## 3 Results  
### Potential Binding Sites for Collagen Type I Subsequence  
A recent study on fibromodulin interaction with collagen and activation of lysyl oxidase tested the ability of collagen III sequences to bind to collagen I [42]. A binding motif from part of the study was found to be GLKGHR. The study further showed which parts of the motif bind to the collagen by showing that a similar peptide GLAGHA binds significantly less than GLKGHR. The free-binding energies from our method are consistent with these results and predict binding behaviors for alkaline (pH 9) and acidic (pH 2) conditions. We verified that our hydropathy-based free-energy-binding screening method correctly predicted the result of this known study. See Figure S1. We initiated our search using a collagen-binding domain analogue (TKKTLRT) that was derived from the sense peptide TKKTLRT for collagen type I \(\alpha\)(2) [36]. This peptide was engineered by a rational hydropathy feature inspired by a leucine-rich repeat (LRR) within the decorin glycoprotein. We first compared the most probable binding sites of TKKTLRT and a collagenase collagen-binding peptide (SQNPVQP) (Figure 1). To find the binding sites, we provided a first-order approximation of the free energy of binding for well-studied collagen-binding peptides TKKTLRT, SQNPVQP, and LRR-10 (leucine-rich repeat-10) to collagen type I [10]. Then we included a more pH-stable version of the hydrophobic binding site in LRR-10 (LRE LHL NNN) into an analogue of TKKTLRT by inserting a leucine residue (TKK LTL RT) and predicted the peptide binding at different pH levels. Our screening tool is based on the Wimley-White scale, which uses measured free energy differences in solvation among water, octanol, and POPC (bilayer membrane molecule) of penta-peptides to infer the free energy changes of each of the side chains of the canonical amino acids. Our screening method focuses on the free energy difference between water and octanol, with octanol being considered as completely hydrophobic for our first approximation. Our screening tool uses the electrostatic interaction rules of electronegativity to determine the difference between attractive and repulsive interfaces. We averaged the hydropathy in segments of three amino-acid sub-sequences. Using the screening tool, we determined the predicted free energies of binding between TKKTLRT and the collagen sub-sequence for which TKKTLRT is the DNA complement. We also included SQNPVQP as a near match for the hydrophobicity trend in TKKTLRT. We observed that while all potential binding energies using this method were positive, some were near zero (See Figure 2). Zero potential free energy means that the process may happen if another reaction releasing energy takes place nearby. The normal fluctuation of free energy is described by the product of the Boltzmann's constant and the absolute temperature of the system. For 25 \({}^{\circ}\)C, the normal fluctuation is \(+/-0.693\) kcal/mol, referred to as kT. For body temperature at 37 \({}^{\circ}\)C, the kT value is about 4% larger (0.721 kcal/mol). The kT values in the figures for this study use 25 \({}^{\circ}\)C, though which kT levels apply between the room temperature value and the body temperature value are close to the same. While the interaction between TKKTLRT and its antisense collagen sequence is not favored according to this approximation, the interaction is still allowable. The approximation also implies that the interaction between either TKKTLRT or SQNPVQP and collagen at this site is highly reversible. Stronger hydrophobicity interactions are possible if we consider sequences which are not between sense/antisense pairs. Functional applications that label collagen, however, are more reliable if the stability of the fusion-tag interface to collagen is based upon a robust and stable interaction. For higher-stability binding interactions, we considered a stronger binding example to pattern our hydropathy relationship.