Polyomavirus BK Replication Dynamics In Vivo and In Silico to Predict Cytopathology and Viral Clearance in Kidney Transplants

Authors

  • G. A. Funk,

    1. Transplantation Virology, Institute for Medical Microbiology, Department of Biomedicine, University of Basel, Basel, Switzerland
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  • R. Gosert,

    1. Transplantation Virology, Institute for Medical Microbiology, Department of Biomedicine, University of Basel, Basel, Switzerland
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  • P. Comoli,

    1. Pediatric Hematology/Oncology, Fondazione IRCCS Policlinico San Matteo, University of Pavia, Pavia, Italy
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  • F. Ginevri,

    1. Pediatric Nephrology Unit, G. Gaslini, Genova, Italy
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  • H. H. Hirsch

    Corresponding author
    1. Transplantation Virology, Institute for Medical Microbiology, Department of Biomedicine, University of Basel, Basel, Switzerland
    2. Infectious Diseases & Hospital Epidemiology, University Hospital Basel, Basel, Switzerland
      * Corresponding author: Hans H. Hirsch, hans.hirsch@unibas.ch
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* Corresponding author: Hans H. Hirsch, hans.hirsch@unibas.ch

Abstract

Fast BK virus (BKV) replication in renal tubular epithelial cells drives polyomavirus-BK-associated nephropathy (PVAN) to premature kidney transplant (KT) failure. BKV also replicates in urothelial cells, but remains asymptomatic in two-thirds of affected KT patients. Comparing 518 day-matched plasma-urine samples from 223 KT patients, BKV loads were ∼3000-fold higher in urine than in plasma (p < 0.000001). Molecular and quantitative parameters indicated that >95% of urine BKV loads resulted from urothelial replication and <5% from tubular epithelial replication. Fast BKV replication dynamics in plasma and urine with half-lives of <12 h accounted for daily urothelial and tubular epithelial cell loss of 4×107 and 6×107, respectively. BKV dynamics in both sites were only partly linked, with full and partial discordance in 36% and 32%, respectively. Viral expansion was best explained by models where BKV replication started in the kidney followed by urothelial amplification and tubular epithelial cell cross-feeding reaching a dynamic equilibrium after ∼10 weeks. Curtailing intrarenal replication by 50% was ineffective and >80% was required for clearing viremia within 7 weeks, but viruria persisted for >14 weeks. Reductions >90% cleared viremia and viruria by 3 and 10 weeks, respectively. The model was clinically validated in prospectively monitored KT patients supporting >80% curtailing for optimal interventions.

Introduction

Polyomavirus-BK-associated nephropathy (PVAN) has emerged as a leading viral cause of early kidney transplant (KT) failure with prevalence rates of 1–10% (1–3). PVAN is mainly caused by high-level replication of the human polyomavirus type 1, also called BK virus (BKV), in renal tubular epithelial cells (4–7). BKV is closely related to JC virus that causes progressive multifocal leukoencephalopathy (8) and only exceptionally PVAN (9,10). Histologically, PVAN is characterized by viral cytopathic changes of renal tubular epithelial cells, with enlarged nuclei, cell rounding, detachment and denudation of basal membranes (11). Increasing inflammatory cell infiltrates and eventually tubular atrophy and fibrosis characterize progression from PVAN pattern A to pattern B and C, with graft loss increasing from <10% to 50% and >80%, respectively (12). Plasma BKV loads correlate closely with replication in the transplanted kidney and are widely used to monitor onset and resolution of PVAN (2,3,13,14). BKV plasma kinetics after graft nephrectomy revealed a short BKV half-life (t1/2) of 2 h–18 h, indicating that in steady-state, >99% of plasma BKV loads must be replaced every day (15). Based on plasma BKV dynamics alone, the cytopathic loss was estimated as at least 106 tubular epithelial cells per day driving the course of PVAN (15). On the other hand, high-level BKV viruria of >107 genome equivalents (copies/mL) is observed in 20–40% of KT patients and paradigmatically precedes BKV viremia, thereby identifying KT patients at increased risk for PVAN (2,13,16). However, two-thirds of viruric KT patients do not develop viremia or evidence of tissue-invasive disease (2,3), yet abundant BKV replication has been demonstrated in the urothelial cell layer (11,17,18). To investigate the role of urothelial BKV replication, we studied BKV loads in 518 day-matched plasma-urine BKV samples from 223 KT patients. We extracted quantitative and kinetic parameters and tested mathematical models of BKV replication in urothelial and renal tubular epithelial cells.

Materials and Methods

Patients and sample

Data were prospectively collected during 2002–2006 at the Institute for Medical Microbiology, University of Basel, Switzerland, and between 2005 and 2008 at the Pediatric Nephrology Unit, Genova, Italy. The studies were conducted according approved IRB protocols at both sites. Two hundred twenty-three KT patients contributed 518 day-matched blood-urine samples. Three hundred thirty-five samples were BKV positive in plasma and urine, 183 samples tested positive for BKV in the urine only. Thirty-one patients provided longitudinal data (≥4 samples) to obtain kinetic estimates. This resulted in 177 (median 8, range 3–26) dynamic episodes available for analysis. From serum creatinine concentrations of 26 patients, the glomerular filtration rate (GFR) was calculated according to Cockroft–Gault (shown in green in Figure 3). For the clinical validation of the results, six pediatric KT patients with persistent viremia and viruria were included who were part of a prospective study monitoring BKV replication and preemptive intervention for which urine and plasma BKV loads had been measured in Basel (19).

Figure 3.

Longitudinal BKV load data of 6 representative KT patients (from a total of n = 31). Kinetic estimates as well as fully discordant and partially discordant dynamic episodes were extracted from day-matched BKV plasma and urine samples. X-axes = time (weeks); y-axes = Log10 transformed BKV load data (copies/mL). Open squares (solid line) = urine BKV loads; filled diamonds (dotted line) = plasma BKV loads; green dotted = proportion of urine viral load explained by glomerular filtration and concentration of plasma BKV loads. The gray area indicates the limit of detection (500 copies/mL) where below which BKV loads were arbitrarily taken as 100 copies/mL. [Correction added after publication 30 September 2008; the letter “A“ was removed from the panel for Pat 00107].

Analysis of the noncoding control region (NCCR)

BKV DNA was extracted from 200 μL plasma or urine using a commercial kit (QIAmp, Qiagen, Hombrechtikon, Switzerland ). NCCR amplification used a standard nested PCR approach as described (20). By dilution series and statistical cloning analysis, the sensitivity to detect rearranged (rr-)NCCR BKV variants was determined to be at 5% of ww-NCCR BKV. BKV loads in urine and plasma were determined by quantitative real-time PCR as previously described (2), with the linear range from 102 to 108 copies/mL and a coefficient of variation of 29.6 derived from 168 PCR standard curves (15). The detection limit of the PCR was set as 500 copies/mL. Viral loads >108 copies/mL were obtained by 10-fold dilution series. Control plasmids were added as inhibition controls.

Kinetic estimates

BKV doubling times (t2) and half-lives (t1/2) in plasma and urine were calculated according to previously described standard formulae (15,21). Viral load slopes were obtained by the expression s = (ln(V1)–ln(V0))/(t1–t0) and, depending on the sign of s, the respective t2 or t1/2 were calculated by the formula ln(2)/s.

Statistical analysis

We used the Mann–Whitney U test or Student's t-test for independent samples, the Wilcoxon signed-ranks test for paired samples, and Fisher's exact test for count data. Two-sided p-values < 0.05 were regarded as statistically significant. Kinetic estimates were compared by the Spearman correlation coefficient, rs. Regression analyses were performed with Mathematica 5.2 (Wolfram Research Inc., Champaign, IL).

Mathematical models

We extended a 1-compartment model (15) to a 2-compartment model with six state variables:

image(1)
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where E is uninfected kidney tubular epithelial cells; I is infected tubular epithelial cells; Vp is plasma virus; U is uninfected urothelial cells; Y is infected urothelial cells and Vu is urine virus. The term p1 E (1–E/Emax) indicates that new epithelial cells E are derived from proliferation of existing E cells. In single-layered kidney tubules, reepithelialization of denuded areas was restricted to the division of adjacent epithelial cells, while in the multilayered urothelium, cell loss was compensated by proliferation of cells from the basal layer (22–25) (for further details, see Supporting Information).

Results

Urine viral load in patients with and without viremia

We compared urine BKV loads in 223 consecutive KT patients with and without concomitant BKV viremia in day-matched plasma samples (Figure 1A). Urine BKV loads were significantly higher in viremic patients than in nonviremic patients (median: 8.1 vs. 4.5 log10 copies/mL; p<10−9, Mann–Whitney U test). Thus, urine BKV loads appeared to be linked to the viremic state. We then analyzed urine BKV loads in patients who shifted either from plasma-negative to positive states (n = 14) or vice versa (n = 25). In both subgroups, switching occurred within a median of 50 days (interquartile range [IQR] 15–93 days and 35– 71 days, respectively). However, unlike for the overall population (Figure 1A), urine BKV loads were not significantly different for patients switching to the viremic state (Figure 1B). Urine BKV loads were higher the shorter the time interval to the viremic state was (linear regression, R2= 0.33, p = 0.03; y = 11.4–2.5x). Thus, urine BKV loads were 7 log10 and 9 log10 copies/mL at ∼63 days and at ∼10 days, respectively, before viremia was documented. In the second group, urine BKV loads were lower as patients shifted to the plasma-negative state, but again without reaching statistical significance. We concluded that urine BKV loads displayed a partial quantitative and dynamic linkage to the BKV viremic state in KT patients.

Figure 1.

BKV load in urine of KT patients with and without BKV viremia. (A) Urine BKV loads of 125 patients without viremia (183 samples); urine BKV loads of 125 patients with viremia (335 samples). (B) Urine BKV loads of patients shifting from plasma BKV-negative to positive (left, n = 14), and vice versa (right, n = 25). Thick line: 2nd quartile (median), box: 1st to 3rd quartile, filled squares: outliers defined (1.5-fold upper or lower quartiles), p-values by the Mann–Whitney U test.

Correlation of urine and plasma BKV loads

To investigate quantitative relationships between viruria and viremia, we compared BKV loads in 335 day-matched plasma and urine samples from 125 viremic KT patients (Figure 2). Urine loads exceeded plasma loads in all but one case (334/335, 99.7%) being on average ∼3000-fold (3.5 log10 copies/mL) higher (8.1 vs. 4.6 log10 copies/mL, p < 10−9, Wilcoxon matched pairs test). Linear regression indicated a significant correlation (R2= 0.44, p < 10−6; y = 0.63 + 0.5x). Thus, 100-fold increases in viruria were ‘on average’ associated with 10-fold increases in viremia. However, urine and plasma loads rarely exceeded 11 and 8 log10 copies/mL, respectively. Using a quadratic regression model (y = 3.3–0.25x + 0.005x2), the resulting convex curve largely overlapped with the linear curve between urine BKV loads of 5.5 log10 and 9.5 log10 copies/mL, but provided better accommodation of extreme data points (Figure 2). At urine viral loads <5.5 log10 copies/mL, large increases in viruria were associated with moderate increases in viremia, but for urine viral loads >9.5 log10 copies/mL, viremia increased more steeply (slope 0.5 to 1). We concluded that BKV replication displayed a dynamic linkage progressively governed by increasing plasma viral loads.

Figure 2.

Correlation of plasma and urine BKV loads (335 day-matched samples from 125 KT patients). Diagonal: parity line with equally high urine and plasma BKV loads. Thick line, linear regression (90% confidence interval, dashed line; quartiles, concentric circles); thin convex line, quadratic regression.

Genomic BKV variants in urine and plasma

To investigate the contribution of plasma BKV to urine BKV loads, we compared the architecture of the BKV NCCR in both samples from 26 patients. We employed a nested PCR assay detecting rearranged (rr-)NCCR in mixtures of archetype (ww-)NCCR with a sensitivity as low as 5%. BKV rr-NCCR were more frequently detected in plasma than in day-matched urine samples (plasma 14/26, 54%; urine 2/26, 8%; p < 0.0007, Fisher's exact test) as reported previously (20). In 12 (46%) patients, the majority species in plasma consisted of rearranged rr-NCCR BKV variants, while archetype ww-NCCR BKV was detected in day-matched urine samples. This discordance of viral NCCR architecture in same day-matched plasma and urine samples provided direct molecular evidence that the majority BKV species in plasma and urine represented distinct viruses from separate replication sites.

Contribution of plasma virus to the urine viral load

To estimate the contribution of plasma BKV to the 3000-fold higher urine BKV loads by glomerular filtration, we compared 166 serum creatinine measurements from these 26 patients. The GFR according to Cockroft–Gault was 40 mL/min (median, IQR 24–52) thereby concentrating plasma by a factor of 29 (IQR 17–37). If this factor was assumed for BKV, plasma loads (median 4.2 log10 copies/mL; IQR 3.4–5.6) contributed ∼2% (IQR 0.1–11%) to total urine BKV loads (median 8.2 log10 copies/mL; IQR 6.8–9.3). For 152/166 samples (92%), concentration of plasma BKV loads explained less than 20% of the day-matched urine BKV load, and in 62/166 samples (37%), this proportion was even <1%. Only for 14/166 episodes (8%), GFR concentrated plasma BKV corresponded numerically to >20% of the matching urine BKV load (Figure 3, green dashed line).

To estimate the proportion of intrarenal BKV replication represented by plasma BKV loads, the average plasma BKV contribution of ∼2% (IQR 0.1–11%) was divided by the GFR concentration factor of 29 (IQR 17–37) to provide the plasma BKV load before concentration. Since the molecular NCCR data and the sensitivity of the nested PCR limited the overall contribution of intrarenal replication to <5% of urine BKV loads, we estimated that plasma BKV loads reflected ∼1.4% (IQR 0.1–6%) of the total intrarenal replication ([0.02/29]×[100/0.05]= 1.4).

BKV kinetics in plasma and urine

To compare urine and plasma BKV dynamics, we examined 177 kinetic episodes of rising or falling viral loads in the 31 patients (Figure 3). The shortest viral doubling times (t2) and half lives (t1/2) are listed in Table S1. Patient 00107 had a short t2 of 13–18 h and a t1/2 of 11–13 h and the median over all patients was t2 of 6–11 days and a t1/2 of 5–9 day. As a first approximation of the dynamics, we compared t2 in both sites and found significant correlations (rs= 0.59, p = 0.002, Spearman correlation analysis). Similarly, t1/2 in both compartments were correlated (rs= 0.85, p < 0.001). We next examined the number of episodes with concordant kinetic changes in both sampling compartments. Of 177 kinetic episodes examined, parallel increases or decreases of BKV loads were observed in 64% (Table S1). Fully discordant kinetic episodes defined as increasing BKV loads in one, but decreasing in the other compartment were found in 63 (36%) episodes. When allowing the urine BKV slope to deviate no more than ±50% from the matching plasma BKV slope, partial dynamic discordance was observed in another 32% yielding a total of 121 (68%) mismatching episodes. We concluded that both replication compartments were kinetically linked, but not very tightly.

BKV replication-dependent cytopathic loss

Given the short BKV t1/2 in plasma and urine of <12 h, and the lytic mode of BKV replication, we estimated the associated cytopathic loss of urothelial and tubular epithelial cells (15). In a dynamic steady-state with viral plasma and urine loads of 5×104 and 108 copies/mL, respectively (Figure 2), host cell loss amounted to ∼6×105 tubular epithelial cells and ∼6×107 urothelial cells per day. Since plasma BKV loads corresponded to ∼1% (IQR 0.1–6%) of intrarenal replication, total tubular epithelial cell loss amounted to ∼6×107 cells per day. Urothelial cell loss was to be reduced by ≤10% to ∼4×107 cells/day for the contributing intrarenal replication. If the urine BKV t1/2 was assumed to be as short as 2 h as previously determined for plasma BKV t1/2 after allograft nephrectomy (15), urothelial cytopathic loss was increased by 10-fold from 4×107 to 4×108 per day.

Mathematical modeling studies

To explore the dynamics of viral replication in renal tubular epithelial cells and in urothelial cells, we constructed a basic model integrating two replication sites (see the material and methods section; Figure 4; and SI Model description), and derived four variants:

Figure 4.

Replication sites and viral flux. The transplanted kidney (brown box) and the urinary tract (yellow box). Abbreviations: E= renal tubular epithelial cells; I= infected tubular epithelial cells; Vp= plasma virus; U= urothelial cells; Y= infected urothelial cells; Vu= virus in urine; rate constants: p1, p2= cell proliferation rates; d1, d2= death rates of uninfected cells; u1, u2= death rates of infected cells; i, j= infection parameters; e= viral efflux rate; r= viral reflux rate (for details, see Supplement model description and Table S2).

  • (i) In model K→U, replication starts in the kidney, and virus is released into the urinary tract infecting a minority of urothelial cells (at rate e*Vp U) while the majority is shed (at rate s*Vp) without infecting urothelial cells.
  • (ii) In model K→U↔K, replication starts in the kidney, then infects urothelial cells, and a bidirectional viral flux (at rates e*Vp U, s*Vp and r*Vu E) feeds both replication sites.
  • (iii) In model U→K, replication starts in urothelial cells, and reaches tubular epithelial cell replication by vesico-uretral reflux (at rate r*Vu E).
  • (iv) In model U→K↔U, replication starts in urothelial cells, and reaches tubular epithelial cell replication by vesico-uretral reflux, followed by bidirectional viral flux into both replication sites (at rates r*Vu E, s*Vp and e*Vp U). Since urothelial replication rates were fast and high, dynamics of model U→K↔U deviated only minimally from those of model U→K in the simulations, and could be omitted henceforth.

In the simulations, we considered three phases of replication dynamics: (i) viral expansion to last ∼100 days in line with clinical observations (2,13,14); (ii) steady state equilibrium; (iii) viral contraction by curtailing virus replication by 50%, 80%, 90% or 99% (Figure S1). During viral expansion, models K→U, U→K and K→U↔K indicated distinct dynamics (Figure 5). The best accommodation of increasing viral loads during the first ∼100 days was obtained by model K→U↔K (Figure 5C). Both of the other models explained the generally observed viral characteristics less satisfactorily with viral load increases being either too flat or appearing too early reaching steady states in urine and plasma after 70 days and 240 days (Figure 5A), or 40 and 120 days (Figure 5B), respectively. During viral contraction, however, the dynamic differences of all three models appeared negligible (Figure 5).

Figure 5.

Mathematical models. (A) Model K→U. Replication starts in kidney allograft. Viral flux is unidirectional to urinary tract (e = 10−9, r = 0). (B) Model U→K. Replication starts in the urinary tract. Viral flux is unidirectional to the kidney (e = 0, r = 10−7). (C) Model K→U↔K. Replication starts in the kidney, reaches the urinary tract followed by bidirectional viral flux cross-feeding into both replication compartments (e = 10−9, r = 10−7). Model parameters indicated in Supplement model description and Table S2.

The robustness of the models was assessed in silico by a sensitivity analysis based on the reproductive number R0 during viral expansion in tubular epithelial and in urothelial cell compartments (Supplement model description and Table S1). Thereby, we identified three key parameters for the intrarenal compartment, and two key parameters for the urothelial compartment: Viral expansion in the intrarenal replication compartment was sensitive to Emax, the ‘carrying capacity’ of uninfected tubular epithelial cells, and, interestingly, two urothelial parameters, namely the urothelial viral decay rate c2, and r, the viral reflux from urinary tract to the allograft (Figure 4). Viral expansion in the urothelial compartment was sensitive to Umax, the ‘carrying capacity’ of uninfected urothelial cells and the death rate of infected urothelial cells u2, whereas viral efflux from the graft to the urothelial compartment e was less than linear (Table S1).

Viral expansion in model K→U↔K showed viruria and viremia increasing above the detection limit at day 35 and day 60, respectively. In the first ∼30 days, plasma and urine viral loads slowly increased with a viral t2 of ∼11 days, the latter due to viral efflux and GFR concentration of plasma virus. During this phase, every infected tubular epithelial cell gave rise to R0K∼1.1 secondary infected cells. After day 30, urine BKV loads sharply increased due to replication in urothelial cells, but plasma BKV loads remained below our current diagnostic detection limit. Within 3 weeks, urine BKV loads increased with an estimated t2 of ≤1day to a plateau of >1010 copies/mL, raising plasma viral loads by cross-feeding intrarenal replication. During this phase, each infected urothelial cell gave on average rise to R0U >7 secondary infected urotelial cells, while the intrarenal R0K increased to ∼3.4. After ∼70 days, a dynamic equilibrium state in the urinary compartment was reached (R0U≈1), while the increase in plasma viral load slowed down toward R0K≈1.1.

Viral contraction in model K→U↔K by curtailing replication to 50% below the maximal replication equilibrium reduced plasma BKV loads by 2–4 log10 units, but did not allow clearing plasma BKV loads, and left viruria unaffected (Figure 5D). Curtailing virus replication by 80%, viremia was cleared after 7 weeks, but viruria persisted for another >14 weeks. However, curtailing by ≥90% led to a parallel decline of plasma and urine viral loads within ∼3 and ∼10 weeks, respectively. Together, these results suggested that model K→U↔K provided the best approximation of BKV expansion in KT patients, and that curtailing BKV replication by >80% is required for significant effects on clearance and intrarenal cytopathic loss.

Clinical validation studies.  We applied the model K→U↔K to the data of a prospectively sampled KT patient with PVAN who was treated with reducing immunosuppression (tacrolimus trough levels <6 ng/mL; mycophenolate mofetil to 500 mg qd). During viral expansion, the observed plasma and urine BKV loads (black) overlapped with simulated data (red) generated by model K→U↔K (Figure 6A). Two phases of viral contraction were observed corresponding to 60% curtailing at day 120 and 85% curtailing after day 220. The total cytopathic loss during BKV replication was calculated as 1.3×1011 tubular epithelial cells and 5.1×1011 urothelial cells (Figure 6B). Up to the histological diagnosis of PVAN (day 93), 5×1010 tubular epithelial cells had been lost in the allograft according to this model.

Figure 6.

Data of a prospectively sampled patient with PVAN superimposed with solutions of model K→U↔K. (A) Measured BKV load in urine (open squares, black dashed line) and plasma (filled diamonds, black line). Red dashed line = fitted urine viral load; red line = fitted plasma viral load. Data points that were below current limits of detection by PCR (the gray area) were set as 100 copies/mL. Asterisks indicate biopsy-proven PVAN. (B) Simulated BKV dynamics in plasma (solid lines) and urine (dashed lines). Abbreviations: E= kidney tubular epithelial cells; I= infected tubular epithelial cells; Vp= plasma virus; U= urothelial cells; Y= infected urothelial cells; Vu= virus in urine. Model parameters: p1= 0.6, p2= 1.5, d1= 0.003, d2= 0.006, i= 2.5×10−7, j= 1.1×10−7, b1=b2= 6000, u1=u2= 0.33, c1= 10, c2= 1, e= 10−9, r= 2×10−7. Curtailing viral replication 0% (0 < t ≤ 115 days); uniform reduction from 0% to 60% (115 < t ≤ 130 days); 60% reduction (130 <t ≤ 210 days); 85% reduction (t > 210 days).

We next evaluated the K→U↔K model regarding plasma and urine BKV load dynamics of an external set of six pediatric KT patients with sustained viremia (Figure 7) who were identified and treated as part of a prospective study of preemptive intervention (19). The viral expansion toward equilibrium occurred rapidly over 13 weeks (median, range 10–37) posttransplant. The median t2 over all six patients was urine ∼1.7 days and plasma ∼3.7 days. The fastest BKV doubling times were observed in patients UPN 6015634 and 7018831 with a urine t2 of ∼1 day and a plasma t2 of ∼1.5 days (weeks 2–4). The median t1/2 were in urine ∼5.2 days and in plasma ∼9 days. The shortest BKV half-life was observed in patient UPN 7015260 with a urine t1/2 of ∼2 days (weeks 22–24) and a plasma t1/2 of ∼8.3 days (weeks 10–12). Intervention in these patients was achieved solely by reducing maintenance immunosuppression (19). In all but one patient, BKV replication was curtailed >80%, with plasma BKV loads declining from >105 copies/mL to undetectable levels in parallel to urine viral loads, as predicted by the K→U↔K model (Figure 7). In one patient (UPN 3019514; Figure 7), curtailing fell below 80% to 64% between week 50 and 72 posttransplant, and a rebound of urine BKV loads was observed that leveled off as curtailing approached 76%.

Figure 7.

Data of six prospectively sampled pediatric KT patients from an independent prospective cohort. Urine BKV loads (open squares, black dashed line); plasma BKV loads (filled diamonds, black line). Superimposed are simulated dynamics of model K→U↔K in urine (dashed lines) and plasma (solid lines). Symbols, abbreviations and model parameters as in Figure 5. Deviations: UPN3019514:i1= 7×10−7, i2= 2×10−6, b1=b2= 10000, u1=u2= 0.66, c2= 2, e= 10−0, r= 5×10−6, I0= 10−4, Imax=5×103, Emax=3×105. Curtailing of viral replication 0% (0 <t ≤ 15 weeks); 82% (15 < t ≤ 50 weeks); 64% (50 < t ≤ 72 weeks); 76% (t > 74 weeks). UPN4009398:i1= 5×10−7, i2= 2.5×10−7, b1=b2= 10000, e= 10−6, r= 5×10−5, I0= 10−3, Imax=7×103. Curtailing 0% (0 < t ≤ 37 weeks); 99% (37 < t ≤ 45 weeks); 94% (45 < t ≤ 95 weeks); 91% (t > 95 weeks). UPN6015634:i1= 7×10−7, i2= 1×10−6, b1=b2= 10000, u1=u2= 1, c2= 2, e= 10−4, r= 5×10−8, I0= 10−3, Imax=3.3×103. Curtailing 0% (0 < t ≤ 10.5 weeks); 99% (10.5 < t ≤ 26 weeks); 83% (26 < t≤ 35 weeks); 91% (t > 35 weeks). UPN7018831:i1= 8×10−7, i2= 1.3×10−6, b1=b2= 10000, u1=u2= 1.1, e= 10−3, r= 5×10−8, I0= 10−2, Imax=5.5×103, Emax=9×106. Curtailing 0% (0 < t ≤ 10.7 weeks); 96% (t > 10.7 weeks). UPN7015260:i1= 7.5×10−7, i2= 5×10−7, b1=b2= 10000, u1=u2= 0.875, e= 10−3, r= 5×10−7, I0= 10−5, Imax=3.5×103. Curtailing 0% (0 < t ≤ 10 weeks); 99.9% (t > 10 weeks). UPN3036365:i1= 5×10−7, i2= 2.5×10−7, b1=b2= 10000, u1=u2= 0.75, e= 10−1, r= 5×10−7, I0= 10−7, Imax=7×103. Curtailing 0% (0 < t ≤ 19 weeks); 84% (19 < t ≤ 36 weeks); 99% (t > 36 weeks).

Discussion

Mathematical modeling of viral infection dynamics has elucidated important aspects of the pathophysiology and treatment responses of HIV1, chronic hepatitis C and some viruses in transplantation (21,26,27). In this study, we extend our previous work on BKV dynamics in KT patients with PVAN (15) and provide evidence that BKV replication in urothelial and tubular epithelial cells is linked, but can be dissected quantitatively and kinetically. Our analysis indicates that more than 90% of urine BKV load results from local urothelial replication. BKV replication in tubular epithelial cells contributes less than 5% to the total urine BKV load, although the vast majority of intrarenal BKV seems to be directly released into the urine. Conversely, plasma BKV loads represent <2% of tubular epithelial cell replication contributing if anything a minor fraction via glomerular filtration to urine BKV loads. BKV replication dynamics in both sampling sites were found to be fast with estimated viral doubling times and half-lives of ∼2h–12h. Although fast kinetics would allow for rapid equilibration between different replication compartments, we observed that viral load changes in plasma and urine were fully discordant in 36%, and partially discordant in another 32% of kinetic episodes. Hydration status and urine volume cannot affect these results as they were extracted from a multitude of different patients and encompassed longitudinal data from individual patients (Figure 3). Moreover, changes in urine BKV load are several orders of magnitudes higher than changes in urine volume. Thus, BKV replication in urothelial and in tubular epithelial cells must be considered independent, presumably governed by local host cell infection dynamics. This notion is supported by molecular studies detecting different genomic NCCR variants as the replicating viral majority species in day-matched plasma and urine samples as reported (20). Thus, our analyses provide important quantitative and dynamic dimensions to earlier studies demonstrating BKV replication histologically in urothelial and in renal tubular epithelial cells (11,17,18,28).

Nevertheless, BKV replication in both anatomical sites displayed some degree of linkage. First, urine BKV loads were generally lower in nonviremic than in viremic KT patients. In some patients, however, very high urine BKV loads were found in the absence of viremia illustrating the dominant role of local urothelial replication for urine BKV loads. This makes it impossible to predict viremia based solely on urine BKV loads. In viremic KT patients, however, urine viral loads were on average 3.5 log10 units (∼3000-fold) higher than plasma viral loads as described previously (13,29–32). A 10-fold increase in viremia was associated with a 100-fold increase in viruria. The overall relationship was better described by a quadratic regression where increasing plasma loads correlated with progressively smaller increments in urine loads as they approached 10 log10 copies/mL. Interestingly, urine and plasma BKV loads hardly exceeded 11 or 8 log10 copies/mL, respectively. Similar boundaries can be found in other studies (13,30,31,33) suggesting limiting ‘carrying capacities' of host cells that can be infected in the respective replication compartments.

The resulting quantitative and kinetic parameters enabled us to explore BKV replication dynamics in KT patients in mathematical models accommodating two replication sites. Permuting the start sites of BKV replication as well as viral flux rates indicated that viral expansion of model K→U↔K yielded urine and plasma load dynamics best compatible with most of our clinical cases (Figure 5–7). In this model, BKV replication was initiated in renal tubular epithelial cells and carried to urothelial cells where the infectious units were then amplified. A limited ureteric reflux caused multiple infection sites in the allograft that accelerated the slowly expanding local intrarenal replication until a dynamic steady state was reached within 2 months. Unlike stochastic differential equation models, our models are based on ordinary differential equations and hence, deterministic. A sensitivity analysis shifting the individual parameters by two orders of magnitude indicated that viral expansion was governed not only by the ‘carrying capacity’ of the uninfected host cells in either replication compartment as expected, but also by three urothelial factors, namely the urine viral decay rate, the death rate of infected urothelial cells and notably, the viral reflux from the urinary tract to the allograft. Only few of our KT patients showed BKV replication dynamics that appeared to be better captured by the models K→U or U→K with slower or faster expansion dynamics, respectively. In the K→U model, urothelial reflux causing amplification of intrarenal replication was excluded, while being key in the U→K model. In the U→K model, urothelial cell-to-cell spread of BKV from the bladder or distal ureter up to the kidney like toppling dominoes cannot explain the dynamics since the time needed to reach the kidney would exceed 4 years per 1 cm distance given a cell diameter of 20 μm and a viral lifecycle of 2–3 days. Thus, given the importance viral reflux rate for the dynamics of the U→K and the K→U↔K model, we hypothesize that conditions favoring urothelial reflux must be important in the dynamics of PVAN pathogenesis. These include ureter kinking or outright ureter stenosis posttransplant causing transient or persistent hydronephrosis that has been described in a number of PVAN patients throughout the literature (34, 35). However, ureter stenting to maintain urinary drainage has also been associated with an increased risk of BKV viremia (13,36,37). In the therapeutic situation, one might argue that prior urinary backlash with intrarenal viral seeding had occurred prior to stent implantation. The increased risk is less obvious in the prophylactic situation, but in fact, ureter stenting has been shown to enable vesico-ureteric reflux following normal bladder contraction (38) that would allow for intrarenal seeding of urothelial BKV in the absence of prior hydronephrosis (39). In addition, in the K→U↔K model, viral colonization of urothelial cells is likely to start ‘top-down’ close to the exit of the infected tubulus into the pyelon, especially as the renal medulla has been described as one of the earliest replication sites (40). Here, transient local stasis and minimal reflux during postural changes may then be sufficient to recruit new allograft sites in the absence of full hydronephrosis or stenting.

We estimated the average daily cytopathic loss as ∼6×107 cells in the allograft and ∼4×107 cells in the urinary tract for steady-state plasma and urine loads of 5×104 copies/mL and 108 copies/mL, respectively. Thus, the intrarenal impact exceeds our previous estimate by more than one order of magnitude (15), further emphasizing the cytopathic wear of unchecked BKV replication for PVAN pathogenesis. This is illustrated for the shown patient by the short time of only 30 days from the onset of viremia to biopsy-proven PVAN during which the cumulative cell loss amounted to ∼1010 renal tubular epithelial cells. Although both urothelial and tubular epithelial cell loss seem numerically comparable, manifestations of BKV disease are typically confined to the renal parenchyma with inflammation (PVAN B), and progression to fibrosis and tubular atrophy (PVAN C), leaving the urothelia compartment largely unaffected (3,12). Nickeleit et al. have pointed out that denudation of tubular basement membranes and urinary leakage may significantly enhance inflammatory responses to BKV-mediated cell necrosis (11). In the denuded areas, BKV replication dynamics exceed the regeneration responses of the single-cell layer of tubular epithelial cells. By contrast, the urothelium consists of a multilayer of highly regenerative cells (22) that may allow for the higher BKV ‘carrying capacity’ without histologically evident denudation and inflammation. This hypothesis would explain in part the different pathology elicited by similarly high-level replication in patients with postengraftment hemorrhagic cystitis after hematopoietic stem cell transplantation. Thus, as a result of the urothelial BKV replication dynamics explored here, BKV-associated hemorrhagic cystitis in these patients may be the result of partial urothelial denudation as the result of high-level BKV replication in poorly regenerating urothelial cells after urotoxic conditioning regimens together with debilitating inflammation postengraftment (23,39,41,42).

A decade after PVAN emergence, the rescue of a functioning renal allograft remains a key challenge as efficacious interventions are undefined (43). By mathematical modeling of contracting BKV replication, we now provide for the first time estimates as to how effective antiviral or immune interventions must be and how this is reflected in plasma and urine BKV loads. Accordingly, BKV replication must be curtailed by at least 80% as indicated by a decline first in plasma loads then in urine loads. Curtailing BKV replication by only 50% is insufficient as significant cytopathic wear continues despite declining plasma loads of 1–2 log10. Moreover, viruria remains unchanged and thereby the risk of reigniting intrarenal replication by viral reflux. Optimal interventions should curtail BKV replication by ≥90% and can be identified by the rapid and almost parallel decline of plasma and urine BKV loads within <10 weeks. The modeling results, in particular the curtailing threshold of 80%, are supported by the clinical validation for the plasma and urine BKV load responses of six pediatric KT patients (Figure 7) who were identified in a prospective study of preemptive reduction of immunosuppression (19).

In conclusion, our study provides quantitative and kinetic support for a model where BKV replication starts in the kidney and is amplified in the urothelial compartment with partial reflux to the allograft. Fast replication dynamics cause substantial cytopathic loss driving PVAN progression to inflammation, fibrosis and exhausted atrophy of renal tubular cell compartment. Plasma BKV loads should guide monitoring of interventions, the efficacy of which can be further adjusted according to urine BKV loads, to target >80% curtailing for optimal interventions.

Acknowledgement

This work was supported in part by the Swiss National Fonda 3200B0-110040 and the Novartis Jubilee Foundation.

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