Elastic network representation of the backbone beads of the RdRP from PV. The red beads and cyan sticks represent the backbone and springs connecting backbone particles, respectively. 

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... it is widely accepted that a folded protein should be represented as an ensemble of numerous conformations fl uctuating in the neighborhood of its native state. 1,2 Thus, the structure − function relationship should also be extended to include protein dynamics. 2 With the realization that protein motions play important roles during biological processes, the study of protein dynamics has received a large amount of attention during recent years. 1 − 4 However, it is not feasible to take detailed “ snapshots ” of every atom moving within a protein experimentally. Even though nuclear magnetic resonance (NMR) spectroscopy has emerged to study protein dynamics, the ability of NMR spectroscopy is still limited by protein size. Because of the increase in computational power and the signi fi cant improvement in energy functions, atomistic molecular dynamics (MD) simulations have become a complementary technique that is capable of providing detailed information about atomic motions in proteins as a function of time. Since the fi rst MD simulation of a small protein performed in a vacuum with a total simulation time of 9.5 ps in 1977, 1 the length of an atomistic MD simulation for a typical protein − solvent system currently extends to several hundred nanoseconds. Despite the enormous progress made in the development of computer algorithms and processor speed during the past 20 years, conventional atomistic MD simulations are still prohibitive for studying many biological processes, such as protein folding and enzyme catalysis, 5,6 that occur in the range of microseconds to seconds. Thus, to extend the applicability of MD simulations to study biological processes occurring on longer time scales, it is necessary to use a simpli ed representation of protein − solvent systems, instead of an atomic-detail description. Thus, a variety of coarse-grained (CG) models have been developed to allow MD simulations to study many biological processes occurring on longer time scales by reducing the number of degrees of freedom of the protein − solvent system and increasing the integration time step by at least a factor of 10 when compared to those used in atomistic MD simulations. 7,8 Two CG models are of main interest in this work. First, the elastic network model (ENM) has been successfully used to study the slow motions of proteins. The ENM arises from the elastic theory of random polymer networks 9 and was extended to study protein dynamics by using a normal-mode analysis (NMA) and simpli fi ed harmonic potentials. 10,11 The second model, the MARTINI coarse-grained force fi eld, was developed by Marrink and co-workers 12 for modeling lipids and surfactants. The current MARTINI model (MARTINI v2.1) has been extended to simulate protein systems 13 and has also been used to study the interactions between proteins and the lipid bilayer. 14 In the latter case, the native structure of a protein is represented using an ENM. In this approach, the elastic network in the protein is constructed by means of backbone beads (one backbone bead per residue is located at the C α atom position), and any two backbone beads within a distance of 7 Å are connected by a spring with a force constant of 1000 kJ · mol − 1 · nm − 2 . Periole and co-workers 15 systematically inves- tigated the optimum force constant for the restraint applied in the elastic network with di ff erent cuto ff distances, and recommended that the spring constant should be in the range of 500 − 1000 kJ · mol − 1 · nm − 2 when the cuto ff distance in the elastic network is chosen in the range of 8 − 10 Å. The combination of the MARTINI model and the elastic network model was named ELNEDIN by the authors. 15 In this work, instead of using a fi xed force constant for the restraint in the elastic network, we elected to introduce a set of individual force constants that were applied to each pair of nonsequentially connected backbone beads. Individual force constants have also been used in other works 16 − 18 and have been shown to be e ff ective. The preliminary force constants and the equilibrium distance (within a cuto ff value of 12 Å) between backbone beads were obtained from the trajectory of a short atomistic MD simulation (2 ns) of the protein using the Boltzmann inversion method. 19 The implementation of the ENM over MARTINI, that is, imposing additional CG force constants obtained from short atomistic MD simulations preserved at the mesoscale, maintains the structural “ scalfold ” biased toward a reference structure. Additionally, it allows the most important dynamic features captured from time-consum- ing atomistic MD simulations to be preserved at the mesoscale. A similar behavior has been found in other works. 12 − 14 In addition, the use of individual force constants for the elastic network provides a method (termed ENM/MARTINI here) that not only reaches microsecond time scales with good accuracy when compared against atomistic simulations but also reveals the di erent dynamics of single mutations within a protein at the mesoscale level. This last topic is outside the scope of the present work and will be addressed in a forthcoming publication. Here, we apply the hybrid ENM/MARTINI coarse-grained model to study the dynamics of four di ff erent RNA-dependent RNA polymerases from poliovirus (PV), Coxsackie virus B3 (CVB3), human rhinovirus 16 (HRV16), and foot-and-mouth- disease virus (FMDV). An RNA-dependent RNA polymerase (RdRP) is an enzyme that catalyzes the replication of RNA from an RNA template. The crystal structures of the RdRPs from PV, 20 CVB3, 21 HRV16, 22 and FMDV 23 studied in this work have an overall similar topology (see Figure 1). The structure of an RdRP resembles a cupped right hand and contains three subdomains: fi ngers, palm, and thumb. 24 The structural description of the RdRp from poliovirus (PV) is given in ref 20 and summarized here for completeness. For poliovirus, which contains a prototypical RdRP, the fi ngers subdomain begins with a buried N terminus that is part of the index fi nger (residues 1 − 68). The pinky fi nger has two segments, residues 96 − 149, which proceed to the ring fi nger (residues 150 − 179), and residues 180 − 190, which are succeeded by residues of the palm. The middle fi nger (residues 269 − 285) is followed by residues of the palm. A common property of RdRPs is the presence of several conserved structural motifs (A − G). The fi ngers subdomain subdomain contains motifs F (residues 153 − 178) and G (residues 113 − 120). The palm contains the remaining fi ve motifs A (residues 229 − 240), B (residues 293 − 312), C (residues 322 − 335), D (residues 338 − 362), and E (residues 363 − 380). Finally, the thumb is composed of the C-terminal residues 381 461, which form a bundle of α -helices. The strong interactions between fi ngertips and thumb result in a completely encircled active site, forming the entry/exit channel for template-primer RNA and NTP substrates. In the following sections, we provide background information on the ENM and MARTINI force fi elds and simulation methods, discuss our model and systems, and fi nally describe conclusions about the behavior of our systems based on our simulations. Elastic Network Model. In the elastic network model (ENM), 10,11 a folded protein is assumed to be a three- dimensional elastic network in which each amino acid residue is usually represented as a bead using the position of the C α atom. Two beads are connected by a harmonic spring, described by a simpli fi ed harmonic potential function Here, is the Hookean pairwise force constant representing the interaction between two residues in the folded protein; the element Δ R i of Δ R is the fl uctuation vector of the i th residue; and G ̧ is a symmetric matrix known as the Kirchho ff matrix where R cut is the cuto distance giving the range of the interaction between two residues and R ij is the separation between the i th and j th residues. MARTINI Coarse-Grained Model. The MARTINI 12,13 coarse-grained representation of the 20 amino acids is presented in Figure 1 of ref 13 and summarized here. The coarse-grained model uses the four-to-one mapping method. Thus, four heavy atoms of an amino acid, except for an amino acid having a ringlike fragment, are grouped into a bead, with each bead representing an interaction site. For di ff erent ringlike fragments, the model uses di ff erent mappings with higher resolu- tion (up to two-to-one mapping). The type of each interaction site is one of four di ff erent main types: polar (P), nonpolar (N), apolar (C), and charged (Q). In addition to the four main types, di ff erent subtypes are de fi ned either by the hydrogen-bonding capacity (donor, acceptor, both, or none) or by the degree of polarity (increasing from 1 to 5). A detailed description of the interaction type for each amino acid is given in Table 1 of ref 13, and the interested reader is referred to this publication for further information. ENM/MARTINI Coarse-Grained Model. In the hybrid model presented here, the MARTINI coarse-grained force fi eld without any modi fi cation was used with additional harmonic restraints imposed on the nonsequentially connected centers of mass of the backbone beads within a predetermined distance (e.g., 12 Å). Thus, the main di ff erence between the ENM/ MARTINI and MARTINI models is the additional elastic restraint imposed on the backbone beads. The partial three- dimensional structure of the protein, represented only by the backbone beads, is then modeled as an elastic network, as shown in Figure 2. The harmonic restraint V between the i th and j ...