An Information Dynamics Model of Protein-Templated DNA Synthesis: From Qualitative Observations to Quantitative Predictions
Abstract
INFORMATION-DYNAMICS MODEL OF PROTEIN-TEMPLATED DNA SYNTHESIS Computational companion for a theoretical study of the bacterial anti-phage reverse transcriptase Drt3b, which synthesizes strictly alternating poly(AC) DNA without any nucleic acid template.
Background
In 2026, Dr. Pujuan Deng et al. (Science) reported that Drt3b uses its active-site residues (Glu26 and Arg253) as a geometric "mold" to enforce precise A/C alternation. This established a new paradigm of template-directed polymerization in which the template is not a nucleic acid strand but a rule set encoded in protein geometry. WHAT THIS WORK DOES We recast the Drt3b mechanism within the information-dynamics framework. Protein-templated synthesis represents a shift in information topology: conventional polymerases read sequence order from a real-space nucleic acid template, whereas Drt3b generates order from a constraint-space rule set — a two-state automaton (S_A → S_C → S_A) encoded in the active-pocket geometry. The framework has three components: Constraint space: the two-state automaton defined by the active pocket's geometric constraints (strict A/C alternation). Real space: the chemical potential of free nucleotides and the energy barriers modulated by mutation or environment. Coupling: a Boltzmann-weighted stochastic selection rule, P ∝ exp(−E/kT). The energy function is E = 0 for the state-preferred nucleotide, E = Δ for the alternative A/C nucleotide, and E = ∞ for G/T in the A/C-only model. KEY
Results
The framework yields a closed-form master curve for the alternation-defect rate (fraction of adjacent identical bases): ε(Δ) = 2·exp(−Δ) / (1 + exp(−Δ))² = ½·sech²(Δ/2) Alternation-defect rates (analytical ε): Wild-type (hard-exclusion limit, Δ → ∞): 0.000 E26A (calibrated to experimental ε = 0.144, Δ = 2.47 kT): 0.144 R253A (symmetry-based prediction, Δ = 2.47 kT): 0.144 E26A_R253A (residual-barrier prediction, Δ = 1.0 kT): 0.393 Random (4-base) (theoretical limit, Δ = 0): 0.250 A G/T-extended layer, calibrated to the reported E26Q product-level dG fraction of 10.16% (γ_G = ln 4), reproduces the 10% product-level dG fraction. Order-sensitive entropy measures distinguish fidelity loss invisible to marginal composition: the marginal entropy remains 1 bit for all A/C-symmetric systems, whereas the conditional entropy rises from 0 (WT) to 1 bit (random A/C). EXPERIMENTALLY TESTABLE PREDICTIONS Single-state automaton → homopolymer, poly(A) or poly(C), defect rate 0, entropy 0 bits. Three-state automaton {S_A, S_A, S_C} → periodic poly(AAC), marginal entropy 0.918 bit, dinucleotide entropy 1.585 bit. Asymmetric barriers E(C|S_A) = δ_low, E(A|S_C) = δ_high → P(AA)/P(CC) = exp(δ_low − δ_high). For δ_low = 1.0, δ_high = 3.0, this gives ≈ 0.135, i.e. CC exceeds AA by a factor of ≈ 7.4. 5% fidelity crossover at Δ ≈ 3.64 kT, an analytical criterion on a smooth monotonic function. THEORETICAL
Significance
Protein-templated synthesis is an instance of information-field self-organization: a fixed rule set in constraint space drives real-space data toward a unique stationary occupation distribution (π(S_A) = π(S_C) = 1/2). The principle is formally analogous to those previously validated in DNA sequencing by hybridization and RNA inverse folding, suggesting that information dynamics may provide a unified language for understanding how order emerges from noise in molecular biology. From a synthetic-biology perspective, the framework suggests a design principle for programmable template-independent polymerases: by redesigning the active-pocket geometry (constraint space), one can in principle engineer polymerases that synthesize arbitrary periodic sequences (e.g., poly(AAC), poly(ACG)) without nucleic acid templates. The energy barrier Δ serves as a tunable fidelity parameter. REPOSITORY CONTENTS config.py: Energy barriers, seeds, analytical helpers drt3b_two_state_simulator.py: Single-sequence simulator with analytical cross-check drt3b_stochastic_simulator.py: 50-replicate ensemble (mean ± std) drt3b_gt_extension.py: G/T-extended model (E26Q only) drt3b_dinucleotide_complexity.py: Analytical entropy metrics drt3b_delta_scan.py: ε(Δ) curve at T = 1 drt3b_temperature_scan.py: ε(T) at fixed Δ (exploratory) validate_manuscript.py: One-command validation of all numerical claims Requires Python 3.8+. No external dependencies beyond the standard library. EPISTEMIC STATUS Values reported here fall into three distinct categories: model consequences (WT strict alternation), calibrated parameters (E26A Δ, E26Q γ_G), and assumption-dependent predictions (R253A, double mutant, 5% crossover). They should not be conflated. The code is intended as a computational companion to the theoretical model; experimental values are not independently regenerated from raw experimental data.
