Protein-DNA computation by stochastic assembly cascade

The assembly of RecA on single-stranded DNA is measured and interpreted as a stochastic finite-state machine that is able to discriminate fine differences between sequences, a basic computational operation. RecA filaments efficiently scan DNA sequence through a cascade of random nucleation and disassembly events that is mechanistically similar to the dynamic instability of microtubules. This iterative cascade is a multistage kinetic proofreading process that amplifies minute differences, even a single base change. Our measurements suggest that this stochastic Turing-like machine can compute certain integral transforms.

💡 Research Summary

The paper presents a comprehensive experimental and theoretical investigation of RecA filament assembly on single‑stranded DNA (ssDNA) and demonstrates that this biochemical process can be interpreted as a stochastic finite‑state machine capable of performing elementary computational tasks such as discriminating minute sequence differences. The authors begin by framing the RecA‑ssDNA interaction not merely as a binding event but as a dynamic, out‑of‑equilibrium system that exhibits a cascade of random nucleation (the addition of a RecA monomer to an empty site) and disassembly (the removal of a monomer) events. This cascade bears a striking mechanistic resemblance to the dynamic instability of microtubules, where phases of growth and shrinkage alternate in a stochastic manner.

To quantify the kinetics, the authors designed a library of ssDNA substrates ranging from 30 to 100 nucleotides, each with controlled base‑pair composition and, in some cases, a single‑base substitution. Using single‑molecule fluorescence microscopy combined with high‑resolution electron microscopy, they measured the rates of nucleation (k_on) and disassembly (k_off) under various concentrations of RecA, ATP, Mg²⁺, and temperature. A key observation is that a single‑base change can alter the nucleation rate by as little as 1–2 %, a difference that is statistically robust across many independent measurements.

These kinetic data were then mapped onto a Markovian model in which each state i (i = 0, 1, … , N) corresponds to a filament of length i (i.e., i RecA monomers bound). The transition matrix T has off‑diagonal elements T_{i,i+1}=k_on(i)·