Amino Acid Physicochemical Distance Matrix Grantham Modified

Amino-Acid Physicochemical Distance Matrix (Grantham-Modified, Row-Scaled to [0,1])

P0 reference — verbatim Table 18.1 from 2014-schneider-de-novo-molecular-design-book §18.2.1 (Hiss & Schneider, p. ~445). Asymmetric pairwise distance matrix between the 20 standard residues, derived from physicochemical descriptor vectors (modified from Grantham). Each row is scaled to the interval [0, 1]; the matrix is not symmetric — d_ij ≠ d_ji in general.

The matrix powers the residue-mutation transition probability in Simulated Molecular Evolution (SME), Particle Swarm Optimization (PSO), and Ant Colony Optimization (ACO) for peptide design (Schneider 2014 §18.2.1, Eq. 18.5):

P(i → j) = exp(−d_ij² / (2σ²)) / Σ_j exp(−d_ij² / (2σ²))

Lower d_ij → higher mutation acceptance. Smaller σ → more conservative mutations.

Verbatim Table 18.1

Rows are the parent residue, columns are the target residue. Diagonal d_ii = 0 (self-mutation). Cells below extracted directly from MinerU-parsed Table 18.1 of the book; some cells in column C are reported as “1” in the source (max distance, scaled).

	A	R	N	D	C	Q	E	G	H	I	L	K	M	F	P	S	T	W	Y	V
A	0	0.57	0.57	0.65	1	0.47	0.55	0.31	0.44	0.48	0.49	0.54	0.43	0.58	0.14	0.51	0.30	0.76	0.57	0.33
R	0.62	0	0.48	0.53	1	0.24	0.30	0.69	0.16	0.54	0.57	0.14	0.51	0.54	0.57	0.61	0.39	0.56	0.43	0.53
N	0.64	0.49	0	0.13	0.80	0.26	0.24	0.46	0.39	0.86	0.88	0.54	0.82	0.91	0.52	0.26	0.37	1	0.82	0.76
D	0.70	0.53	0.13	0	0.85	0.34	0.25	0.52	0.45	0.93	0.95	0.56	0.88	0.98	0.60	0.36	0.47	1	0.88	0.84
C	0.91	0.84	0.65	0.72	0	0.72	0.79	0.74	0.81	0.92	0.92	0.94	0.91	0.95	0.79	0.52	0.69	1	0.90	0.89
Q	0.59	0.28	0.30	0.40	1	0	0.19	0.56	0.16	0.71	0.73	0.34	0.66	0.75	0.49	0.44	0.27	0.84	0.64	0.62
E	0.63	0.32	0.25	0.26	1	0.17	0	0.58	0.24	0.79	0.81	0.33	0.74	0.82	0.55	0.47	0.38	0.89	0.72	0.71
G	0.33	0.68	0.43	0.51	0.86	0.47	0.53	0	0.53	0.73	0.75	0.69	0.69	0.83	0.23	0.30	0.32	1	0.80	0.59
H	0.49	0.17	0.39	0.47	1	0.14	0.23	0.56	0	0.54	0.57	0.18	0.50	0.57	0.44	0.51	0.27	0.66	0.48	0.48
I	0.47	0.49	0.75	0.85	1	0.55	0.68	0.68	0.47	0	0.03	0.52	0.05	0.11	0.48	0.72	0.45	0.31	0.17	0.15
L	0.48	0.52	0.77	0.87	1	0.57	0.70	0.70	0.50	0.03	0	0.54	0.08	0.11	0.49	0.73	0.46	0.31	0.18	0.16
K	0.52	0.13	0.47	0.50	1	0.26	0.28	0.63	0.16	0.50	0.53	0	0.47	0.50	0.51	0.60	0.39	0.54	0.42	0.48
M	0.43	0.46	0.72	0.82	1	0.52	0.64	0.65	0.44	0.05	0.08	0.48	0	0.14	0.44	0.69	0.41	0.34	0.18	0.11
F	0.55	0.47	0.77	0.86	1	0.57	0.68	0.75	0.49	0.10	0.11	0.50	0.14	0	0.56	0.76	0.50	0.20	0.11	0.24
P	0.16	0.61	0.54	0.64	1	0.45	0.55	0.25	0.46	0.56	0.58	0.61	0.51	0.67	0	0.44	0.22	0.87	0.65	0.40
S	0.56	0.62	0.26	0.37	0.63	0.38	0.45	0.32	0.50	0.80	0.82	0.68	0.76	0.88	0.42	0	0.33	1	0.81	0.70
T	0.39	0.48	0.44	0.57	1	0.28	0.44	0.40	0.32	0.60	0.62	0.52	0.54	0.69	0.26	0.39	0	0.86	0.62	0.46
W	0.69	0.47	0.81	0.84	1	0.60	0.71	0.86	0.53	0.28	0.28	0.51	0.31	0.19	0.68	0.82	0.60	0	0.17	0.41
Y	0.58	0.40	0.74	0.82	1	0.51	0.63	0.76	0.43	0.17	0.19	0.44	0.19	0.11	0.57	0.74	0.47	0.19	0	0.28
V	0.33	0.50	0.69	0.79	1	0.50	0.63	0.57	0.44	0.15	0.17	0.51	0.11	0.26	0.35	0.65	0.36	0.46	0.29	0

— Verbatim from Schneider 2014, Table 18.1, Ch. 18 (Hiss & Schneider). Reference [42] of Ch. 18 (Schneider & Wrede physicochemical distance scales).

Useful diagonal observations

• I↔L↔M↔V form a tight aliphatic-hydrophobe cluster: pairwise distances 0.03–0.17. Conservative substitutions for h09 RADA-like assemblies expecting hydrophobic burial.
• D↔E distance 0.25–0.26 (acidic conservation).
• K↔R distance 0.13–0.14 (basic conservation, near-neutral).
• N↔D distance 0.13 (amide ↔ acid; classic conservative-mutation pair).
• Q↔E distance 0.17–0.19 (long-chain analogue of N↔D).
• F↔Y↔W form an aromatic cluster: F↔Y 0.11, Y↔W 0.17–0.19.
• C is the most isolated residue (distances ≈1 to most). Cysteine engineering (h26 disulfide design) cannot be modeled as a “conservative” SME mutation — must be designed explicitly.
• G↔A↔P small/flexible cluster: G↔A 0.31, A↔P 0.14, G↔P 0.23–0.25.

How to use in STRC

• h09 hydrogel — RADA16 / EAK16 conservative ablation series: to test which residues are load-bearing for self-assembly, mutate within physicochemical-distance ≤0.20 windows (e.g., R↔K, D↔E, A↔V, N↔Q). Larger jumps (≥0.5) test self-assembly robustness.
• h09 ACO peptide library (per Recipe — Ant Colony Optimization for Peptide Sequence Design): when the ACO update step needs a residue-similarity prior, use 1 − d_ij from this matrix.
• h09 SME mutation step-size σ choice: Schneider 2014 §18.2.1 example uses σ = 0.1 (conservative) and σ = 0.5 (broad). σ = 0.05 yields essentially-identical libraries. For h09 RADA16-class peptides expecting β-sheet propensity, σ ≈ 0.15 is a sensible midpoint — preserves residue class with occasional inter-class jump.
• h26 cysteine disulfide engineering: because column-C distances are mostly = 1 (max), cysteine substitution is the worst case for SME-type continuous evolution. Use explicit design (Rosetta DESIGN, AF3 disulfide-finder) instead.
• NOT to be used for evolutionary-conservation analyses — this is a physicochemical-mutation matrix, not a BLOSUM/PAM substitution-likelihood matrix.

Connections

• [part-of] rada16-geometry
• [source] 2014-schneider-de-novo-molecular-design-book
• [applies] index
• [applies] index
• [see-also] Recipe — Ant Colony Optimization for Peptide Sequence Design
• [see-also] Recipe — Therapeutic Peptide Stability Modifications