Chelated Magnesium Logic Gate Regulates Riboswitch Pseudoknot Formation

Abstract

Magnesium plays a critical role in the structure, dynamics, and function of RNA. The precise microscopic effect of chelated magnesium on RNA structure is yet to be explored. Magnesium is known to act through its diffuse cloud around the RNA, through outer-sphere (water-mediated), inner sphere, and often chelated ion-mediated interactions. A mechanism is proposed for the role of experimentally discovered site-specific chelated magnesium ions on the conformational dynamics of SAM-I riboswitch aptamer in bacteria. This mechanism is observed with atomistic simulations performed in a physiological mixed salt environment at a high temperature. The simulations were validated with phosphorothioate interference mapping experiments that help to identify crucial inner-sphere Mg²⁺ sites prescribing an appropriate initial distribution of inner and outer-sphere magnesium ions to maintain a physiological ion concentration of monovalent and divalent salts. A concerted role of two chelated magnesium ions is newly discovered since the presence of both supports the formation of the pseudoknot. This constitutes a logical AND gate. The absence of any of these magnesium ions instigates the dissociation of long-range pseudoknot interaction exposing the inner core of the RNA. A base triple is the epicenter of the magnesium chelation effect. It allosterically controls RNA pseudoknot by bolstering the direct effect of magnesium chelation in protecting the functional fold of RNA to control ON and OFF transcription switching.

Introduction

RNA folding into stable secondary and tertiary structures is the most important phenomenon for specific gene expression. RNA consists of a series of negatively charged phosphate groups in its phosphodiester backbone, but it still folds into a well-shaped compact structure overcoming the huge electrostatic repulsion.¹ The presence of positively charged metal ions, hence, crucial not only for charge neutralization but they also coherently décor the ion-atmosphere of RNA, in such a way, that the RNA gets its optimal ambiance to fold and function.^2–9 Among different prevalent metal ions in cellular composition, magnesium is eventually unique in stabilizing the compact fold of RNA.^{3, 10} It creates a more effective ion-atmosphere by directly interacting with the negatively charged phosphate group of RNA backbone. ^11–12 However, physiologically, RNA hovers in a mixed-salt environment where it interacts with both monovalent potassium (K⁺) and divalent magnesium (Mg²⁺) ions. ^13–15

In solution, Mg²⁺ forms a hexa-hydrated complex with six water molecules surrounding in an octahedral manner, in the first solvation layer, ^16–17 while the ion-atmosphere of RNA involves three kinds of Mg²⁺ ions: (i) the diffused ions, which are dynamic in nature, (ii) the outer-sphere ions, which are interacting with RNA but separated from the RNA by a single hydration layer, and (iii) the inner sphere ions which are directly interacting with the phosphate groups of RNA^{4, 14, 18}. Although this classification is done based on the characteristics of Mg²⁺ ions, it is valid for monovalent K⁺, as well. ¹⁹ In general, it is hypothesized in many theoretical studies that an essential contribution to the stabilization of the native structure RNA comes from the diffuse ions. ^20–23 For the inner-sphere ions to make direct contact with the phosphate groups of RNA, it is essential for them to partially dehydrate. ^{3, 24} The partial dehydration of a hexa-hydrated Mg²⁺ complex to come into the direct contact of phosphate groups of RNA is energetically less favorable due to huge entropy loss.³ This explanation is also augmented by the slow exchange rate of a water molecule in the first solvation layer of Mg²⁺ (in the order of microseconds).²⁵ While all these explanations support the hypothesis that the stability of RNA structure is mostly contributed by the outer-sphere ions than an inner-sphere prototype, it is rather recently when a special type of inner-sphere ion coordination has been found to interact directly with a number of phosphate groups and thus, supporting the inner-core of the RNA fold. ^{6, 9, 26–28} These inner-sphere ions that hold more than one phosphate groups together are called chelated ions. Also, for chelated ions, it might be true that they generate electric stress due to loss of entropy, but we cannot rule out the fact that the strong electrostatic interactions with multiple phosphate groups of RNA may out-compete the entropy loss turning it into a favorable interaction.²⁹ This demands a thorough calculation characterizing the free energy of chelation accounting for a real RNA system that is immersed in a solution of monovalent and divalent ion mixture mimicking the physiological functional ion-environment for RNA. Although this is computationally highly challenging, our research in this direction is underway.

To unravel the microscopic picture of the ion-chelation effect on RNA structure, the slow exchange rate between Mg²⁺ and water appears as the bottleneck that narrows the revenue of characterization of the ion-atmosphere with different computational approaches. Even a long-extended simulation often falls short to accurately probe such slow exchange dynamics with the aid of available empirical force-fields relevant for biomolecular simulations. In one of our previous works, we have performed ten 2μs simulations of riboswitch S-adenosylmethionine-1 (SAM-1) in explicit water, using the salt buffer as potassium chloride and magnesium ions.³⁰ The simulation revealed slow RNA fluctuations with increasing magnesium concentrations. We found the strong association of outer-sphere magnesium ions with RNA that is mostly responsible to restrict the RNA dynamics.^{3, 30} The slowness is also reflected in our estimated diffusion coefficient which is in the range of 10μm²/s.³⁰ In these early studies, we found the biomolecular force-fields, such as AMBER, CHARMM27 work well for a nucleic acid system with other small ions ^31–36. However, understanding ion-binding properties and solvation free energy are different with Mg²⁺. Several attempts were made to study the correct structural, dynamic, and thermodynamic properties of the ion-atmosphere of RNA. ^{25, 34–35} In 2012, Villa and co-workers introduced some new parameters and validated them with the available experimental results to deal with such slow kinetics.²⁵

Because of this slow timescale issue and a high degree of flexibility in the RNA structure, most of the models of RNA are limited to describe its ion-atmosphere filled with only non-specific diffused ions, at a low salt concentration range. Debye-Hückel (DH) electrostatics and non-linear Poisson Boltzmann (NLPB) are used to treat the ionic environment as a continuum. ^37–40 In these approaches, molecular details such as ion-ion correlations and the discrete effects of the ions are generally ignored. To account for the ion-ion correlation, recently we have developed a generalized Manning counter-ion condensation model.^41–43 This model additionally accounts for the irregular structure of RNA at physiological ionic concentrations but the effects of inner-sphere ions were neglected.

The effect of site-specific Mg²⁺ is thought to be the most critical for the function of many RNA systems, including riboswitches which is a key gene-regulatory RNA component abundantly found in bacteria.⁵ In recent times, many such chelation sites are being identified in the X-ray crystal structure of other RNA systems^26–28 but their precise role in RNA fold stabilization has not been explored. In the crystallographic study of 58-nucleotide ribosomal RNA, one chelated K⁺, and one chelated Mg²⁺ are found. ^{4, 44–45} In hammerhead and glmS ribozymes, chelated Mg²⁺ was found to exert greater impact in their folding and catalysis⁴⁶. In Thermotoga petrophila fluoride riboswitch, the fluoride ion is found encapsulated by three chelated Mg²⁺ ions, regulating gene expression through transcription termination mechanism.²⁸

In our early wet-lab experiments, we found three inner-sphere Mg²⁺sites that are profoundly impactful for the stability of SAM-I riboswitch.⁶ These are considered as hotspots for RNA stability. Two of these Mg²⁺ chelated sites are consistent with the crystal structure of Batey and co-workers. ⁹ While our early structured-based model study shows that the presence of outer-sphere Mg²⁺ ion can induce open-to-closed transitions for SAM-I riboswitch, ⁴⁷ it is not known whether these transitions result from the implicit effect of site-specifically bound, chelated Mg²⁺ ions or independently from the dense outer-sphere cloud of Mg²⁺ surrounding the RNA. In this work, we will use SAM-I riboswitch aptamer as a best-characterized RNA model to initiate the first study of chelated-Mg²⁺-RNA interactions in a mixed salt environment by performing extensive atomistic simulations combining knowledge from our phosphorothioate interference mapping experiments.

Result:

Phosphorothioate interference mapping experiments and extensive atomistic simulations identify inner-sphere Mg²⁺ hotspots.

The location of each inner-sphere Mg²⁺ ion is vital for a compact RNA fold. Our phosphorothioate interference mapping experiments help in identifying crucial inner-sphere Mg²⁺ sites prescribing an appropriate distribution of inner and outer-sphere magnesium ions to maintain a physiological ion concentration of monovalent and divalent salt for the RNA simulation. We have performed phosphorothioate interference mapping experiments in combination with expression platform (EP) switching assay by perturbing the site-specifically bound Mg²⁺ ions (Figure 2). The conformational switching selection scheme for phosphorothioate interference is described in the method section. In our experiment, phosphate to phosphorothioate substitution substantially reduces the binding affinity of localized Mg²⁺ which were otherwise closely interacting with the phosphate oxygens of RNA backbone. In these experiments, aptamer RNA was randomly incorporated with a phosphorothioate nucleotide where we used a level of ∼5% with different α-phosphorothioate-NTPs during transcription. The 3′ terminus of the RNA was fluorescently labeled and purified. The RNA aptamer was then folded with 2 mM Mg²⁺ and different concentrations of SAM varying from 10 µM to 100 µM. Selections were performed using RNase H to cleave destabilized aptamers following our previous experimental protocol.⁶ Similar to our earlier work, we have verified the loss of a specific Mg²⁺ interaction by performing a rescue experiment using a buffer with [Mg²⁺] = 1 mM, [Mn²⁺] = 1 mM, and the lowest concentration of SAM (10 µM). Manganese, being a softer Lewis acid than magnesium, can make more close and stable interaction with the sulfur of phosphorothioate backbone. By performing capillary electrophoresis following cleavage of the phosphorothioate linkages with molecular iodine, fractional traces of each phosphorothioate position were resolved.

Figure 2: Phosphorothioate interference mapping assay and extended equilibrium simulations together identify potential inner-sphere Mg²⁺ sites.

Phosphorothioate interference mapping experiments show positions where interference is high. Capillary electrophoresis traces of selected and unselected RNA included with ATPαS. To fold the RNA various concentrations of SAM were taken and a rescue operation is also performed with 1 mM Mn²⁺ along with 1 mM Mg²⁺ keeping minimum SAM concentration (10μM). Electropherograms for UTPαS interference assay are shown elsewhere.⁶ Traces are integrated and the areas are normalized to peaks that display no selection. As the concentration of SAM increases, the trace population of phosphorothioate returns to normal.

Earlier our experiment found strong interference at A10 and U64 that are anyway connected via site1 chelated Mg²⁺. In addition to those nucleotides, our current assays could capture significant interference at U26 (which belongs to the PK motif), A36 (which belongs to the kink-turn region), and U63 due to its proximity to U64 those are just beneath the PK motif.

We have performed three independent sets of 1μs simulations starting from the crystal structure (pdb:2gis⁹) where two chelated Mg²⁺ (site 1 and site 2) ions pre-exist. In this study, our major concern was to simulate an RNA but under an appropriate ion-environment condition. Each simulation reaches an equilibrium structure where we find three additional inner-sphere Mg²⁺ ions consistently reach near U26, A36 location as we find in the experiment (Figure S1). Although our phosphorothioate interference mapping experiments were adept in identifying most of the inner-sphere Mg²⁺, we didn’t find significant interference at A84 and A85 locations where the crystal structure found a potential chelated Mg²⁺ binding site as interference will only arise if only the pro-Rp oxygen is interacting with the Mg. ⁶ This certainly raises a question regarding the binding affinity and the impact of site2-chelation center on RNA structure stabilization.

Preferential interaction coefficients quantitatively characterize RNA ion environment.

The physiological ion-environment of RNA is an extremely complex environment due to the presence of multiple essential entities involving Mg²⁺, K⁺, Cl^-, water. Besides, various complex physical phenomena, like counter-ion condensation, chelation, and ion-pair effect including other electrostatic coupling effects make it extremely challenging to isolate the contribution from any one or two species towards RNA structural stabilization. While our phosphorothioate interference mapping assay suggests that the chelated Mg²⁺ at site1 may impart a significant stabilization effect to the RNA core, it does not pinpoint which RNA interactions are most sensitive to the chelation effect.

As mentioned before, due to the slow timescale issue, it is a daunting task to capture RNA conformational degrees of freedom by any canonical simulations at room temperature. Consequently, any free energy simulations along one/two order parameter plane are also challenging knowing the fact that RNA conformational change is a multi-dimensional problem. Hence, we decided to minimally perturb the system by imposing the high-temperature effect making the system moderately flexible such that we can isolate RNA’s structural sensitivity toward different ion-environment. To precisely capture the effect of inner and outer-sphere ionic effects on RNA conformations we have first generated three independent ion-environmental conditions individually at two different temperatures, referring to T= 300K and T*=450K. The ion-environmental conditions are as follows: (i) (+) Chelated Mg²⁺, (+) 2mM [Mg²⁺]; this is a reference system where SAM-I aptamer includes the presence of site1, site2 chelation maintaining a 2mM Mg²⁺ concentration. (ii) (+) Chelated Mg²⁺, (−) 2mM [Mg²⁺]; this is to understand the impact of two chelated Mg²⁺ and their coupled behavior in the absence of any outer-sphere/bulk Mg²⁺. Here K⁺ only helps in maintaining a neutralized ion-environment condition. (iii) (−) Chelated Mg²⁺, (−) 2mM [Mg²⁺]; this is an extreme condition is generated where there is no Mg²⁺ at all; only K⁺ ions are there to stabilize the RNA structure.

In an early study, we have observed the highly negative-charged RNA to accommodate excess cations in its ions-solvation layer over their bulk concentrations. This excess cationic effect can efficiently be characterized both theoretically and experimentally by quantifying preferential interaction coefficient, (Γ_i). The definition and calculation methods are described in the method section where we have depicted how we have obtained a corrected electroneutral bulk concentration as enlisted in Table 1. We observe a Γ_Mg²⁺ of 9.74 at 2mM [Mg²⁺] with the new Mg²⁺ parameters in the context of a nucleic acid reported by Villa and co-workers while earlier our predictions were based on Mg²⁺ parameters by Åqvist where the Mg²⁺-water exchange rate was underestimated by several orders of magnitude.^{25, 48} In Mg²⁺ -RNA titration experiments, for adenine-binding and other riboswitch systems it is shown that Γ_Mg²⁺ significantly varies its magnitude depending on its conformational state. ^{4, 11} Although we have chosen particularly a high temperature (450K) to accelerate the slow conformational change by enhancing the rate of Mg²⁺-water exchange, the enhanced rate, however, marginally affects Γ_Mg²⁺. At the higher temperature of 450K, we find Γ_Mg²⁺ of 9.69 which does not deviate much from the value we find at 300K. This signifies that in the presence of both chelated, inner and outer-sphere Mg²⁺ ions, except local, large conformational changes are less probable at 450K within our simulation timescale. Thus, we can consider the ion-environment of RNA at T*=450K as a new reference set with which other ionic conditions at the same temperature can be compared. In other ionic conditions, where only chelated Mg²⁺ ions present, the calculation of Γ_Mg²⁺ is irrelevant and left black. However, just to mechanistically understand individual site1 and site-2 chelation mediated effects on RNA structure, we have generated two other unphysical situations making one of them absent, as a separate event. In this situation, a substantial number of K⁺ ions are accommodated in the ion-solvation layer of RNA reflected in the calculation of Γ_K⁺ while Cl^-ions stay dispersed in Table 2.

Table 1:

Number of ions needs to satisfy the different ion-environment conditions. In each condition-dependent simulation, raw salt concentration []* corrected bulk concentrations [] determined (using the aforesaid approach) and calculated preferential interaction coefficients,Γ.

Chelated Mg2+	+	+	+	+	-	-
[Mg2+] =2.0 mM	+	+	-	-	-	-
Temp ➔	T	T*	T	T*	T	T*
NMg2+	11	11	2	2	0	0
NK+	116	116	138	138	138	138
NCl-	46	46	50	50	46	46
[Mg2+ ]* mM a	2.8	2.86	-	-	-	-
[K+]* mM	112	110.3	120.6	117	115.0	116.0
[Cl−]* mM	95	94.9	103.1	103	95.1	99
[Mg2+] mM b	2.2	2.3	-	-	-	-
[K+] mM	100.5	99.5	111.1	109.5	104	107.2
[Cl−] mM	105	104.1	111.1	109.5	104	107.2
ΓMg2+	9.74	9.69	-	-	-	-
ΓK+	58.59	59.16	74.53	75.58	78.54	76.88
ΓCl−	−13.98	−13.47	−13.50	−12.42	−13.41	−15.12

^aRaw concentration: Raw concentrations are determined 20 Å beyond RNA (asterisk),

^bCorrected bulk concentrations are determined using a small potential perturbation approximation method.

Table 2:

Number of K⁺/Cl^- ions needed when only one/none site-specific chelated Mg²⁺ present. These are unphysical ion-environment conditions at high temperature, T*, purposefully built to understand site-specific chelation effects. In each condition-dependent simulation, raw salt concentration []* corrected bulk concentrations [] determined (using the aforesaid approach) and calculated preferential interaction coefficients,Γ.

site1 Mg2+	+	-
site2 Mg2+	-	+
[Mg2+] =2.0 mM	-	-
Temp ➔	T*	T*
NMg2+	1	1
NK+	138	138
NCl−	48	48
[Mg2+ ]* mM a	-	-
[K+]* mM	114	115
[Cl−]* mM	99.2	99.6
[Mg2+] mM b	-	-
[K+] mM	106.0	106.7
[Cl−] mM	106.0	106.7
ΓMg2+	-	-
ΓK+	77.57	76.17
ΓCl-	−12.43	−12.83

^aRaw concentration: Raw concentrations are determined 20 Å beyond RNA (asterisk),

^bCorrected bulk concentrations are determined using a small potential perturbation approximation method.

Contact probability maps isolate the macroscopic structural impact of Mg²⁺ chelation.

The preferential interaction coefficient and its change are mostly affected by the outer-sphere Mg²⁺ than site-specifically bound Mg²⁺ which are strongly bound to the phosphate groups of RNA. However, these site-specifically bound inner-sphere/chelated ions have the tremendous potential not only to reorganize its local ion density of outer-sphere Mg²⁺ /K⁺, but their presence or absence can also control the global conformational dynamics of RNA. Here we monitor and compare the RNA conformational dynamics by generating contact probability maps (CPM) for the different ion-environmental conditions as shown in Figure 3. From our CPM analysis comparing the conformational changes at two different temperatures (T and T*), each under the ionic environment of 2mM [Mg²⁺] and 100mM [K⁺], we find the RNA only to instigate a slight local conformational fluctuation at the referred higher temperature (Figure 3a and 3b). At this temperature limit when we analyze an unphysical condition keeping only two chelated Mg²⁺ at 100mM [K⁺], we observe a noticeable change in the P1 and P3 juxtaposition. In early Small Angle X-ray Scattering (SAXS) and Fluorescence Resonance Energy Transfer (FRET) experiments including our early structure-based electrostatic simulations of SAM-I aptamer show the involvement of both metabolite and magnesium ions in the structural stabilization of P1-P3 juxtaposition^{8, 47, 49}. This juxtaposition secures SAM-binding elements, P1 and P3. Our early atomistic molecular simulations study explained the integrated role of metabolite (SAM) and Mg²⁺ mechanistically where we found that SAM essentially connects the P1-helix with P3, where the independent effect of small, dynamic Mg²⁺ is not sufficient to make this connection stable due to the high degree of flexibility of the 5′-end of P1-helix. The same argument holds for metabolite alone where the independent effect of SAM is not sufficient to connect P1 and P3 connection as it costs huge electrostatic barrier. In the present study, while metabolite presents in its binding pocket, due to the absence of 2mM [Mg²⁺] (major constituents are a collection outer-sphere Mg²⁺ ions), we have observed the significant deformation in the P1-P3 tertiary interaction disrupting the binding pocket (Figure 3c). This is consistent with our early simulation study which accounts only for outer-sphere Mg²⁺ ions. ⁴⁷ Subsequently, when we removed the exposed chelated-Mg²⁺ from the site2, we observed some of the pseudoknot contacts connecting P2 and P4 helices become highly sensitive (Figure 3d and 3e). This sensitivity becomes severe when the core-chelated-Mg²⁺ is removed from site 1. As a result, most of the pseudoknot contacts are deformed and an extended RNA conformation is formed. At another extreme condition when this RNA system is projected to a no Mg²⁺ condition, a residual portion of secondary structure from P2 and P4 is the only survivor motifs in the structure (Figure 3f). However, our CPM analysis at room temperature (T=300K) detects no significant structural changes due to the slow kinetics of RNA fluctuations (Figure S2).

Figure 3: Contact probability maps detect RNA pseudoknot (PK) deformation in the absence of Mg²⁺-chelation.

Contact probability maps are analyzed comparing the following ionic conditions: (a) In the presence of site1 and site 2 chelated magnesium ions and outer-sphere ions maintaining 2 mM [Mg²⁺] (this is a controlled condition at 300K). (b) the same as (a) but at a stimulating temperature (T*=450K); (c) In the presence of site1 and site2 but in the absence of outer-sphere Mg²⁺ ions maintaining a 2 mM [Mg²⁺]; In the absence of outer-sphere and site2 chelated Mg²⁺ ion but the presence of site1 chelated Mg²⁺ ion. In the absence of outer-sphere and site1 chelated Mg²⁺ ion but the presence of site2 chelated Mg²⁺ ion, only. (f) No Mg²⁺ present. Residue-level contact probability for each of these variable conditions (bottom) is compared with that of the controlled condition where ~2.0 mM [Mg²⁺] and 100 mM [K⁺] are maintained at 300K. A remarkable difference is detected near the PK region (Residue index (RI): 65–68; 25–28) if any/both the chelated Mg²⁺ removed.

Mg²⁺ chelation modulates RNA fluctuation by terminating tertiary pseudoknot connection.

Earlier, by single-molecule FRET (smFRET) and our various structure probing experiments including Nucleotide Analog Interference Mapping (NAIM), 2-aminopurine switching assay, ligand titration, and SHAPE probing, we have observed that Mg²⁺ binding to the aptamer promotes the formation of the pseudoknot interaction.^5–8 However, from all these experiments it is difficult to pinpoint whether the stabilization results from any site-specifically bound Mg²⁺ or from the collective effect of outer-sphere Mg²⁺. In our simulations, as the Mg²⁺ ion-environment changes, a measurable effect on RNA fluctuations is expected. To characterize this dynamical effect of the RNA, we have calculated the average root mean square fluctuation (RMSF) along with residue index at varying ionic conditions (Figure 4a). It is expected that P1 being a terminal helix shows large RMSF values. However, it is a highly non-trivial outcome that as we impose a condition like one or no Mg²⁺ which means when we remove any of chelated Mg²⁺ or both at a time, the PK tertiary interaction consistently shows high RMSF compared to other non-terminal location of the RNA. This implies that the presence of both the chelated is required in securing the pseudoknot connection (Figure 4b, 4c). This coupled effect is very analogous to the AND gate of the digital logic gate concept that helps to understand the binary input-output mechanism of electronic devices. AND gate results in a HIGH output only if all the inputs to the AND gate are HIGH. Now when one looks back to Figure 1c, it becomes clearer that if we imagine SAM-I aptamer as an RNA device, the presence of both the chelated Mg²⁺ ions is required as a supportgate of the pseudoknot fold (Figure 4d).

Figure 4: Root mean square fluctuation (RMSF) measurements capture the amplified flexibility of the PK region.

(a) RMSF calculations have been performed accounting backbone phosphate groups at four most sensitive conditions: (color code: red, green, blue, yellow) in comparison to the controlled condition (black). RMSF change reflected near PK region (r25-r28) close to P2 helix when any/both chelated magnesium is removed. RMSF amplified near PK region (r65-r68) close to P4 specifically when core chelated Mg²⁺ is removed. (b) RMSF calculation identified two prime sensitive non-local tertiary interactions: PK and P1-P3 junction which are deformed when any/both chelated Mg²⁺ disappear. (c) Stabilization of PK and P1-P3 juxtaposition explicitly requires support from both the chelated Mg²+, in a site-specific way. (d) This collective input effect of two chelated Mg²+ in the stabilizing of PK device of RNA represents a biological analog of binary ‘AND’ logic Gate which promotes the high output as a result of all high from all inputs.

Figure 1: An equilibrium structure of SAM-I aptamer RNA along with its interactive Mg²⁺ ion-environment.

The snapshot is extracted from one of the equilibrium trajectories of SAM-I generated maintaining 300K temperature, ~100 mM KCl, ~2.0 mM bulk Mg²⁺ concentration. (a) SAM-I with all helices. (b) 180⁰ reorientation of (a). Inner (red) and outer-sphere (violet) Mg^{2 +} ions are indicated in (b). The inner Mg^{2 +} binding sites are consistent with our phosphorothioate interference experimental results. (c).Two chelated Mg²⁺ are identified: (i) one in the RNA core, close to SAM ligand-binding site. The core chelated magnesium is indicated as site1-Mg²⁺ coordinating A10 and U64. (ii) The exposed chelated magnesium coordinating A84 and A85. The exposed chelated magnesium is referred to as site2-Mg²⁺.

Chelation induces dynamical anti-correlation between PK and P1-P3 tertiary junction.

The importance of PK specifically on SAM-I structure-function has been elucidated in several experimental studies whereas the tertiary PK motif is distantly located from the metabolite binding site.^{5–9, 50} Despite its distant location, the formation of the PK was found crucial for ligand binding and riboswitch activity. The functional impact of PK was more established where using in vitro transcription assays the wild-type riboswitch is compared with the G55C/G56C mutant. It was found that the riboswitch activity is severely affected by the disruption of the pseudoknot even in the presence of SAM.⁸ Also, these studies found that disruption of the pseudoknot interaction instigates the deformation of the P1-P3 close juxtaposition. Consistent with these early smFRET results, we have also observed an intricate interplay between these two tertiary motifs (PK connection and P1-P3 connection) (Figure 5). PK is essentially a long-range tertiary connection between the PK segment near P2 (indicated as PK_P2) and the PK segment near P4 (indicated as PK_P4). At the physiological ionic environment ([Mg²⁺] ~2.0mM, [K⁺] ~100mM), we have observed a weak anti-correlated pattern in the dynamics of PK and P1-P3 connecting distances (Figure 5a) (correlation coefficient ~ - 0.3). This steady anti-correlated dynamical flow is disturbed when we eliminate any important ion component/s from its ion-atmosphere. If we eliminate all the outer-sphere Mg²⁺, the time-dependent distance profile clearly shows the most affected P1-P3 juxtaposition (Figure 5b). Again, when we eliminate any of the chelated Mg²⁺ (site1/site2) or both the chelated Mg²⁺, we immediately observe the deformation of PK (Figure 5c and 5d). Almost in every case, when we remove the chelated Mg²⁺, we observe that PK deformation is followed by P1-P3 deformation (Figure Figure 5c-5e). This observation correlates well with the same observed in the early smFRET experiment. ⁸

Figure 5: Two important tertiary connections, PK and P1-P3 helical juxtaposition in SAM-I show anti-correlated dynamical behavior.

Distance trajectories for non-local PK connection and P1-P3 connection at different ion-atmospheric conditions as labeled: (a) (+) site1 Mg²⁺ , (+) site2 Mg²⁺, (+) 2mM [Mg²⁺]; (b) (+) site1 Mg²⁺ , (+) site2 Mg²⁺, (−) 2mM [Mg²⁺]; (c) (+) site1 Mg²⁺ , (−) site2 Mg²⁺, (−) 2mM [Mg²⁺]; (d) (−) site1 Mg²⁺ , (+) site2 Mg²⁺, (−) 2mM [Mg²⁺]; (e) (−) site1 Mg²⁺ , (−) site2 Mg²⁺, (−) 2mM [Mg²⁺]. Here, all the dynamics were analyzed under T* (450K) temperature. P1-P3 connection is found to be sensitive towards outer-sphere Mg²⁺ ions. PK connection shows its sensitivity towards chelation effects. In most of ionic conditions, P1-P3 shows higher flexibility and metabolite exploits this connection in order to switch transcription ON/OFF. Chelation guards the residual RNA fold both in ON and OFF states.

Chelation safeguards non-local base-triple to inhibit large-scale PK deformation.

As illustrated in Figure 1, it appears from the crystal structure of SAM-I riboswitch that the site1 and site2 chelated Mg²⁺ are located in such a way that they can safeguard the base-pair formation between A85 and U64. On the other hand, our ionic condition-dependent analysis shows that in the absence of chelated Mg²⁺, a large-scale deformation in the PK region. Although U64 is an adjacent base of the PK region, the question yet to answer, which microscopic event/mechanism instigates such a large deformation in PK and thereby, promoting the global unfolding of the RNA. To understand this, we have performed a normal mode analysis which helps us to explore the correlated motion between different distant dynamic regions/domains in this RNA. The lowest and most correlated modes are shown with the directions of motion along with the normal mode in Figure 6a (in the presence of all ions including chelation) and Figure 6b (in the absence of site1/core chelated Mg²⁺). We have also analyzed the pairwise cross-correlation maps (Figure S3-S5). Both the analyses capture large-scale PK breathing dynamics which is governed by the correlated dynamics between distant P2 and P4 helices. After investigating all the modes, we find the epicenter of the dynamical correlation under the effect of chelation lies beneath a competitive base-triple where A85, U64 forms a triple-connection with A24 (Figure 6c). This is an event of love-triangle where A24 and A64 compete for U64. This competition is exhibited in their anti-correlated dynamical behavior even when we monitor the distance time-trajectory of A24-U64 and U64-A85 (Figure 6d). When we remove any of site1/site2 chelated Mg²⁺, this microscopic fluctuation around this base-triple amplifies, A24-U64 (close to PK) breaks and instigates a large change in the PK region (Figure 6e). In most of our trajectories, we have observed that when the U64-A85 connection breaks, this instigates the deformation of the P1-P3 connection affecting SAM-binding. On the other hand, chelation induced A24-U64 deformation affects PK folding. ⁸ As a result of PK deformation ultimately the RNA core gets exposed (Figure 6b). However, we did not notice any noticeable influence of SAM in our simulation sets at varying ionic conditions where it mostly stays in its active site except in the absence of Mg²⁺. However, a future atomistic study is necessary to understand the influence of ligand in connection to the chelation effect.

Figure 6: Normal mode analysis pinpoints a competitive non-local base-triple and their anti-correlated dynamics safeguard the tertiary fold of PK.

From normal mode analysis, only the lowest frequency mode along the direction of motion is shown for (a) in the presence of site1 chelated Mg²⁺ (all ion components present) and (b) in the absence of site1 chelated Mg²⁺. This lends support to the large-scale PK breathing motion in the absence of site1 Mg²⁺. (c) A competitive base-triple, A24-U64-A85 at the RNA core is found to dictate the deformation of PK and P1-P3 long-range tertiary interactions. (d) When all ion components are present (the controlled condition) including core/site1 Mg²⁺, an anti-correlated dynamical behavior is observed in distances between A24-U64 and A85-U64. (e) In the absence of core/site1 Mg²⁺, A24-U64 breaks, immediately resulting in PK opening which is followed by the separation of A85-U64 leading to P1-P3 deformation. This example explicitly shows how the relevant microscopic fluctuation amplifies and transmits to cause global conformational changes in RNA.

Discussion:

A nucleic acid system operates its biological function when it acquires a suitable functional ambiance. That ambiance is created by its ion-atmosphere, a multi-layered sheath surrounding this highly charged polymer. The ion-atmosphere is composed of different types of ions. Some decide to interact with RNA directly (site bound ion, other inner-sphere ions), some interact indirectly screened by water (outer-sphere ions), and some stay diffused (mostly in a hexa-hydrated form). ³ The transformation of a particular ion to any of these interactive forms occurs through the hydration/dehydration process to interact with RNA which then governs the structure, dynamics, and thermodynamics of the RNA-ion complex. The mode of transformation of the ion-cloud is again well-correlated with the functional fold of RNA to perform specific activities. In the present case, SAM-I riboswitch functions in the transcription regulation process by transforming between its ON and OFF alternative folds not only in the presence of metabolite but these folds have their independent Mg²⁺ concentration dependence. This we have explicitly observed in our early experimental and simulation studies by analyzing the population profile of the transcription-OFF/transcription-ON as a function of [Mg²⁺]. ⁴² It reveals that the ratio is maximized at an intermediate Mg²⁺ concentration of 4.0 mM Mg²⁺. Beyond this concentration, the stability of the expression platform starts to enhance at the cost of aptamer stability, specifically by affecting P1 and P4 helices. However, even in this transcription-ON state, a residual RNA tertiary fold stays intact at the aptamer level where the tertiary PK region remains protected to perform the required function in the transcription activation process. Here comes the functional role of chelated Mg²⁺ in stabilizing an active fold of RNA, the current study reveals. Below we summarize the key highlights of this study and new findings on the role of ion chelation effects on RNA structure:

1. The present study attempts here to mimic the mixed salt environment with a correct bulk concentration of K⁺, Mg²⁺, Cl^- guided by the calculations of preferential interaction coefficient which quantitatively captures the heterogeneity in the RNA ion solvation layer (Table 1). In simulation studies, the assessment of correct bulk concentration is essentially attributed to the correct distribution of inner and outer-sphere ions. Mg²⁺ being an effective modulator of RNA ion-environment, the number of inner-sphere Mg²⁺ ion and their site-dependence is corroborated by our phosphorothioate interference mapping experiments of SAM-I aptamer.

2. Our phosphorothioate interference mapping and crystallographic data reveal the presence of two primary chelated Mg²⁺ ions: one residing at the core connecting two non-local (in sequence) phosphate groups in the backbone (near 4-way helical junction) and the other is rather exposed connecting two local (in sequence) phosphate groups (near 1–4 helical-stack region).

3. To understand the structural and functional importance of these chelated Mg²⁺ ions in stabilizing the RNA core, we have created different ion-atmospheric conditions including a control one as a reference and two unphysical situations at high temperature solely to understand site-specific chelation effects on RNA. All together when we compare and analyze the RNA structure under such ion-atmospheric conditions, we find the importance of outer-sphere Mg²⁺ in stabilizing flexible P1-P3 helical juxtaposition that controls the switching of transcription activation process by shifting the population from the stable aptamer to the stable expression platform. In the current study, the key finding is the profound role of chelated Mg²⁺ ion in stabilizing the pseudoknot motif of the SAM-I aptamer. Our contact problity map (Figure 3) indeed that while two specific chelated Mg²⁺ ions are responsible for stabilizing the PK motif bringing P2 and P4 helices together, outer-sphere/diffuse Mg²⁺ ions exert significant stabilization effects over flexible P1-P3 helical junction (Figure 5(b)). The importance of Mg²⁺ ions in stabilizing the PK motif has been observed in several early experiments creating a no-Mg²⁺ ionic condition. ^5–7 To further address this point , we would like to emphasize that in various experiments such as single-molecule FRET (smFRET), Nucleotide Analog Interference Mapping (NAIM), 2-Aminopurine switching assay, Ligand titration, and SHAPE probing, it is observed that Mg²⁺ ions binding to the aptamer promote the formation of the pseudoknot (PK) interactions. 5–8 However, from all these experiments it is very difficult to conclude whether the stabilization of PK interaction comes from the site-specifically bound Mg²⁺ or from the collective effects of outer-sphere Mg²⁺/diffused Mg²⁺. From our study, we could distinguish that the Site1/Core chelated Mg²⁺, which is essentially coordinating two non-local phosphates groups, A10 (belongs to P2 region) and U64 (in the P4 helix) through strong electrostatic interactions, helps to bring two large distant helices P2 & P4 close to form PK. In fact, both the site-specific chelated Mg²⁺ ions (Site1 and Site2) mechanistically control structural stabilization of PK motif evident from our rigorous analysis of contact probability maps (Figure 3c-3f), RMSF calculations (Figure 4a), Distance trajectories of non-local PKs, and P1-P3 connections (Figure 5c-5e) at different physiological ionic conditions. Most importantly, we find the microscopic basis of PK stabilization where two competitive base-pairs (A24-A64 and A64-A85) in a base triple A24-U64-A85 play a crucial role in PK stabilization (Figure 6e). This is also verified by our normal mode analysis (Figure 6b). We have also observed that the chelated Mg²⁺ ions induced PK stabilization supports the RNA core in such a way that its deformation instigates the deformation of all the tertiary interactions including P1-P3 helical juxtaposition. In close connection with these observations, the early smFRET result correctly pointed out that PK supports the idea that it may be used as a lever to correctly position P3 close to P1, via the P2-P3 helical stacking. ^{9, 49, 51} Although it is a distant tertiary motif, it can severely affect the metabolite-binding at the P1-P3 junctional region and in turn, the transcription activation process. This is excellent functional evidence of allosteric regulation in RNA via PK.

In connection with all experimental and simulation results, at this far, we understand the functional role of PK where it helps tightly pack the RNA core of the aptamer. The stability of PK gravely depends on the chelated Mg²⁺. Most importantly, we find that the placement of two chelated Mg²⁺ ions is highly crucial those work in concert to support the long-range PK connection. We have observed ripped PK if any one of chelated Mg²⁺ disappears. This outcome is analogously found in the binary AND logic gate where all the high inputs are necessary to get an output. This describes the collective effect of two chelated Mg²⁺ following a gating mechanism that supports the close-packed RNA core of SAM-I aptamer.

RNA aptamers have already entered the clinical pipeline in virus detection and antiviral therapy, along with more than nine ongoing clinical trials for various types of cancer, coronary artery bypass graft surgery. A detailed thermodynamic understanding of the chelation effect will indeed enable greater control of aptamer/riboswitch regulation. This study anticipates the chelation concept to uphold an upcoming technology in the application of RNA aptamer-based virus detection and therapeutics.

METHODS

RNA System

SAM-I aptamer is a well-deserved RNA candidate to study the impact of Mg²⁺ chelation on RNA structure due to the following reasons: (i) As it is the first discovered riboswitch, its structural information at least at the aptamer level is well characterized compared to other RNA systems; (ii) Existence of two chelated Mg²⁺ ions those are intricately associated with the RNA fold; (iii) Presence of two different types of chelated Mg²⁺ ions; one type helps connect two sequentially non-local phosphate groups together (e.g. site1 Mg²⁺) and the other type connects two sequentially local phosphate groups (e.g. site2 Mg²⁺). SAM-I aptamer structure, on the other hand, has two partially overlapped domains: the aptamer domain and the expression platform. In general, the aptamer domain has high binding affinity to small metabolites and accordingly expression platform responses with a large conformational change close to the promotor region of RNA and that results in gene transcription to be off or on. The ligand/metabolite of this riboswitch is SAM which is a small co-factor involved in methyl group transfers. ⁹ In the absence of SAM, a large termination helix formed to activate gene transcription. In the presence of SAM, the aptamer domain forms a very compact conformation that it terminates the transcriptional processes. So far X-ray crystallography has resolved the structures for the ligand-bound aptamer domain of the SAM-I riboswitch from Bacillus subtilis yitJ and Thermoanaerobacter tengcongensis.^52–53 In this study, we have chosen the SAM-I riboswitch aptamer from Thermoanaerobacter tengcongensis as a candidate RNA system.⁹

RNA preparation

SAM-I aptamer sequence is derived from the Thermoanaerobacter tengcongensis Met F-Met H2 element. The aptamer sequence used includes sequence additions to the 50 and 30 (before and after P1 helix) to improve primer extension reads. Templates for RNA transcription were prepared as previously described.^6–7 PCR was used to prepare transcription templates using Ex-Taq polymerase (TaKaRa) for the amplification of long synthetic templates. Following purification, the transcription templates were transcribed using Ampliscribe high-yield transcriptions kits (Epicentre). The RNA was precipitated by the addition of 1 volume 7M ammonium acetate and centrifuged. Homogeneity was checked by PAGE (10% polyacrylamide, 7 M urea, 0.5x TBE). Phosphorothioate incorporated aptamers were prepared using the High yield transcription kit. The standard reaction was supplemented by the addition of α-phosphorothioate-NTP (Glen Research) at a 1:20 ratio to its parent NTP (0.375 mM:7.5 mM). After purification, the level of incorporation was verified by 30-fluorescent labeling, iodine cleavage, and capillary electrophoresis.

Phosphorothioate interference mapping

Our expression platform switching assay was used as a selection screen in a phosphorothioate interference assay similar to our previous studies.⁶ Here, aptamer stability is challenged by adding an expression platform oligomer. The oligomer is a chimera of DNA and 20-O-Methyl RNA with the following sequence. Formation of the expression platform anti-terminator helix between the oligomer and the aptamer domain creates a hybrid DNA/RNA duplex. The duplex is a substrate for cleavage by RNase H. Reactions were incubated at 37ºC for 2 h and then purified by HPLC (Dionex DNApac column), 0–40% buffer B (buffer A, 25mM Tris–HCl pH 8.0, buffer B, 25 mM Tris–HCl pH 8.0 and 1 M NaClO4) in 45 min. The aptamer RNA was randomly incorporated with one of the four a-phosphorothioate-rNTPs. After purification, the RNA was precipitated, and 3’-end labeled using amine reactive Alexa-488 SPD (Molecular Probes, ~1 mM) in 100 mM NaBO4 pH 8.3. Reactions were incubated at RT for 6h, precipitated (3 volumes ethanol, 300 mM NaOAc pH 6.5) and purified using the above HPLC gradient to separate labeled from unlabeled. The labeled RNA was then spiked into unlabeled phosphorothioate incorporated RNA at a level sufficient for capillary electrophoresis analysis following selection. RNA (0.5mM final concentration) was folded in HMK buffer (containing either 2 mM MgCl₂ or 1 mM MgCl₂ with 1 mM MnSO₄) supplemented with 10 mM, 30 mM or 100 mM SAM as indicated. After equilibration with RNase H and the chimeric oligomer for 1 h at 37º C, the labeled RNA was desalted (micro-biospin P6 columns), lyophilized and resuspended in Hi-Di formamide. RNase H cleavage removes the label from aptamers unfit to compete for shared sequence. Populations of each phosphorothioate position are resolved by phosphorothioate cleavage with iodine after selection and analyzed with capillary electrophoresis. Phosphorothioate containing diester linkages were cleaved by the addition of 1/10th volume of 100 mM iodine in ethanol and heating to 95ºC for 2 min.

Atomistic explicit solvent simulation details at variable RNA ion-atmospheric conditions:

Our simulations started with the crystal structure of the SAM-I aptamer (PDB-ID: 2GIS⁹) where two potential chelated Mg²⁺ ions, namely, site1 and site2 already exist. MD simulations of the SAM-I riboswitch were performed first generating the following ion-environment conditions in the presence of metabolite, SAM, at two different temperatures, T= 300K and T*=450K. The ion-environmental conditions are as follows: (i) (+) Chelated Mg²⁺, (+) 2mM [Mg²⁺], (ii) (+) Chelated Mg²⁺, (−) 2mM [Mg²⁺], (iii) (−) Chelated Mg²⁺, (−) 2mM [Mg²⁺]. However, just to mechanistically understand individual site1 and site-2 chelation mediated effects on RNA structure, we have generated two other unphysical situations making one of them absent, each at a time: (iv) (+) site1 Mg²⁺, (−) site2 Mg²⁺ at T*, (−) 2mM [Mg²⁺] at T*; (v) (−) site1 Mg²⁺, (+) site2 Mg²⁺, (−) 2mM [Mg²⁺] at T*. The control sets of simulations (condition (i)) were prepared under a physiological mixed salt environment where ~100mM [K⁺] and ~2.0 mM [Mg²⁺] bulk concentrations were maintained. Physiological bulk concentration generation is a daunting task due to preferential interactions for Mg²⁺ with RNA where in most cases monovalent K⁺ is replaced by Mg²⁺ with its long life-time³⁰. Due to this preferential interaction, RNA stability is often attributed to the number of excess ions that do not count toward the bulk concentration. This collective excess ion-effect is quantified by the preferential interaction coefficient as presented in Table 1 and Table 2. Therefore, taking into account all the ion-exchange phenomena and the slow diffusiveness of hexa-hydrated Mg²⁺, the equilibration method of an RNA system is tricky and needs comprehensive measures where we followed our early established protocol.^{30, 44}

Equilibration method of RNA ion-atmosphere:

The equilibration of ion-induced sampling is tricky to obtain the correct distribution of outer-sphere and inner-sphere ions as there is a combination of ions (K⁺, Mg²⁺). Here the challenges are twofold: (i) Due to the strong coulombic attraction between RNA backbone and Mg²⁺, all Mg²⁺ ions tend to drive fast to condense onto the RNA without forming an appropriate hydration shell; (ii) Even if they interact with water, in certain cases, once they stick to a negatively charge RNA site, the potential barrier will not allow it to unbind easily. In such explicit solvent simulations of RNA, at first, RNA was placed in a waterless box and a required number of ions were added. The ions in our simulations are a combination of excess ions that balance the RNA charge and bulk ions accounting for physiological ion concentration range. To prevent them from condensing onto the RNA without an appropriate hydration shell initially ions were placed randomly with larger van der Waals radii. These ions were equilibrated using stochastic dynamics and a dielectric constant of 80 to mimic water for 10 ns until the electrostatic energy converged keeping RNA frozen. Then, the simulation box was filled with water and annealed to 300K over 500 ps where RNA and ions were frozen. Following our early protocol, we have first released the Mg²⁺ first and equilibrate it for 2ns and then released RNA where we gradually lowered the position restraining force by 1000, 100, 0 kcal/mol/nm² at constant volume spending 2 ns for each³⁰. This process collects 10ns NVT equilibration. Another 10 ns of unrestrained equilibration was added under constant pressure. As the simulations were conducted at different ionic conditions and temperatures, to maintain the correct density range, the production run was performed under constant volume. Each of the ionic Individual simulations was 400 ns (3sets each), for a total of 7.2 μs of sampling has been performed. In all simulation sets apart from the case of no magnesium ion present, the ligand, SAM, was stably interacting with the RNA (inside the binding pocket near P1-P3 juxtaposition). In general, the time scale of unbinding/dissociation rate of SAM is quite large compared to our simulation time scale (in the order of a few ns). So conclusively, unrestrained SAM was interacting with the RNA during all the MD production run in all different ion-environmental conditions, except where there was no Mg²⁺ present at the system (in the absence of Site1, Site2 Chelated Mg²⁺ ions and 2 mM Mg²⁺ concentration, only K⁺ ions are there to stabilize the RNA structure). In this condition, we observed that SAM was disoriented and loosely bound near its binding site.

Parameters:

All simulations were performed using the Gromacs version 2018.3. AMBER99 force field⁵⁴ with extensions parmbsc0⁵⁵ and chiOL3.⁵⁶ The ligand, SAM is parametrized for AMBER using GAMESS quantum mechanics software⁵⁷ and the R.E.D. software package. ⁵⁸ Atmic charges were calculated using the Restrained ElectroStatic Potential method.⁵⁹ The other forcefield parameters were taken from GAFF (the Generalized Amber ForceField).⁶⁰ The biomolecular force fields, such as AMBER and CHARMM parameters for magnesium, which were used in simulating the riboswitches, result in an exchange rate of water from the first solvation shell that is orders of magnitude smaller than the experimental estimate, the newly derived Mg²⁺ by Villa and coworkers have been used in combination with TIP3P water model following ref. ²⁵. Further, to avoid crystallization at a higher concentration limit modified K⁺ parameters were used.⁶¹ Other than the new Mg²⁺/TIP3P addition, the RNA solution with the updated force field is well tested.⁴¹ While the majority of RNA simulations avoid accounting for direct RNA-ion interactions, our MD simulation protocol predicts stable RNA-Mg²⁺ interaction sites independently which is validated by our phosphorothioate interference mapping experiments.

Quantification of preferential interaction coefficient of ion atmosphere:

The stability of a compact RNA structure depends on the stability of solution containing associated counter-ions. While anions are dispersed in the solution, cations become excess near the RNA over their bulk concentrations. The effect is quantified for ions of species i by preferential interaction coefficient, Γ_i, which depends both on the identity of the RNA and on the bulk concentrations of the ions. The ion-preferential interaction coefficient, Γ₂₊ is defined as (∂m₂₊/∂m_RNA)_μ2+. m_RNA and m₂₊ are the molal concentrations of RNA and divalent ion, I²⁺, respectively. μ₂₊ is the chemical potential of the divalent metal cation I²⁺. Molal and molar concentrations are effectively same if the concentration of salt ions and RNA are in the dilute range. The energetic stabilization by I²⁺ is quantified by the I²⁺-RNA interaction free energy. Experimental estimation for Γ²⁺ has been obtained for several systems using the fluorescent dye 8-hydroxyquinoline-5-sulfonic acid (HQS) and other spectroscopic studies. ^{4, 18, 62} Γ²⁺ can also be predicted from well-equilibrated explicit-solvent molecular dynamics simulations.^{30, 41} Γ for any ionic species, i will be measured as follows: First, the concentration of an ionic species will be measured by the time average of the ratio of these molecule counts multiplied by the molarity of pure water.

$${\left[C_i\right]}^{\ast }=55.51M\frac{N_i}{N_{H_{2}O}}$$ (1)

However, unlike the case near the RNA where ions interact differently with the RNA due to large electrostatic potentials, at 20 Å, the electrostatic potential is under a smooth, small perturbation. Ion densities in a small potential well will respond linearly with their concentration, charge, and the well depth. The corrected bulk concentrations [Ci ] (which must be electroneutral) are given by:

$$\left[C_i\right]={\left[C_i\right]}^{*}-q_i{\left[C_i\right]}^{*}\frac{{\displaystyle \sum _j{q}_j{\left[j\right]}^{*}}}{{\displaystyle \sum _j{q}_j^2{\left[j\right]}^{*}}}$$ (2)

Here q_i is the charge, [C_i ]* denotes the raw concentration, and [C_i ] denotes the corrected concentration. From the corrected concentration the preferential interaction coefficients are calculated by the following expression:

$${\mathrm{\Gamma }}_i=N_i-N_{H_{2}O}\frac{\left[C_i\right]}{55.51M}$$ (3)

We found the measurement as shown in Table 1 and Table 2 simulating SAM-I riboswitch aptamer.

In an early study, by performing 2-μs atomistic explicit solvent molecular dynamics simulations of the SAM-I riboswitch with varying ion concentrations we have investigated the dynamic interplay between RNA and Mg²⁺ by essentially focusing on the outer-sphere Mg²⁺ ion. As we have increased ion concentrations we have observed the highly negative-charged RNA to accommodate excess cations in its ions-solvation layer over their bulk concentrations.³⁰ We have seen this concentration dependent ions-solvation redistribution effect also in SAM-II riboswitch which accommodates increasing numbers of Mg²⁺ up to certain Mg²⁺ content.⁴³ Subsequent additions of Mg²⁺ do not effectively add to the 1st layer of Mg²⁺ solvation promoting a saturation effect. While anions are dispersed in the solution, these excess cations substantially contribute towards RNA stabilization and can be measured by experiments.