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Parikh vectors
6RWL_1 7ZTS_1 3MMJ_1 Letter Amino acid
24 45 19 V Valine
24 57 32 A Alanine
12 36 23 R Arginine
11 13 13 H Histidine
6 28 6 M Methionine
8 27 13 F Phenylalanine
9 39 17 P Proline
9 38 7 N Asparagine
5 7 0 C Cysteine
23 42 11 I Isoleucine
13 60 22 L Leucine
16 48 19 D Aspartic acid
24 29 21 K Lycine
6 36 16 Y Tyrosine
24 18 13 Q Glutamine
22 37 23 E Glutamic acid
22 36 20 G Glycine
11 51 15 S Serine
14 43 16 T Threonine
7 7 8 W Tryptophan 

6RWL_1|Chains A, B, C, F[auth E], I, J, K, N[auth M]|Pol protein|Simian immunodeficiency virus (11723)
>7ZTS_1|Chains AA[auth AB], AB[auth AC], AC[auth AD], AD[auth AE], A[auth AA], BA[auth AG], BB[auth AH], BC[auth AI], BD[auth AJ], B[auth AF], CA[auth AL], CB[auth AM], CC[auth AN], CD[auth AO], C[auth AK], DA[auth AQ], DB[auth AR], DC[auth AS], DD[auth AT], D[auth AP], EA[auth AV], EB[auth AW], EC[auth AX], ED[auth AY], E[auth AU], FA[auth BA], FB[auth BB], FC[auth BC], FD[auth BD], F[auth AZ], GA[auth BF], GB[auth BG], GC[auth BH], G[auth BE], HA[auth BJ], HB[auth BK], HC[auth BL], H[auth BI], IA[auth BN], IB[auth BO], IC[auth BP], I[auth BM], JA[auth BR], JB[auth BS], JC[auth BT], J[auth BQ], KA[auth BV], KB[auth BW], KC[auth BX], K[auth BU], LA[auth BZ], LB[auth CA], LC[auth CB], L[auth BY], MA[auth CD], MB[auth CE], MC[auth CF], M[auth CC], NA[auth CH], NB[auth CI], NC[auth CJ], N[auth CG], OA[auth CL], OB[auth CM], OC[auth CN], O[auth CK], PA[auth CP], PB[auth CQ], PC[auth CR], P[auth CO], QA[auth CT], QB[auth CU], QC[auth CV], Q[auth CS], RA[auth CX], RB[auth CY], RC[auth CZ], R[auth CW], SA[auth DB], SB[auth DC], SC[auth DD], S[auth DA], TA[auth DF], TB[auth DG], TC[auth DH], T[auth DE], UA[auth DJ], UB[auth DK], UC[auth DL], U[auth DI], VA[auth DN], VB[auth DO], VC[auth DP], V[auth DM], WA[auth DR], WB[auth DS], WC[auth DT], W[auth DQ], XA[auth DV], XB[auth DW], XC[auth DX], X[auth DU], YA[auth DZ], YB[auth EA], YC[auth EB], Y[auth DY], ZA[auth ED], ZB[auth EE], ZC[auth EF], Z[auth EC]|Major capsid protein|Saccharomyces cerevisiae BY4741 (1247190)
>3MMJ_1|Chains A, B|Myo-inositol hexaphosphate phosphohydrolase|Selenomonas ruminantium (971)
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 \(w=f(c)\)
6RWL , Knot 128 290 0.83 40 185 281 
GFLDGIEKAQEEHEKYHNNWRAMAEDFQIPQVVAKEIVAQCPKCQVKGEAMHGQVDASPKTWQMDCTHLEGKVIIVAVHVASGYIEAEVLPAETGKETAHFLLKLAARWPVKHLHTDNGDNFTSSAVQAVCWWAQIEHTFGVPYNPQSQGVVESMNHQLKTIITQIRDQAEKIETAVQMAVLIHNFKRKGGIGGYSAGERIIDIIASDLQTTKLQNQISKIQNFRVYFREGRDQQWKGPATLIWKGEGAVVIQDGQDLKVVPRRKCKIIKDYGRKDVDSETSMEGRQEKD
7ZTS , Knot 269 697 0.84 40 291 650 
MSSLLNSLLPEYFKPKTNLNINSSRVQYGFNARIDMQYEDDSGTRKGSRPNAFMSNTVAFIGNYEGIIVDDIPILDGLRADIFDTHGDLDMGLVEDALSKSTMIRRNVPTYTAYASELLYKRNLTSLFYNMLRLYYIKKWGSIKYEKDAIFYDNGHACLLNRQLFPKSRDASLESSLSLPEAEIAMLDPGLEFPEEDVPAILWHGRVSSRATCILGQACSEFAPLAPFSIAHYSPQLTRKLFVNAPAGIEPSSGRYTHEDVKDAITILVSANQAYTDFEAAYLMLAQTLVSPVPRTAEASAWFINAGMVNMPTLSCANGYYPALTNVNPYHRLDTWKDTLNHWVAYPDMLFYHSVAMIESCYVELGNVARVSDSDAINKYTFTELSVQGRPVMNRGIIVDLTLVAMRTGREISLPYPVSCGLTRTDALLQGTEIHVPVVVKDIDMPQYYNAIDKDVIEGQETVIKVKQLPPAMYPIYTYGINTTEFYSDHFEDQVQVEMAPIDNGKAVFNDARKFSKFMSIMRMMGNDVTATDLVTGRKVSNWADNSSGRFLYTDVKYEGQTAFLVDMDTVKARDHCWVSIVDPNGTMNLSYKMTNFRAAMFSRNKPLYMTGGSVRTIATGNYRDAAERLRAMDETLRLKPFKITEKLDFRVAAYAIPSLSGSNMPSLHHQEQLQISEVDAEPINPIGEDELPPDIE
3MMJ , Knot 137 314 0.83 38 193 301 
QTVTEPVGSYARAERPQDFEGFVWRLDNDGKEALPRNFRTSADALRAPEKKFHLDAAYVPSREGMDALHISGSSAFTPAQLKNVAAKLREKTAGPIYDVDLRQESHGYLDGIPVSWYGERDWANLGKSQHEALADERHRLHAALHKTVYIAPLGKHKLPEGGEVRRVQKVQTEQEVAEAAGMRYFRIAATDHVWPTPENIDRFLAFYRTLPQDAWLHFHSEAGVGRTTAFMVMTDMLKNPSVSLKDILYRQHEIGGFYYGEFPIKTKDKDSWKTKYYREKIVMIEQFYRYVQENRADGYQTPWSVWLKSHPAKA

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 \(c\).

\(|P_{f(6RWL_1)}(2) \setminus P_{f(7ZTS_1)}(2)|=45\), \(|P_{f(7ZTS_1)}(2) \setminus P_{f(6RWL_1)}(2)|=151\). 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 1:11101100100000000001011100101101110011100100010101101010101001010000101011111101101010101111001000101110111011100100001001000110110111010001111001000111001000100110010001001001101111100100011111001100110111001000010001001001010100100001011101110101111100100101110000011000100010000010100000
Pair \(Z_2\) Length of longest common subsequence
6RWL_1,7ZTS_1 196 3
6RWL_1,3MMJ_1 174 4
7ZTS_1,3MMJ_1 166 3

Newick tree

 
[
	6RWL_1:95.66,
	[
		3MMJ_1:83,7ZTS_1:83
	]:12.66
]

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 \((0.85)(0.8)(\frac{987 }{\log_{20} 987}-\frac{290}{\log_{20}290})=187.\)
Status Protein1 Protein2 d d1/2
Query variables 6RWL_1 7ZTS_1 239 168
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]