Collagen Fibril Formation and Its Applications in Nano-technology

Zhongmin Shen

Our goal is to develop nano-technology in building artificial tissues for medical purpose, based on the self-assembly process of native collagen fibers. Native mature collagen fibrils are usually very long compared to their diameter. Early collagen fibrils have major implications for tissue morphogenesis and repair. Thus we will investigate early fibrils or fibril segments, and try to find the biological rules in the self-assembly process which can be our design criteria to stimulate collagen fibers. Much of what is known about collagen self-assembly has resulted from the studies of type I collagen. Thus our investigation will primarily focus on the self-assembly of type I collagen. We will consider the following self-assembly process at two stages:

Collagen Molecules à Collagen Fibrils à Collagen Fibers

Self-Assembly of Collagen Molecules into Collagen Fibrils

Procollagens are converted into collagens by specific enzymic cleavage of terminal propeptides by the procollagen metalloproteinase. A collagen molecule consists of an uninterrupted triple helix of approx. 300 nm in length and 1.5 nm in diameter flanked by short extra-helical telopeptides. The telopeptides are critical for fibril formation. Each collagen molecule is oriented with N-terminal and C-terminal. The wound molecule has total length of 4.34D (D = 67 nm).

The assembly of collagen molecules into fibrils is an entropy-driven process. This process is driven by the loss of solvent molecules from the surface of protein molecules and results in assemblies with a circular cross-section. However, the molecular mechanism of assembly process is not clear enough yet. We would like find suitable mathematical equations to model the dynamic system of self-assembly of collagen fibrils.

A Brief Summary on the Self-assembly of Collagen Fibrils at Early Stage.

In a cell-free system (in vitro), fibrils generated initially have a near-paraboloidal pointed tip and a blunt end [1]. The growth is exclusively from the pointed tip, and the pointed tip has collagen molecule oriented with N-terminal closest to the fibril end [2]. As growth proceeds, the blunt end becomes a new pointed tip for growth in the other direction [3]. Fibrils formed in this way are bipolar (N-N).

Growth at a blunt end only occurs at high pCcollagen concentrations. This suggests that the occurrence of bipolar fibrils, in part, depends on the initial concentration of pCcollagen. The N-telopeptide is crucial for the formation of the polarized 4D-staggered fibrils. The loss of N-telopeptides leads to the formation of D-periodic symmetrical fibrils with molecules in anti-parallel contact. The C-telopeptide has dual role, promoting a lateral accretion of linear aggregates as well as participating in the formation of the early linear assemblies[11]. The level of C-proteinase has a major effect on the shape of the fibrils. At a constant initial concentration of pCcollagen, when the level of C-proteinase increases, the slope of the axial mass distributions of alpha-tips increases, and hence the fibrils become more symmetrical. The loss of part of the C-telopeptides leads to the formation of D-periodic tactoids. Complete removal of both telopeptides prevents the formation of fibrils.

In vitro, fibrils formed from acid-soluble collagen molecules are unipolar, D-periodic, and have two smoothly tapered ends. Early fibrils have length of about 90 D-periods and a maximal cross-section diameter containing about 160 molecules [12][13]. Long and exclusively unipolar fibrils form when pCcollagen is absent during early fibril formation.

In developing chick tendon, it is observed that some fibrils are N-N bipolar, some are C-N unipolar. In 18-day chick embryos about half of the early fibrils are bipolar and half are unipolar. Bipolar fibrils are shape-asymmetrical.

Echinoderm fibrils are all bipolar, and symmetrical about a plane through the central anti-parallel D-period. The aspect ratio (length/diameter) is constant in the fibrils from each species of echinoderms, regardless of length. The constant aspect ratio means that growing fibrils must increase their diameter in proportional to their increase in length, with the result that fibrils of various lengths have the same shape. This suggests that the assembly of echinoderm bipolar fibrils is different from that of vertebrate bipolar fibrils. A specific model to account for this growth process has not been developed yet.

Fibrils, whether they are in vivo or in vitro, all have growing tips with almost linear axial mass distributions near the ends. In vitro, the tip shape is established at an early time in the assembly pathway and remains unchanged during growth of the fibrils.

It has been reported that the occurrence of preferred diameters of multiples of 8 nm. The diameter measurement was made on dehydrated, plastic-embedded samples where shrinkage is typically 27% [4] [5] [6] [7]. The corrected value for the preferred diameter increment is then 11 nm, resulting in fibrils of diameter 22, 33, 44, 55 nm, etc. [8] [9]. This suggests that collagen fibrils consist of microfibrils and each microfibril consists of five strands of molecules.

In organisms the collagen fibril diameter is clearly controlled at the cellular level. The way this is controlled is not yet clear but it has been suggested that specific glycosaminoglycans play a key function in this. It is likely that surface transformations of growing fibers, induced by specific sugars, inhibit lateral association.

Based on experimental data, we make the following fundamental hypothesis on the self-assembly of collagen fibrils of same type from same species.

Laws of Collagen Assembly: All collagen fibrils of same type from same species in the same biological environment have similar shape. Hence the aspect ratio (diameter/length) is a constant (the diameter is measured on the largest circular cross-section of the fibril). They are spindle-shaped and oriented. They are either bipolar (Nßà N) or unipolar (Nà C). The axial mass distribution is almost linear near the ends.

Based on experimental data, we suggest the following rules of assembly.

Rules of Collagen Assembly for Simulation:

Primitive element (template) is a molecule. It is cylindrical, oriented with N-terminal end and C-terminal end, 4.34D in length, and r in radius (r=0.75 nm when dehydrated in vitro and r=1 nm in diameter in vivo, about 25% shrinkage ).

1. Two molecules oriented N- to C- from left to right could fuse side-by-side register, the N-terminal of one molecule being connected to the C-terminal of another with overlap of 0.34D in length.
2. Two molecules oriented N- to C- from left to right could fuse end-to-end register, the N-terminal of one molecule being connected to the C-terminal of another with gap of 0.66D in length.
3. The N-terminal of an oriented molecule can not be connected to the N-terminal of another, side-by-side or end-to-end.
4. The C-terminal of an oriented molecule can not be connected to the C-terminal of another, side-by-side or end-to-end.

The Collagen Molecule Packing Problem: The above four rules determine the formation of unipolar collagen fibrils. It suggests that microfibrils are formed into fibrils, each microfibril consisting of 5k, or 5k+2 molecules, k=1,2, …. However, the energy efficiency implies that only the case, k =1, occurs, namely, each microfibril consists of exactly five molecules in a generic circular cross section. This supports the three dimensional microfibrillar model suggested by Smith [18].

The Smith-model is quite popular nowadays. There is independent evidence for a well-defined micro-fibrillar substructure. This evidence is derived from electron microscopy, studies of in vitro assembly, the pattern of covalent cross-links and sequence analysis.

Assuming that collagen fibrils have micro-fibrillar substructures, we would like to investigate how the microfibrils are packed together in the most efficient way. We are going to construct possible packing models and exam them one by one using available experimental data. Below are few promising packing models under our investigation.

According to Rules #1-#4, bigger circular loops, consisting of 5k, 5k+2 with k =2, 3 …,. are allowed. In the model on the right, each circular loop consists of 5+10k, k=0, 1, 2, … We shall analyze the diffraction behavior of these circular models, to see if these models can explain the observed diffraction patterns. The surface is clearly correlated with the thickness. After every layer the surface is altered. It is reasonable to expect that lateral association ceases, even independently, after some surface curvature is attained. We shall analyze the lateral periodicity of fibrils, with the help of electron microscopy. The lateral periodicity in cross-sections of fibers might have implication on building up models. Despite all the improvements, the mystery about the lateral packing is not quite solved. In the future improvement of the collagen model can be expected from new surface scanning techniques like AFM (atomic force microscopy) and STM (scanning tunneling microscopy), from NMR and from X-ray diffraction when it is possible to obtain better and more complete diffraction data.

Fibrils grow layer by layer. We can use the observed preferred diameter increment to infer the assembly process from microfibrils into fibrils. Let r be the radius of a collagen molecule, R be the radius of the microfibril and I be the radius of the electron-lucent lumen inside the microfibril. They are related by

,

If r = 0.75 nm, then R = 2.025 nm and I = 0.525 nm. The preferred diameter increment is then 4R~8 nm, resulting in fibrils of diameter 12, 20, 28, 36 nm, etc. This is supported by lab observations made on dehydrated samples [4] [5] [6] [7]. If r = 1.015 nm, then R = 2.74 nm and I = 0.71 nm. The preferred diameter increment is then 4R~11 nm, resulting in fibrils of diameter 22, 33, 44, 55 nm, etc. This is supported by lab observations [8] [9].

Samples in Vivo

Dyhydrated Samples in Vitro

In either case, the center of the fibril is empty, possibly filled with liquid-like stuffs. It is reported that some fibrils in the dermis of the sea cucumber Cucumaria frondosa are circular with numerous electron-lucent interiors [14].

A trick of nature to make the collagen fibers stronger is the change in handedness at each level of coiling. This keeps the rope from uncoiling like in real ropes made by men. The experimental data suggests that each microfibril is wound up by exactly five strands. Each strand is formed by a sequence of collagen molecules, head to tail, with gap 0.66D = 44.22 nm. Thus the helical length of a molecule in a strand is shorter than the stretched one. The central axis of a molecule in a microfibril can be parameterized by

, ,

where is the helical length and k is the winding number of the molecule. Then the stretched length L of the molecule is given by

We obtain a formula for the winding number k,

In the dehydrated case (in vitro), r = 0.75 nm, L = 300 nm, = 4.34D =290.78 nm. We obtain k = 9.2. This suggests that the molecule is wound around the axis at least 9 times. In vivo, r=1.0 nm, L=300 nm, =290.78 nm. We obtain k=7. Thus, the molecule is wound around the axis about 7 times. This needs to be tested by experiments.

If Rule #4 is replaced by the following Rule #4*, then bipolar fibrils can be formed.

4*. (Formation of bipolar fibrils) Two microfibrils oriented N- to C- in the opposite direction can be connected at their C-terminal ends. The anti-parallel arrangement of the molecules is such that the C-terminals of oppositely directed molecules are in axial register. This arrangement allows for axial continuity of the intermolecular crosslinks in fibrils.

In order to simulate the dynamic process of assembly, we set up the following rules.

Dynamic Rules of Collagen Assembly for Simulation

(a) A fibril is spirally built from molecules. It grows layer by layer in two opposite directions at possibly different speed.

(b) The (k+1)-th layer starts to grow when the k-th completes n circle. Here n is not necessarily an integer, but a constant for all layers in the growing fibril.

(c) The shape of fibril tips remains unchanged, and the aspect ratio (left length/right length of asymmetrical fibril) remains unchanged.

(e) The rate of growth of number of molecules in a growing fibril is proportional to the volume of free molecules.

Dynamic Rules (a)-(b) will be tested and modified, based on experiments in various biological environments. Rule (c) can be derived from (a) and (b) as follows.

The k-th layer has radius. Let ι denote the axial increment for each added molecule and let υ denote the speed of adding molecules spirally. Assume that the system provides sufficiently many molecules so that υ is constant, independent of the size of the fibril. Usually,unipolar fibrils grow faster on the left side (N-terminal) and slower on the right side (C-terminal). After t steps, the axial length of k-th layer with inner radius is given by

This shows that the tip of fibril is paraboloidal. Moreover, the shape is determined by the coefficient. This analysis enables us to simulate the assembly of fibrils.

Fusion of Collagen Fibrils into Collagen Fibers

Diameter distributions are narrow and unimodal during the early stages of development [4]. Diameters show a multi-modal distribution during the late stages of development [5]. This suggests the occurrence of the fusion of fibrils into fibers. It is important to understand how early fibrils are converted into larger fibers. We set up the following rules for our models, based on the fusion theory of fibrils in vivo.

Rules of Fusion:

1. The side-by-side or end-on-end fusion of unipolar and bipolar fibrils is allowed, the C-tip being connected to the N-tip.
2. Two unipolar fibrils with molecules oriented N- to C- from left to right could fuse in side-by-side register to result in a thicker fibril, or in end-on-end register to give a longer fibril.
3. The side-by-side or end-on-end fusion of two oppositely directed unipolar fibrils (one fibril oriented C- to N- from left to right and the other from right to left) is not allowed.
4. The end-on-end fusion of two oppositely directed unipolar fibrils (i.e., one fibril oriented N- to C- from left to right and the other from right to left) yields a bipolar fibril. But the side-by-side fusion is not allowed.
5. The fusion of two bipolar fibrils is allowed only when the molecular switch regions of two neighboring bipolar fibrils are perfectly aligned

Below is an example for the fusion of two unipolar fibrils in side-by-side register, resulting in a thicker and longer fibril.

How are native fibrils aggregated into fibers? This is still a mystery. We test the above rules of fusion by stimulation. It is certain that in a mixed population of unipolar and bipolar fibrils, the end-on-end fusion by Rule# 1 has the effect of decreasing the unipolar population, resulting in a population enriched in bipolar fibrils, unable to fuse further.

References

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