A model is developed and analyzed for type IV collagen turnover in the kidney glomerular basement membrane (GBM), which is the primary structural element in the glomerular capillary wall. The model incorporates strain dependence in both deposition and removal of the GBM, leading to an equilibrium tissue strain at which deposition and removal are balanced. The GBM thickening decreases tissue strain per unit of transcapillary pressure drop according to the law of Laplace, but increases the transcapillary pressure drop required to maintain glomerular filtration. The model results are in agreement with the observed GBM alterations in Alport syndrome and thin basement membrane disease, and the model-predicted linear relation between the inverse capillary radius and inverse capillary thickness at equilibrium is consistent with published data on different mammals. In addition, the model predicts a minimum achievable strain in the GBM based on the geometry, properties, and mechanical environment; that is, an infinitely thick GBM would still experience a finite strain. Although the model assumptions would be invalid for an extremely thick GBM, the minimum achievable strain could be significant in diseases, such as Alport syndrome, characterized by focal GBM thickening. Finally, an examination of reasonable values for the model parameters suggests that the oncotic pressure drop—the osmotic pressure difference between the plasma and the filtrate due to large molecules—plays an important role in setting the GBM strain and, thus, leakage of protein into the urine may be protective against some GBM damage.

References

References
1.
Drumond
,
M. C.
, and
Deen
,
W. M.
, 1994, “
Structural Determinants of Glomerular Hydraulic Permeability
,”
Am. J. Physiol.
,
266
(
1
), pp.
F1
F12
.
2.
Deen
,
W. M.
,
Lazzara
,
M. J.
, and
Myers
,
B. D.
, 2001, “
Structural Determinants of Glomerular Permeability
,”
Renal Physiol.
,
281
(
4
), pp.
F579
F596
.
3.
Haraldsson
,
B.
,
Nystrom
,
J.
, and
Deen
,
W. M.
, 2008, “
Properties of the Glomerular Barrier and Mechanisms of Proteinuria
,”
Physiol. Rev.
,
88
(
2
), pp.
451
487
.
4.
Mohamed
,
E. I.
, and
de Lorenzo
,
A.
, 2002, “
Modeling Combined Transport of Water and Test Macromolecules Across the Glomerular Capillary Barrier: Dynamics of the Permselectivity
,”
Eur. Biophys. J.
,
31
(
3
), pp.
163
171
.
5.
Kriz
,
W.
,
Kretzler
,
M.
, and
Provoost
,
A. P.
, 1996, “
Stability and Leakiness: Opposing Challenges to the Glomerulus
,”
Kidney Int.
,
49
(
6
), pp.
1570
1574
.
6.
Singh
,
P.
, and
Thomson
,
S. C.
, 2010, “
Renal Homeostasis and Tubuloglomerular Feedback
,”
Curr. Opin. Nephrol. Hyperten.
,
19
(
1
), pp.
59
64
.
7.
Walker
,
F.
, 1973, “
The Origin, Turnover and Removal of Glomerular Basement-Membrane
,”
J. Pathol.
,
110
(
3
), pp.
233
244
.
8.
Endlich
,
N.
,
Kress
,
K. R.
, and
Reiser
,
J.
, 2001, “
Podocytes Respond to Mechanical Stress In Vitro
,”
J. Am. Soc. Nephrol.
,
12
(
3
), pp.
413
422
.
9.
Endlich
,
N.
, and
Endlich
,
K.
, 2006, “
Stretch, Tension and Adhesion—Adaptive Mechanisms of the Actin Cytoskeleton in Podocytes
,”
Eur. J. Cell Biol.
,
85
(
3
), pp.
229
234
.
10.
Petermann
,
A. T.
,
Pippin
,
J.
, and
Durvasula
,
R.
, 2005, “
Mechanical Stretch Induces Podocyte Hypertrophy In Vitro
,”
Kidney Int.
,
67
(
1
), pp.
157
166
.
11.
Flynn
,
B. P.
,
Bhole
,
A. P.
, and
Saeidi
,
N.
, 2010, “
Mechanical Strain Stabilizes Reconstituted Collagen Fibrils Against Enzymatic Degradation by Mammalian Collagenase Matrix Metalloproteinase 8 (MMP-8)
,”
PLos ONE
,
5
(
8
), p.
e12337
.
12.
Zareian
,
R.
,
Church
,
K. P.
, and
Saeidi
,
N.
, 2010, “
Probing Collagen/Enzyme Mechanochemistry in Native Tissue With Dynamic, Enzyme-Induced Creep
,”
Langmuir
,
26
(
12
), pp.
9917
9926
.
13.
Bhole
,
A. P.
,
Flynn
,
B. P.
, and
Liles
,
M.
, 2009, “
Mechanical Strain Enhances Survivability of Collagen Micronetworks in the Presence of Collagenase: Implications for Load-Bearing Matrix Growth and Stability
,”
Philos. Trans. R. Soc. London, Ser. A
,
367
(
1902
), pp.
3339
3362
.
14.
Kriz
,
W.
, and
Endlich
,
K.
, 2005, “
Hypertrophy of Podocytes: A Mechanism to Cope With Increased Glomerular Capillary Pressures?
,”
Kidney Int.
,
67
(
1
), pp.
373
374
.
15.
Taber
,
L. A.
, 1998, “
A Model for Aortic Growth Based on Fluid Shear and Fiber Stresses
,”
ASME J. Biomech. Eng.
,
120
(
3
), pp.
348
354
.
16.
Renkin
,
E. M.
, and
Gilmore
,
J. P.
, 1973,
Handbook of Physiology: Renal Physiology
,
Williams and Wilkins
,
Washington, D.C.
, pp.
185
248
.
17.
Singer
,
M. A.
, and
Morton
,
A. R.
, 2000, “
Mouse to Elephant: Biological Scaling and Kt/V
,”
Am. J. Kidney Dis.
,
35
(
2
), pp.
306
309
.
18.
Maluf
,
N. S.
, and
Gassman
,
J. J.
, 1998, “
Kidneys of the Killerwhale and Significance of Reniculism
,”
Anat. Rec.
,
250
(
1
), pp.
34
44
.
19.
Bohle
,
A.
,
Aeikens
,
B.
, and
Eenboom
,
A.
, 1998, “
Human Glomerular Structure Under Normal Conditions and in Isolated Glomerular Disease
,”
Kidney Int.
, Suppl.,
67
, pp.
S186
S188
.
20.
Marquez
,
B.
,
Zouvani
,
I.
, and
Karagrigoriou
,
A.
, 2003, “
A Simplified Method for Measuring the Thickness of Glomerular Basement Membranes
,”
Ultrastruct. Pathol.
,
27
(
6
), pp.
409
416
.
21.
Osawa
,
G.
,
Kimmelstiel
,
P.
, and
Seiling
,
V.
, 1966, “
Thickness of Glomerular Basement Membranes
,”
Am. J. Clin. Pathol.
,
45
(
1
), pp.
7
.
22.
Akaoka
,
K.
,
White
,
R. H.
, and
Raafat
,
F.
, 1995, “
Glomerular Morphometry in Childhood Reflux Nephropathy, Emphasizing the Capillary Changes
,”
Kidney Int.
,
47
(
4
), pp.
1108
1114
.
23.
Yun
,
J. C. H.
and
Kenney
,
R. A.
, 1978, “
Structural Changes After Infusion of Mannitol in the Cat Kidney
,”
Kidney Blood Pressure Res.
,
1
(
5
), pp.
283
295
.
24.
Marion
,
M. S.
, and
Carlson
,
E. C.
, 1989, “
Ultrastructural Analyses of Acellular Glomerular Basement Membranes and Mesangial Matrix in a Spontaneously Diabetic Rhesus Monkey
,”
Acta Anat.
,
135
(
2
), pp.
119
128
.
25.
Nyengaard
,
J. R.
, 1993, “
Number and Dimensions of Rat Glomerular Capillaries in Normal Development and After Nephrectomy
,”
Kidney Int.
,
43
(
5
), pp.
1049
1057
.
26.
Shirato
,
I.
,
Tomino
,
Y.
, and
Koide
,
H.
, 1991, “
Fine Structure of the Glomerular Basement Membrane of the Rat Kidney Visualized by High-Resolution Scanning Electron Microscopy
,”
Cell Tissue Res.
,
266
(
1
), pp.
1
10
.
27.
Shea
,
S. M.
, 1979, “
Glomerular Hemodynamics and Vascular Structure. The Pattern and Dimensions of a Single Rat Glomerular Capillary Network Reconstructed From Ultrathin Sections
,”
Microvasc. Res.
,
18
(
2
), pp.
129
143
.
28.
Guo
,
M.
,
Ricardo
,
S. D.
, and
Deane
,
J. A.
, 2005, “
A Stereological Study of the Renal Glomerular Vasculature in the db/db Mouse Model of Diabetic Nephropathy
,”
J. Anat.
,
207
(
6
), pp.
813
821
.
29.
Endo
,
H.
,
Akihisa
,
N.
, and
Sasaki
,
M.
, 2002, “
The Renal Structure in an Asian Elephant (Elephas Maximus)
,”
Anat. Histol. Embryol.
,
31
(
5
), pp.
269
272
.
30.
Hudson
,
B. G.
,
Tryggvason
,
K.
, and
Sundaramoorthy
,
M.
, 2003, “
Alport’s Syndrome, Goodpasture’s Syndrome, and Type IV Collagen
,”
New Engl. J. Med.
,
348
(
25
), pp.
2543
2556
.
31.
Foster
,
K.
,
Markowitz
,
G. S.
, and
D’Agati
,
V. D.
, 2005, “
Pathology of Thin Basement Membrane Nephropathy
,”
Semin. Nephrol.
,
25
(
3
), pp.
149
158
.
32.
Rana
,
K.
,
Wang
,
Y. Y.
, and
Buzza
,
M.
, 2005, “
The Genetics of Thin Basement Membrane Nephropathy
,”
Semin. Nephrol.
,
25
(
3
), pp.
163
170
.
33.
Wang
,
Y. Y.
, and
Savige
,
J.
, 2005, “
The Epidemiology of Thin Basement Membrane Nephropathy
,”
Semin. Nephrol.
,
25
(
3
), pp.
136
139
.
34.
Lees
,
G. E.
,
Helman
,
R. G.
, and
Kashtan
,
C. E.
, 1998, “
A Model of Autosomal Recessive Alport Syndrome in English Cocker Spaniel Dogs
,”
Kidney Int.
,
54
(
3
), pp.
706
719
.
35.
Beirowski
,
B.
,
Weber
,
M.
, and
Gross
,
O.
, 2006, “
Chronic Renal Failure and Shortened Lifespan in COL4A3+/− Mice: An Animal Model for Thin Basement Membrane Nephropathy
,”
J. Am. Soc. Nephrol.
,
17
(
7
), pp.
1986
1994
.
36.
Kashtan
,
C. E.
, 2000, “
Alport Syndrome: Abnormalities of Type IV Collagen Genes and Proteins
,”
Ren. Fail.
,
22
(
6
), pp.
737
749
.
37.
Kashtan
,
C. E.
, and
Segal
,
Y.
, 2011, “
Genetic Disorders of Glomerular Basement Membranes
,”
Nephron. Clin. Practi.
,
118
(
1
), pp.
c9
c18
.
38.
Kashtan
,
C. E.
, 1998, “
Alport Syndrome and Thin Glomerular Basement Membrane Disease
,”
J. Am. Soc. Nephrol.
,
9
(
9
), pp.
1736
1750
.
39.
Gunwar
,
S.
,
Ballester
,
F.
, and
Noelken
,
M. E.
, 1998, “
Identification of a Novel Disulfide-Cross-Linked Network of α3, α4, and α5 Chains of Type IV Collagen and Its Implications for the Pathogenesis of Alport Syndrome
,”
J. Biol. Chem.
,
273
(
15
), pp.
8767
8775
.
40.
Gunwar
,
S.
,
Ballester
,
F.
, and
Noelken
,
M. E.
, 1998, “
Glomerular Basement Membrane—Identification of a Novel Disulfide-Cross-Linked Network of Alpha 3, Alpha 4, and Alpha 5 Chains of Type IV Collagen and Its Implications for the Pathogenesis of Alport Syndrome
,”
J. Biol. Chem.
,
273
(
15
), pp.
8767
8775
.
41.
Wyss
,
H. M.
,
Henderson
,
J. M.
, and
Byfield
,
F. J.
, 2011, “
Biophysical Properties of Normal and Diseased Renal Glomeruli
,”
Am. J. Physiol: Cell Physiol.
,
300
(
3
), pp.
C397
C405
.
42.
Meehan
,
D. T.
,
Delimont
,
D.
, and
Cheung
,
L.
, 2009, “
Biomechanical Strain Causes Maladaptive Gene Regulation, Contributing to Alport Glomerular Disease
,”
Kidney Int.
,
76
(
9
), pp.
968
76
.
43.
Rayat
,
C. S.
,
Joshi
,
K.
, and
Dey
,
P.
, 2007, “
Glomerular Morphometry in Biopsy Evaluation of Minimal Change Disease, Membranous Glomerulonephritis, Thin Basement Membrane Disease and Alport’s Syndrome
,”
Anal. Quan. Cytol. Histo.
,
29
(
3
), pp.
173
182
.
44.
Kalluri
,
R.
,
Shield
,
C. F.
, and
Todd
,
P.
, 1997, “
Isoform Switching of Type IV Collagen is Developmentally Arrested in X-Linked Alport Syndrome Leading to Increased Susceptibility of Renal Basement Membranes to Endoproteolysis
,”
J. Clin. Invest.
,
99
(
10
), pp.
2470
2478
.
45.
Lewko
,
B.
and
Stepinski
,
J.
, 2009, “
Hyperglycemia and Mechanical Stress: Targeting the Renal Podocyte
,”
J. Cell. Physiol.
,
221
(
2
), pp.
288
295
.
46.
Brownlee
,
M.
, 2001, “
Biochemistry and Molecular Cell Biology of Diabetic Complications
,”
Nature (London)
,
414
(
6865
), pp.
813
820
.
47.
Bohlender
,
J. M.
,
Franke
,
S.
, and
Stein
,
G.
, 2005, “
Advanced Glycation End Products and the Kidney
,”
Ren. Physiol.
,
289
(
4
), pp.
F645
F59
.
48.
Bailey
,
A. J.
,
Sims
,
T. J.
, and
Avery
,
N. C.
, 1993, “
Chemistry of Collagen Cross-Links: Glucose-Mediated Covalent Cross-Linking of Type-IV Collagen in Lens Capsules
,”
Biochem. J.
,
296
(
2
), pp.
489
496
.
49.
Mott
,
J. D.
,
Khalifah
,
R. G.
, and
Nagase
,
H.
, 1997, “
Nonenzymatic Glycation of Type IV Collagen and Matrix Metalloproteinase Susceptibility
,”
Kidney Int.
,
52
(
5
), pp.
1302
1312
.
50.
Cochrane
,
S. M.
and
Robinson
,
G. B.
, 1995, “
In Vitro Glycation of Glomerular Basement Membrane Alters its Permeability: A Possible Mechanism in Diabetic Complications
,”
FEBS Lett.
,
375
(
1-2
), pp.
41
44
.
51.
Boyd-White
,
J.
, and
Williams
,
J. C.
, Jr.
, 1996, “
Effect of Cross-Linking on Matrix Permeability. A Model for AGE-Modified Basement Membranes
,”
Diabetes
,
45
(
3
), pp.
348
353
.
52.
Brownlee
,
M.
, and
Spiro
,
R. G.
, 1979, “
Glomerular Basement Membrane Metabolism in the Diabetic Rat. In Vivo Studies
,”
Diabetes
,
28
(
2
), pp.
121
125
.
53.
Hasslacher
,
C.
,
Reichenbacher
,
R.
, and
Gechter
,
F.
, 1984, “
Glomerular Basement Membrane Synthesis and Serum Concentration of Type IV Collagen in Streptozotocin-Diabetic Rats
,”
Diabetologia
,
26
(
2
), pp.
150
154
.
54.
Cohen
,
M. P.
,
Surma
,
M. L.
, and
Wu
,
V. Y.
, 1982, “
In Vivo Biosynthesis and Turnover of Glomerular Basement Membrane in Diabetic Rats
,”
Am. J. Physiol.
,
242
(
4
), pp.
F385
F389
.
55.
Iglesias-de la Cruz
,
M. C.
,
Ziyadeh
,
F. N.
, and
Isono
,
M.
, 2002, “
Effects of High Glucose and TGF-Beta1 on the Expression of Collagen IV and Vascular Endothelial Growth Factor in Mouse Podocytes
,”
Kidney Int.
,
62
(
3
), pp.
901
913
.
56.
Zatz
,
R.
, and
Brenner
,
B. M.
, 1986, “
Pathogenesis of Diabetic Microangiopathy. The Hemodynamic View
,”
Am. J. Med.
,
80
(
3
), pp.
443
453
.
57.
Carmines
,
P. K.
, 2010, “
The Renal Vascular Response to Diabetes
,”
Curr. Opin. Nephrol. Hypertens.
,
19
(
1
), pp.
85
90
.
58.
Osterby
,
R.
,
Bangstad
,
H. J.
, and
Nyberg
,
G.
, 2001, “
On Glomerular Structural Alterations in Type-1 Diabetes. Companions of Early Diabetic Glomerulopathy
,”
Virchows Arch.
,
438
(
2
), pp.
129
135
.
59.
O’Rourke
,
M. F.
, 2007, “
Arterial Aging: Pathophysiological Principles
,”
Vasc. Med.
,
12
(
4
), pp.
329
341
.
60.
Cooper
,
M. E.
,
Allen
,
T. J.
, and
O’Brien
,
R. C.
, 1988, “
Effects of Genetic Hypertension on Diabetic Nephropathy in the Rat–—Functional and Structural Characteristics
,”
J. Hypertens.
,
6
(
12
), pp.
1009
1016
.
61.
Nielsen
,
B.
,
Gronbaek
,
H.
, and
Osterby
,
R.
, 1999, “
Effect of the Calcium Channel Blocker Nitrendipine in Normotensive and Spontaneously Hypertensive, Diabetic Rats on Kidney Morphology and Urinary Albumin Excretion
,”
J. Hypertens.
,
17
(
7
), pp.
973
981
.
62.
Valentin
,
A.
and
Humphrey
,
J. D.
, 2009, “
Modeling Effects of Axial Extension on Arterial Growth and Remodeling
,”
Med. Biol. Eng. Comput.
,
47
(
9
), pp.
979
987
.
63.
Gleason
,
R. L.
, Jr.
and
Humphrey
,
J. D.
, 2005, “
A 2D Constrained Mixture Model for Arterial Adaptations to Large Changes in Flow, Pressure and Axial Stretch
,”
IMA J. Math. Appl. Med. Biol.
,
22
(
4
), pp.
347
369
.
64.
Rachev
,
A.
,
Stergiopulos
,
N.
, and
Meister
,
J. J.
, 1996, “
Theoretical Study of Dynamics of Arterial Wall Remodeling in Response to Changes in Blood Pressure
,”
J. Biomech.
,
29
(
5
), pp.
635
642
.
65.
Lu
,
X.
,
Pandit
,
A.
, and
Kassab
,
G. S.
, 2004, “
Biaxial Incremental Homeostatic Elastic Moduli of Coronary Artery: Two-Layer Model
,”
Am. J. Physiol. Heart Circ. Physiol.
,
287
(
4
), pp.
H1663
H1669
.
66.
Jacobsen
,
J. C.
,
Mulvany
,
M. J.
, and
Holstein-Rathlou
,
N. H.
, 2008, “
A Mechanism for Arteriolar Remodeling Based on Maintenance of Smooth Muscle Cell Activation
,”
Am. J. Physiol. Regulatory Integrative Comp. Physiol.
,
294
(
4
), pp.
R1379
R1389
.
67.
Pries
,
A. R.
,
Reglin
,
B.
, and
Secomb
,
T. W.
, 2005, “
Remodeling of Blood Vessels: Responses of Diameter and Wall Thickness to Hemodynamic and Metabolic Stimuli
,”
Hypertension
,
46
(
4
), pp.
725
731
.
68.
Mundel
,
P.
, and
Reiser
,
J.
, 2010, “
Proteinuria: An Enzymatic Disease of the Podocyte?
,”
Kidney Int.
,
77
(
7
), pp.
571
580
.
69.
Alford
,
P. W.
, and
Taber
,
L. A.
, 2008, “
Computational Study of Growth and Remodelling in the Aortic Arch
,”
Comput. Methods Biomech. Biomed. Eng.
,
11
(
5
), pp.
525
538
.
70.
Abrahamson
,
D. R.
,
Isom
,
K.
, and
Roach
,
E.
, 2007, “
Laminin Compensation in Collagen α3(IV) Knockout (Alport) Glomeruli Contributes to Permeability Defects
,”
J. Am. Soc. Nephrol.
,
18
(
9
), pp.
2465
2472
.
71.
Rumpelt
,
H. J.
,
Steinke
,
A.
, and
Thoenes
,
W.
, 1992, “
Alport-Type Glomerulopathy: Evidence for Diminished Capillary Loop Size
,”
Clin. Nephrol.
,
37
(
2
), pp.
57
64
.
72.
Srinivasan
,
M.
,
Uzel
,
S. G.
, and
Gautieri
,
A.
, 2009, “
Alport Syndrome Mutations in Type IV Tropocollagen Alter Molecular Structure and Nanomechanical Properties
,”
J. Struct. Biol.
,
168
(
3
), pp.
503
510
.
73.
Sander
,
E. A.
,
Stylianopoulos
,
T.
, and
Tranquillo
,
R. T.
, 2009, “
Image-Based Multiscale Modeling Predicts Tissue-Level and Network-Level Fiber Reorganization in Stretched Cell-Compacted Collagen Gels
,”
Proc. Natl. Acad. Sci. U.S.A.
,
106
(
42
). pp.
17675
17680
.
74.
Hadi
,
M. F.
,
Sander
,
E. A.
, and
Ruberti
,
J. W.
, 2012, “
Simulated Remodeling of Loaded Collagen Networks Via Strain–Dependent Enzymatic Degradation and Constant-Rate Fiber Growth
,”
Mech. Mater.
,
44
, pp.
72
82
.
75.
Welling
,
L. W.
and
Grantham
,
J. J.
, 1972, “
Physical Properties of Isolated Perfused Renal Tubules and Tubular Basement Membranes
,”
J. Clin. Invest.
,
51
(
5
), pp.
1063
1075
.
76.
Jorgensen
,
F.
, and
Bentzon
,
M. W.
, 1968, “
The Ultrastructure of the Normal Human Glomerulus
,”
Lab. Invest.
,
18
(
1
), pp.
42
.
77.
Bolton
,
G. R.
,
Deen
,
W. M.
, and
Daniels
,
B. S.
, 1998, “
Assessment of the Charge Selectivity of Glomerular Basement Membrane Using Ficoll Sulfate
,”
Am. J. Physiol.
,
274
(
5
), pp.
F889
F896
.
78.
Durvasula
,
R. V.
,
Petermann
,
A. T.
, and
Hiromura
,
K.
, 2004, “
Activation of a Local Tissue Angiotensin System in Podocytes by Mechanical Strain
,”
Kidney Int.
,
65
(
1
), pp.
30
39
.
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