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Effect of Supercoiling on the Mechanical and Permeability Properties of Model Collagen IV Networks

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Abstract

Collagen IV networks in the glomerular basement membrane (GBM) are essential for the maintenance and regulation of blood filtration in the kidneys. The GBM contains two different types of collagen IV networks: [α1(IV)]2α2(IV) and α3(IV)α4(IV)α5(IV), the latter of which has a higher number of supercoils (two or more collagens coiling around each other). To investigate the effects of supercoiling on the mechanical and permeability properties of collagen IV networks, we generated model collagen IV networks in the GBM and reconnected them to create different levels of supercoiling. We found that supercoiling greatly increases the stiffness of collagen IV networks but only minimally decreases the permeability. Also, doubling the amount of supercoils in a network had a bigger effect than doubling the stiffness of the supercoils. Our results suggest that the formation of supercoils is a specialized mechanism by the GBM that provides with a network stiff and strong enough to withstand the high hydrostatic pressures of filtration, yet porous enough that filtration is not hindered. Clinically, understanding the effects of supercoiling gives us insight into the mechanisms of GBM failure in some disease states where the normal collagen IV structure is disrupted.

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Abbreviations

GBM:

Glomerular basement membrane

RVE:

Representative volume element

n i :

Node number

α s :

Smallest angle

M :

Midline

p m :

Percent of length of midline/supercoil ratio

r :

Radius

F :

Force (N)

E :

Elastic modulus (GPa)

E sc :

Supercoil elastic modulus (GPa)

A :

Collagen IV cross-sectional area (nm2)

A sc :

Supercoil cross-sectional area (nm2)

B :

Non-linearity parameter (Unitless)

e G :

Green strain (Unitless)

λ :

Stretch ratio (Unitless)

σ ij :

Cauchy stress tensor (MPa)

V :

Volume of RVE (nm3)

x i :

Boundary nodal position (nm)

Φ :

Collagen IV volume fraction (Unitless)

l :

Length of collagen IV segment (nm)

d ij :

Drag coefficient tensor of single segment (nm−1)

R ij :

Direction cosines matrix (rad)

C ij :

Coefficients matrix of drag (nm)

V n :

Volume of collagen IV network (nm3)

D ij :

Drag coefficient tensor of whole network (nm−2)

k ij :

Darcy permeability (nm2)

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Acknowledgments

This work was carried out in part using computing resources at the University of Minnesota Supercomputing Institute and was supported by the National Science Foundation Graduate Research Fellowship and Grant No. NSF CMMI 1300649. This work was also supported by resources and the use of facilities at the Minneapolis VA Health Care System.

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Authors and Affiliations

  1. Department of Biomedical Engineering, University of Minnesota, 7-105 Nils Hasselmo Hall, 312 Church St. SE, Minneapolis, MN, 55455, USA

    Lazarina Gyoneva & Victor H. Barocas

  2. Division of Renal Diseases and Hypertension, Department of Medicine, University of Minnesota, 717 Delaware Street SE Suite 353, Minneapolis, MN, 55414, USA

    Yoav Segal

  3. Minneapolis VA Health Care System, One Veterans Drive, Minneapolis, MN, 55417, USA

    Yoav Segal

  4. Department of Chemical Engineering and Materials Science, University of Minnesota, 151 Amundson Hall, 421 Washington Ave SE, Minneapolis, MN, 55455, USA

    Kevin D. Dorfman

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  1. Lazarina Gyoneva
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  2. Yoav Segal
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  4. Victor H. Barocas
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Correspondence to Victor H. Barocas.

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Associate Editor Gerhard A. Holzapfel oversaw the review of this article.

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Gyoneva, L., Segal, Y., Dorfman, K.D. et al. Effect of Supercoiling on the Mechanical and Permeability Properties of Model Collagen IV Networks. Ann Biomed Eng 43, 1695–1705 (2015). https://doi.org/10.1007/s10439-014-1187-1

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