Strain Stiffening

When you impose a small strain on a sample its response will be roughly linear. In other words, the amount of force necessary to deform the sample a given amount is roughly constant. As you increase the strain most materials will start to weaken and eventually break (strain weaken). Interestingly, many biopolymer networks exhibit the opposite behavior. Namely, as you increasingly strain them, they stiffen before they break. (strain stiffening).

There has been a lot of theoretical work trying to predict and model how individual filament dynamics give rise to strain stiffening. We are taking an experimental approach and directly visualize the individual filaments using confocal microscopy as the networks undergo shear.

Biopolymer Systems

We are currently looking at 3 biopolymer systems, collagen, fibrin, and actin bundled with filamin. These all have the basic property that they form a network of fibers and show strain stiffening behavior. But the mechanical properties, thickness, etc. of the different fiber systems differ substantially. All the samples are fluorescently labeled.

Shear Cell

In order to visualize a biopolymer network undergoing shear we use a shear cell that sits on top of a confocal microscope. Basically, this consists of two plates with the sample sandwiched between them. The lower plate is a coverslip, so the fibers can be imaged using the microscope. While the upper plate can be moved using a micrometer. In this way a shear deformation can be imposed on the gel. Confocal images are taken at different shear positions.

Rheometer

We use a rheometer to measure the bulk mechanical properties of our samples. In particular, we are interested in the strain stiffening behavior of biopolymer networks. This is illustrated by the picture on the right. G' is the elastic modulus (red) and G"(blue) is the viscous or loss modulus. At low strains, G' is roughly constant. This is referred to as linear regime. At about 10%, G' starts to increase. This is called strain stiffening.

Raw Data from Confocal

Fluorescent images of fibrin fibers in the xy plane before and after shear. (click to see a movie going through the z direction)

Qualitative

One way to qualitatively understand what is going on in our system is by looking at 3D projections of the raw confocal data. Below is a projection from unsheared and sheared networks.

Fibrin before & after shear (click for a movie of the 3D rotation)

Actin bundled w. Filamin (50:1) before & after shear (click for a movie of the 3D rotation) (raw data taken by Jiayu Liu)

Quantitative Analysis

Finding Fiber Backbones

To understand the full 3D structure of the network, we have developed software tools that pulls in the raw confocal data and finds the midline or 'backbone' of the fibers. This is essentially a 1 pixel line which traces the center of each fiber. Every fiber is also individually labeled. The overall output of the program is precise x, y, z information as well as individual fiber information (size, connectivity, branch points, etc.) (we primarily use two algorithms. One developed in our lab and another implemented by Andy Stein at U. Michigan). (Eventually, there should be a webpage with detailed information about our code & algorithm, but until then If you are interested in using it please send an email to ljawerth@fas.harvard.edu. )

Angles as a function of shear

By analyzing the 3D moments at each point in the image we can can determine fiber angles throughout the volume. Looking at histograms of the angles we can see the amount of alignment in the direction of shear.

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For more information please contact louise jawerth ljawerth at fas.harvard.edu (August 2007)