Abstract
Riboswitches are non-coding RNA that regulate gene expression by folding into specific three-dimensional structures (holo-form) upon binding by their cognate ligand in the presence of Mg2+. Riboswitch functioning is also hypothesized to be under kinetic control requiring large cognate ligand concentrations. We ask the question under thermodynamic conditions, can the riboswitches populate holo-form like structures in the absence of their cognate ligands only in the presence of Mg2+. We addressed this question using thiamine pyrophosphate (TPP) riboswitch as a model system and computer simulations using a coarse-grained model for RNA. The folding free energy surface (FES) shows that with the initial increase in Mg2+ concentration ([Mg2+]), TPP AD undergoes a barrierless collapse in its dimensions. On further increase in [Mg2+], intermediates separated by barriers appear on the FES, and one of the intermediates has a TPP ligand-binding competent structure. We show that site-specific binding of the Mg2+ aids in the formation of tertiary contacts. For [Mg2+] greater than physiological concentration, AD folds into its holo-form like structure even in the absence of the TPP ligand. The folding kinetics shows that it populates an intermediate due to the misalignment of the two arms in the TPP AD, which acts as a kinetic trap leading to larger folding timescales. The predictions of the intermediate structures from the simulations are amenable for experimental verification.
Introduction
The mechanism of gene regulation by riboswitches in bacteria is a fascinating problem. Riboswitches are non-coding RNA present in the 5′ untranslated region of the mRNA and are composed of two domains: the aptamer domain (AD) and the expression platform (EP). An interplay of the structural transitions between the AD and EP play a critical role in gene regulation. 1–3 Structural transitions between the two domains are influenced by Mg2+ and the binding of a cognate ligand to the AD.
The Mg2+ influence RNA folding through diffuse and site-specific binding.4 In diffuse binding, Mg2+ non-specifically binds to the negatively charged phosphate groups and renor-malizes charge on the RNA chain5 leading to the initial collapse. Whereas in site-specific binding, Mg2+ bind in the pockets created by the specific arrangement of nucleotides and aid in the stabilization of secondary and tertiary structures.6,7 However, for the functioning of riboswitches, in addition to the Mg2+, cognate ligand binding is equally essential. The cognate ligand binding to the AD leads to structural changes in both the AD and EP domains, which signal the attenuation or initiation of the transcription or translation process. Riboswitches are important drug targets since they are involved in the critical functional role of gene regulation in bacteria and also absent in the human genome.8,9
Experiments10–22 and simulations23–31 probing the folding of ADs in the presence of Mg2+ and their cognate ligands provide evidence that the ADs populate multiple intermediates in their folding pathways. Functional studies on TPP,32 Adenine,33 Mg2+,34 c-di-GMP,35 SAM-I36 and FMN37,38 riboswitches further demonstrate that higher concentrations of cognate ligands are required than their intrinsic affinity to effectively regulate gene expression, indicating that riboswitch functioning is under kinetic control rather than thermodynamic control. Despite significant progress in our understanding of the functioning of riboswitches, the role of cations and cognate ligands in the mechanism of structural transitions in the AD and EP is not completely clear. An interesting question that requires comprehensive understanding is if Mg2+ alone is sufficient to populate the holo-form like structures in the absence of the cognate ligand under thermodynamic conditions? To address this question, we studied the role of [Mg2+] on the stability of intermediates populated in the folding free energy surface (FES) of the AD of thiamine pyrophosphate (TPP) sensing riboswitch.
The TPP riboswitch is widely distributed along the three phylogenic branches: bacteria, archaea, and eukarya. It is found in 48 out of the 59 human bacterial pathogens making it the most abundant riboswitch in human pathogens.39 The TPP AD is ≈ 80 nt long, and in the native state (holo-form), it is a junction-type riboswitch with a tuning-fork-like structure40 composed of two arms (Figure 1A and S1 in supporting information (SI)). The P2−3 arm is composed of P2-P3 helices joined by the junction J32, and the P4−5 arm is composed of P4-P5 helices joined by the junction J45, respectively. The P1 helix acts as a base holding both the arms from P2 and P4 helices (Figure 1A). The P2−3 arm has the binding pocket for the 4-amino-5-hydroxymethyl-2-methyl-pyrimidine (HMP) moiety of the TPP ligand. The P4−5 arm binds to the pyrophosphate (PP) moiety of the ligand through the mediation of Mg2+.
Single-molecule FRET12,18 and SAXS41–43 studies have shown that physiological [Mg2+] is indispensable for the cognate ligand to bind to the TPP AD. Single-molecule FRET18 study proposed that a Y-shaped intermediate mediated by Mg2+ gets populated during the initial stages of folding even in the absence of the cognate TPP ligand. Upon binding of the TPP ligand, the AD attains the prerequisite folded state that regulates the downstream gene expression. Studies on other riboswitches reveal that the AD domains can sample the holo-form like conformations even in the absence of cognate ligand but in [Mg2+] greater than the physiological concentration.44,45 Experiments studying TPP AD folding also suggest that multiple structural ensembles are populated depending on [Mg2+] and TPP-ligand.12 Further, the timescales associated with the transitions among these ensembles varied from µs to s, indicating significant variations in the barrier heights separating the basins.
Computer simulations using all-atom7,30,46–51 and coarse-grained models52–61 are playing an important role in elucidating various aspects of RNA folding. The stability of folded state compared to the unfolded state of RNA is very sensitive to the charge and the concentration of the cations.62,63 Mg2+ is known to be remarkably efficient in facilitating the formation of native-like tertiary contacts and the folded state even in the millimolar concentration. In contrast, submolar to molar concentration of K+ is required for the monovalent ion-driven folding of RNA.63–68 Mg2+ preferentially accumulates around the phosphate groups (P sites) of specific nucleotides and initiates folding by stabilization of the secondary structures and subsequently leading to the hierarchical formation of tertiary contacts.56,69,70 During various stages of RNA folding, the inherently hierarchical nature of structural reorganization can result in the population of intermediates with an increase in [Mg2+].
We studied the effect of [Mg2+] on the folding FES of TPP AD using molecular dynamics simulations and a coarse-grained RNA model.56 We find that with the increase in [Mg2+], AD initially undergoes barrierless compaction in size followed by the formation of intermediate states. We show that Mg2+ binding to the P sites of specific nucleotides leads to the formation of tertiary contacts that stabilize the holo-form like folded state even in the absence of the TPP ligand. Interestingly, folding kinetics show that the AD can populate a kinetic trap due to the misaligned orientation of the arms leading to a larger folding time.
Methods
We studied the effect of [Mg2+] on the folding mechanism of TPP AD from Escherichia coli thiM mRNA using the three interaction site (TIS) RNA model56,71 and Langevin dynamics simulations. The TIS model for the TPP AD is constructed using the crystal structure (PDB: 2GDI).40
TIS Model of RNA
We used the TIS model developed by Denesyuk and Thirumalai,56,71 where each nucleotide is represented by three sites mimicking the phosphate (P), sugar (S), and base (B) groups. The centers of the sites are placed at the center of mass of the P, S, and B groups, respectively. In this model, the monovalent (K+, Na+, and Cl−) and divalent ions (Mg2+) are explicitly present in the simulation. The Hamiltonian for the TIS model has seven components and is given by
The components in the Hamiltonian correspond to the bond length (UBL), bond angle (UBA), excluded volume repulsion between different sites (UEV), electrostatic interaction between charged sites (UEL), single-strand base stacking interaction between consecutive bases (UST), hydrogen bonding interaction (UHB) and tertiary stacking interaction between two non-consecutive bases (UTST), respectively. The force field details and parameters can be found in the works of Denesyuk and Thirumalai.56,71 Below we provide a brief description of the force field.
The harmonic bond length and bond angle potentials account for the RNA chain connectivity and stiffness. The excluded volume repulsion between a pair of interacting sites, either RNA or ions, is given by a modified Lennard-Jones potential. The electrostatic interaction between a pair of charged sites is given by the Coulomb potential scaled by the temperature-dependent dielectric constant of water. The charge is -1 for phosphate group, -1 for Cl−, +2 for Mg2+, +1 for K+, and +1 for Na+ ions, respectively. The consecutive bases in the RNA chain have base stacking interactions, which depend on the sequence. The list of base pairs involved in the native hydrogen bond network in the folded structure of TPP AD is obtained using the crystal structure (PDB: 2GDI) and WHAT IF web server (https://swift.cmbi.umcn.nl) 72(Table S1-S4). All the base pairs, which have a hydrogen bond between them, interact using the hydrogen bonding potential. Non-canonical base pair hydrogen bonds and tertiary base stacking interactions present in the crystal structure are also taken into account in the model (Table S5-S6). This model is successful in quantitatively accounting for the folding thermodynamics of various RNA systems such as Azoarcus ribozyme,56 the central domain of 16S ribosomal RNA70 and RNA pseudoknots68 demonstrating that it is reliable and transferable to study various other RNA systems.
Simulations
We performed simulations to study TPP AD folding as [Mg2+] is varied from 1 mM to 6.5 mM. The [K+] is fixed at 30 mM in all the simulations. The simulations are performed in a cubic box of length 200 Å. The two Na+ ions present in the crystal structure are added to the simulation box. The number of Mg2+ and K+ ions in the simulation box are computed using their concentration and box volume. Cl− ions are added to maintain charge neutrality in the simulation box. All ions are explicitly modeled as beads with charge and excluded volume. We used Langevin dynamics simulations to study the folding dynamics of TPP AD at temperature, T = 310 K. To compute the thermodynamic properties of TPP AD folding, we used 5% viscosity of water, η = 5 × 10−5 Pa·s to enhance conformational sampling. To study the TPP folding kinetics at [Mg2+] = 6.5 mM, we used the viscosity of water, η = 10−3 Pa·s. The equation of motion for the RNA sites and ions in Langevin dynamics is given by where mi is the mass (in amu), ζi (= 6πηRi) (in amu/fs) is the friction coefficient, ri is the position, is the deterministic force, Ri is the radius (in Å) of ith site in the system. is the random force on the ith site with a white-noise spectrum. The random force auto-correlation function is given by, where n = 0, 1, …, δ0,n is Kronecker delta function, and kB is the Boltzmann constant. The Langevin equation is integrated using the velocity Verlet algorithm with a time step h (= 2.5 fs).56,73 System coordinates are saved after every 5,000 steps (τf = 12.5 ps) to compute the properties. The initial 1 µs of simulation data is ignored in computing the properties. For each [Mg2+], at least ≈ 13 µs of simulation data is collected to compute the average properties. The atomistic coordinates of the AD are generated using the coarse-grained coordinates and TIS2AA74 program, which uses the fragment-assembly approach75 and energy minimization embedded in AmberTools.76 We used VMD to generate the three dimensional structures of the AD.77
Data Analysis
The radius of gyration Rg, of the TPP AD is computed using the equation, , where N (= 240) is the total number of RNA sites in the TIS model of TPP AD, and is the vector connecting the sites i and j. The average fraction of helix formation for a given helix H, is computed using the equation where is the number of hydrogen bonds present in the helix H in ith conformation and ⟨ ⟩is the total number of hydrogen bonds present in the helix H in the crystal structure. denotes the average over all the conformations. A hydrogen bond is considered to be present if its energy is lower than the thermal energy (kBT).56
Local [Mg2+] Around P sites
The local [Mg2+] in the vicinity of the P site of the ith nucleotide in molar units is computed69 using the relation where ρi(r) is the number density of the Mg2+ at a distance r from the ith P site, Vc is the spherical volume of radius rc, and NA is the Avogadro’s number. The cutoff radius rc is given by rc = RMg + RP + Δr, where RMg and RP are the radii of Mg2+ and P sites, and Δr is the margin distance. We used Δr = 1.7 Å to ensure that we take into account only the tightly bound local Mg2+ around the P sites.
FES Calculation
The total number of native contacts in the TPP AD is computed using the TIS model of the folded crystal structure (PDB: 2GDI).40 A pair of sites i and j in the folded structure are defined to have a native contact between them if |i − j| > 10, and the distance between the sites rij is less than 15 Å (Figure S1). The fNC for ith TPP AD conformation is computed using the equation where Nnc(i) the number of native contacts present in ith conformation and Nnc(cry) is the number of native contacts present in the crystal structure.
The FES corresponding to the TPP AD folding (G) is projected onto the fraction of native contacts fNC, and it is calculated using the equation where P (fNC) is the probability distribution of fNC.
Fraction of Tertiary Contacts (TCs)
The TPP AD has two critical tertiary contact (TC) forming sites, the three-way junction (TC3WJ) and the arm-tip (TCAT). The TC3WJ involves contacts between the nucleotide segments A12 - U20, C48 - U59, and A80 - G86 (Figure S2A). The TCAT involves contacts between the nucleotide segments G21 - C24, and A69 - G72 (Figure S2A). Apart from the two TCs mentioned above, TPP AD has a third tertiary contact (TCRB) between U54 (J24) and U79 (J45) located at the base of the P4−5 arm. The total number of tertiary interactions in a particular TC in the TPP AD native state is equal to the number of native contacts between the sites belonging to the nucleotides involved in forming that specific TC. The fraction of tertiary contacts fTC for a particular TC is computed using the equation where is the number of native contacts present between the sites belonging to the nucleotides involved in the formation of that specific TC in the ith conformation and is the total number of native contacts present in that specific TC in the crystal structure. We label a TC as formed (F) if ⟨fTC ⟩ is ≥ 0.5 and as ruptured (R) otherwise.
Role of Mg2+ in Tertiary Contact Formation
The contribution of Mg2+ binding to the P sites in the formation of TCs is inferred by computing the free energy difference (ΔΔGTC) in the TC formation with and without Mg2+ binding.70 The free energy contribution to the TC formation due to Mg2+ binding to the ith P site is given by where PTC,i(F, MgB) is the joint probability that TC is formed (F), and Mg2+ is bound (MgB) to the ith P site, PTC,i(R, MgU) is the joint probability that TC is ruptured (R) and Mg2+ is not bound (MgU) to the ith P site. Similarly PTC,i(R, MgB) and PTC,i(F, MgU) are defined. An Mg2+ is considered bound to the ith P site if the distance between the centers of the P site and ion is less than 4.6 Å.
TPP AD Folding Kinetics
To decipher the kinetic intermediates populated in the TPP AD folding pathways, we computed an inter-arm angle (ΩIA) between the helical arms to characterize their orientation. The arm with helices P2 and P3 is represented using a vector joining the center of mass of nucleotides C15 and G51, and the center of mass of nucleotides C22 and G37. Similarly, the other arm with helices P4 and P5 is represented using a vector joining the center of mass of nucleotides C57 and G82, and the center of mass of nucleotides U64 and A75. The inter-arm angle ΩIA is defined to be the angle between the vectors and (Figure S2B). We computed a dihedral angle (ΘJ) to characterize the orientation of the junction J24. ΘJ is computed using the position of the S sites of the nucleotides U14, G51, C57 and G86 belonging to P1, P2, P4, and P1 helices, respectively. The length of J24 motif is the distance between the P sites of the nucleotides G51 and C57 (Figure S2B).
Results
Mg2+ Facilitates TPP AD Folding
In physiological conditions, noncoding RNA molecules fold to a unique native state to perform their regulatory activities. RNA molecules have a cooperative interaction network,78,79 which guides folding to the native state and suppresses the formation of non-native structures from the early stages of folding.80 The cooperativity in RNA folding further depends on the ions present in solution.81–89 To study the effect of Mg2+ on TPP AD folding, we computed ⟨Rg ⟩ and ⟨fNC⟩ as a function of [Mg2+] (Figure 1B). As we increase the [Mg2+] from 1 mM to 6.5 mM, the TPP AD undergoes a transition from an unfolded state (Rg ≈ 40 Å and fNC ≈ 0.3) to a compact folded state (⟨Rg ⟩ ≈ 21 Å and ⟨ fNC ≈ ⟩ 0.7). The plot shows two major folding transitions (Figure 1B). The first transition occurs in the range 1.5 mM < [Mg2+] < 2 mM, where ⟨ Rg ⟩ decreases from ≈ 38 Å to 34 Å (fNC changes from 0.31 to 0.37), and the second transition occurs in the range 4 mM < [Mg2+] < 4.5 mM, where ⟨Rg⟩ decreases from ≈ 30 Å to 22 Å (⟨fNC⟩ changes from 0.44 to 0.67). The multiple transitions indicate that TPP AD populates intermediates when folding is initiated by increasing [Mg2+]. The changes in ⟨Rg⟩ and ⟨fNC⟩ with the increase in [Mg2+] shows that TPP AD can fold to its native-like state only beyond physiological [Mg2+] (≈ 4 mM90–92) in the absence of the TPP ligand.
Folding Intermediates and Holo-Form Like Structure
The FES projected onto fNC shows that AD populates four different states depending on the [Mg2+] (Figure 2). As [Mg2+] is increased, the equilibrium shifted towards populating compact intermediate states. Experiments have shown that Mg2+ contributes to both specific and non-specific compaction in the dimensions of the RNA unfolded state.18,41,85,93,94 In the early stages of folding, we observed barrierless collapse of the AD as [Mg2+] is increased from 1 mM to 2 mM, where the FES retains its shape and only its minimum is shifted from fNC = 0.29 to 0.38, indicating compaction in the AD size (Figure 2). The decrease in ⟨Rg ⟩ and the disrupted tertiary contacts confirm compaction in the AD size without the formation of any tertiary structure (Figure 1B and 3A). For [Mg2+] ≤ 2 mM, the AD unfolded state is the global minimum on the FES. Upon increasing [Mg2+] (≥ 3 mM), intermediate states separated by energy barriers appear on the FES along with the shift in energy minima to higher fNC. For [Mg2+] ≥ 5 mM, the global minimum on the FES is the AD native-like folded state (holo-form) with fNC ≥ 0.7.
For [Mg2+] = 3 mM, the TPP AD exists in three states: unfolded (fNC = 0.32), openarm Y-shaped (fNC = 0.41) and closed-arm Y-shaped (fNC = 0.55) (Figure 2). As [Mg2+] increases to 5 mM, the FES shows that the TPP AD populates four states: unfolded (fNC = 0.3), open-arm (fNC = 0.44), closed-arm (fNC = 0.58) and holo-form like folded state (fNC = 0.71) (Figure 2). However, with the increase in [Mg2+] from 3 mM to 5 mM, the most stable state shifts from the open-arm Y-shaped (fNC = 0.41) to the holo-form state (fNC = 0.71) (Figure 2). The increase in stability of the holo-form like state (fNC = 0.71) for [Mg2+] ≥ 4.5 mM is due to the formation of both TC3W J and TCAT (Figure 3A). The transitions between the open and closed-arm Y-shaped intermediates indicate that at [Mg2+] = 3 mM, AD populates conformations, which can either facilitate or hinder the formation of the ligand binding pocket.
Stability of the Helical Arms
Out of all the five helices present in the AD, the P1 helix located at the basal region, which holds the two helical arms together, is thermodynamically the least stable helix and remains unfolded for [Mg2+] < 2 mM (Figure 1A, 2 and 3A). The lower stability of the P1 helix was also observed in previous studies.25,95 A single-molecule FRET experiment18 has shown that the P1 helix is highly dynamic and can exist in the unfolded form in the absence of Mg2+. Unfolded P1 helix leads to unzipping of the P4 helix in low [Mg2+] (< 2 mM) (Figure 2). The two arms of the AD retain their shape as the helices P2, P3, and P5 remain stable even in low [Mg2+] (= 1 mM) (Figure 3A). Monovalent cations ([K+] = 30 mM), which neutralize the RNA backbone charge, are sufficient to stabilize the P2, P3 and P5 secondary structures. However, the P1 helix is unfolded in the presence of K+ ions and low [Mg2+]. When [Mg2+] ≥ 2 mM, the P1 helix is stabilized, and it further stabilizes the P2−3 and P4−5 helical arms forming a Y-shaped structure (Figure 2). Fluorescence spectroscopy experiment96 has shown that at physiological [Mg2+], P1 helix orients the P2−3 and P4−5 arms forming a three-way-junction (3WJ).
Site-Specific Mg2+ Binding Facilitates TC Formation
To understand the role of Mg2+ in TPP AD folding, we computed the average local Mg2+ concentration (⟨c*⟩) around the AD at nucleotide resolution (Eq. 4). We found that Mg2+ are not randomly diffused along the RNA backbone but are bound to specific nucleotides and assist the formation of tertiary contacts.4,56,69,97,98 When [Mg2+] = 1 - 2 mM, Mg2+ are dominantly distributed around the nucleotides, NN (nucleotide number) = A43 to A45, which belong to the J32 junction (Figure 3B). Due to the lack of Mg2+ in the core region and the three-way-junction (3WJ) (Figure 1A, 3B), the electrostatic repulsion between the P2, P4 helices and J24 junction (basal inter-arm motif) hinders the close approach of the P2−3 and P4−5 arms to form TCs and the folded state (Figure 2).
As [Mg2+] is increased to 3 - 4 mM, Mg2+ accumulates preferentially around the core region (cavity formed by the P3, J32, P2, J24, P4 and P5 motifs) and the 3WJ region (NN = G33 - A35; A43 - A45; C48 - C49; U54 - A56; C57 - C58; C74 - G76; U14 - G16, A84 - G86, respectively) (Figure 3B, S2B). The condensed Mg2+ decrease the effective negative charge on the P sites of the basal inter-arm motif weakening the electrostatic repulsion between the P2−3 and P4−5 arms. As a result, the helical arms approach each other, and the Y-shaped intermediate state is populated (Figure 2).
When [Mg2+] is large (≥ 5 mM), Mg2+ are condensed in the core and 3WJ regions with comparatively increased binding preference to the P3 (NN = C23 - C24), J32 (NN = G19 - U20 and U39 - A41 and A43 - A45), P2 (NN = G17 - G18 and C48 - G51), J24 (NN = C55 ≥- A56), P4 (NN = C57 - U59), P5 (NN = C73 - A75), and L5 (NN = U71 - G72) motifs (Figure 3B). The increased accumulation of Mg2+ on the helical arms and the J24 junction further weakens the inter-arm electrostatic repulsion and allows the arms to form TCs, which stabilizes the holo-form like folded structure even in the absence of the TPP ligand.
The nucleotides with high preferential binding of Mg2+, A43 and C74 to G76 are involved in the TPP ligand binding to the AD. A43 forms stacking interaction with the HMP group of the TPP ligand, and C74 - G76 bind to the pyrophosphate tail of TPP ligand bridged by Mg2+ (Figure S3).40 Mg2+ prefers binding to A43 even in low [Mg2+], whereas the ions show binding preference towards C74 - G76 when [Mg2+] ≥ 3 mM. The fact that Mg2+ prefers to bind to the nucleotides involved in TPP ligand recognition and binding illustrates that Mg2+ aids in the formation and stabilization of the scaffolding for ligand binding pocket.18,40 The SAXS experiments42,43 on E. coli thiM mRNA show that in high [Mg2+] (≈ 10 mM), TPP AD samples compact conformations similar to the holo-form like structures, whose Rg is greater than the ligand-bound structures by ≈ 2 Å. The experiments provide evidence that the T-loop (U39 - A47) region where the TPP ligand binds (Figure S2B) could be partially unfolded in the absence of the ligand.
TC Formation is Cooperative
We computed the average fraction of TCs in TPP AD, ⟨ fTC ⟩, to probe the cooperativity and hierarchy in TC formation with the variation in [Mg2+]. The two TCs located at the 3WJ (TC3W J) and the arm-tip of AD (TCAT) exhibit [Mg2+] dependent formation (Figure 3A). Both the TCs form cooperatively and show a sharp transition in the range 4 mM < [Mg2+] < 4.5 mM, which coincides with the second transition observed in both ⟨ Rg ⟩ and ⟨ fNC ⟩ (Figure 1B) establishing that the compaction in AD dimensions is due to the formation of these TCs. The enhanced stability of the Y-shaped intermediates and the holo-form like state require the complete formation of these two TCs. The TC3W J forms first and stabilizes the two helical arms, which subsequently approach each other to form TCAT (Figure 3A). The tertiary structures do not form in the early stages of folding but during the AD assembly to the native-like state in the late stages of folding shows that TPP AD follows the quasi-hierarchical folding model. 99 TCRB remains disrupted even in high [Mg2+]. We hypothesize that TPP ligand binding to the AD is essential to stabilize TCRB. The crystal structure of the TPP AD shows that the pyrophosphate domain of the TPP ligand interacts with G78 (J45) mediated by Mg2+ and water molecules (Figure S3C).
Mg2+ Binding to Specific P Sites Decreases the Free Energy for TC Formation
To decipher the contribution of site-specific Mg2+ binding to the formation of a TC, we computed the difference in the stability of that TC due to Mg2+ binding and unbinding to the P site of ith nucleotide, ΔΔGTC(i) (Eq. 8).70 Negative value of ΔΔGTC(i) for a TC indicates that Mg2+ binding to the ith P site favors the formation of that TC. We computed ΔΔGTC(i) for [Mg2+] = 4 mM, 4.5 mM and 5 mM, which correspond to the second transition in AD folding where TC formation is observed (Figure 1B and 3A). For [Mg2+] = 4 mM, conformations with both the TCs in the ruptured state are predominantly populated. With the increase in [Mg2+] (≥ 4.5 mM), the AD dominantly populates conformations with the formed TCs (Figure S4).
Although, AD with the disrupted TC3WJ is the most stable state at [Mg2+] = 4 mM, Mg2+ are already bound to the P sites located in the 3WJ region (NN = G19, C50 - A53, A56 - C58, A85) (Figure 3A,B). The bound Mg2+ significantly favor the TC3W J formation as ΔΔGTC(i) < -0.5 kBT for i belonging to the 3WJ nucleotides (Figure 4A). With the increase in [Mg2+] (≥ 4.5 mM), the probability of TC3W J formation increased (Figure 3A). However, the ΔΔGTC(i) values remain almost unchanged (Figure 4A), but the ⟨c*⟩ around the NN forming the TC3W J shows a significant increase with the increase in [Mg2+] (≥ 4.5 mM) (Figure 3B, S5). We hypothesize that at [Mg2+] = 4 mM, as lower number of Mg2+ accumulate in the 3WJ region, the backbone electrostatic repulsion may still prevail in the region and hinder the TC3W J formation. With increasing [Mg2+] (≥ 4.5 mM), sufficient number of Mg2+ accumulate in the 3WJ region (Figure 3B) and diminish the backbone electrostatic repulsion to stabilize the TC3W J (Figure 3A, 4A).
During the second transition in AD folding ([Mg2+] = 4 - 4.5 mM), TCAT formation is favored by Mg2+ binding to the nucleotides located at the interior region mainly to the nucleotides located at both 3WJ (NN = G19 - U20, C50 - A53, A56 - U59 and A85) and arm-tip (NN = C22 - C23, A70 - G72) regions of the AD (Figure 4B,C). The lower value of due to Mg2+ binding to the 3WJ nucleotides (NN = G51 - C58) compared to the arm-tip nucleotides, indicates that Mg2+ binding in the 3WJ region can expedite the TCAT formation, located at a distant site through allosteric interactions. At [Mg2+] = 4.5 mM, AD dominantly populates the conformations with formed TCAT (Figure 3A). Mg2+ binding to both 3WJ (NN = G51, C58) and arm-tip (NN = C23 - C24, A70 - G72) nucleotides almost equally contribute towards TCAT formation. After the second transition ([Mg2+] = 5 mM), TCAT formation is governed by the Mg2+ binding to the nucleotides located at the periphery of AD (Figure 4B,D). Most of these peripheral nucleotides, NN = C30 - U32 (L3), A44 - A47 (J32) and A67 - U71 (L5), belong to motifs devoid of any three-dimensional structures. The favorable free energy for TCAT formation due to Mg2+ binding to the peripheral nucleotides can probably lead to the proper orientation of the junction and loop region so that AD can fold to its holo-form like conformation.
ΔΔGTC(i) data reveals that the nucleotides located near the 3WJ region facilitate the AD folding to its holo-form like state by stabilizing both the TCs. The stabilization of TCs due to the site-specific Mg2+ binding to the nucleotides in the 3WJ region irrespective of [Mg2+] establishes that Mg2+ binds to specific nucleotides of an RNA molecule that drive and stabilize the TC formation leading to the RNA folded state.70
TPP AD Folds Through Slow and Fast Folding Pathways
We spawned 60 folding trajectories to study the AD folding kinetics in the absence of the TPP ligand starting from different unfolded conformations at T = 310 K and [Mg2+] = 6.5 mM. The initial unfolded conformations are taken from the [Mg2+] = 1.0 mM simulation, where the unfolded state is the most stable state (Figure 2). Upon initiating folding, we find that the AD folds through fast and slow folding pathways. We labeled trajectories where TPP AD folds in less than 0.5 µs as fast folding pathways and the other trajectories as slow folding pathways. 16 out of the 60 spawned folding trajectories follow the fast folding pathway and the rest fold through the slow folding pathway. In the slow folding pathway, an intermediate, which acts as a kinetic trap, is populated, leading to a longer folding time (Figure 5B,D).
The helices P2, P3 and P5 are stable in the unfolded state at [Mg2+] = 6.5 mM (Figure 3A). The Mg2+ mediated formation of the least stable switch helix P1 is essential for the formation of 3WJ and open-arm Y-shaped intermediate for the folding of the AD in the absence of ligand. The initial barrier that AD has to overcome to fold is the relative orientation of the two helical arms P2−3 and P4−5 with respect to each other. In the early stages of folding, the arms fluctuate relative to each other as inferred from the inter-arm angle, ΩIA (see Methods) (Figure 5A,B and 6A,A1). Stochastic fluctuations rotate the P4−5 arm around the J24 junction as an axis to align it parallel to the P2−3 arm (Figure 6B,B1). The parallel alignment of both the arms also facilitates the formation of P1 helix at the base (Figure 6C1,C1). The fluctuations in ΩIA show that the parallel orientation of the helical arms is necessary but not sufficient for the AD to proceed to fold to its native state (Figure 5A,B).
Misaligned Orientation of P2-J24(L)-P4 and P1-P2/P4-J24(S)-P1 Motifs Leads to a Kinetic Trap
The kinetic trap in the slow folding pathway is due to the population of a conformation where although both the arms are aligned parallel to each other, their orientation is misaligned, and this conformation with a lifetime greater than 1 µs acts as a kinetic trap (Figure 5B,D and 6D,D′). In the kinetic trap, the nucleotides G51 - C57 (P2-J24(L)-P4 motif) are misaligned with respect to the nucleotides 14U - 15C and G82 - A85 (P1-P2/P4-J24(S)-P1 motif). We quantified this misalignment using the dihedral angle ΘJ (see Methods). For both the slow and fast folding pathways, ΘJ initially fluctuates due to the unfolded P1 and P4 helices. After the formation of the helices, the magnitude of the fluctuations in ΘJ decreased. If the AD is stuck in the kinetic trap, ΘJ fluctuates around -0.1 rad (Figure 5B). The misaligned arms prevent the formation of pre-organized 3WJ, which facilitates the formation of the TCAT tertiary structure. To escape from the kinetic trap, J24(L), P4 and P5 rotate around the P4−5 arm (Figure 6C1,D,C′,D′). After escaping from the kinetic trap, a U-shaped loop is formed by the longer part of the J24 junction (J24(L)) joining the P2 and P4 helices, which allows the helical arms to come closer to acquire native-like folded state competent to form the ligand-binding pocket (Figure 6C2,E,E′). The loop-formation by the folded J24(L) junction pulls the helical arms together leading to the formation of TCAT and holo-form like folded state. The inter-arm angle, ΩIA and show large fluctuations when the AD is unfolded, and fluctuations subside only after the AD is completely folded.
Mg2+ Binding to Specific P Sites Facilitates Folding to the Native State
To probe the effect of Mg2+ on TPP AD folding, we computed c* around the P sites of nucleotides involved in the formation of TCs (PTC sites) (Figure S6 and S7) and fTC as a function of time (tkin) (Figure 5C,D). In the slow folding pathway, during the early stages of folding (tkin ⪅ 0.39 µs), c* varies between 0 - 1 mM for all the PTC sites and none of the TCs are formed. After the population of the kinetic trap due to the misalignment of the two arms (0.39 µs < tkin < 1.41 µs), TC3W J fluctuates between states with fTC = 0.4 to 0.5, as the AD attempts to escape from the kinetic trap (Figure 5D). The fTC plot shows hierarchy in the formation of the TCs and the formation of TC3W J is a prerequisite for the formation of TCAT (Figure 5C,D). Both the TCs form after native-like reorganization of the J24 motifs at tkin > 1.41 µs. Similar time-dependent trends are also observed in c* for fast-folding pathways, where the formation of the TCs is facilitated by Mg2+ accumulation around the PTC sites. Hierarchy in TC formation where TC3W J anchors the formation of TCAT is also observed in the fast folding pathways as well. Both thermodynamics and kinetics folding studies confirm that AD folding follows a quasi-hierarchical model, where TCs are not formed during the early stages of folding, and they form only during the AD assembly in the late stages of folding.
Conclusion
In this study, we showed that TPP AD populates intermediates when its folding is induced by Mg2+ in agreement with the experiments.12 We found that at physiological [Mg2+] (≈ 4 mM), AD populated a closed-arm Y-shaped and a holo-form like folded conformations. The holo-form like conformation is not the global minimum in the FES at around physiological [Mg2+] but becomes the global minimum in higher [Mg2+] (≥ 5 mM) even in the absence of the TPP ligand. These results indicate that holo-form like riboswitch conformations are only marginally stable at physiological conditions in the absence of their cognate ligands. Therefore at physiological conditions, TPP-ligand binding to the AD is indispensable for gene regulation and further supports the hypothesis that gene regulation by riboswitches is under kinetic control. The population of holo-form like conformations in the absence of cognate ligand but in high [Mg2+] is also observed in preQ1, Fluoride and SAM-I ri-boswitch.28,44,45,100,101 Experiments on preQ1 riboswitch have shown that Mg2+ can further shift the aptamer-ligand sensing mechanism from induced-fit to conformation selection.45 The unique ability of Mg2+ to stabilize the holo-form like AD conformations in the absence of the cognate ligand poses an interesting unanswered question whether only Mg2+ can lead to the population of holo-form like structures in the AD of all riboswitches without their cognate ligands and what is the optimum Mg2+ concentration required?
Supporting Information Available
Structural details of P2-J24(L)-P4 and P1-P2/P4-J24(S)-P1 motifs is provided in supporting information. Figure S1: Native contact map of AD; Figure S2: 3D structure of the AD with highlighted TC3W J and TCAT forming nucleotides and 2D schematic structure of the AD with definition of parameters used to characterize the kinetic results; Figure S3: Atomistic representation of RNA residues involved in the TPP ligand binding; Figure S4: Time profile of fTC for both TC3W J and TCAT showing the formation of TCs at [Mg2+] = 4 to 5 mM; Figure S5: ⟨ c* ⟩ for [Mg2+] = 4 to 5 mM; Figure S6-S7: Time profile of c* at TC forming nucleotide resolution for fast and slow folding trajectories; Table S1-S6: Various parameters used to model the TPP AD using TIS model is given in the tabular format in the supporting information.
For Table of Contents Use Only
Acknowledgement
A part of this work is funded by the grant to G.R. by the National Supercomputing Mission (MeitY/R&D/HPC/2(1)/2014). S.K. acknowledges research fellowship from the Indian Institute of Science, Bangalore. We acknowledge National Supercomputing Mission (NSM) for providing computing resources of “PARAM Brahma” at IISER Pune, which is implemented by C-DAC and supported by the Ministry of Electronics and Information Technology (Me-itY) and Department of Science and Technology (DST), Government of India.
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