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Dr Carlo Knupp 


Research Interests

Corneal Transparency

corneal stroma
 Electron Micrograph of corneal stroma. The dark dots in the middle of the micrographs are collagen fibrils seen in cross section. These fibril are arranged in lamellae and their orientation changes between adjacent lamellae. Micrographs courtesy of Dr R. D. Young.

 

Why are corneas transparent?

 

Mammalian corneas, like much of the extracellular matrix, are made essentially of collagen and proteoglycans. However, unlike the rest of the extracellular matrix, they are exquisitely transparent. To understand why we need first to understand how light interacts with each collagen fibril in the cornea.

 

single collagen fibril

 

The top-left corner of the image above contains the representation of a single collagen fibril seen in cross section.

 

In the bottom-left corner, light is coming from the left and is represented as straight lines. You can think of this incoming light as ripples on the surface of a pond. The darker lines represent a wave-crest while the lighter lines a trough. When light interacts with the collagen fibrils, it forces the electrons of the atoms in the fibril to oscillate. Because accelerating charges produce electromagnetic waves, a secondary wave is produced. This wave has the same wavelength of the incoming wave, but it radiates in all directions in the plane. The crest of the secondary wave is represented in red, the trough in grey.

 

In the top-right corner the secondary wave is drawn on top of a greyscale representation of the wave itself. Since we are actually interested in the energy associated with the wave, we draw here the square of the wave amplitudes, so that crests and troughs look identical.

 

In the bottom-right corner we only draw the greyscale (intensity) representation of the secondary wave.

 

secondary wave

 

When two fibrils are present, the secondary waves produced by each fibril interfere. This means that the two sets of secondary waves simply add together, so that where two crests or two troughs meet we will have a wave twice as deep, but where a crest meets a trough the waves cancel out. Correspondingly, the greyscale representation of the intensity of the resulting wave in the top and the bottom right panels of the figure above is not two even sets of concentric rings radiating from the fibrils: the wave intensity is distributed unevenly in the plane. But what happens when more than two fibrils are present?

 

Wave interference

 

The figure above represents a situation in which many fibrils are randomly placed. Wave interference will take place also in this case, and the secondary waves from all fibrils will add together. As you might expect, the intensity of the resulting wave is not uniformly distributed in space. Most of the intensity from the secondary waves is travelling in the forward direction, but a considerable portion is travelling in other directions. This means that if the fibrils in the cornea were randomly distributed, not all the light would be transmitted through the cornea, but a considerable portion would be reflected back. What would happen if the fibrils were not randomly distributed?

 

hexagonal lattice

 

In the figure above, the collagen fibrils are regularly placed on an hexagonal lattice. Secondary waves from these fibrils cancel out in all directions except the forward direction: light is travelling undisturbed through the cornea. A cornea with an ordered collagen fibril distribution of this type is therefore transparent.

 

It turns out that strict positional order for the collagen fibrils is not an absolute requirement for cornea transparency. It is in fact sufficient that the distance between adjacent collagen fibrils is approximately the same, as long as this distance is markedly less than the wavelength of the incoming wave. In addition, a final requirement is that the diameter of the fibrils must be the same for all fibrils.

 

To understand how the arrangement of the collagen fibrils in the cornea is maintained, we can look at it directly using a transmission electron microscope and reconstruct what we see in three dimensions.

 

ElectronTomography of the Cornea

 

By tilting a corneal specimen in the electron microscope, collecting a series of images at different tilt angles, and recombining these images using suitable computational algorithms, we can reconstruct the structure of the corneal stroma and observe the way proteoglycans and collagen fibrils interact with each other. These interactions are fundamental in maintaining the arrangement of the collagen fibrils, so important for transparency.

 

three dimensional reconstruction of a mouse cornea
Above is an image of a three dimensional reconstruction of a mouse cornea. Collagen fibrils,
seen in cross-section, are painted in blue. Proteoglycans in yellow. We can see here that the
proteoglycans link two or more adjacent fibrils. The way proteoglycans extend from a collagen
fibril to a neighbouring one is not ordered and crystal-like, but it is sufficient to keep
neighbouring fibrils at defined distances (Reconstruction by Dr C. Pinali).

 

From reconstructions of bovine and mouse corneas, we proposed a model of how the distance between adjacent collagen fibrils is maintained thanks to the action of the proteoglycans. The model is based on the idea that proteoglycans are able to give rise to two opposite forces acting on the fibrils: an attractive force trying to pull fibrils close to each other and a repulsive one trying to push fibrils apart. The distance between fibrils in the cornea is the distance where the two opposing forces cancel out.

 

Donnan effect

 

The repulsive force arise because of the Donnan effect. Since the proteoglycans are negatively charged they attract positive ions present in the corneal stroma. In turn, these ions attract water molecules by a process analogous to osmosis. Water accumulates between the fibrils and exert pressure that make the fibrils move apart.

 

thermal motion of the proteoglycans

 

The Attractive forces are due to thermal motion of the proteoglycans. Proteoglycans are continuously bombarded by molecules present in the stroma. The overall effect of the collisions is that the proteoglycans change their shape. They are no longer fully extended and their terminal ends are forced to move close to each other. Since these ends are linked to the collagen fibrils, also the fibrils move closer to each other.

 

The combination of these repulsive and attractive forces keep the fibrils at regular distances from each other. Note that the fibrils are not fixed in space in a crystalline way. They are able to vibrate and move around, making the cornea a fluid and resilient system.

 

 

References:

 

Lewis PN, Pinali C, Young RD, Meek KM, Quantock AJ, Knupp C. (2010) “Structural interactions between collagen and  proteoglycans are elucidated by three-dimensional  electron tomography of bovine cornea”. Structure. 18(2), 239-245.

 

Knupp C, Pinali C, Lewis PN, Parfitt GJ, Young RD, Meek KM, Quantock AJ (2010) “The architecture of the cornea and structural basis of its transparency” Advances in protein chemistry and structural biology,78, 25-49.