How it works

An immune system as a reaction network, and one of the few chemistries that fixes its own rate constants. Antibodies are bitstrings with two sites; when one antibody's paratope matches another's epitope, the recogniser is replicated and the recognised destroyed. The crucial move is that the reaction rate is computed from the *degree* of complementarity between the strings, over all alignments - structure determines kinetics. Species below a concentration threshold are periodically culled and new ones injected, so the species set turns over.

S

antibodies X_i as binary strings with two binding sites (epitope e, paratope p); antigens Y_j with an epitope · implicit

R

Recognition of an epitope by a paratope replicates the recogniser and destroys the recognised. Matching specificity: m_ij = sum_k G( sum_n [ e_i(n+k) XOR p_j(n) ] - s + 1 ), G(x)=x for x>0 else 0, over all alignments -l_p < k < l_e. · arity 1, 2

A

ode, ssa · metadynamics: periodically drop species below a concentration threshold and inject new ones

Parameters

What to look for

• clonal selection
• idiotypic network memory
• constructive dynamics via metadynamics

Implementation decisions

• Strings are random bits from the seed. Each term of eqs. 11.5-11.6 is one mass-action reaction whose rate the matching strengths prescribe: stimulation X_i + X_j -> 2X_i + X_j (c m_ji), suppression X_i + X_j -> X_j (c k1 m_ij), antigen stimulation X_i + Y_j -> 2X_i + Y_j (c m), antigen removal Y_j + X_i -> X_i (k3 m), decay X_i -> (k2). A self-interaction i = j uses 2X_i on the left.
• The book says strings bind when 's > min(l_e, l_p)', which contradicts its own definition of G. Here an alignment contributes when at least s bits are complementary, which is what eq. 11.4 computes.
• The book gives no parameter values; defaults are N = 10, M = 2, 8-bit sites, s = 6, c = k1 = k3 = 1, k2 = 0.5. Metadynamics (mutation and replacement) acts between network snapshots and is not generated; mutation_ops is dropped.

Banzhaf & Yamamoto, Artificial Chemistries (2015), §11.2.2

Preview at default parameters

12 species · 88 reactions · status complete · seed 1

X1 + X2 -> 2 X1 + X2  [mass-action k=1.0]
X1 + X4 -> X4  [mass-action k=1.0]
X1 + X5 -> X5  [mass-action k=1.0]
X1 + X6 -> 2 X1 + X6  [mass-action k=1.0]
X1 + X7 -> 2 X1 + X7  [mass-action k=1.0]
X1 + X8 -> X8  [mass-action k=1.0]
X1 + X10 -> 2 X1 + X10  [mass-action k=1.0]
X2 + X1 -> X1  [mass-action k=1.0]
2 X2 -> 3 X2  [mass-action k=2.0]
2 X2 -> X2  [mass-action k=2.0]
X2 + X3 -> X3  [mass-action k=1.0]
X2 + X4 -> 2 X2 + X4  [mass-action k=1.0]
X2 + X5 -> X5  [mass-action k=3.0]
X2 + X7 -> 2 X2 + X7  [mass-action k=2.0]
X2 + X7 -> X7  [mass-action k=2.0]
X2 + X9 -> 2 X2 + X9  [mass-action k=1.0]
X2 + X10 -> 2 X2 + X10  [mass-action k=2.0]
X3 + X2 -> 2 X3 + X2  [mass-action k=1.0]
X3 + X5 -> 2 X3 + X5  [mass-action k=1.0]
X3 + X5 -> X5  [mass-action k=1.0]
X3 + X6 -> X6  [mass-action k=1.0]
X3 + X8 -> 2 X3 + X8  [mass-action k=2.0]
X3 + X10 -> X10  [mass-action k=2.0]
X4 + X1 -> 2 X4 + X1  [mass-action k=1.0]
X4 + X2 -> X2  [mass-action k=1.0]
2 X4 -> 3 X4  [mass-action k=2.0]
2 X4 -> X4  [mass-action k=2.0]
X4 + X5 -> 2 X4 + X5  [mass-action k=1.0]
X4 + X5 -> X5  [mass-action k=1.0]
X4 + X7 -> 2 X4 + X7  [mass-action k=1.0]
X4 + X8 -> X8  [mass-action k=1.0]
X4 + X9 -> 2 X4 + X9  [mass-action k=2.0]
X4 + X10 -> 2 X4 + X10  [mass-action k=1.0]
X5 + X1 -> 2 X5 + X1  [mass-action k=1.0]
X5 + X2 -> 2 X5 + X2  [mass-action k=3.0]
X5 + X3 -> 2 X5 + X3  [mass-action k=1.0]
X5 + X3 -> X3  [mass-action k=1.0]
X5 + X4 -> 2 X5 + X4  [mass-action k=1.0]
X5 + X4 -> X4  [mass-action k=1.0]
2 X5 -> 3 X5  [mass-action k=1.0]
… 48 more

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