A substrate recursion principle for biological information, with empirical anchoring through a templating-mode taxonomy

Abstract

Biological inheritance can be treated as a class of catalytic templating reactions in which a daughter molecule, generated by a kinetic kernel acting on a parent template, is itself a substrate for the next round of the same catalysis. We give the physicochemical conditions under which such a reaction can support unbounded heritable molecular distinguishability. Four conditions on the template-operator pair organize the analysis: nonzero per-site information content under the activesite recognition kernel (R1), a count of independently variable recognized positions that grows without bound as the reaction extends (R2), catalytic closure under iteration, possibly through a reversible involution such as Watson-Crick complementation (R3), and stochastic drift of the kernel in its recognition alphabet (R4). A fifth, scope-defining condition (R5) restricts the principle to kernels that are intrinsic physicochemistry rather than externally optimized search. These conditions are necessary for two distinct outcomes, separable as two necessity results. The capacity theorem states that linear scaling of substrate Shannon capacity with reaction extent requires R1, R2, and R3 but not R4: a perfect copier transmits an exponentially large configurational ensemble while producing no novelty. The generation theorem states that diversification of the heritable configuration set beyond the deterministic closure of a finite initial repertoire additionally requires R4, because branching trajectories in the recognized alphabet are what produce innovation. Populationlevel kinetics follow as a corollary that organizes six attested templating reactions into a taxonomy, and as a finite-population, finite-horizon proposition tested over five inheritance kinetic schemes, in which only individual-level stochastic drift reaches the target within the model class. We test the framework on the recently characterized bacterial defense system Drt3b, which makes alternating poly(AC) DNA without using a nucleic acid template. The framework classifies Drt3b as a cyclic two-state catalytic templating channel with a 1-bit capacity ceiling, and predicts that the Glu26-to-Gln active-site mutant incorporates dG at 10% probability at the dA-selecting state; the published biochemistry reports 10.16%. Across 1,232 Drt3b homologs, the framework predicts and recovers a 15.7-fold elevation of dG misincorporation in six clades carrying the natural Glu26-to-Asp substitution at this gate. Substitutions at two universal gate residues, Arg253 (architectural) and Gly248 (selectivity), provide single-experiment site-directed mutagenesis tests of the frameworks predictions. POPULAR SUMMARYA bacterial defense protein called Drt3b, recently characterized in E. coli, synthesizes DNA with a strict alternating ACAC pattern without copying any template. Two conserved active-site residues, Glu26 and Arg253, are modeled as enforcing an alternating two-state catalytic cycle that selects which nucleotide enters at each step. This is sequence without a sequence template, and it does not fit the textbook picture of inheritance. We treat inheritance as a class of catalytic templating reactions and ask which chemistries can support openended evolution. Two distinct requirements emerge. Capacity, the ability to transmit exponentially many distinct heritable configurations, requires three conditions on the template-catalyst pair: more than one monomer state recognized at each position, a position count that grows unboundedly with the reaction extent, and applicability of the catalysis to its own product. Generation of novel heritable configurations beyond what is already present requires a fourth condition: stochastic drift of the catalysis in its recognition alphabet. A perfect copier has capacity but cannot innovate; a drifting copier has both. Drt3b fails the second capacity condition, because its cycle has two states regardless of product length. The framework classifies six attested biological templating reactions as instances or partial instances of the same chemical specification, and it identifies two single-residue substitutions at Drt3bs active site whose measured effects would test its predictions.