Supporting Online Information for
Calcium oxalate monohydrate aggregation induced by aggregation of desialylated Tamm-Horsfall protein
P. Viswanathan, J.D. Rimer, A.M. Kolbach, M.D. Ward, J.G. Kleinman and J.A. Wesson
* To whom correspondence should be addressed. Email: or
SOI A: THP Western blot and PAGE analyses
SOI B: Equilibrium binding model
SOI C: Equilibrium binding model equations
Reference List
Figs. S1 to S8
Table S1
SOI A: THP Western blot and PAGE analyses
Figure S1. A quantitative Western blot for THP (inset) was probed with anti-THP and a chemiluminescent image was acquired. Purified THP (25-100 ng) produced a linear standard curve (y = 7.8x – 27.4; R2 = 0.99) over this range. The urinary macromolecules (UMs) were loaded at the varied total protein concentrations (25-400 ng).
Figure S2. PAGE mobility shifts of ds-THP-S vs. n-THP. Purified THP samples (20 ng) were stained with SYPRO Ruby overnight and were visualized using UV-Transillumination with a 600-nm emission filter. The estimated molecular weights for ds-THP and n-THP were 79.6 kDa and 80.5 kDa, respectively.
SOI B: Equilibrium binding model
The possible role of aggregate surface coverage of COM was explored using an “aggregate binding model” that assumes ds-THP aggregates with a 1-µm diameter (consistent with the particle sizing measurements) and an adjustable equilibrium binding constant for the ds-THP aggregate on the COM surface, while accounting for total protein and COM masses. The model (represented schematically in Figure S3) assumes (i) spherical shapes for protein molecules, protein aggregates and COM particles, (ii) monodisperse aggregate size, (iii) protein adsorbates that retain their size and shape measured in bulk solution when adsorbed on the crystal surface, (iv) an area occupied by an adsorbed aggregate that equals its cross-sectional area, as determined from its diameter, and (v) surface coverage described only in terms of the amount of surface covered, independent of any specific aggregate packing arrangement on the surface.
Figure S3. Schematic diagram illustrating two possible ds-THP adsorbates: individual proteins (Dprotein ~ 6 nm) and aggregates (Daggregate ~ 103 nm) of proteins (not drawn to scale). The inset contains a scanning electron micrograph of COM seeds used in these studies, which have a weight average particle diameter of 10 µm. While the weight average diameter corresponds roughly to the particle size corresponding to the largest mass fraction of COM crystal in the distribution of particle sizes, smaller particles, like the COM aggregates shown in the inset, are far more numerous.
Binding of ds-THP aggregates to the COM crystal surface can be described by equations (1) and (2) in the manuscript, which are rewritten here,
(1)
(2)
where K (units of liter/m2) is the equilibrium constant and [ds-THP]A,o and [COM]A,o denote the total concentration of ds-THP aggregates and COM, respectively. The COM concentration, [COM]A, is expressed in terms of the seed surface area per solution volume (m2/L), whereas [ds-THP]A represents the total cross-sectional area per solution volume (m2/liter) of either an individual protein molecule or a spherical 1-µm diameter protein aggregate (Table S1). The protein concentration defined in this manner describes the total surface area that can be covered by all the available protein molecules in molecularly dispersed form or by the 1 m-sized protein aggregates. This enables the volumetric protein concentration to be described in terms of area surface coverage so that the equilibrium model is dimensionally correct. The term x, which represents the concentration of adsorbed protein (either as individual molecules or aggregates) in m2/liter, corresponds to the fractional coverage of COM by ds-THP ( = x/[COM]A,o). The value of is governed by the magnitude of the equilibrium constant, K, an adjustable parameter used to simulate the dependence of fractional coverage on MR, using values of MR explored in the experimental measurements described above. In this manner, any correspondence between the features of the RD vs. MR obtained experimentally and vs. MR obtained through modeling would support a causal relationship between COM aggregation promotion, protein aggregate formation, and aggregate binding at the crystal surfaces.
Table S1. Protein binding model parameters.
Parameters / COMSeed / ds-THPMolecule / ds-THPAggregateMolecular weight, Mw (kDa) / 73.91
Density, (g/cm3) / 2.2 / 1.0 / 0.642
Diameter, D (nm) / 1.0 x 104 / 6.23 / 1.0 x 103
Surface area, (nm2/particle)4 / 3.1 x 108 / 29.8 / 7.9 x 105
1Based on 13 % mass loss from desialylation of native THP; 2Density of randomly packed ds-THP spheres; 3Approximated as D = 2(3Mw/(4NA))1/3; 4Calculated based on spherical geometries for COM seeds, ds-THP molecules and aggregates.
B1: Limiting Condition of Infinite Equilibrium Constant
The aggregate binding model can be considered initially assuming K = ∞, tantamount to all protein in solution adsorbing on the COM surface, and at two limiting extremes – binding of individual proteins, assumed to 6.2 nm spheres, and binding of 1-µm protein aggregates to COM surfaces. Based solely on surface area considerations, = 3 at the lowest experimental MR value for individual ds-THP molecules, approaching = 500 at the higher MR values, corresponding to 3 and 500 layers of protein spheres on the COM surface. This argues that, under the experimental conditions used, molecularly dispersed ds-THP is more than sufficient to cover fully the surface area of COM seeds. Aggregation substantially lowers the concentration of free protein in solution, as a 1-µm aggregate of randomly packed ds-THP molecules contains approximately 106 individual protein molecules. Under these conditions, adsorption would be dominated by the 1-µm aggregates observed experimentally. At the lower experimental MR values the amount of 1-µm ds-THP aggregates is insufficient to cover all available COM surface area ( < 1). The fractional coverage of the aggregates – which increase in number but not size with increasing ds-THP concentration – would increase proportionally with increasing MR values, reaching full coverage (i.e. = 1.0) at MR = 0.12 (Figure S4). This value actually corresponds to the MR value at which COM aggregation promotion declines to negligible amounts for fixed COM, suggesting that aggregation promotion is favored for a partial coverage of ds-THP aggregates; however, full coverage is reached at an MR value well below the point where COM aggregation is negligible (i.e. RD > 1.1) for the case of fixed ds-THP, suggesting the condition of K = ∞ cannot simultaneously account for the experimental behavior observed at both fixed COM and fixed ds-THP.
Figure S4. Fractional coverage of ds-THP aggregates on COM seed surfaces. Left axis: Bulk aggregation data are plotted as a function of ds-THP/COM mass ratios for constant compositions of COM (300 µg, circles, solid lines) and ds-THP (21 µg, triangles, dashed lines). Particles of COM (~10 µm aggregates of individual crystals) were suspended in 5 mL solutions and changes in aggregation state were measured by particle sizing. Normalized COM particle diameters, RD, are shown with error bars (two standard deviations) and interpolated lines drawn through data points. Right axis: Fractional surface coverage of ds-THP assuming adsorption of ds-THP aggregates to COM particle surfaces with equilibrium constant K = ∞. Calculations are identical for fixed COM and fixed ds-THP. Note that the fractional coverage increases linearly with increasing MR, wherein > 1 at MR > 0.12. Assuming that only a single monolayer of protein adsorbs on the COM surface, the fractional coverage cannot exceed 1.0 (i.e.1), and thus we plot = 1 at MR > 0.12.
The correlation between and RD suggests that aggregation promotion is favored at partial coverage (low , low MR), at which an optimal number of ds-THP aggregates can bridge two opposing crystal surfaces directly, forming crystal-aggregate-crystal contacts through binding of carboxylate groups on the external surfaces of the ds-THP aggregates to calcium sites on the COM surfaces. Higher aggregate coverage attained at larger MR values (i.e. increasing ) would create a condition wherein direct bridging is obstructed by aggregate-aggregate interactions (see Figure S5). The negative charge on the aggregate surfaces could produce repulsive interactions, which in addition to blocking of binding sites, would frustrate COM aggregation at high coverage. Aggregation promotion would cease (identified experimentally when RD equals that of the control at RD = 1.1) at *, which corresponds to a coverage at which the repulsive aggregate-aggregate interactions between opposing crystal surfaces dominate the attractive crystal-aggregate-crystal bridges. This overall behavior contrasts with that for n-THP, which does not form aggregates and covers the COM surfaces at very low concentrations, to the extent that aggregation promotion is prohibited and a small amount of disaggregation is observed across the entire range of MR values.
B2: Condition of Finite Equilibrium Constant
Thermodynamic data for the equilibrium binding constant of THP with COM surfaces is not available in the literature; thus, K was used a fitting parameter in the model. The condition of K = ∞ described above is an illustrative extreme, as in reality aggregate binding would be governed by a finite value of K. The fractional coverage depends on both K and MR, and must be determined numerically using Eqs. (S1) and (S2). A constant, , is used to convert concentration from units of moles to surface area (eq. S3), where D and are the diameter and mass density, respectively, for COM seeds and ds-THP. The values for ds-THP aggregates and molecularly-dispersed ds-THP are 8.6 and 892, respectively.
Fixed COM
(S1)
Fixed ds-THP
(S2)
(S3)
Assuming an idealized ordered arrangement of protein units (protein molecules or aggregates) on the COM surface, the maximum number of crystal-protein-crystal contacts (attractive interactions) would occur at = 0.5, as depicted in Figure S5 (A and B). If the arrangement of adsorbed protein spheres was random, the formation of crystal-protein-crystal contacts would be partially obstructed by repulsive protein-protein interactions at = 0.5 (Figure S5C). This effect would be true at any coverage, but would lead to maximal attractive interactions at < 0.5. Moreover, the number of crystal-protein-crystal bridges will be further reduced if > 0.5 for both ordered and random arrangements of adsorbed proteins. Therefore, K was adjusted such that < 0.5 over the MR range where RD > 1.1 for the experimental data regardless of whether ds-THP or COM was fixed.
Figure S5. Illustrations of the interaction between two opposing COM crystals with adsorbed ds-THP aggregates. (A and B) COM crystals with adsorbed ds-THP aggregates ( = 0.5) uniformly arranged on the surface provides the maximum number of crystal-aggregate-crystal bridges without any repulsive aggregate-aggregate interactions. (C) A more realistic situation is random ds-THP aggregate adsorption ( = 0.5) on COM, which increases the number of unfavorable interactions between protein aggregates (red crosses) on opposing crystal surfaces. The MR value where a maximum in COM aggregation promotion is observed experimentally corresponds to = 0.2 for ds-THP aggregates (D), which likely corresponds to the most favorable number of attractive crystal-aggregate-crystal interactions that bridge two opposing crystal surfaces relative to repulsive aggregate-aggregate interactions that frustrate COM aggregation.
In the case of molecularly dispersed protein, no value of K could be found that satisfied this condition. This is exemplified in Figure S6A for K = 1.0 L/m2, where the equilibrium binding model reveals that = 0.5 over nearly the entire range of MR where RD > 1.1 for fixed ds-THP, while the fractional coverage climbs above = 0.5 at MR values where RD > 1.1 for fixed COM. Values of K > 1 L/m2 increases the fractional coverage across the entire MR range for both curves, which further contradicts the aforementioned idealized behavior. In the case of the protein aggregate, it is possible to adjust K to values that satisfy the idealized model, that is, < 0.5 can be generated for MR values at which RD > 1.1 for both fixed ds-THP and fixed COM (Figure S6B).
Figure S6. Equilibrium binding model analyses of protein adsorption on COM surfaces for (A) molecularly-dispersed ds-THP and (B) ds-THP aggregates. Data are plotted as a function of ds-THP/COM mass ratio, MR, for fixed COM (300 µg, circles, solid lines) and fixed ds-THP (21 µg, triangles, dashed lines). Left axes: normalized COM particle diameters, RD, with error bars (two standard deviations) and interpolated lines drawn through data points. Measurements were obtained by particle sizing using COM seeds (~10 µm aggregates of individual crystals) suspended in 5 mL ds-THP solutions at various MR values. Right axes: fractional surface coverage, , of (A) molecularly-dispersed ds-THP molecules and (B) ds-THP aggregates on the COM surface. The equilibrium binding constant K was adjusted to achieve < 0.5 at MR values where RD > 1.1
Plots of against MR for both ds-THP fixed and COM fixed experiments for K = 113 L/m2 illustrate that approaches a plateau near 0.5 for the fixed ds-THP experiments, as MR is increased over the range of MR values, while increases toward 1 for the model of COM fixed experiments. These profiles correspond to the intuitive model predictions, where the fixed COM experiments demonstrate a rapid decline in RD as rises toward saturation, while in the fixed ds-THP experiments show a much more gradual decline in RD as reaches an apparent plateau at approximately half coverage. The model with K = 113 L/m2 predicts a maximum in COM aggregation promotion at 10-20 % coverage of ds-THP aggregates on the COM surface, and further increases in frustrate COM aggregation. Changes in K shift the curves to higher or lower fractional coverage, for example, reducing K below 113 L/m2 decreases for both sets of experimental conditions, and furthers the separation between model curves.
The decline in RD in fixed ds-THP data set, which is characterized by a long tail rather than a steep descent to RD = 1.1, can be readily explained in the context of our model. Two factors contribute to the apparent broadening of the aggregation-promoting region at fixed ds-THP concentration. First, in fixed ds-THP experiments, MR is increased by decreasing the quantity of COM added to the system, thus the total mass decreases with increasing MR. In contrast, when COM is fixed and ds-THP is varied, MR is increased by increasing the quantity of ds-THP, thus the total mass increases with increasing MR. At the MR values beyond the maximum in Figure S6 the total mass of COM and ds-THP is less for measurements performed at fixed THP than at fixed COM. At infinite K, the fractional surface coverage of COM, , would be the same regardless of the concentration of COM and ds-THP (which can be regarded as “reactants”). This would yield equivalent RD values at equivalent MR regardless of the reactant concentrations. In the case of fixed ds-THP, at any finite value of K, for a given MR value will be smaller than at fixed COM because of the smaller reactant concentration (i.e. the dashed curve vs. the solid curve in Figure S6B), thus reducing the aggregate coverage of the COM surface to values that enable crystal-aggregate-crystal bridges and larger values of RD. Consequently, when ds-THP is fixed such that the overall reactant concentration is small RD will exhibit a slower decline from its maximum than when COM is fixed, leading to the apparent broadening. Second, protein aggregation is phase separation phenomenon, such that at protein concentrations below a critical threshold, ds-THP in solution remains molecularly dispersed. At ds-THP concentrations above this threshold, the amount of molecularly dispersed ds-THP will be equal to the critical concentration, while any remaining protein will be phase separated (aggregates). Consequently, at large MR, the fraction of ds-THP in the aggregated state will increase as the total ds-THP concentration increases in the fixed COM series, leading to increased fractional surface coverage on COM and rapidly decreasing RD, compared with the measurements at fixed ds-THP, wherein the aggregate concentration is unchanging.
The slight shift of the maximum RD to lower MR values at fixed ds-THP, compared with fixed COM, can be explained by similar reasoning, albeit the effect of total mass is reversed. At the low MR values (to the left of the maximum), the total reactant concentration is larger for fixed ds-THP experiments because small MR values correspond to large amounts of added COM. Consequently, at fixed ds-THP a low MR will produce a larger fractional surface coverage of COM compared with the fixed COM condition as well as a larger amount of aggregated ds-THP. Both factors will favor maximal COM aggregation promotion at lower MR, due to higher aggregate coverage, than observed at the same MR values when COM is fixed.
The total concentration of crystal and protein, [ds-THP]A,o + [COM]A,o, for fixed ds-THP and fixed COM were calculated using the total surface area of spherical COM seeds and the cross-sectional areas of spherical ds-THP (either molecularly-dispersed or aggregate ds-THP). The surface area of molecularly-dispersed ds-THP is two orders of magnitude higher than that of ds-THP aggregates (Figure S7). Moreover, the total concentration for molecularly-dispersed ds-THP is constant over the entire range of MR values, which results in constant (Figure S6A) at MR values where experimental RD exhibits significant changes.
Figure S7. Total area concentration, [COM]A,o + [ds-THP]A,o, for molecularly-dispersed and aggregate ds-THP as a function of experimental MR values at fixed ds-THP. Concentrations are obtained from the total surface area of spherical COM seeds and the projected cross-sectional area of spherical ds-THP molecules and aggregates. The formation of ds-THP aggregates reduces the total available surface area of protein by two orders of magnitude. The y-axis is plotted in log scale to compare concentrations of molecularly-dispersed ds-THP and ds-THP aggregate data. The total concentration is nearly constant over the entire MR range for molecularly-dispersed ds-THP, whereas there is a more gradual decrease in total concentration for ds-THP aggregates over the same MR range.
Experimental measurements at fixed COM and fixed ds-THP vary the mass of ds-THP and COM mass, respectively, to achieve a given MR value (Figure S8). At fixed COM, the mass of ds-THP increases linearly with increasing MR, while at fixed ds-THP there is a nonlinear, inverse relationship between COM mass and MR (Figure S8), wherein the total mass is larger at low MR values and decreases significantly with increasing MR.