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Parikh vectors
9DAZ_1 2MHM_1 1AHW_1 Letter Amino acid
51 4 13 D Aspartic acid
60 12 13 G Glycine
46 4 10 I Isoleucine
119 8 13 L Leucine
73 4 10 P Proline
14 2 5 C Cysteine
27 5 3 H Histidine
24 2 3 M Methionine
97 3 8 V Valine
48 4 13 Y Tyrosine
39 3 7 R Arginine
71 7 10 N Asparagine
68 7 10 E Glutamic acid
64 15 14 K Lycine
96 4 32 S Serine
67 8 10 A Alanine
58 2 9 Q Glutamine
50 4 6 F Phenylalanine
83 9 21 T Threonine
29 1 4 W Tryptophan 

9DAZ_1|Chains A, C|Aminopeptidase N,Immunoglobulin gamma-1 heavy chain|Felis catus (9685)
>2MHM_1|Chain A|Cytochrome c iso-1|Saccharomyces cerevisiae (559292)
>1AHW_1|Chains A, D|IMMUNOGLOBULIN FAB 5G9 (LIGHT CHAIN)|Mus musculus (10090)
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 \(w=f(c)\)
9DAZ , Knot 432 1184 0.86 40 341 1044 
MGILPSPGMPALLSLVSLLSVLLMGCVAETGTDQSKPWNVYRLPKTLIPDSYNVTLRPYLTPNNKGLYVFTGTNIVRFTCKESTNIVIIHSKRLNYTSHQGHMVALSGVGGFHPQPVIVRTELVELTEYLVVHLQEPLVAGRQYEMNSEFQGELADDLAGFYRSEYMENGVKKVLATTHMQATEARKSFPCFDEPAMKATFNITIIHPNNLVALSNMLPRGPSVPFGEDPTWKVTEFETTPIMSTYLLAYIVSEFSYVETRAPSGVLIRIWARPSAINQGHGDYALKVTGPILDFFSQHYDTPYPLNKSDQIALPDFNAGAMENWGLVTYRESALLYDRQSSSSGNQERVVTVIAHELAHQWFGNLVTLEWWNDLWLNEGFASYVEYLGADFAEPTWNLKDLMVLNDVYRVMAVDALASSHPLSTPASEINTPAQISEVFDSISYSKGASVLRMLSNFLTEDLFKMGIASYLHTYKYGNTIYLNLWEHLQQVVDKQPTIKLPDTVSAIMDRWILQMGFPVITVDTQTGTISQQHFLLDPQSVVTRPSQFNYLWIVPISSVRSGSPQAHYWLPGVEKAQNDLFKTTANDWVLLNLNVTGYYLVNYDNENWKKIQTQLQTDLSVIPVINRAQVIHDAFNLASAQKVPVTLALNNTLFLIQETEYMPWQAALSSLSYFKLMFDRSEVYGPMKRYLKKQVTPLFNHFERVTKNWTDHPQTLMDQYSEINAVSTACSYGVPECEKLAATLFAQWKKNPQNNPIHPNLRSTVYCNAIAQGGEEEWNFVWEQFLKAELVNEADKLRGALACSNQVWILNRFLSYTLDPNLIRKQDVTSTLSSISSNVVGQTLVWDFVQSNWKKLFQDYGTGSFSFSNLIQAVTRRFSTEFELQQLEQFKKNNMDTGFGSATRALEQALEKTKANLKWVKENKDVVLRWFTENSGGSLVPRGSGSGSGDPEPKSCDKTHTCPPCPAPELLGGPSVFLFPPKPKDTLMISRTPEVTCVVVDVSHEDPEVKFNWYVDGVEVHNAKTKPREEQYNSTYRVVSVLTVLHQDWLNGKEYKCKVSNKALPAPIEKTISKAKGQPREPQVYTLPPSRDELTKNQVSLTCLVKGFYPSDIAVEWESNGQPENNYKTTPPVLDSDGSFFLYSKLTVDKSRWQQGNVFSCSVMHEALHNHYTQKSLSLSPGK
2MHM , Knot 59 108 0.85 40 93 105 
TEFKAGSAKKGATLFKTRCLQCHTVEKGGPHKVGPNLHGIFGRHSGQAEGYSYTDANIKKNVLWDENNMSEHLTNPAKYIPGTKMAFGGLKKEKDRNDLITYLKKATE
1AHW , Knot 100 214 0.83 40 146 208 
DIKMTQSPSSMYASLGERVTITCKASQDIRKYLNWYQQKPWKSPKTLIYYATSLADGVPSRFSGSGSGQDYSLTISSLESDDTATYYCLQHGESPYTFGGGTKLEINRADAAPTVSIFPPSSEQLTSGGASVVCFLNNFYPKDINVKWKIDGSERQNGVLNSWTDQDSKDSTYSMSSTLTLTKDEYERHNSYTCEATHKTSTSPIVKSFNRNEC

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 \(c\).

\(|P_{f(9DAZ_1)}(2) \setminus P_{f(2MHM_1)}(2)|=256\), \(|P_{f(2MHM_1)}(2) \setminus P_{f(9DAZ_1)}(2)|=8\). 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 1:11111011111110110110111110110010000011010011001110000101010101000110110100110100000001111000010000001011110111110101111000110100011101001111100001000101011001111000001001100111000101001000110100111010101011010011110011101101111001010100100011100011101100100100011011110111010110010100110101111011000000101100000111101011110011110000011100000000100001101110011001110110101100111001110010011101101010100111100100111101110001100110010011010011001000011011011001100011011110010000010010101100100110001010110010111001110111111010000101000011101001100100100111111001001010100111110010001100010011110101010011000000100100010001011111001011001101101001110111000111100000111011100100101110000101110001000101110010010001000100110000010110010001110000111011101000100011010100010001110110001011100110101100100101111000011110011000101011000010001001000111001110110001001100010101010011011000100010100100100001001110100110011000010101100000111011000011011101010101010100000000011011101111101111110100011100010100111010000101010101011010010001000000000011011011000110100000010001111110001001010100101001110000100001010011011010011101000101000000011110001011100010100001001011000110011000000001010110
Pair \(Z_2\) Length of longest common subsequence
9DAZ_1,2MHM_1 264 4
9DAZ_1,1AHW_1 217 6
2MHM_1,1AHW_1 159 3

Newick tree

 
[
	9DAZ_1:13.74,
	[
		1AHW_1:79.5,2MHM_1:79.5
	]:52.24
]

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 \((0.85)(0.8)(\frac{1292 }{\log_{20} 1292}-\frac{108}{\log_{20}108})=320.\)
Status Protein1 Protein2 d d1/2
Query variables 9DAZ_1 2MHM_1 405 219.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]