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Research Papers

# Deformation-Dependent Enzyme Mechanokinetic Cleavage of Type I Collagen

[+] Author and Article Information
Karla E.-K. Wyatt

Laboratory for Soft Tissue Research, Tissue Engineering, Regeneration and Repair Program, Hospital for Special Surgery, 535 East 70th Street, New York, NY 10021; Department of Biomedical Engineering, City College of New York, Steinman Hall, Room T-401, Convent Avenue at 140th Street, New York, NY 10031

Jonathan W. Bourne

Department of Physiology and Biophysics, Weill Graduate School of Cornell University, 1300 York Avenue, Room E-509, New York, NY 10021; Laboratory for Soft Tissue Research, Tissue Engineering, Regeneration and Repair Program, Hospital for Special Surgery, 535 East 70th Street, New York, NY 10021

Peter A. Torzilli1

Laboratory for Soft Tissue Research, Tissue Engineering, Regeneration and Repair Program, Hospital for Special Surgery, 535 East 70th Street, New York, NY 10021; Program in Physiology, Biophysics and Systems Biology, Weill Graduate School of Cornell University, 1300 York Avenue, Room E-509, New York, NY 10021torzillip@hss.edu

1

Corresponding author.

J Biomech Eng 131(5), 051004 (Mar 24, 2009) (11 pages) doi:10.1115/1.3078177 History: Received February 04, 2008; Revised November 17, 2008; Published March 24, 2009

## Abstract

Collagen is a key structural protein in the extracellular matrix of many tissues. It provides biological tissues with tensile mechanical strength and is enzymatically cleaved by a class of matrix metalloproteinases known as collagenases. Collagen enzymatic kinetics has been well characterized in solubilized, gel, and reconstituted forms. However, limited information exists on enzyme degradation of structurally intact collagen fibers and, more importantly, on the effect of mechanical deformation on collagen cleavage. We studied the degradation of native rat tail tendon fibers by collagenase after the fibers were mechanically elongated to strains of $ε=1–10%$. After the fibers were elongated and the stress was allowed to relax, the fiber was immersed in Clostridium histolyticum collagenase and the decrease in stress $(σ)$ was monitored as a means of calculating the rate of enzyme cleavage of the fiber. An enzyme mechanokinetic (EMK) relaxation function $TE(ε)$ in $s−1$ was calculated from the linear stress-time response during fiber cleavage, where $TE(ε)$ corresponds to the zero order Michaelis–Menten enzyme-substrate kinetic response. The EMK relaxation function $TE(ε)$ was found to decrease with applied strain at a rate of $∼9%$ per percent strain, with complete inhibition of collagen cleavage predicted to occur at a strain of $∼11%$. However, comparison of the EMK response ($TE$ versus $ε$) to collagen’s stress-strain response ($σ$ versus $ε$) suggested the possibility of three different EMK responses: (1) constant $TE(ε)$ within the toe region $(ε<3%)$, (2) a rapid decrease $(∼50%)$ in the transition of the toe-to-heel region $(ε≅3%)$ followed by (3) a constant value throughout the heel $(ε=3–5%)$ and linear $(ε=5–10%)$ regions. This observation suggests that the mechanism for the strain-dependent inhibition of enzyme cleavage of the collagen triple helix may be by a conformational change in the triple helix since the decrease in $TE(ε)$ appeared concomitant with stretching of the collagen molecule.

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## Figures

Figure 1

(a) The collagen-enzyme mechanokinetic automated test system used to mechanically stretch the collagen fiber between grips attached to two stepper motors. The load applied to the fiber is monitored using a 250 g load cell attached to the right grip, while images of the fiber’s elongation and diameter are recorded using a digital camera (not shown) attached to a microscope. Two personal computers (not shown) were used to simultaneously control the motors and record the load and camera images. (b) The collagen fiber is affixed to the test grips by gluing the fiber within a groove and hole and then positioning the fiber within a 1 mm wide by 25 mm long channel. PBS is slowly dripped into the channel during the fiber elongation and load-relaxation phases, and then replaced with bacterial collagenase during the enzyme mechanokinetic cleavage phase. (c) Schematic of the CEMKATS used to mechanically stretch the collagen fiber and measure the resulting fiber load and elongation during the elongation, relaxation, and enzyme-cleavage phases. The fiber is stretched using two stepper motors, and the load is continuously recorded using a load cell. The fiber elongation (gage marks) and diameter are recorded using a digital camera attached to a microscope. The stepper motors and recording transducers are interfaced to two personal computers for continuous and simultaneous control and data recording, respectively.

Figure 2

The local fiber axial strain (change in distance between gage marks) and radial strain (change in diameter) at the center of the fiber were recorded using a microscope and digital camera image capture at (a) time t=0, unstrained initial lengths, lo and do, (b) time=tp, at the end of the elongation phase at peak stress, lp and dp, (c) time=tr, after mechanical stress relaxation, lr and dr, and (d) time=te, after collagenase cleavage, le and de. The initial, elongation, and relaxation lengths ((a), (b), and (c), respectively) were used to determine the fiber’s axial and radial strains. Fiber images (right) are for an initial 3% grip-to-grip strain.

Figure 3

Typical mechanical-elongation (a), mechanical stress-relaxation (c), and enzyme-cleavage (e) responses for the rat tail tendon fibers subjected to a constant applied strain (3%) and degradation by bacterial collagenase, respectively. The peak stress occurs at the end of the mechanical-elongation phase (b). Immediately after the fiber is exposed to the collagenase (d) there is a small transient increase in fiber stress due to the osmotic stress. The mechanical stress-relaxation response (c) was curve-fit using Eq. 1 (dotted line) and extended beyond (d) to predict the continued mechanical stress relaxation (f). This was used to correct the enzyme-cleavage response (g). The linear portion of the corrected enzyme-cleavage response (h) was used to calculate the EMK relaxation function. For clarity the data shown in (a), (e), and (g) are plotted at 1 s intervals, and in (c) at every 100 s.

Figure 4

Plot of the fiber’s axial (εl, gray squares) and radial (εd, black squares) strains at the end of the mechanical-elongation (tp) and mechanical stress-relaxation (tr) phases. The radial strain was always greater than the axial strain at both times. After mechanical stress-relaxation both strains increased significantly. A best-fit linear model ±95% confidence intervals is shown for the axial (gray lines) and radial (black lines) strains.

Figure 5

The Poisson's ratio (εd/εl) at the end of the mechanical-elongation (peak, gray squares) and mechanical stress-relaxation (equilibrium, black squares) phases decreased with increasing axial strain (εl) at the peak and equilibrium times, tp and tr, respectively. For both phases the data fit best to an exponential-linear model (gray and black lines, respectively). Note that the greatest decrease in the Poisson's ratio occurs for εl(tr)≤3%.

Figure 6

The peak stress at the end of the mechanical-elongation phase (peak ◼), at time tp, linearly increased with increasing axial peak strain. However, the equilibrium stress at the end of the stress-relaxation phase (equilibrium ▼), time tr, was independent of the equilibrium stress. A best-fit linear model ±95% confidence intervals is shown for the peak and equilibrium phases. Note that after stress-relaxation the equilibrium strains increased by 1.71±0.37, as shown in Fig. 4.

Figure 7

The Enzyme MechanoKinetic (EMK) relaxation function TE(εl) is plotted as a function of the axial strain at the end of the mechanical-elongation (gray squares) and mechanical stress-relaxation phases (black squares), εl(tp) and εl(tr), respectively. A best-fit linear model ±95% confidence intervals is shown for the peak (gray dashed line) and equilibrium (solid black line). Note that a sharp transition in TE(εl) appears to occur at εl≃3%.

Figure 8

Nonlinear curve fits to the EMK relaxation function TE(εl) as a function of the axial strain εl(tr) after mechanical stress relaxation. (a) Schematic representation of fiber elongation in the toe (εl=0–3%), heel (3–5%), and linear (>5%) regions of the stress-strain response. In the toe region the fiber crimp pattern straightens, followed by stretching of the fiber in the heel and linear regions. Adapted from Refs. 40,42. (b) Best-fit four-parameter logistic models are shown with variable slope (dashed black line) and constant slope (solid black line). The mean±standard error of the mean for TE(εl) in each region are also shown (gray, solid, and dotted, respectively). Note that the transition in TE(εl) occurs for εl=2.9–3.4%.

## Errata

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