Belonging to the Flaviviridae family, hepatitis C virus (HCV) is the only member of the Hepacivirus genus. It has infected nearly 200 million individuals around the globe. The viral genome is a 9.6 kb single-stranded, positive-sense RNA, which not only encodes viral proteins but also encrypts regulation of viral replication steps (Moradpour et al., 2007). The 5′-untranslated region (UTR) contains a highly structured internal ribosomal entry site (IRES) that initiates translation of the polyprotein encoded in the open reading frame (ORF). The polyprotein translated from the single ORF is processed by host and viral proteases to produce structural proteins and nonstructural proteins. Minus-strand RNA synthesis initiates at the 3′-UTR by viral nonstructural protein 5B (NS5B), which also produces positive-strand RNA using the minus-strand RNA as template (Moradpour et al., 2007).

Both viral protein translation and minus-strand RNA synthesis occur on the genomic RNA (gRNA). Hence, mechanism must exist to prevent collision of these two replication machineries. While viral and host proteins contribute significantly to the regulation, dynamic RNA structures and RNA:RNA interactions in the gRNA also play a pivotal role. Current knowledge has posited the 3′-UTR of the gRNA as the key regulatory element. It serves as a hub participating in long-range interactions with the 5BSL3.2 stem loop in the ORF (You et al., 2004; Friebe et al., 2005; You and Rice, 2008), as well as the 5′- internal ribosome entry site (IRES) (Romero-López and Berzal-Herranz, 2009; Romero-Lopez et al., 2012; Romero-López et al., 2014). The base pair complementarities between 5BSL3.2 and the 3′-tail of the gRNA (3′X, 98 nucleotides), are critical for viral replication (You et al., 2004; Friebe et al., 2005; You and Rice, 2008), and nucleotide accessibility probing of the 3′-UTR has demonstrated its structural changes in the presence of upstream elements (Romero-Lopez et al., 2012; Romero-López et al., 2014; Tuplin et al., 2012). However, lack of accurate models of the RNA:RNA interaction network has hampered functional and mechanistic interpretations. One of the main challenges for studying RNA:RNA interactions is about how to understand and predict the effects of metal ions, which are essential for neutralizing/screening RNA backbone charges (Brion and Westhof, 1997; Tinoco and Bustamante, 1999; Davis et al., 2007; Fürtig et al., 2010).

Ions bound to an RNA structure can be classified into three types (Cate and Doudna, 1996; Draper et al., 2005; Tan and Chen, 2005): site-specific bound (SSB) ions (Cate and Doudna, 1996), diffusively bound (DB) ions (Draper et al., 2005), and tightly bound (TB) ions (Tan and Chen, 2005). SSB ions are fully or partially dehydrated and trapped at specific sites such as the pocket regions in the RNA structure (Misra and Draper, 2001). Because of the chelation with the electronegative atomic groups of RNA, SSB ions have relatively specific binding sites in the RNA (Ando et al., 2003; Lilley, 2003; Forconi and Herschlag, 2009; Kellerman et al., 2014; Bobyr et al., 2015). DB ions are fully hydrated and bound to RNA diffusively (Draper et al., 2005). These ions can diffuse at a distance from the surface of RNA. TB ions are clustered around RNA surface to form a high local concentration (Tan and Chen, 2005). TB ions form a mid-state between SSB and DB ions (Sun et al., 2017a): on the one hand, TB ions do not involve SSB-like specific binding sites and are hydrated, on the other hand, TB ions cannot move around like DB ions, because the local high concentration and the resultant ion-ion coupling (correlation) can significantly lower the ion mobility. The ion correlation prevents a fluid-like model mean-field treatment for the TB ions. The TB ions should be treated as explicit, discrete particles.

Molecular dynamic (MD) simulations can account for the ion correlation effect since the ions are treated as explicit particles (Joung and Cheatham, 2009; Kuczera et al., 2009; Hayes et al., 2014). However, the simulations are limited by the computational time (Dong et al., 2008). Mean-field based non-simulation models, such as the non-linear Poisson-Boltzmann (NLPB) model (Zhou, 1994; Misra and Draper, 1998, 1999; Luo et al., 2002; Claudia et al., 2007) and the counterion condensation (CC) theory (Manning, 1978) cannot treat ion correlations. As a result, although NLPB has been highly successful in predicting the electrostatic effects for (weakly correlated) monovalent ions, the theory may under-estimate ion-mediated stabilization effect for (strongly correlated) multivalent ions such as Mg²⁺ ions (Bai et al., 2007; Gebala et al., 2015). With the increasing recognition of the importance of ion correlation effect, several new models have been developed (Mak and Henke, 2013; Henke and Mak, 2014), such as three-dimensional reference interaction site model (3D-RISM) (Giambaşu et al., 2014, 2015), which can simultaneously account for the ion correlation and solvation (dehydration/hydration) effects, and the generalized counterion condensation theory (Hayes et al., 2015), which adds a Mg²⁺-Mg²⁺ interaction term to the traditional CC theory. These models have shown promising potential in the prediction of the ion binding effects (Sun et al., 2017b).

The tightly bound ion (TBI) model (Tan and Chen, 2005) is one of the reliable models for the prediction of the ion effects in RNA folding. Extensive theory-experiment comparisons have shown that TBI model may provide improved predictions (Tan and Chen, 2010; He and Chen, 2012). The key feature of the model is to sample discrete multi-ion distributions for the TB ions and for each distribution, to evaluate the multi-ion correlated electrostatic free energy for the system (RNA and the ion solution). Through the use of the Generalized Born model, the TBI model can quantify the different energetics components, such as the solvent polarization effects in ion-RNA interactions (He and Chen, 2013). The ability to treat ion correlation and fluctuation, which can be important for multivalent ions such as Mg²⁺, makes TBI an ideal model for the HCV gRNA folding system, which involves Mg²⁺ ions.

Since the original TBI framework was first reported, several new models have been developed in the TBI framework. Most recently, using a novel sampling-resampling algorithm, the Monte Carlo tightly bound ion model (MCTBI) (Sun and Chen, 2016) was developed in order to enhance the computational efficiency, and the partial charge-based tightly bound ion model (PCTBI) (Sun et al., 2017a) was developed to account for more detailed RNA charge distribution. These new models have led to 1,000-fold improvement in computational time and thus allow us to treat large RNAs (several hundred nucleotides) (Sun et al., 2017c). More importantly, these new models enable accurate predictions for RNA-RNA interactions, such the 5BSL3.2:3′X kissing interactions in HCV gRNA below, where high-resolution charge distribution can be very important. However, the above models do not account for the heterogeneity of RNA conformations. Thus, in order to predict RNA structural changes, we need to sample RNA conformations using RNA folding models such as Vfold (Xu et al., 2014) and molecular dynamics (MD) simulations, and compute the ion-induced free energy changes for the different conformations. In what follows, we focus on the major conclusions and the analysis for the ion binding effects in the 5BSL3.2:3′X HCV kissing complex formation (Kranawetter et al., 2017; Sun et al., 2017a).

Since the demonstration of the importance of sequence complementarity of 5BSL3.2 and 3′X, efforts have been made to investigate the long-range kissing interaction at the 3′-end of gRNA. Starting from the 2D structure (base pair assignments) derived from the NMR experiment, the Vfold RNA folding model (Xu et al., 2014) gives the initial 3D structures. Starting from the initial 3D structures, MD simulation generates ensembles of 3D conformations. In the simulations, the base pairs in the initial structures are constrained by a harmonic potential U(r)=k(r-r0)2 with k = 1.0 kcal/mol and r₀ = 3.5 Å. For each 3D conformation, the use of the PCTBI model gives the electrostatic free energy for the RNA-ion system: ΔG3D=ΔGion+ΔGRNA, where ΔG_ion is the electrostatic free energy induced by the ions (including the TB and DB ions) and ΔG_RNA is the mutual electrostatic interaction between RNA backbone charges. The Boltzmann-weighted free energy ΔG = < ΔG_3D > describes the energy landscape of the system for the given ion condition.

The combined theory-experiment studies described above demonstrate a general approach for the prediction and data interpretation for RNA structure and functions. The results for the metal ion effects are biologically significant. For the HCV system, the undocked and docked kissing-loop conformations are likely associated with distinct replications steps. Blocking the 5BSL3.2:3′X kissing-loop interaction suppressed viral protein translation without affecting RNA synthesis (Tuplin et al., 2015). Host protein EWSR1 was discovered to promote HCV RNA synthesis by preferentially interacting with 5BSL3.2 in the absence of 3′X (Oakland et al., 2013). Thus, the 3′-end of gRNA may fine-tune various functions utilizing a Mg²⁺ modulated structural equilibrium. The Mg²⁺ effect on the HCV gRNA is not limited to the 3′-end. It was recently reported that the IRES switched from an elongated structure to a closed comma-shaped structure when the Mg²⁺ concentration increased, and the structural change might be related to the observed different translation activities (Swaminathan, 2003; Romani, 2011; Garcia-Sacristan et al., 2015). Thus, the Mg²⁺-dependent structural equilibria in the HCV gRNA are likely an adaptive property to the intracellular Mg²⁺ concentration in liver cells for viral replication.

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.