Sensing the structural and conformational properties of single-stranded nucleic acids using electrometry and molecular simulations

Inferring the 3D structure and conformation of disordered biomolecules, e.g., single stranded nucleic acids (ssNAs), remains challenging due to their conformational heterogeneity in solution. Here, we use escape-time electrometry (ETe) to measure with sub elementary-charge precision the effective electrical charge in solution of short to medium chain length ssNAs in the range of 5–60 bases. We compare measurements of molecular effective charge with theoretically calculated values for simulated molecular conformations obtained from Molecular Dynamics simulations using a variety of forcefield descriptions. We demonstrate that the measured effective charge captures subtle differences in molecular structure in various nucleic acid homopolymers of identical length, and also that the experimental measurements can find agreement with computed values derived from coarse-grained molecular structure descriptions such as oxDNA, as well next generation ssNA force fields. We further show that comparing the measured effective charge with calculations for a rigid, charged rod—the simplest model of a nucleic acid—yields estimates of molecular structural dimensions such as linear charge spacings that capture molecular structural trends observed using high resolution structural analysis methods such as X-ray scattering. By sensitively probing the effective charge of a molecule, electrometry provides a powerful dimension supporting inferences of molecular structural and conformational properties, as well as the validation of biomolecular structural models. The overall approach holds promise for a high throughput, microscopy-based biomolecular analytical approach offering rapid screening and inference of molecular 3D conformation, and operating at the single molecule level in solution.


S2. PB calcula3on geometry and boundary condi3ons
As outlined in the main text and the Methods, we calculate theoreMcal effecMve charge values,  %&'% , of model structures in a Poisson Boltzmann framework that resembles the experimental ETe geometry.In Fig. S2 below we provide schemaMc representaMons of this geometry and highlight the governing equaMons and boundary condiMons in the relevant domains.(A) IllustraMon of the experimental ETe geometry, whereby molecules can either reside in 'slit' (1) or 'pocket' (2) states.The effecMve charge of the molecule can be deduced from the relaMonship Δ (' =  ())  * where Δ (' =  "'+# −  ,-%.(# and  * is the electrostaMc potenMal at the midplane of the slit.ElectrostaMc potenMal distribuMons for a molecule in the 'slit state' (B), and (C) the 'pocket state', i.e., effecMvely in free soluMon.The governing PB equaMon in the electrolyte and constant surface charge boundary condiMons of the silica walls are depicted.The distance between the center of the molecule and the edges of the box was set to large distance of 5 /0 as depicted in order to enable the implementaMon the zero electric field boundary condiMon on the outer walls of the geometry.

S3. Determining the renormalized charge for a covalently aFached ATTO532 dye molecule
As discussed in the main text and the Methods, since our experimental structures contain aWached fluorescent ATTO-532 dyes (which themselves carry a total structural charge  "#$ = −1 e), the contribuMon of the dye molecule must be added to the effecMve charge of model structures that do not include any dyes in order to generate,  %&'% values, that can be compared with experimental measurements.Since an MD model for ATTO-532 was not available in the AMBER-dyes library and the dye is structurally very similar to ATTO-488, we performed a study calculaMng the effecMve charge of model half-helix structures with and without an aWached ATTO-488-dye molecule 1 .The difference in the effecMve charge of these two structures yielded an esMmate the renormalized charge of the ATTO-dye molecule,  %&'%,23( .RepeaMng this procedure for various values of  !we found a dependence of this  %&'%,23( on the number of bases,  !, of the aWached polymer chain (see Fig. S3).The results are in line with the expectaMon of  → 1 for small values of  ! and  < 1 for larger  ! .In parMcular for large  !, we have  %&'%,23( = -0.62 e which is very close to the value of -0.46 e obtained for dsNAs in previous work 2 .The value of  ()),23( for a given  ! is added to the effecMve charge of dye-free model ssNA structures to obtain a value that can be compared to the experimental measurements (see Methods).

S4. Conforma3onal analysis of model ssNAs
In this secMon we describe further conformaMonal analyses of model ssNA structures obtained using both atomisMc and coarse-grained modelling approaches, and provide some discussion comparing the results with those inferred from SAXS data in the experimental literature.We also present conformaMonal  4 vs  landscapes for all other ssNA models used in this work.

S4.1. OrientaMonal correlaMon analysis
It has been demonstrated in Refs.3,4 that the properMes of ssNA polymer chains may be inferred from experimental SAXS data via a 'model building and iteraMve refinement' scheme that seeks to produce model ssNA structures that theoreMcally reproduce the measured SAXS profiles.One such property that can be inferred in this way is the direcMonal persistence of the polymer chain, as captured by the orientaMonal correlaMon funcMon (OCF).The OCF is defined as 〈̂5.̂6〉, where (5.̂6) are two phosphate site bond vectors in the ssNA chain, separated by  bonds and where the dot product between two such vectors is computed as a funcMon of the number of bonds that separate them (| − |) (see Fig. S4).The OCF can also be readily calculated as an output from analysing the molecular simulaMon trajectories in this work, and comparison with the experimentally inferred OCF data in Refs.3,4 may provide an extra measure with which to validate ssNA structural models.We note that the experimental salt concentraMon for the SAXS measurements in Refs.3,4 was 20 mM NaCl, close to our measurement salt concentraMon of ≈ 1 mM.
The calculated OCF data for poly-dT and poly-dA modelled with the AMBER forcefield in this study showed very liWle difference between the two sequences, with both exhibiMng a strong oscillatory moMf which can be assigned to a highly stacked helical polymer chain configuraMon (see Fig. S4).Such poor agreement in the OCF profiles between the experimentally inferred and simulated data for the AMBER forcefields suggest that the models greatly over-esMmate the tendency of nucleobases to form stacked helical coils.We found that the CHARMM-36 forcefield performed beWer than AMBER in capturing the OCF profiles for poly-dT and poly-dA (see Fig. S4).A clear difference in the orientaMonal correlaMon funcMon (OCF) between dT and dA for the CHARMM models was observed, with that of dA exhibiMng a slight oscillatory moMf, and with dT exhibiMng a more gradual decay -characterisMcs also present in the experimentally inferred OCF profiles.
Recently, efforts to improve exisMng molecular dynamics forcefields for the purpose of modelling ssNAs have been made, as exhibited in the DES-Amber and CUFIX forcefields [5][6][7][8][9] .The combinaMon of conformaMonal constraints, hydrogen bonding, base stacking, salt and solvaMon effects that influence ssNA structure in an all atom MD model are challenging to accurately incorporate, and in reality no forcefield is able to closely match the experimental data across the wide range of soluMon condiMons seen in experiments 10 .For DES-Amber poly-dT we noMced a strong tendency for thymine bases to also form stacked helical regions, similar to the AMBER forcefield on which the model is based, resulMng in an oscillatory moMf in the OCF (see Fig. S4).However this behaviour is not inferred for poly-dT from the experimental SAXS data as previously discussed 3 .In modelling poly-rU30, all models considered found good agreement with the experimentally inferred OCF in Ref. 4, with the OCF profiles exhibiMng a gradual decay with increased bond separaMon, whilst sMll retaining a small posiMve value of 〈̂5.̂6〉 over separaMons of | − | = 10.The DES-AMBER RNA model showed the best agreement with the SAXS data and is a rare example of a model considered in this work that is able to capture both local (OCF) and global (reflected in values of  4 and ) polymer chain properMes when comparing to the available experimental SAXS and smFRET data.

S4.2. Conforma3onal landscapes of MD simulated ssNAs
Here we present  7 vs  landscapes for the other ssNA models not shown in Fig. 4 of the main text.

S5. Discussion comparing gel electrophoresis and effec3ve charge measurements
We performed polyacrylamide gel electrophoresis on our  != 30 and 60 single stranded homopolymeric nucleic acid species (see Fig. 3B and Methods).Echoing the observaMons in electrometry, the various species migrated differently, despite having the same total structural charge.We observed the following order of increasing electrophoreMc mobility: poly-dA > mixed sequence > -dT > -rU (see Fig. 3B).The ordering of mobiliMes may of course be compared with the magnitude of measured effecMve charge values.The simplest view of electrophoreMc mobility of a charged object in soluMon suggests  ∝ | ()) |/, where  represents the "Stokes' drag" of the object in the medium.In the Ogston sieving regime, which we may expect to hold for ssDNA oligomers, we expect the mobility to be inversely related to molecular contour length  % reflecMng the inverse relaMonship between the electrical mobility and Stokes' drag.Since  ()) for poly-dT is larger than that of -rU the electrophoreMc mobiliMes observed for rU and dT may be raMonalised based on measured trends in  ()) values alone.
However the qualitaMve trend observed in electrophoreMc mobility observed for DNA (poly-dA > mixed sequence > -dT) appears to be the opposite of that indicated by the magnitude of the effecMve charge.This trend may be explained by base stacking interacMons that cause poly-dA to adopt more compact conformaMons than poly-dT, implying a lower value of  for poly-dA 11,12 .Indeed, the observed trend in gel electrophoreMc mobiliMes reflects the order of base-stacking energies reported in the literature, namely AA > mixed > TT > UU 13,14 Nonetheless, for ssDNA it has been demonstrated that molecular affiniMes for the gel matrix can impact the observed electrical mobility which therefore may not be a solely a funcMon of from physical properMes (such as effecMve charge and stokes drag) that are governed by molecular 3D conformaMonal properMes 15 .This disparity between molecular effecMve charge and electrophoreMc mobility has also been noted in a previous study in which pure poly-dT was measured to have the fewest associated excess counterions using AES and hence the largest | ()) |, and yet the smallest mobility when compared to sequences which included a number of other subsMtuted nucleobases 12 .

S6. Computa3onal tes3ng of the rod model for ssDNA
To further test the relaMonship between the quanMMes  and  % , we performed a comparison of  %&'% values determined for molecular models of  != 60 base poly-dT constructed using oxDNA, assuming a width parameter  = 0.2 nm with those determined for rod models of radius  = 0.4 nm and variable .EquaMng the  %&'% value in the two models, we obtained a value of the axial charge spacing of  ≈ 0.5 nm in the rod model that were about 50% smaller than the corresponding average contour length per base of  % ≈ 0.75 nm inferred both from our molecular-model structures (see Fig. 4D) and also in previous molecular simulaMon studies 16 , thus confirming the qualitaMvely expected  <  % relaMonship.This analysis sheds light on the relaMonship between the values of physically similar parameters obtained from interpreMng experimental data using different models of polyelectrolyte conformaMon.

S7. On the rela3onship between the experimental readouts of ETe and that of ion coun3ng methods such as atomic emission spectroscopy (AES)
Atomic emission spectroscopy (AES) is a measurement technique that infers an excess ion concentraMon in the ion atmosphere, , around the molecule relaMve to bulk soluMon.Similar to the effecMve  ()) as measured by ETe,  also reports on the phenomenon of molecular charge renormalizaMon.In order to make a direct link between these two closely related quanMMes, we suggested the approximate relaMonship  9 ∝  1 +  2 , where the coefficients in the equaMon depend on molecular geometry and salt concentraMon.In order to deduce this relaMonship we calculated the counterion excess  9 and charge renormalizaMon factor  for rigid rod models of ssDNA with different  and  values (see Fig. S7).
The number of associated ions  of valence  5 associated with a molecule can be computed by solving the Poisson-Boltzmann equaMon for the molecule immersed in bulk electrolyte, as described in the Methods and Supplementary InformaMon SecMon S2, by integraMng the excess ion number density, as given in Ref. 17:  5 =  +  : ∫(e /; !<=/? " @ − 1)  (S1) Indeed, we find that for a highly charged molecule we have a large value of || resulMng in strong charge renormalizaMon which entails both a larger value of excess counterions as well as a lower magnitude of  ()) (smaller ).Eq.S1 clearly indicates that a large value of − 5  (overall posiMve for a negaMvely charged molecule) entails a larger the excess counterion concentraMon in the molecule's ion atmosphere (see Fig. S7).We note that the quanMty  9 /| "#$ | (inferred to be ≈ 0.71 and 0.74 for our 60 base poly-dT and poly-dA species respecMvely (see Fig. S7B), can be directly compared with the number of excess counterions per phosphate as reported by AES (reported to be ≈ 0.68 and 0.71 for 30 base poly-dT and poly-dA respecMvely in Ref. 18).Furthermore, the magnitude of the difference in  9 /| "#$ | between poly-dA and poly-dT of around 4% can be seen to correspond to about an 11% difference in  ( : = 0.63 and  A = 0.70 as measured by ETe for ssDNA species of  != 60 in this work), highlighMng the higher sensiMvity of ETe compared to AES in the low salt regime (see Fig. S7B), parMcularly in relaMon to the relevant measurement precision in each case.It is also worth noMng in this context that the indicated relaMve differences in molecular species in this example are comparable, or oren smaller than, the reported experimental uncertainty in ion counMng methods.However these differences are at least one order of magnitude larger than a typical measurement precision in ETe.

Fig. S2 .
Fig. S2.Schema3c representa3ons of model ssNA structures in PB free energy calcula3ons.(A) IllustraMon of the experimental ETe geometry, whereby molecules can either reside in 'slit' (1) or 'pocket' (2) states.The effecMve charge of the molecule can be deduced from the relaMonship Δ (' =  ())  * where Δ (' =  "'+# −  ,-%.(# and  * is the electrostaMc potenMal at the midplane of the slit.ElectrostaMc potenMal distribuMons for a molecule in the 'slit state' (B), and (C) the 'pocket state', i.e., effecMvely in free soluMon.The governing PB equaMon in the electrolyte and constant surface charge boundary condiMons of the silica walls are depicted.The distance between the center of the molecule and the edges of the box was set to large distance of 5 /0 as depicted in order to enable the implementaMon the zero electric field boundary condiMon on the outer walls of the geometry.

Fig. S3 :
Fig. S3: Renormalisa3on of the charge of an ATTO dye molecule as a func3on of the aFached ssNA fragment length.Values of the effecMve charge of an ATTO dye,  ()),23( , coupled to model 'half-helix' ssDNA structures of varying number of bases  ! . ()),23( is determined as the difference in calculated effecMve charge of structures with and without an aWached dye.The value of  ()),23( for a given  ! is added to the effecMve charge of dye-free model ssNA structures to obtain a value that can be compared to the experimental measurements (see Methods).

Fig. S6 :
Fig. S6: (A) Original and (B) contrast enhanced full-length gel electrophoresis images of ssNA samples for  != 30 and 60, imaged under 532 nm excitaMon where only the fluorescently labelled DNA, and not the fragments in the molecular weight standard DNA ladder, are visible.Cropped versions of these full-length figures are shown in Fig. 3C.(C) Image of the same gel as in (A) and (B) stained with GelRed and visualised to display both the ladder (O'RangeRuler 5 bp DNA Ladder, Thermo ScienMfic) and the test samples.

Fig. S7 :
Fig. S7: (A) RelaMonship between the counterion excess  9 and the charge renormalizaMon factor  for rigid rod models of ssNAs ( != 60,  "#$ = −61 e) calculated for our experimental framework as described in SecMon S2 for a bulk salt concentraMon  B = 1.2 mM.Data points are shown for rod models characterised by  = 0.4 nm and  = 0.35 − 0.65 nm (pink open circles), 'line charge' rod models with  = 0.05 nm and  = 0.35 − 0.65 nm (orange open circles) and rod models with  = 0.4 nm and extreme values of the axial base spacing  = 0.1 and 1.4 nm (green open circles).A linear fit to all data suggests the relaMonship  9 = −25.441+ 61.222 in the range of rod geometries and at the salt concentraMon probed (black dashed line).(B) Normalised plot of the data presented in (A), where  9 has been normalised by | "#$ |. 60 base poly-dT and -dA are measured by ETe in this work to have average charge renormalizaMon factors  A = 0.70 and  : = 0.63 respecMvely.These  values correspond  9 /| "#$ | values of ≈ 0.71 and 0.74, shown by red and blue arrows on the ordinate.Thus a ≈ 4% difference in the fracMonal excess counterion values, which is also termed number of Na + per phosphate in the AES literature, corresponds to an approximately10% disparity in .This is consistent with experimental AES results that reveal correspondingly small differences of ≈4% between poly-dT and -dA, and highlights the sensiMvity of ETe compared to AES in this regime4,18,19 .