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Parikh vectors
7XPK_1 1XIS_1 6MDC_1 Letter Amino acid
8 10 25 N Asparagine
1 10 19 H Histidine
3 7 12 M Methionine
10 23 18 F Phenylalanine
7 47 19 A Alanine
4 1 8 C Cysteine
13 28 44 E Glutamic acid
12 37 39 G Glycine
14 11 40 K Lycine
9 19 43 V Valine
13 11 25 I Isoleucine
4 16 34 T Threonine
2 6 7 W Tryptophan
5 35 31 R Arginine
9 37 30 D Aspartic acid
6 11 24 Q Glutamine
15 39 39 L Leucine
7 19 19 P Proline
10 11 30 S Serine
7 9 20 Y Tyrosine 

7XPK_1|Chains A, C|BAH domain-containing protein|Oryza sativa Japonica Group (39947)
>1XIS_1|Chain A|XYLOSE ISOMERASE|Streptomyces rubiginosus (1929)
>6MDC_1|Chains A, B|Tyrosine-protein phosphatase non-receptor type 11|Homo sapiens (9606)
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 \(w=f(c)\)
7XPK , Knot 78 159 0.83 40 122 156 
GGIKMDTQFYDSFTFDNVKYSLYDNVYLFKSGESEPYIGKIIKIWQQNQAKKVKILWFFLPDEIRKHLSGPVMEKEIFLACGEGVGLADINPLEAIGGKCTVLCISKDERNRQPSPRELAMADYIFYRFFDVNSCTLSEQLPEKIAGVEGNLLLNSKVE
1XIS , Knot 158 387 0.81 40 205 356 
NYQPTPEDRFTFGLWTVGWQGRDPFGDATRRALDPVESVRRLAELGAHGVTFHDDDLIPFGSSDSEREEHVKRFRQALDDTGMKVPMATTNLFTHPVFKDGGFTANDRDVRRYALRKTIRNIDLAVELGAETYVAWGGREGAESGGAKDVRDALDRMKEAFDLLGEYVTSQGYDIRFAIEPKPNEPRGDILLPTVGHALAFIERLERPELYGVNPEVGHEQMAGLNFPHGIAQALWAGKLFHIDLNGQNGIKYDQDLRFGAGDLRAAFWLVDLLESAGYSGPRHFDFKPPRTEDFDGVWASAAGCMRNYLILKERAAAFRADPEVQEALRASRLDELARPTAADGLQALLDDRSAFEEFDVDAAAARGMAFERLDQLAMDHLLGARG
6MDC , Knot 211 526 0.83 40 259 482 
SMTSRRWFHPNITGVEAENLLLTRGVDGSFLARPSKSNPGDFTLSVRRNGAVTHIKIQNTGDYYDLYGGEKFATLAELVQYYMEHHGQLKEKNGDVIELKYPLNCADPTSERWFHGHLSGKEAEKLLTEKGKHGSFLVRESQSHPGDFVLSVRTGDDKGESNDGKSKVTHVMIRCQELKYDVGGGERFDSLTDLVEHYKKNPMVETLGTVLQLKQPLNTTRINAAEIESRVRELSKLAETTDKVKQGFWEEFETLQQQECKLLYSRKEGQRQENKNKNRYKNILPFDHTRVVLHDGDPNEPVSDYINANIIMPEFETKCNNSKPKKSYIATQGCLQNTVNDFWRMVFQENSRVIVMTTKEVERGKSKCVKYWPDEYALKEYGVMRVRNVKESAAHDYTLRELKLSKVGQGNTERTVWQYHFRTWPDHGVPSDPGGVLDFLEEVHHKQESIMDAGPVVVHCSAGIGRTGTFIVIDILIDIIREKGVDCDIDVPKTIQMVRSQRSGMVQTEAQYRFIYMAVQHYIETL

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 \(c\).

\(|P_{f(7XPK_1)}(2) \setminus P_{f(1XIS_1)}(2)|=50\), \(|P_{f(1XIS_1)}(2) \setminus P_{f(7XPK_1)}(2)|=133\). 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 1:111010001000101001000100010110010001011011011000010010111111100100010111100011110101111101011011110001101000000001010011110011001101000010001100111101011100010
Pair \(Z_2\) Length of longest common subsequence
7XPK_1,1XIS_1 183 3
7XPK_1,6MDC_1 199 4
1XIS_1,6MDC_1 154 4

Newick tree

 
[
	7XPK_1:10.02,
	[
		1XIS_1:77,6MDC_1:77
	]:24.02
]

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 \((0.85)(0.8)(\frac{546 }{\log_{20} 546}-\frac{159}{\log_{20}159})=112.\)
Status Protein1 Protein2 d d1/2
Query variables 7XPK_1 1XIS_1 143 101
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]