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Parikh vectors
6SNY_1 6UMB_1 8FXR_1 Letter Amino acid
2 4 0 Y Tyrosine
4 4 1 Q Glutamine
5 2 1 I Isoleucine
6 19 3 L Leucine
0 2 1 M Methionine
4 5 0 W Tryptophan
11 8 0 D Aspartic acid
1 14 2 G Glycine
23 5 1 K Lycine
1 10 7 P Proline
2 14 3 S Serine
8 10 4 A Alanine
2 4 4 C Cysteine
29 13 0 E Glutamic acid
0 6 0 H Histidine
4 9 1 F Phenylalanine
12 16 3 R Arginine
6 5 1 N Asparagine
2 10 2 T Threonine
2 17 4 V Valine 

6SNY_1|Chain A|Synthetic EPCR binding protein|synthetic construct (32630)
>6UMB_1|Chain A|E3 ubiquitin-protein ligase TRIM7|Homo sapiens (9606)
>8FXR_1|Chains AF[auth a2], A[auth a1], BF[auth a6], B[auth a5], CF[auth b1], C[auth a7], D[auth b2], E[auth b5], GE[auth b6], HE[auth b7], IE[auth c], JE[auth d], MA[auth d1], NA[auth d2], ND[auth d5], OA[auth d6], OD[auth d7], PA[auth e], PD[auth e1], QD[auth e2], T[auth e5], U[auth e6], V[auth e7], W[auth f], ZE[auth g]|Linking protein 2, gp128|Agrobacterium phage Milano (2557550)
Protein code \(c\) LZ-complexity \(\mathrm{LZ}(w)\) Length \(n=|w|\) \(\frac{\mathrm{LZ}(w)}{n /\log_{20} n}\) \(p_w(1)\) \(p_w(2)\) \(p_w(3)\) Sequence \(w=f(c)\)
6SNY , Knot 53 124 0.68 36 68 110 
NNWEQQKKNIEDDLDRYKKRAEELRKEAEKARKEARKTEDPTEEAKKEWEKRCKELEERARKLEDEAKDRVNDLFDSNFFQVIYSGDNDEEEWKKEKDRAEKEIEEWFKRIKEKCEEIKKRLEQ
6UMB , Knot 85 177 0.82 40 134 172 
SHMKEEKVELTLDPDTANPRLILSLDLKGVRLGERAQDLPNHPCRFDTNTRVLASCGFSSGRHHWEVEVGSKDGWAFGVARESVRRKGLTPFTPEEGVWALQLNGGQYWAVTSPERSPLSCGHLSRVRVALDLEVGAVSFYAVEDMRHLYTFRVNFQERVFPLFSVCSTGTYLRIWP
8FXR , Knot 24 38 0.76 30 34 36 
MVKLNCRPLCQAPTASRLVSPPCFICRGVAPSAPVTPG

Let \(P_w(n)\) be the set of distinct subwords (intervals) in a word \(w\). Let \(p_w(n)\) be the cardinality of \(P_w(n)\). Let \(f(c)\) be the sequence in FASTA with 4-symbol Protein Data Bank code \(c\).

\(|P_{f(6SNY_1)}(2) \setminus P_{f(6UMB_1)}(2)|=43\), \(|P_{f(6UMB_1)}(2) \setminus P_{f(6SNY_1)}(2)|=109\). Let \( Z_k(x,y)=|P_x(k)\setminus P_y(k)|+|P_y(k)\setminus P_x(k)| \) be a LZ76 style (set of subwords) Jaccard distance numerator for \(P(k)\).Hydrophobic-polar version of Sequence 1:0010000001000100000010010001001000100000100010001000000100010010001000100110001101100100000010000001000100110010000001000100
Pair \(Z_2\) Length of longest common subsequence
6SNY_1,6UMB_1 152 3
6SNY_1,8FXR_1 96 2
6UMB_1,8FXR_1 140 3

Newick tree

 
[
	6UMB_1:79.68,
	[
		6SNY_1:48,8FXR_1:48
	]:31.68
]

Let d be the Otu--Sayood distance d.
Let d1 be the Otu--Sayood distance d1. (This makes the 4TYN sequence AAAAAA a close match...)
A roughly speaking expected distance is \((0.85)(0.8)(\frac{301 }{\log_{20} 301}-\frac{124}{\log_{20}124})=55.0\)
Status Protein1 Protein2 d d1/2
Query variables 6SNY_1 6UMB_1 76 60.5
Was not able to put for d
Was not able to put for d1

In notation analogous to [Theorem 16, Kjos-Hanssen, Niraula and Yoon (2022)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]

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