Information-Thermodynamic Analysis of the DNA--RNA Polymerase Complex via Interface Dissipation: large Based on Observer--Observed Swap Symmetry

TL;DR

This work reframes RNAP transcription as an information-thermodynamics problem by introducing interface dissipation, a swap-symmetric, partition-invariant measure of irreversibility that remains meaningful under different observer–target decompositions. It develops a minimal Brownian-ratchet CTMC in which DNA-structure–driven pre/post fluctuations are rectified by binding and polymerization of the correct rNTP, yielding forward motion without directly propelling via chemical free energy. Dissipation is decomposed into pre/post fluctuations, binding, and polymerization contributions, with a path-space KL framework to compute the total dissipation $\dot\Sigma_{XY}$ and the interface dissipation $\dot\Sigma_{\mathrm{int}}=\dot\Sigma_{XY}-\tfrac{1}{2}(\dot\Sigma_X+\dot\Sigma_Y)$, where $\dot\Sigma_X$ and $\dot\Sigma_Y$ are marginal dissipations estimated from forward/reverse likelihood ratios. The authors provide a practical protocol for estimating these quantities from single-molecule data (via Gillespie simulations and finite-memory KL estimators), show how to infer the forward/backward ratio $K_{\delta}$ from traces, and discuss how $\Sigma_{\mathrm{int}}$ isolates input-dependent irreversibility, offering a partition-invariant lens on information-to-motion narratives in molecular machines.

Abstract

RNA polymerase (RNAP) is a molecular machine that reads information encoded in the base sequence of a DNA template while producing mechanical motion (transcription elongation; forward/backward stepping; backtracking) through chemical-potential differences of nucleoside triphosphates (NTPs) and fluctuations under external conditions. A prior work formulated a mismatch in free-energy accounting as the involvement of a term originating from genetic information (e.g.\ $k_BT\log P(N)$), and interpreted RNAP as a Maxwell's demon / Szilard-engine-like device that converts information into motion. However, in information thermodynamics, the bookkeeping of information and dissipation can depend on how one partitions the composite system into a device and a target (observer/observed labeling).

Figures (6)

• Figure 1: Simultaneous estimation of the mean velocity and total dissipation rate in the locking--rectification CTMC. RNAP translocation fluctuations between pre/post conformations are modeled as $(m,\mathrm{pre},b)\rightleftarrows(m,\mathrm{post},b)$, with the forward/backward rate ratio $K_\delta:=k_{-1}/k_{1}$ fixed from the literature (or single-molecule traces). Binding/unbinding of the correct rNTP occurs only in the post state, $(m,\mathrm{post},0)\rightleftarrows(m,\mathrm{post},1)$, and polymerization commitment after binding induces $(m,\mathrm{post},1)\to(m+1,\mathrm{pre},0)$ (with depolymerization included as a minimal reverse process for mathematical consistency). Each marker corresponds to one Gillespie trajectory with effective observation time $T_{\mathrm{eff}}=T-T_{\mathrm{burn}}$. The velocity is estimated from the polymerization and depolymerization counts as $v:=(N_{+}-N_{-})/T_{\mathrm{eff}}$ and the dissipation rate is reported as $\dot\Sigma_{XY}:=\Sigma_{XY}/T_{\mathrm{eff}}$ (Eq. \ref{['eq:est-sigmaXY']}). The scatter reflects finite-time and finite-sampling trajectory fluctuations.
• Figure 2: Convergence diagnostics for the interface-dissipation-rate estimator. With fixed sampling interval $\Delta t$, estimate $\widehat{\dot{\Sigma}}_{\mathrm{int}}^{(r)}$ for multiple Markov orders $r$, and plot the mean estimate as a function of observation length $T$. The result illustrates that $r=1$ is stable, whereas $r\ge2$ is more susceptible to sparse-estimation effects in finite data.
• Figure 3: Convergence diagnostics for the total dissipation rate estimator. Under the same settings, estimate $\widehat{\dot{\Sigma}}_{XY}^{(r)}$ (corresponding to $S=(X,Y)$ in Eq. \ref{['eq:KLrate-int']}) and compare across observation lengths $T$.
• Figure 4: Transcription-length trajectories of the locking-rectification CTMC. Define $M(t)=N_{+}(t)-N_{-}(t)$ as a proxy for transcription length, and evaluate $\mathbb{E}[M(t)]$ (solid line) and $\pm 1$ SD (shaded band) from many independent trajectories. Estimate the drift $\mu$ via the linear regression in Eq. \ref{['eq:muD-fit2']}.
• Figure 5: Estimating the diffusion coefficient via variance growth. From the same set of trajectories, evaluate $\mathop{\mathrm{Var}}\nolimits[M(t)]$ and estimate $D$ based on $\mathop{\mathrm{Var}}\nolimits[M(t)]\simeq 2Dt$.

Theorems & Definitions (8)

• Definition 1: Interface dissipation
• Remark 2: How we use it in this manuscript
• Definition 3: Projection to the variables used previously
• Definition 4: Meaning of the prior state function in the present manuscript
• Proposition 5: Inclusion by coarse-graining and monotonicity of dissipation
• proof
• Proposition 6: Estimating $K_\delta$ from occupation times and transition counts
• proof