (D), a direct relationship is evident in DM, and no relationship is evident in CTRL. In (E), a marginal inverse relationship is evident in DM, and no relationship is evident in CTRL. Cd: Cadmium; cr: creatinine; β₂M: β₂-microglobulin; TD_β2M/C_cr: amount of β₂M undergoing tubular degradation per volume of glomerular filtrate; DM: group with diabetes mellitus; CTRL: control group without diabetes; E_Cd/C_cr: amount of Cd excreted per volume of glomerular filtrate; F_β2M: rate of glomerular filtration of β₂M; [β₂M]_s: serum concentration of β₂M; FrTD_β2M: fractional tubular degradation of filtered β₂M; eGFR: estimated glomerular filtration rate.

TD_β2M/C_cr was weakly related to FrTD_β2M in DM and unrelated to FrTD_β2M in CTRL [Figure 5D]. The relationship in DM was created by points from eight subjects with atypically low FrTD_β2M and TD_β2M/C_cr at the low end of the observed range. The weakness of the relationship in DM and its absence in CTRL were due to the primacy of I_β2M in determining [β₂M]_s and TD_β2M/C_cr. TD_β2M/C_cr was weakly and inversely related to eGFR in DM and unrelated to eGFR in CTRL [Figure 5D]. We have no explanation for this difference.

In DM, SLRs showed that TD_β2M/C_cr was directly related to F_β2M, [β₂M]_s, and FrTD_β2M [Figure 5]; in an MLR, [β₂M]_s and FrTD_β2M persisted as independent determinants of TD_β2M/C_cr, and F_β2M did not [Table 4]. In CTRL, TD_β2M/C_cr was directly related to F_β2M and [β₂M]_s but not FrTD_β2M; an MLR showed persistence of both associations, but the p-value for the association of TD_β2M/C_cr with [β₂M]_s was much lower (i.e., the association was more significant). In both groups, [β₂M]_s, the sum of E_β2M/C_cr + TD_β2M/C_cr, was the predominant determinant of TD_β2M/C_cr because [β₂M]_s and TD_β2M/C_cr were virtually equal.

Regressions of E_β2M/C_cr on its determinants

Figure 6 depicts the relationships between E_β2M/C_crv - the amount of β₂M excreted per volume of filtrate - and relevant variables. While E_β2M was clearly related to E_Cd in more severely intoxicated subjects^[7,35], we found in the present study that E_B2M/C_cr was weakly and directly related to E_Cd/C_cr in DM and unrelated to E_Cd/C_cr in CTRL [Figure 6A]. E_β2M/C_cr was equally related to F_β2M and [β₂M]_s in CTRL (R² = 0.11 for both SLRs), but unrelated to those variables in DM [Figure 6B and C]. E_B2M/C_cr rose with TD_B2M/C_cr in CTRL and was unrelated to TD_B2M/C_cr in DM [Figure 6E].

Figure 6. Linear regressions of E_β2M/C_cr on potential determinants. Scatter diagrams present data from diabetics (DM, blue) and non-diabetic controls (CTRL, orange). The graphs plot E_β2M/C_cr against (A) E_Cd/C_cr, (B) F_β2M, (C) [β₂M]_s, (D) eGFR, (E) TD_β2M/C_cr, and (F) FrTD_β2M. In (A), a positive relationship is evident in DM, and no relationship is evident in CTRL. In (B) and (C), positive relationships are evident in CTRL, and no relationships are evident in DM. Inverse relationships are evident in both groups in (D). In (E), a positive relationship is evident in CTRL, and no relationship is evident in DM. In (F), strong inverse relationships are evident in both groups. Cd: Cadmium; cr: creatinine; β₂M: β₂-microglobulin; E_β2M/C_cr: amount of β₂M excreted per volume of glomerular filtrate; DM: group with diabetes mellitus; CTRL: control group without diabetes; E_Cd/C_cr: amount of Cd excreted per volume of glomerular filtrate; F_β2M: rate of glomerular filtration of β₂M; [β₂M]_s: serum concentration of β₂M; eGFR: estimated glomerular filtration rate; TD_β2M/C_cr: amount of β₂M undergoing tubular degradation per volume of glomerular filtrate; FrTD_β2M: fractional tubular degradation of filtered β₂M.

At a constant FrTD_β2M, we expect both E_B2M/C_cr and TD_B2M/C_cr to rise as F_β2M rises, as occurred in CTRL. Under this hypothetical condition, E_B2M/C_cr should correlate with F_β2M, the mathematical determinants of F_β2M ([β₂M]_s and eGFR), and TD_B2M/C_cr. SLRs demonstrated those relationships in CTRL but not DM. In an MLR, the relationship between E_B2M/C_cr and TD_B2M/C_cr persisted in CTRL, while the associations with F_β2M and [β₂M]_s were no longer observed [Table 4].

E_B2M/C_cr was inversely related to eGFR in DM (R² = 0.32) and CTRL (R² = 0.10), and the slope of the line relating the two variables was steeper in DM [Figure 6D]. Similarly, in DM and CTRL, E_β2M/C_cr was strongly and inversely related to FrTD_β2M, which accounted respectively for 68% and 59% of variation in E_β2M/C_cr [Figure 6F]. These observations can be understood from equation 9, which states that E_β2M/C_cr = (1 - FrTD_β2M)[β₂M]_s. E_β2M/C_cr falls as FrTD_β2M rises if [β₂M]_s remains constant; similarly, since [β₂M]_s = I_β2M/GFR (equation 2), E_β2M/C_cr varies inversely with GFR if FrTD_β2M and I_β2M remain constant.

In DM, approximately 15% of subjects had FrTD_β2M ≤ 0.996; in all but one of these subjects, E_β2M/C_cr was ≥ 30 µ/L of filtrate. The remainder of DM showed FrTD_β2M ≥ 0.996; in this subset, no subject had E_β2M/C_cr > 30 µg/L of filtrate. From our data, it appears that E_β2M/C_cr > 30 µg/L coincided with FrTD_β2M < 0.996, but E_β2M/C_cr was nevertheless quite variable at a given FrTD_β2M; for example, at FrTD_β2M of 0.998, E_β2M/C_cr varied between 1 and 20 µg/L of filtrate [Figure 6F]. Equation 9 indicates that this observation resulted from the variability of [β₂M]_s.

MLRs revised some relationships suggested by SLRs [Table 4]. In DM, the regression of E_β2M/C_cr on E_Cd/C_cr disappeared, while the regression of E_β2M/C_cr on eGFR persisted; variation in FrTD_β2M and eGFR then accounted for 73% of the variation in E_β2M/C_cr. In CTRL, regressions of E_β2M/C_cr on F_β2M and [β₂M]_s disappeared, while the regression of E_β2M/C_cr on TD_β2M/C_cr persisted; variation in FrTD_β2M, TD_β2M/C_cr, and eGFR then accounted for 85% of the variation in E_β2M/C_cr. Thus, in MLRs, E_β2M/C_cr was not related to E_Cd/C_cr in either group, but it was inversely related to eGFR and especially to FrTD_β2M in both groups, as equation 9 predicts.

Comparison of regressions in DM and CTRL

Table 5 shows that several physiologically important regressions were unaffected by diabetes. SLRs that were significant in both groups included F_β2M on [β₂M]_s (and vice versa), FrTD_β2M on E_Cd/C_cr, FrTD_β2M on eGFR, TD_β2M/C_cr on F_β2M, TD_β2M/C_cr on [β₂M]_s, E_β2M/C_cr on eGFR (inverse), and E_β2M/C_cr on FrTD_β2M (inverse). In CTRL, E_Cd/C_cr disappeared as a determinant of FrTD_β2M in an MLR, presumably because of a linkage between eGFR and E_Cd/C_cr [Figure 1], but all other associations common to the two groups persisted in MLRs [Table 4].

Several notable SLRs were significant in neither group. They included regressions of [β₂M]_s and TD_β2M/C_cr on E_Cd/C_cr and eGFR, and the regression of F_β2M on E_Cd/C_cr. SLRs of FrTD_β2M on F_β2M and [β₂M]_s, TD_β2M/C_cr on FrTD_β2M, and E_β2M/C_cr on E_Cd/C_cr were significant in DM but not CTRL. SLRs of eGFR on E_Cd/C_cr, F_β2M on eGFR, and E_β2M/C_cr on F_β2M, [β₂M]_s, and TD_β2M/C_cr were significant in CTRL but not DM. These differences probably resulted from wider ranges and greater variability of I_β2M and FrTD_β2M in DM.

Diabetes appears to have depressed FrTD_β2M in a significant minority of subjects [Figure 4A-E]. The 13 lowest values of FrTD_β2M were seen in DM, and they were not uniformly attributable to high E_Cd/C_cr or low eGFR. E_β2M/C_cr rose accordingly in the same subjects [Figure 6F]; a tentative inference from these data is that in some patients, diabetes imposed a small but easily demonstrable limitation on tubular degradation of β₂M. In an individual diabetic with moderate Cd exposure, reduced reabsorption of β₂M may not be due to Cd toxicity or nephron loss.

Arguments as to whether diabetes enhances the nephrotoxicity of Cd, or vice versa, may be moot. Because GSC_β2M approaches 1^[11,12], increased E_β2M at a given F_β2M is necessarily a consequence of proximal tubular dysfunction. Glomerular disease does not increase E_β2M. However, diabetes, which indisputably affects glomeruli, may also impair tubular handling of β₂M, and may do so in advance of any increase in albuminuria^[22,41]. In non-diabetic subjects, glycosuria promoted β₂M excretion acutely, and in diabetics, improvement of glycemic control (and therefore of glycosuria) gradually reduced E_β2M^[23].

Cd toxicity almost certainly causes albuminuria by interfering with the function of megalin, the brush border protein that mediates proximal tubular reabsorption of β₂M^[14]. A large body of research suggests that GSC_alb is high enough, in the range of 10^-2, to permit daily filtration of many grams of albumin. All but a few grams are retrieved by the process of fluid phase endocytosis, which is separate from megalin-mediated endocytosis, and returned to the circulation by transcytosis^[42-45]. If a large amount of albumin is normally filtered each day, it seems unlikely that microalbuminuria in DM is due to increased permeability of the glomerular barrier^[27]. A more logical inference is that β₂-microglobulinuria and albuminuria are tubular phenomena in both Cd nephropathy and early diabetic nephropathy. In the present study, the 13 lowest values of FrTD_β2M were seen in DM, and most of the affected subjects exhibited minimal Cd excretion [Figure 4].

Comparison of regressions in women and men

Supplementary Table 1 presents correlations of F_β2M, FrTD_β2M, and E_β2M/C_cr with possible determinants in diabetic and control women and men. F_β2M correlated more closely with eGFR in diabetic and control women than in their male counterparts. FrTD_β2M was less closely associated with E_Cd/C_cr and eGFR in control men than in diabetic women and men and control women. E_β2M/C_cr correlated less strongly with eGFR in control men than in diabetic women and men and control women. E_β2M/C_cr correlated with F_β2M and TD_β2M/C_cr in control men only. We have no explanation for these gender-related differences.

Strengths and weaknesses

In the present study, we analyzed β₂M homeostasis in diabetics and non-diabetics with modest Cd intoxication. To perform the analysis, we employed equations developed from the premise that plasma is normally in equilibrium with respect to β₂M. In other words, we assumed that the entry of β₂M into plasma is balanced by renal disposition of the protein through tubular degradation and urinary excretion. Equations that followed from this assumption provided guidance in the selection of regressions for examination, and the significant associations that we document confirmed the validity of the framework. To the best of our knowledge, our method for estimating I_β2M has not been previously employed. We are providing new information concerning the effects of diabetes on β₂M homeostasis, the apparent effect of eGFR on I_β2M in CTRL, the superiority of FrTD_β2M as an indicator of β₂M degradation, the clear effect of GFR on FrTD_β2M, the strong inverse relationships of E_β2M/C_cr to eGFR and FrTD_β2M, and the inevitable inadequacy of excretion-based parameters for precise quantification of tubular β₂M handling.

Attributes of the study sample limit the general applicability of our data. Most subjects were not seriously intoxicated with Cd, and documentation of FrTD_β2M > 99% in all participants suggests that tubular effects of Cd and GFR were modest. In contrast, a mean FrTD_β2M of 82.7% was documented in severely intoxicated women in Japan^[34]. Although conclusions drawn from the present study may not be applicable to more seriously afflicted individuals, our methods are suitable for the investigation of such subjects.