Accessible Contact Volume (ACV)

• ACV is defined as the three-dimensional volume a fluorophore can access when attached to an RNA structure, considering linker flexibility and steric hindrance.
• ACV bridges static RNA conformations with dynamic FRET predictions by converting fixed structures into dye-position ensembles via Monte Carlo sampling in FRETraj.
• The ACV framework aids in RNA structure selection by correlating simulated FRET histograms with experimental data, enhancing model accuracy.

Accessible contact volume (ACV) denotes the three-dimensional region of space that a fluorophore center can occupy when attached to an RNA conformation, subject to the geometry and steric constraints of its covalent attachment point on the RNA, the length and flexibility of the chemical linker, and hard-sphere repulsion from the RNA scaffold. In the FRET-guided RNA-structure-selection framework of Weber et al., ACV is the formal device that converts each static RNA fold into an ensemble of dye positions and, from that ensemble, into a predicted FRET-efficiency distribution. Within that treatment, ACV captures the static heterogeneity of dye position on nanosecond timescales and provides the link between predicted RNA 3D structures, single-molecule FRET observables, and conformational-state selection (Weber et al., 22 Sep 2025).

1. Definition and physical interpretation

The ACV of a dye attached to an RNA conformation is defined as the three-dimensional region of space that the fluorophore center can occupy, given the geometry and steric constraints of its covalent attachment point on the RNA, the length and flexibility of the chemical linker, and hard-sphere repulsion from the RNA scaffold (Weber et al., 22 Sep 2025). In a single fixed RNA fold, the linker can rotate through thousands of conformations, and the dye therefore sweeps out a volume around the attachment site. The ACV is that volume, under the assumption that dye-chain dynamics are fast compared to the fluorescence lifetime.

This interpretation makes ACV a representation of positional heterogeneity even when the underlying biomolecular structure is held fixed. In Weber et al., the ACV formalism is implemented in the FRETraj package, which is used to convert each static RNA conformation into an ensemble of dye positions. A plausible implication is that ACV separates dye-motion heterogeneity from conformational heterogeneity of the RNA itself: the former is represented within a single structure, whereas the latter is represented across a collection of structures.

In a FRET experiment, each donor-acceptor pair samples two overlapping ACVs, and the instantaneous distance between dyes is then a random variable drawn from the convolution of those two volumes. This is the central physical reason that ACV-based modeling does not reduce a labeled RNA conformation to a single donor-acceptor distance.

2. Formal relation to Förster efficiency

The ACV-based calculation of average transfer efficiency in FRETraj is described through uniform probability densities over the donor and acceptor ACVs. If $p_D(r_D)$ and $p_A(r_A)$ are the uniform probability densities over the donor and acceptor ACVs, each normalized to unity over its volume, the theoretical ensemble-averaged transfer efficiency is

$$\langle E \rangle = \int_{V_D} d^3r_D \int_{V_A} d^3r_A p_D(r_D) p_A(r_A) \times [1 + (|r_D - r_A|/R_0)^6]^{-1}.$$

In practice, FRETraj draws $N_D$ samples $\{r_D^i\}$ from the donor ACV and $N_A$ samples $\{r_A^j\}$ from the acceptor ACV and estimates

$$\langle E \rangle \simeq \frac{1}{N_D N_A} \sum_{i=1..N_D} \sum_{j=1..N_A} [1 + (|r_D^i - r_A^j|/R_0)^6]^{-1}.$$

For the sCy3/sCy5 dye pair, $R_0 \approx 5.5\ \mathrm{nm}$, so this procedure directly yields a predicted mean FRET efficiency for each fixed RNA conformation (Weber et al., 22 Sep 2025). The broader or more distant the two accessible volumes are, the lower the average $\langle E \rangle$.

The paper does not reproduce the full double-integral derivation, nor the full parametrization of ACV generation. Instead, the detailed mathematics are delegated to the FRETraj references, and FRETraj is invoked as a “black box.” That division of labor is important for interpretation: the Weber et al. study uses ACV operationally to score RNA conformations against smFRET data rather than to rederive the geometry model.

3. Computational realization in FRETraj

For each retained RNA structure, whether from a 3-D predictor or an MD snapshot, FRETraj performs a sequence of steps that produce ACVs and then convert them into predicted FRET observables (Weber et al., 22 Sep 2025).

First, the program reads the PDB atom indices at which donor (Cy3) and acceptor (Cy5) linkers are attached. Each dye is then represented by a spherical fluorophore of given radius, for example approximately $p_A(r_A)$0–$p_A(r_A)$1, together with a flexible linker of specified length, characterized by the number of rotatable bonds and typical bond-angle and dihedral statistics.

The linker is subsequently grown stochastically one rotatable bond at a time by Monte Carlo sampling. Trial positions of the dye center are generated, and any conformation that causes steric overlap, that is, a hard-sphere clash with RNA atoms, is rejected. Sampling continues until the software has collected a user-specified number of allowed dye positions, often thousands. The aggregate of accepted dye-center positions is then saved as an ACV point cloud in .pkl files, from which uniform sampling yields $p_A(r_A)$2 or $p_A(r_A)$3.

A single FRETraj function then pairs donor and acceptor clouds to compute $p_A(r_A)$4 for that RNA conformation. Weber et al. summarize this stage by reporting that “ACVs of both dyes were calculated for each structure … Photon emission events were simulated by FRETraj …” Explicit numerical values for dye radii or linker parameters are inherited from the internal FRETraj defaults for sCy3/sCy5 rather than being restated in the study.

4. Role in FRET-guided RNA 3D-structure selection

In Weber et al., ACV is embedded in an integrative workflow for RNA conformational-state selection rather than being treated as an isolated dye model (Weber et al., 22 Sep 2025). The study predicts 3D structures of a ribosomal RNA tertiary contact comprising a GAAA tetraloop and a kissing loop using RNAComposer, FARFAR2, and AlphaFold3, thereby yielding a collection of candidate conformations. These models are structurally validated based on Watson-Crick base-pairing patterns and filtered using an eRMSD threshold.

For each retained structure, the accessible contact volume of the sCy3/sCy5 dye pair is computed using FRETraj to predict FRET distributions. The resulting theoretical distributions are then compared and weighted against experimental smFRET data to identify conformational states compatible with the observed FRET states.

Within this workflow, ACV plays a specific mediating role. It is the mechanism by which a static RNA conformation is converted into a dye-position ensemble, and the dye-position ensemble is the mechanism by which a structure is converted into a predicted transfer-efficiency observable. This suggests that ACV is not merely an annotation on top of a structural model; it is the operational bridge between RNA structural hypotheses and the experimentally measured FRET histogram.

5. From single-structure efficiencies to FRET distributions

For each of the 1,000 filtered structures from RNAComposer, FARFAR2, or AlphaFold3, or for each MD snapshot, FRETraj first returns a single $p_A(r_A)$5, described as the mean transfer efficiency based on that structure’s donor and acceptor ACVs (Weber et al., 22 Sep 2025). Collectively, the set $p_A(r_A)$6 over structures defines a theoretical distribution of FRET efficiencies.

FRETraj then simulates photon-counting bursts for each structure in proportion to its weight. Under uniform weighting, the weight is $p_A(r_A)$7; under reweighting, the weights are adjusted to match the experimental smFRET histogram. The simulated bursts are intended to mimic experimental burst-histogram broadening, including shot noise, direct excitation, and $p_A(r_A)$8-correction. The output is a fully instrument-corrected in silico FRET histogram that can be compared directly with the measured smFRET data.

This construction clarifies a recurrent point of confusion. A plausible misconception is that ACV produces only a corrected donor-acceptor distance. In the Weber et al. formulation, ACV instead yields a structure-specific ensemble average, and distributions over many structures are obtained only after collecting the $p_A(r_A)$9 values across the retained structural ensemble and, if desired, applying photon sampling and reweighting.

6. Numerical behavior, interpretive value, and limits

The numerical examples in Weber et al. show how ACV-derived efficiencies behave before and after photon sampling and before and after reweighting to experimental data (Weber et al., 22 Sep 2025). Without photon sampling, the reported FRET means and widths are $$\langle E \rangle = \int_{V_D} d^3r_D \int_{V_A} d^3r_A p_D(r_D) p_A(r_A) \times [1 + (|r_D - r_A|/R_0)^6]^{-1}.$$0 for RNAComposer, $$\langle E \rangle = \int_{V_D} d^3r_D \int_{V_A} d^3r_A p_D(r_D) p_A(r_A) \times [1 + (|r_D - r_A|/R_0)^6]^{-1}.$$1 for FARFAR2, $$\langle E \rangle = \int_{V_D} d^3r_D \int_{V_A} d^3r_A p_D(r_D) p_A(r_A) \times [1 + (|r_D - r_A|/R_0)^6]^{-1}.$$2 for AlphaFold3, and $$\langle E \rangle = \int_{V_D} d^3r_D \int_{V_A} d^3r_A p_D(r_D) p_A(r_A) \times [1 + (|r_D - r_A|/R_0)^6]^{-1}.$$3 for MD. With photon sampling and uniform weighting, the corresponding values are $$\langle E \rangle = \int_{V_D} d^3r_D \int_{V_A} d^3r_A p_D(r_D) p_A(r_A) \times [1 + (|r_D - r_A|/R_0)^6]^{-1}.$$4, $$\langle E \rangle = \int_{V_D} d^3r_D \int_{V_A} d^3r_A p_D(r_D) p_A(r_A) \times [1 + (|r_D - r_A|/R_0)^6]^{-1}.$$5, $$\langle E \rangle = \int_{V_D} d^3r_D \int_{V_A} d^3r_A p_D(r_D) p_A(r_A) \times [1 + (|r_D - r_A|/R_0)^6]^{-1}.$$6, and $$\langle E \rangle = \int_{V_D} d^3r_D \int_{V_A} d^3r_A p_D(r_D) p_A(r_A) \times [1 + (|r_D - r_A|/R_0)^6]^{-1}.$$7.

After reweighting structures to reproduce the experimental smFRET histogram, whose reported mean and width are $$\langle E \rangle = \int_{V_D} d^3r_D \int_{V_A} d^3r_A p_D(r_D) p_A(r_A) \times [1 + (|r_D - r_A|/R_0)^6]^{-1}.$$8, the predicted means shift to $$\langle E \rangle = \int_{V_D} d^3r_D \int_{V_A} d^3r_A p_D(r_D) p_A(r_A) \times [1 + (|r_D - r_A|/R_0)^6]^{-1}.$$9 for RNAComposer, $N_D$0 for FARFAR2, $N_D$1 for AlphaFold3, and $N_D$2 for MD. These values demonstrate that accounting for the ACV-derived $N_D$3 and then reweighting according to the experimental FRET occupancy can bring in silico and experimental FRET into closer agreement. Weber et al. further note that this can occur at the cost—especially in some tools—of relying on only a few high-occupancy conformers.

The broader significance assigned to ACV in this study is therefore methodological. ACVs are the engine that converts a single static RNA fold into a dye-position ensemble; FRETraj’s Monte Carlo procedure enforces steric constraints; and the resulting $N_D$4 values serve both as unweighted predictions and as the basis for the FRET-guided reweighting scheme. At the same time, the study also delineates the formal limits of its exposition: it does not reproduce the full ACV integral machinery or list every geometric parameter in detail, because those aspects are inherited from the underlying FRETraj references. A plausible implication is that ACV, in this context, is best understood as a rigorously defined but operationally encapsulated component of an integrative RNA-modeling workflow rather than as a standalone geometric observable.