The regular molecular structure of tendon with large numbers of collagen protein molecules (nearly 100% of dry mass in extensor tendons of young animals) regularly aligned parallel to the axis of the tendon provides greater than millionfold amplification to make accurate molecular measurements feasible. It is reasoned that the contraction or expansion of tendon length and diameter with dehydration is the result of removing water from molecular surfaces. As a result, the measurement of the contraction of tendon is directly proportional to change in the dimension of the collagen molecule, such that relative changes in length , diameter , and volume are proportional to changes in molecular dimension, where the zero reference is the length , diameter , and volume for completely dry tendon and collagen.
The SHM molecular hydration model for collagen identifies two bound water fractions or bridges due to binding of water by electric dipoles on the backbone. The compartmental capacities are calculated from collagen amino acid composition, e.g., the Ramachandran single water bridge includes one water molecule per tripeptide unit such that and the total bound water on the backbone is g/g , where 91.2 Da is the collagen mean amino acid residue molecular mass. The differences in binding energies and motional restrictions per water molecule for each different hydration compartments predicts differing changes in relative diameter, relative length, and relative volume for both collagen and tendon as a function of hydration h(g/g).
Summary of the comparison of micro-CT and calibrated gold standard micrometer measurements provides the correction equations for (a) accurate imaging diameter, (b) accurate imaging volume, (c) validation of density measurement, and (d) validation of differential density measurement to reduce systematic imaging error. The plots of mass as a function of corrected volume for tendon phantoms in (c) and the differential mass versus differential volume between two phantom sizes in (d) shows the highly linear dependence over the range of phantom sizes. The slope allows calculation of the density of Lucite from the slope of phantom mass versus volume and the density of removed Lucite from the differential measurements versus to validate both density measurements. The intercept is not significantly different from zero and the correlation coefficient is equal to 1 (rounding off to four decimal places). It is noted that although six phantoms were initially evaluated for (c) micrometer mass versus volume (6 points) and (d) differential density versus differential volume (six phantoms yielding 15 differential pairs), only four phantom measures are reported in CT calibration curves (a) and (b) as these four encompassed the experimental range of tendon measurements. Longer phantoms ( and ) were outside the usable tendon range and decreased measurement accuracy due to geometric distortion caused by the short source-axis distance of the CT unit.
This figure summarizes micro-CT measurements on bovine extensor tendons for (a) relative length, (b) relative diameter, (c) relative volume, (d) density, and [(e) and (f)] differential density as a function of hydration. Results are consistent with three linear segments as predicted by the SHM model. Statistically significant slope changes (see Table I) occur at or for all quantities, while significant changes in only three of five quantities (relative length, diameter, and density) occur at or . A whisker plot of the differential density shows mean and variance of change between SHM water categories (see text for details).
The interpretation of the dilatometry results of these experiments is founded on SHM geometric concepts summarized in these images. Each tripeptide unit of collagen has one direct hydrogen bond (top panel) that exists even with no water . Each triplet can hold a single water bridge and a double water bridge as shown in panels 2 and 3. The four water bridge molecules per tripeptide unit together form main chain polar hydration and are buried deep in the crevices of the collagen molecule as shown at the right in the diagram from Bella. Secondary water molecules to 11 shown in lighter gray in panels 4 and 5 from polar water clusters by hydrogen bonding to the water bridges now shown in darker shades to indicate primary bonding status. Polar water cluster hydration is outside the grooves but remains closer to the surface (higher density) than hydrophobic hydration indicated by the double arrow in bottom panel for to 24 (lower density). Together, the network of water molecules covers the entire surface of the collagen molecule with a monolayer of water as shown in the diagram from Bella et al. on the right. The diagram at the bottom right shows the decrease in the effective dielectric coefficient at the molecular level when increasing numbers of neighboring water molecules cause reduction of the alignment of water bridges by competitive electrostatic interactions with water bridge molecules.
(a) These plots of rat tail tendon normalized NH and OH spectral parameters as a function of interaxial spacing show that the reference separation 17.0 Å at and the SHM dilatometry prediction of change at provides a good description of optical parameters. The change in slope of the Raman spectral parameters of NH and OH show that hydrogen bonding of water to the collagen causes significant changes in hydrogen bonding energies. (b) The plot of hydration force necessary to remove water from the collagen surface show the increased binding of water molecules in the polar water cluster fraction. Both optical and hydration force are consistent with SHM predictions.
The presence of cavities on the protein surface creates a nonrecoverable volume when the adjacent molecules approach one another during dehydration shown by the large arrow. This nonrecoverable volume becomes filled with air and causes the density of the tendon to decrease because of the low density of air. The recoverable volume fractions and nonrecoverable volume fractions are calculated from measured differential densities for each SHM hydration compartment.
(a) This graph compares the measured density of tendon to the various methods of calculating collagen/protein density. The density of collagen calculated by summation of the mass of the amino acid components divided by the van der Waals volumes (p. 141, Ref. 37) gives as the radius of the theoretical test particle is zero. The collagen density in water solution accounts for increased collagen molecule volume caused by stand-off of the center of the water molecule as discussed by Creighton (Ref. 37) and Zamyatin (Ref. 36) This accounts for the density decrease noted by arrow Ia for collagen. When protein chains are folded, the volume occupied by the protein increases and the density is further decreased by small crevices in the structure that become inaccessible to water molecule as shown by the range of sedimentation densities for 20 amino acids (p. 266, Ref. 37) indicated by arrow Ib. When one measures the dry state density with autoexclusion (zone or volume encompassed by a molecule that cannot be occupied by the center of mass of another identical molecule) by tropocollagen, the combination of test molecule standoff and large folding induced cavities decreases the density to 1.077 g/ml due to air-filled cavities as indicated by arrow II. The smaller water molecule can, however, fill some of the air cavities left unfilled by very large collagen molecules and most especially those cavities located in the grooves of the collagen for SHM backbone hydration to 0.263 g/g. The maximum density at occurs at , while the density at native hydration agrees well with the literature value 1.2 g/ml for native mammalian tendon. (b) This plot of globular protein density [(, measured by sedimentation (p. 266, Ref. 37)] versus molecular weight shows a highly significant decrease as a function of molecular weight which, when extrapolated to , predicts a density which agrees well with the density of tendon in the SHM polar region to 0.724 g/g (see text for discussion).
Summary of the SHM piecewise segmental analysis of native bovine extensor tendon micro-CT dilatometry (Fig. 4).
Calculation of nonrecoverable water volume on collagen from mean differential water densities.
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