## 3 Results
### Potential Binding Sites for Collagen Type I Subsequence
Positive binding sites are energetically unfavorable, while negative binding sites are favorable. Binding sites significantly below \(-\)kT are likely to be stable. Each circle represents a potential three-amino-acid binding site between a peptide and collagen. The potential binding free energy was calculated from  
the Wimley-White hydropathy scale values for the amino acids within the binding site. The three-amino-acid binding sites are labeled with the peptide sub-sequence when the potential free energy is below \(-0.693\) kcal/mol. When the histidine is protonated, the free energy shifts from \(-1.2\) kcal/mol to \(-0.5\) kcal/mol. Potential binding sites are gold for collagenase sub-sequence (SQNPVQP), cyan for LRR-10 (LRELHLNNN), and magenta for the COL1A2 sense peptide (TKKTLRT). The radius of the circle sizes is related to the magnitude of the polarity of the peptide residues. The middle leucine residues of the COL1A2 sub-sequence mark the potential free energy change of binding when the histidine in the LRR-10 sequence transitions from uncharged to protonated. The potential energy of binding at the GLL/LLG collagen site is similar for the protonated histidine site and the non-protonated histidine site with the asparagine residue (H0-L-N, a shift of one amino acid residue for LRR-10 from L-H0-L). kT, which is the Boltzmann's constant multiplied by the temperature of \(25\,^{\circ}\)C, is \(0.693\) kcal/mol. This value is close to a mean estimate of the free energy fluctuations of a surrounding environment near room temperature. We see that the LHL interaction between LRR-10 and COL1A2 is below \(-\)kT when the surrounding environment is non-acidic or alkaline, meaning it is predicted to be unlikely to reverse under standard conditions. The prediction denotes that the favorable free energy necessary to couple for the reverse reaction of unbinding to happen is not likely to occur under standard conditions. LRR-10 also has likely interactions with collagen when the histidine is protonated. The shift in the binding free energy moves the binding site to above \(-\)kT, predicting that the binding is more likely to be reversible. When the histidine is protonated, other nearby binding sites of LRR10 may lead to more resonance structures which are close in energy, leading to rearrangements of LRR10 on the surface, with interactions of L, R+, E\(-\) and G, P, Q being favored the same as the L, H+, L interaction to within a difference of about 0.2 kcal/mol. Both of the potential binding sites for LRR-10 are shown in Figure 4.  
Figure 4: Free energy of binding estimates for sets of three adjacent residues for LRR-10 (LRELHLNNN) on human collagen type I alpha chain 2 (COL1A2) residues 861–871. The binding site (LHL) reference view is in (**A**), with views of \(90^{\circ}\) rotations along the indicated axis in (**B–D**). Each circle represents the same potential three-amino-acid binding site between the LRR-10 peptide and collagen at different rotations. How the rearrangement of LRR-10 when bound to collagen based on protonation state affects its binding is an open question beyond our single-site binding model. However, our binding models indicate that the histidine residue in the leucine-rich repeat motif seems to serve as a logical switch determining if the hydrophilic feature is a match for this hydropathic interface of COL1A2. If we consider the case when the histidine residue is replaced by a polar, uncharged amino acid like threonine, we can propose a proton-independent type of binding site for COL1A2 matching the hydropathic interface at this site. We describe this peptide sequence (TKKLTLRT) as a high-stability binding peptide because the collagen-binding prediction is nearly completely pH independent. See Figure 5 for the LTL binding site within the TKKLTLRT structure. We introduced the LTL peptide sequence from the previous peptide to result in TKK-LTL-RT. We compared TKK-LTL-RT to LREN-LTL-NNN to see which candidate high-stability collagen-binding peptide has the more favorable binding prediction to COL1A2.