Viewed in renal physiology as a refined filtration device, the glomerulus filters large volumes of blood plasma while keeping proteins within blood circulation. Effects of macromolecule size and macromolecule hydrodynamic interaction with the nanostructure of the cellular layers of the glomerular capillary wall on the glomerular size selectivity are investigated through a mathematical simulation based on an ultrastructural model. The epithelial slit, a planar arrangement of fibers connecting the epithelial podocytes, is represented as a row of parallel cylinders with nonuniform spacing between adjacent fibers. The mean and standard deviation of gap half-width between its fibers are based on values recently reported from electron microscopy. The glomerular basement membrane (GBM) is represented as a fibrous medium containing fibers of two different sizes: the size of type IV collagens and that of glycosaminoglycans (GAGs). The endothelial cell layer is modeled as a layer full of fenestrae that are much larger than solute size and filled with GAGs. The calculated total sieving coefficient agrees well with the sieving coefficients of ficolls obtained from in vivo urinalysis in humans, whereas the computed glomerular hydraulic permeability also falls within the range estimated from human glomerular filtration rate (GFR). Our result indicates that the endothelial cell layer and GBM significantly contribute to solute and fluid restriction of the glomerular barrier, whereas, based on the structure of the epithelial slit obtained from electron microscopy, the contribution of the epithelial slit could be smaller than previously believed.

References

1.
Mattern
,
K. J.
,
2008
, “
Permeability Studies in Biomimetic Glycosaminoglycan-Hydrogel Membranes
,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
2.
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
.
3.
Deen
,
W. M.
,
Lazzara
,
M. J.
, and
Myers
,
B. D.
,
2001
, “
Structural Determinants of Glomerular Permeability
,”
Am. J. Physiol. Renal Physiol.
,
281
(
4
), pp.
579
596
.
4.
Layton
,
A. T.
, and
Edwards
,
A.
,
2014
,
Mathematical Modeling in Renal Physiology
,
Springer
,
Berlin
.
5.
Maddox
,
D. A.
,
Deen
,
W. M.
, and
Brenner
,
B. M.
,
1992
, “
Glomerular Filtration
,”
Handbook of Physiology, Renal Physiology
, E. E. Windhager, ed., Oxford University Press, New York, pp. 545–638.
6.
Deen
,
W. M.
,
Bridges
,
C. R.
,
Brenner
,
B. M.
, and
Myers
,
B. D.
,
1985
, “
Heteroporous Model of Glomerular Size Selectivity: Application to Normal and Nephrotic Humans
,”
Am. J. Physiol.
,
249
(
3
), pp.
F374
F389
.
7.
Rippe
,
B.
, and
Haraldsson
,
B.
,
1994
, “
Transport of Macromolecules Across Microvascular Walls: The Two-Pore Theory
,”
Physiol. Rev.
,
74
(
1
), pp.
163
219
.
8.
Tencer
,
J.
,
Frick
,
I.-M.
,
Oquist
,
B. W.
,
Alm
,
P.
, and
Rippe
,
B.
,
1998
, “
Size-Selectivity of the Glomerular Barrier to High Molecular Weight Proteins: Upper Size Limitations of Shunt Pathways
,”
Kidney Int.
,
53
(
3
), pp.
709
715
.
9.
Öberg
,
C. M.
, and
Rippe
,
B.
,
2014
, “
A Distributed Two-Pore Model: Theoretical Implications and Practical Application to the Glomerular Sieving of Ficoll
,”
Am. J. Physiol. Renal Physiol.
,
306
(
8
), pp.
F844
F854
.
10.
Curry
,
F. E.
, and
Michel
,
C. C.
,
1980
, “
A Fiber Matrix Model of Capillary Permeability
,”
Microvasc. Res.
,
20
(
1
), pp.
96
99
.
11.
Ohlson
,
M.
,
Sorensson
,
J.
,
Lindstrom
,
K.
,
Blom
,
A. M.
,
Fries
,
E.
, and
Haraldsson
,
B.
,
2001
, “
Effects of Filtration Rate on the Glomerular Barrier and Clearance of Four Differently Shaped Molecules
,”
Am. J. Physiol. Renal Physiol.
,
281
(
1
), pp.
F103
F113
.
12.
Öberg
,
C. M.
, and
Rippe
,
B.
,
2013
, “
Quantification of the Electrostatic Properties of the Glomerular Filtration Barrier Modeled as a Charged Fiber Matrix Separating Anionic From Neutral Ficoll
,”
Am. J. Physiol. Renal Physiol.
,
304
(
6
), pp.
F781
F787
.
13.
Drumond
,
M. C.
, and
Deen
,
W. M.
,
1994
, “
Structural Determinants of Glomerular Hydraulic Permeability
,”
Am. J. Physiol.
,
266
(
1
), pp.
F1
F12
.
14.
Drumond
,
M. C.
, and
Deen
,
W. M.
,
1995
, “
Hindered Transport of Macromolecules Through a Single Row of Cylinders: Application to Glomerular Filtration
,”
ASME J. Biomech. Eng.
,
117
(
4
), pp.
414
422
.
15.
Edwards
,
A.
,
Daniels
,
B. S.
, and
Deen
,
W. M.
,
1999
, “
Ultrastructural Model for Size Selectivity in Glomerular Filtration
,”
Am. J. Physiol. Renal Physiol.
,
276
(
6
), pp.
F892
F902
.
16.
Rodewald
,
R.
, and
Karnovsky
,
M. J.
,
1974
, “
Porous Substructure of the Glomerular Slit Diaphragm in the Rat and Mouse
,”
J. Cell Biol.
,
60
(
2
), pp.
423
433
.
17.
Blouch
,
K.
,
Deen
,
W. M.
,
Fauvel
,
J.-P.
,
Bialek
,
J.
,
Derby
,
G.
, and
Myers
,
B. D.
,
1997
, “
Molecular Configuration and Glomerular Size Selectivity in Healthy and Nephrotic Humans
,”
Am. J. Physiol.
,
273
(
3
), pp.
F430
F437
.
18.
Gagliardini
,
E.
,
Conti
,
S.
,
Benigni
,
A.
,
Remuzzi
,
G.
, and
Remuzzi
,
A.
,
2010
, “
Imaging of the Porous Ultrastructure of the Glomerular Epithelial Filtration Slit
,”
J. Am. Soc. Nephrol.
,
21
(
12
), pp.
2081
2089
.
19.
Rice
,
W. L.
,
Hoek
,
A. N. V.
,
Paunescu
,
T. G.
,
Huynh
,
C.
,
Goetze
,
B.
,
Singh
,
B.
,
Scipioni
,
L.
,
Stern
,
L. A.
, and
Brown
,
D.
,
2013
, “
High Resolution Helium Ion Scanning Microscopy of the Rat Kidney
,”
PLoS One
,
8
(
3
), p.
e57051
.
20.
Deen
,
W. M.
,
Robertson
,
C. R.
, and
Brenner
,
B. M.
,
1974
, “
Concentration Polarization in an Ultrafiltration Capillary
,”
Biophys. J.
,
14
(
5
), pp.
412
431
.
21.
Brady
,
J. F.
,
1994
, “
Hindered Diffusion
,”
American Institute of Chemical Engineers Annual Meeting
, San Francisco, CA, Nov. 13–18, p. 320.
22.
Clague
,
D. S.
, and
Phillips
,
R. J.
,
1996
, “
Hindered Diffusion of Spherical Macromolecules Through Dilute Fibrous Media
,”
Phys. Fluids
,
8
(
7
), pp.
1720
1731
.
23.
Phillips
,
R. J.
,
2000
, “
A Hydrodynamic Model for Hindered Diffusion of Proteins and Micelles in Hydrogels
,”
Biophys. J.
,
79
(
6
), pp.
3350
3354
.
24.
Oseen
,
C. W.
,
1927
,
Neuere Methoden und Ergebnisse in der Hydrodynamik
,
Akademische Verlagsgesellschaft
,
Leipzig, Germany
.
25.
Dufresne
,
E. R.
,
Altman
,
D.
, and
Grier
,
D. G.
,
2001
, “
Brownian Dynamics of a Sphere Between Parallel Walls
,”
Europhys. Lett.
,
53
(
2
), pp.
264
270
.
26.
Johnson
,
E. M.
,
Berk
,
D. A.
,
Jain
,
R. K.
, and
Deen
,
W. M.
,
1996
, “
Hindered Diffusion in Agarose Gels: Test of Effective Medium Model
,”
Biophys. J.
,
70
(
2
), pp.
1017
1026
.
27.
Johansson
,
L.
, and
Löfroth
,
J. E.
,
1993
, “
Diffusion and Interaction in Gels and Solutions IV: Hard Sphere Brownian Dynamics Simulations
,”
J. Chem. Phys.
,
98
(
9
), pp.
7471
7479
.
28.
Tsai
,
D. S.
, and
Strieder
,
W.
,
1986
, “
Effective Conductivities of Random Fiber Beds
,”
Chem. Eng. Commun.
,
40
(
1–6
), pp.
207
218
.
29.
Kosar
,
T. F.
, and
Phillips
,
R. J.
,
1995
, “
Measurement of Protein Diffusion in Dextran Solutions by Holographic Interferometry
,”
AIChE J.
,
41
(
3
), pp.
701
711
.
30.
Kosto
,
K. B.
, and
Deen
,
W. M.
,
2004
, “
Diffusivities of Macromolecules in Composite Hydrogels
,”
AIChE J.
,
50
(
11
), pp.
2648
2658
.
31.
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
.
32.
Edwards
,
A.
,
Deen
,
W. M.
, and
Daniels
,
B. S.
,
1997
, “
Hindered Transport of Macromolecules in Isolated Glomeruli I: Diffusion Across Intact and Cell-Free Capillaries
,”
Biophys. J.
,
72
(
1
), pp.
204
213
.
33.
Brinkman
,
H. C.
,
1947
, “
A Calculation of the Viscous Force Exerted by A Flowing Fluid on a Dense Swarm of Particles
,”
Appl. Sci. Res. A
,
1
, pp.
27
34
.
34.
Sugihara-Seki
,
M.
,
2004
, “
Motion of a Sphere in a Cylindrical Tube Filled With a Brinkman Medium
,”
Fluid. Dyn. Res.
,
34
(
1
), pp.
59
76
.
35.
Edwards
,
A.
,
Daniels
,
B. S.
, and
Deen
,
W. M.
,
1997
, “
Hindered Transport of Macromolecules in Isolated Glomeruli—II: Convection and Pressure Effects in Basement Membrane
,”
Biophys. J.
,
72
(
1
), pp.
214
222
.
36.
Punyaratabandhu
,
N.
,
2015
, “
Simulation of Transport of Spherical Particles Through Hydrogel and Row of Parallel Fibers for Applications in Glomerular Filtration in Normal and Nephrotic Humans
,” M.Sc. thesis, Chulalongkorn University, Bangkok, Thailand.
37.
Boyd
,
R. F.
, and
Zydney
,
A. L.
,
1997
, “
Sieving Characteristics of Multilayer Ultrafiltration Membranes
,”
J. Membr. Sci.
,
131
(1–3), pp.
155
165
.
38.
Hora
,
K.
,
Ohno
,
S.
,
Oguchi
,
H.
,
Furukawa
,
T.
, and
Furuta
,
S.
,
1990
, “
Three-Dimensional Study of Glomerular Slit Diaphragm by Quick-Freezing and Deep-Etching Replica Method
,”
Eur. J. Cell Biol.
,
53
(
2
), pp.
402
406
.
39.
Tryggvason
,
K.
, and
Wartiovaara
,
J.
,
2005
, “
How Does the Kidney Filter Plasma?
,”
Physiology
,
20
(
2
), pp.
96
101
.
40.
Amsden
,
B.
,
1998
, “
Solute Diffusion in Hydrogels. An Examination of the Retardation Effect
,”
Polym. Gels Networks
,
6
(
1
), pp.
13
43
.
41.
Drumond
,
M. C.
, and
Deen
,
W. M.
,
1994
, “
Stokes Flow Through a Row of Cylinders Between Parallel Walls: Model for the Glomerular Slit Diaphragm
,”
ASME J. Biomech. Eng.
,
116
(
2
), pp.
184
189
.
42.
Drumond
,
M. C.
,
Kristal
,
B.
,
Myers
,
B. D.
, and
Deen
,
W. M.
,
1994
, “
Structural Basis for Reduced Glomerular Filtration Capacity in Nephrotic Humans
,”
J. Clin. Invest.
,
94
(
3
), pp.
1187
1195
.
43.
Lazzara
,
M. J.
,
Blankschtein
,
D.
, and
Deen
,
W. M.
,
2000
, “
Effects of Multisolute Steric Interactions on Membrane Partition Coefficients
,”
J. Colloid Interface Sci.
,
226
(
1
), pp.
112
122
.
44.
Satchell
,
S.
,
2013
, “
The Role of the Glomerular Endothelium in Albumin Handling
,”
Nat. Rev. Nephrol.
,
9
(
12
), pp.
717
725
.
45.
Sugimoto
,
H.
,
Hamano
,
Y.
,
Charytan
,
D.
,
Cosgrove
,
D.
,
Kieran
,
M.
,
Sudhakar
,
A.
, and
Kalluri
,
R.
,
2003
, “
Neutralization of Circulating Vascular Endothelial Growth Factor (VEGF) by Anti-VEGF Antibodies and Soluble VEGF Receptor 1 (sFlt-1) Induces Proteinuria
,”
J. Biol. Chem.
,
278
(
15
), pp.
12605
12608
.
46.
Davis
,
B.
,
Cas
,
A. D.
,
Long
,
D. A.
,
White
,
K. E.
,
Hayward
,
A.
,
Ku
,
C.-H.
,
Woolf
,
A. S.
,
Bilous
,
R.
,
Viberti
,
G.
, and
Gnudi
,
L.
,
2007
, “
Podocyte-Specific Expression of Angiopoietin-2 Causes Proteinuria and Apoptosis of Glomerular Endothelia
,”
J. Am. Soc. Nephrol.
,
18
(
8
), pp.
2320
2329
.
47.
Wartiovaara
,
J.
,
Öfverstedt
,
L.-G.
,
Khoshnoodi
,
J.
,
Zhang
,
J.
,
Mäkelä
,
E.
,
Sandin
,
S.
,
Ruotsalainen
,
V.
,
Cheng
,
R. H.
,
Jalanko
,
H.
,
Skoglund
,
U.
, and
Tryggvason
,
K.
,
2004
, “
Nephrin Strands Contribute to a Porous Slit Diaphragm Scaffold as Revealed by Electron Tomography
,”
J. Clin. Invest.
,
114
(
10
), pp.
1475
1483
.
48.
Lazzara
,
M. J.
, and
Deen
,
W. M.
,
2001
, “
Effects of Plasma Proteins on Sieving of Tracer Macromolecules in Glomerular Basement Membrane
,”
Am. J. Physiol. Renal Physiol.
,
281
(
5
), pp.
F860
F868
.
49.
Neal
,
C. R.
,
Muston
,
P. R.
,
Njegovan
,
D.
,
Verrill
,
R.
,
Harper
,
S. J.
,
Deen
,
W. M.
, and
Bates
,
D. O.
,
2007
, “
Glomerular Filtration Into the Subpodocyte Space Is Highly Restricted Under Physiological Perfusion Conditions
,”
Am. J. Physiol. Renal Physiol.
,
293
(
6
), pp.
F1787
F1798
.
50.
Pagtalunan
,
M. E.
,
Miller
,
P. L.
,
Jumping-Eagle
,
S.
,
Nelson
,
R. G.
,
Myers
,
B. D.
,
Rennke
,
H. G.
,
Coplon
,
N. S.
,
Sun
,
L.
, and
Meyer
,
T. W.
,
1997
, “
Podocyte Loss and Progressive Glomerular Injury in Type II Diabetes
,”
J. Clin. Invest.
,
99
(
2
), pp.
342
348
.
51.
Stillman
,
I. E.
, and
Karumanchi
,
S. A.
,
2007
, “
The Glomerular Injury of Preeclampsia
,”
J. Am. Soc. Nephrol.
,
18
(
8
), pp.
2281
2284
.
52.
van den Berg
,
J. G.
,
van den Bergh Weerman
,
M. A.
,
Assmann
,
K. J. M.
,
Weening
,
J. J.
, and
Florquin
,
S.
,
2004
, “
Podocyte Foot Process Effacement Is Not Correlated With the Level of Proteinuria in Human Glomerulopathies
,”
Kidney Int.
,
66
(
5
), pp.
1901
1906
.
53.
Zhang
,
A.
, and
Huang
,
S.
,
2012
, “
Progress in Pathogenesis of Proteinuria
,”
Int. J. Nephrol.
,
2012
, p. 314251.
54.
Nieuwdorp
,
M.
,
Mooij
,
H. L.
,
Kroon
,
J.
,
Atasever
,
B.
,
Spaan
,
J. A. E.
,
Ince
,
C.
,
Holleman
,
F.
,
Diamant
,
M.
,
Heine
,
R. J.
,
Hoekstra
,
J. B. L.
,
Kastelein
,
J. J. P.
,
Stroes
,
E. S. G.
, and
Vink
,
H.
,
2006
, “
Endothelial Glycocalyx Damage Coincides With Microalbuminuria in Type 1 Diabetes
,”
Diabetes
,
55
(
4
), pp.
1127
1132
.
55.
Satoh
,
T.
,
Kato
,
H.
,
Kumagai
,
Y.
,
Yoneyama
,
M.
,
Sato
,
S.
,
Matsushita
,
K.
,
Tsujimura
,
T.
,
Fujita
,
T.
,
Akira
,
S.
, and
Takeuchi
,
O.
,
2010
, “
LGP2 Is a Positive Regulator of RIG-I– and MDA5-Mediated Antiviral Responses
,”
PNAS
,
107
(
4
), pp.
1512
1517
.
56.
Jeansson
,
M.
, and
Haraldsson
,
B.
,
2003
, “
Glomerular Size and Charge Selectivity in the Mouse After Exposure to Glucosaminoglycan-Degrading Enzymes
,”
J. Am. Soc. Nephrol.
,
14
(
7
), pp.
1756
1765
.
57.
van den Born
,
J.
,
van den Heuvel
,
L. P.
,
Bakker
,
M. A.
,
Veerkamp
,
J. H.
,
Assmann
,
K. J.
, and
Berden
,
J. H.
,
1992
, “
A Monoclonal Antibody Against GBM Heparan-Sulfate Induces an Acute Selective Proteinuria in Rats
,”
Kidney Int.
,
41
(
1
), pp.
115
123
.
58.
Kanwar
,
Y. S.
,
Rosenzweig
,
L. J.
, and
Kerjasachki
,
D. I.
, 1981, “
Glycosaminoglycans of the Glomerular Basement Membrane in Normal and Nephrotic States
,”
Renal Physiol.
,
4
, pp.
121
130
.
59.
Wijinhoven
,
T. J. M.
,
Lensen
,
J. F. M.
,
Wismans
,
R. G. P.
,
Lamrani
,
M.
,
Momnens
,
L. A. H.
,
Wevers
,
R. A.
,
Rops
,
A. L. W. M. M.
,
van der Vlag
,
J.
,
Berden
,
J. H. M.
,
van den Heuvel
,
L. P. W. J.
, and
van Kuppevelt
,
T. H.
,
2007
, “
In Vivo Degradation of Heperan Sulfates in the Glomerular Basement Membrane Does Not Result in Proteinuria
,”
J. Am. Soc. Nephrol.
,
18
(
3
), pp.
823
832
.
60.
Rossi
,
M.
,
Morita
,
H.
,
Sormunen
,
R.
,
Airenne
,
S.
,
Kreivi
,
M.
,
Wang
,
L.
,
Fukai
,
N.
,
Olsen
,
B. R.
,
Tryggvason
,
K.
, and
Soininen
,
R.
,
2003
, “
Heparan Sulfate Chains of Perlecan are Indispensable in the Lens and Capsule But Not in Kidney
,”
EMBO J.
,
22
(
2
), pp.
236
245
.
61.
Sangani
,
A. S.
, and
Acrivos
,
A.
,
1982
, “
Slow Flow Past Periodic Arrays of Cylinders With Application to Heat Transfer
,”
Int. J. Multiphase Flow
,
8
(
3
), pp.
193
206
.
You do not currently have access to this content.