The performance of fine‐grained and coarse‐grained elastic network models and its dependence on various factors

In a recent work we developed a method for deriving accurate simplified models that capture the essentials of conventional all‐atom NMA and identified two best simplified models: ssNMA and eANM, both of which have a significantly higher correlation with NMA in mean square fluctuation calculations than existing elastic network models such as ANM and ANMr2, a variant of ANM that uses the inverse of the squared separation distances as spring constants. Here, we examine closely how the performance of these elastic network models depends on various factors, namely, the presence of hydrogen atoms in the model, the quality of input structures, and the effect of crystal packing. The study reveals the strengths and limitations of these models. Our results indicate that ssNMA and eANM are the best fine‐grained elastic network models but their performance is sensitive to the quality of input structures. When the quality of input structures is poor, ANMr2 is a good alternative for computing mean‐square fluctuations while ANM model is a good alternative for obtaining normal modes. Proteins 2015; 83:1273–1283. © 2015 Wiley Periodicals, Inc.     

All‐atom and coarse‐grained simulations of the forced unfolding pathways of the SNARE complex

The SNARE complex, consisting of three proteins (VAMP2, syntaxin, and SNAP‐25), is thought to drive membrane fusion by assembling into a four‐helix bundle through a zippering process. In support of the above zippering model, a recent single‐molecule optical tweezers experiment by Gao et al. revealed a sequential unzipping of SNARE along VAMP2 in the order of the linker domain → the C‐terminal domain → the N‐terminal domain. To offer detailed structural insights to this unzipping process, we have performed all‐atom and coarse‐grained steered molecular dynamics (sMD) simulations of the forced unfolding pathways of SNARE using different models and force fields. Our findings are summarized as follows: First, the sMD simulations based on either an all‐atom force field (with an implicit solvent model) or a coarse‐grained Go model were unable to capture the forced unfolding pathway of SNARE as observed by Gao et al., which may be attributed to insufficient simulation time and inaccurate force fields. Second, the sMD simulations based on a reparameterized coarse‐grained model (i.e., modified elastic network model) were able to predict a sequential unzipping of SNARE in good agreement with the findings by Gao et al. The key to this success is to reparameterize the intrahelix and interhelix nonbonded force constants against the pair‐wise residue–residue distance fluctuations collected from all‐atom MD simulations of SNARE. Therefore, our finding supports the importance of accurately describing the inherent dynamics/flexibility of SNARE (in the absence of force), in order to correctly simulate its unfolding behaviors under force. This study has established a useful computational framework for future studies of the zippering function of SNARE and its perturbations by point mutations with amino‐acid level of details, and more generally the forced unfolding pathways of other helix bundle proteins. Proteins 2014; 82:1376–1386. © 2014 Wiley Periodicals, Inc.     

Conventional NMA as a better standard for evaluating elastic network models

Normal mode analysis (NMA) is an important tool for studying protein dynamics. Because of the complexity of conventional NMA that uses an all‐atom model and a semi‐empirical force field, many simplified NMA models have been developed, some of which are known as elastic network models. The quality of these simplified NMA models was assessed mostly by evaluating their predictions against experimental B‐factors, and rarely by comparing them with the original NMA. In this work, we take the effort to create a publicly accessible dataset of proteins with their minimized structures, NMA modes, and mean‐square fluctuations. Then, for the first time, we evaluate the quality of individual normal modes of several widely used elastic network models by comparing them with the conventional NMA. Our results demonstrate that the conventional NMA presents a better and more complete evaluation measure of the quality of elastic network models. This realization should be very helpful in improving current or designing new, higher quality elastic network models. Moreover, using the conventional NMA as the standard of evaluation, a number of interesting and significant insights into the elastic network models are gained. Proteins 2015; 83:259–267. © 2014 Wiley Periodicals, Inc.     

Folding and stability of helical bundle proteins from coarse‐grained models

We develop a coarse‐grained model where solvent is considered implicitly, electrostatics are included as short‐range interactions, and side‐chains are coarse‐grained to a single bead. The model depends on three main parameters: hydrophobic, electrostatic, and side‐chain hydrogen bond strength. The parameters are determined by considering three level of approximations and characterizing the folding for three selected proteins (training set). Nine additional proteins (containing up to 126 residues) as well as mutated versions (test set) are folded with the given parameters. In all folding simulations, the initial state is a random coil configuration. Besides the native state, some proteins fold into an additional state differing in the topology (structure of the helical bundle). We discuss the stability of the native states, and compare the dynamics of our model to all atom molecular dynamics simulations as well as some general properties on the interactions governing folding dynamics. Proteins 2013; 81:1200–1211. © 2013 Wiley Periodicals, Inc.     

Probing the structural dynamics of the SNARE recycling machine based on coarse‐grained modeling

Membrane fusion in eukaryotes is driven by the formation of a four‐helix bundle by three SNARE proteins. To recycle the SNARE proteins, they must be disassembled by the ATPase NSF and four SNAP proteins which together form a 20S supercomplex. Recently, the first high‐resolution structures of the NSF (in both ATP and ADP state) and 20S (in four distinct states termed I, II, IIIa, and IIIb) were solved by cryo‐electron microscopy (cryo‐EM), which have paved the way for structure‐driven studies of the SNARE recycling mechanism. To probe the structural dynamics of SNARE disassembly at amino‐acid level of details, a systematic coarse‐grained modeling based on an elastic network model and related analyses were performed. Our normal mode analysis of NSF, SNARE, and 20S predicted key modes of collective motions that partially account for the observed structural changes, and illuminated how the SNARE complex can be effectively destabilized by untwisting and bending motions of the SNARE complex driven by the amino‐terminal domains of NSF in state II. Our flexibility analysis identified regions with high/low flexibility that coincide with key functional sites (such as the NSF‐SNAPs‐SNARE binding sites). A subset of hotspot residues that control the above collective motions, which will make promising targets for future mutagenesis studies were also identified. Finally, the conformational changes in 20S as induced by the transition of NSF from ATP to ADP state were modeled, and a concerted untwisting motion of SNARE/SNAPs and a sideway flip of two amino‐terminal domains were observed. In sum, the findings have offered new structural and dynamic details relevant to the SNARE disassembly mechanism, and will guide future functional studies of the SNARE recycling machinery. Proteins 2016; 84:1055–1066. © 2016 Wiley Periodicals, Inc.     

Protein folding pathways and state transitions described by classical equations of motion of an elastic network model

Protein topology defined by the matrix of residue contacts has proved to be a fruitful basis for the study of protein dynamics. The widely implemented coarse-grained elastic network model of backbone fluctuations has been used to describe crystallographic temperature factors, allosteric couplings, and some aspects of the folding pathway. In the present study, we develop a model of protein dynamics based on the classical equations of motion of a damped network model (DNM) that describes the folding path from a completely unfolded state to the native conformation through a single-well potential derived purely from the native conformation. The kinetic energy gained through the collapse of the protein chain is dissipated through a friction term in the equations of motion that models the water bath. This approach is completely general and sufficiently fast that it can be applied to large proteins. Folding pathways for various proteins of different classes are described and shown to correlate with experimental observations and molecular dynamics and Monte Carlo simulations. Allosteric transitions between alternative protein structures are also modeled within the DNM through an asymmetric double-well potential.     

A mass weighted chemical elastic network model elucidates closed form domain motions in proteins

An elastic network model (ENM), usually Cα coarse‐grained one, has been widely used to study protein dynamics as an alternative to classical molecular dynamics simulation. This simple approach dramatically saves the computational cost, but sometimes fails to describe a feasible conformational change due to unrealistically excessive spring connections. To overcome this limitation, we propose a mass‐weighted chemical elastic network model (MWCENM) in which the total mass of each residue is assumed to be concentrated on the representative alpha carbon atom and various stiffness values are precisely assigned according to the types of chemical interactions. We test MWCENM on several well‐known proteins of which both closed and open conformations are available as well as three α‐helix rich proteins. Their normal mode analysis reveals that MWCENM not only generates more plausible conformational changes, especially for closed forms of proteins, but also preserves protein secondary structures thus distinguishing MWCENM from traditional ENMs. In addition, MWCENM also reduces computational burden by using a more sparse stiffness matrix.     

Investigating the structural dynamics of the PIEZO1 channel activation and inactivation by coarse‐grained modeling

The PIEZO channels, a family of mechanosensitive channels in vertebrates, feature a fast activation by mechanical stimuli (eg, membrane tension) followed by a slower inactivation. Although a medium‐resolution structure of the trimeric form of PIEZO1 was solved by cryo‐electron microscopy (cryo‐EM), key structural changes responsible for the channel activation and inactivation are still unknown. Toward decrypting the structural mechanism of the PIEZO1 activation and inactivation, we performed systematic coarse‐grained modeling using an elastic network model and related modeling/analysis tools (ie, normal mode analysis, flexibility and hotspot analysis, correlation analysis, and cryo‐EM‐based hybrid modeling and flexible fitting). We identified four key motional modes that may drive the tension‐induced activation and inactivation, with fast and slow relaxation time, respectively. These modes allosterically couple the lateral and vertical motions of the peripheral domains to the opening and closing of the intra‐cellular vestibule, enabling external mechanical forces to trigger, and regulate the activation/inactivation transitions. We also calculated domain‐specific flexibility profiles, and predicted hotspot residues at key domain‐domain interfaces and hinges. Our results offer unprecedented structural and dynamic information, which is consistent with the literature on mutational and functional studies of the PIEZO channels, and will guide future studies of this important family of mechanosensitive channels.     

De novo inference of protein function from coarse‐grained dynamics

Inference of molecular function of proteins is the fundamental task in the quest for understanding cellular processes. The task is getting increasingly difficult with thousands of new proteins discovered each day. The difficulty arises primarily due to lack of high‐throughput experimental technique for assessing protein molecular function, a lacunae that computational approaches are trying hard to fill. The latter too faces a major bottleneck in absence of clear evidence based on evolutionary information. Here we propose a de novo approach to annotate protein molecular function through structural dynamics match for a pair of segments from two dissimilar proteins, which may share even <10% sequence identity. To screen these matches, corresponding 1 µs coarse‐grained (CG) molecular dynamics trajectories were used to compute normalized root‐mean‐square‐fluctuation graphs and select mobile segments, which were, thereafter, matched for all pairs using unweighted three‐dimensional autocorrelation vectors. Our in‐house custom‐built forcefield (FF), extensively validated against dynamics information obtained from experimental nuclear magnetic resonance data, was specifically used to generate the CG dynamics trajectories. The test for correspondence of dynamics‐signature of protein segments and function revealed 87% true positive rate and 93.5% true negative rate, on a dataset of 60 experimentally validated proteins, including moonlighting proteins and those with novel functional motifs. A random test against 315 unique fold/function proteins for a negative test gave >99% true recall. A blind prediction on a novel protein appears consistent with additional evidences retrieved therein. This is the first proof‐of‐principle of generalized use of structural dynamics for inferring protein molecular function leveraging our custom‐made CG FF, useful to all. Proteins 2014; 82:2443–2454. © 2014 Wiley Periodicals, Inc.     

Toward decrypting the allosteric mechanism of the ryanodine receptor based on coarse‐grained structural and dynamic modeling

The ryanodine receptors (RyRs) are a family of calcium (Ca) channels that regulate Ca release by undergoing a closed‐to‐open gating transition in response to action potential or Ca binding. The allosteric mechanism of RyRs gating, which is activated/regulated by ligand/protein binding >200 Å away from the channel gate, remains elusive for the lack of high‐resolution structures. Recent solution of the closed‐form structures of the RyR1 isoform by cryo‐electron microscopy has paved the way for detailed structure‐driven studies of RyRs functions. Toward elucidating the allosteric mechanism of RyRs gating, we performed coarse‐grained modeling based on the newly solved closed‐form structures of RyR1. Our normal mode analysis captured a key mode of collective motions dominating the observed structural variations in RyR1, which features large outward and downward movements of the peripheral domains with the channel remaining closed, and involves hotspot residues that overlap well with key functional sites and disease mutations. In particular, we found a key interaction between a peripheral domain and the Ca‐binding EF hand domain, which may allow for direct coupling of Ca binding to the collective motions as captured by the above mode. This key mode was robustly reproduced by the normal mode analysis of the other two closed‐form structures of RyR1 solved independently. To elucidate the closed‐to‐open conformational changes in RyR1 with amino‐acid level of details, we flexibly fitted the closed‐form structures of RyR1 into a 10‐Å cryo‐electron microscopy map of the open state. We observed extensive structural changes involving the peripheral domains and the central domains, resulting in the channel pore opening. In sum, our findings have offered unprecedented structural and dynamic insights to the allosteric mechanism of RyR1 via modulation of the key collective motions involved in RyR1 gating. The predicted hotspot residues and open‐form conformation of RyR1 will guide future mutational and functional studies. Proteins 2015; 83:2307–2318. © 2015 Wiley Periodicals, Inc.     

Validating and improving elastic network models with molecular dynamics simulations

Elastic network models (ENMs) are a class of simple models intended to represent the collective motions of proteins. In contrast to all‐atom molecular dynamics simulations, the low computational investment required to use an ENM makes them ideal for speculative hypothesis‐testing situations. Historically, ENMs have been validated via comparison to crystallographic B‐factors, but this comparison is relatively low‐resolution and only tests the predictions of relative flexibility. In this work, we systematically validate and optimize a number of ENM‐type models by quantitatively comparing their predictions to microsecond‐scale all‐atom simulations of three different G protein coupled receptors. We show that, despite their apparent simplicity, well‐optimized ENMs perform remarkably well, reproducing the protein fluctuations with an accuracy comparable to what one would expect from all‐atom simulations run for several hundred nanoseconds. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Coarse‐grained and all‐atom modeling of structural states and transitions in hemoglobin

Hemoglobin (Hb), an oxygen‐binding protein composed of four subunits (α1, α2, β1, and β2), is a well‐known example of allosteric proteins that are capable of cooperative ligand binding. Despite decades of studies, the structural basis of its cooperativity remains controversial. In this study, we have integrated coarse‐grained (CG) modeling, all‐atom simulation, and structural data from X‐ray crystallography and wide‐angle X‐ray scattering (WAXS), aiming to probe dynamic properties of the two structural states of Hb (T and R state) and the transitions between them. First, by analyzing the WAXS data of unliganded and liganded Hb, we have found that the structural ensemble of T or R state is dominated by one crystal structure of Hb with small contributions from other crystal structures of Hb. Second, we have used normal mode analysis to identify two distinct quaternary rotations between the α1β1 and α2β2 dimer, which drive the transitions between T and R state. We have also identified the hot‐spot residues whose mutations are predicted to greatly change these quaternary motions. Third, we have generated a CG transition pathway between T and R state, which predicts a clear order of quaternary and tertiary changes involving α and β subunits in Hb. Fourth, we have used the accelerated molecular dynamics to perform an all‐atom simulation starting from the T state of Hb, and we have observed a transition toward the R state of Hb. Further analysis of crystal structural data and the all‐atom simulation trajectory has corroborated the order of quaternary and tertiary changes predicted by CG modeling. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Exploration of conformational changes in lactose permease upon sugar binding and proton transfer through coarse‐grained simulations

Escherichia coli lactose permease (LacY) actively transports lactose and other galactosides across cell membranes through lactose/H⁺ symport process. Lactose/H⁺ symport is a highly complex process that involves sugar translocation, H⁺ transfer, and large‐scale protein conformational changes. The complete picture of lactose/H⁺ symport is largely unclear due to the complexity and multiscale nature of the process. In this work, we develop the force field for sugar molecules compatible with PACE, a hybrid and coarse‐grained force field that couples the united‐atom protein models with the coarse‐grained MARTINI water/lipid. After validation, we implement the new force field to investigate the binding of a ‐d ‐galactopyranosyl‐1‐thio‐ ‐d ‐galactopyranoside (TDG) molecule to a wild‐type LacY. Results show that the local interactions between TDG and LacY at the binding pocket are consistent with the X‐ray experiment. Transitions from inward‐facing to outward‐facing conformations upon TDG binding and protonation of Glu269 have been achieved from ～5.5 µs simulations. Both the opening of the periplasmic side and closure of the cytoplasmic side of LacY are consistent with double electron–electron resonance and thiol cross‐linking experiments. Our analysis suggests that the conformational changes of LacY are a cumulative consequence of interdomain H‐bonds breaking at the periplasmic side, interdomain salt‐bridge formation at the cytoplasmic side, and the TDG orientational changes during the transition.     

Large‐scale comparison of protein essential dynamics from molecular dynamics simulations and coarse‐grained normal mode analyses

A large‐scale comparison of essential dynamics (ED) modes from molecular dynamic simulations and normal modes from coarse‐grained normal mode methods (CGNM) was performed on a dataset of 335 proteins. As CGNM methods, the elastic network model (ENM) and the rigid cluster normal mode analysis (RCNMA) were used. Low‐frequency normal modes from ENM correlate very well with ED modes in terms of directions of motions and relative amplitudes of motions. Notably, a similar performance was found if normal modes from RCNMA were used, despite a higher level of coarse graining. On average, the space spanned by the first quarter of ENM modes describes 84% of the space spanned by the five ED modes. Furthermore, no prominent differences for ED and CGNM modes among different protein structure classes (CATH classification) were found. This demonstrates the general potential of CGNM approaches for describing intrinsic motions of proteins with little computational cost. For selected cases, CGNM modes were found to be more robust among proteins that have the same topology or are of the same homologous superfamily than ED modes. In view of recent evidence regarding evolutionary conservation of vibrational dynamics, this suggests that ED modes, in some cases, might not be representative of the underlying dynamics that are characteristic of a whole family, probably due to insufficient sampling of some of the family members by MD. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Bridging between normal mode analysis and elastic network models

Normal mode analysis (NMA) has been a powerful tool for studying protein dynamics. Elastic network models (ENM), through their simplicity, have made normal mode computations accessible to a much broader research community and for many more biomolecular systems. The drawback of ENMs, however, is that they are less accurate than NMA. In this work, through steps of simplification that starts with NMA and ends with ENMs we build a tight connection between NMA and ENMs. In the process of bridging between the two, we have also discovered several high‐quality simplified models. Our best simplified model has a mean correlation with the original NMA that is as high as 0.88. In addition, the model is force‐field independent and does not require energy minimization, and thus can be applied directly to experimental structures. Another benefit of drawing the connection is a clearer understanding why ENMs work well and how it can be further improved. We discovered that can be greatly enhanced by including an additional torsional term and a geometry term. Proteins 2014; 82:2157–2168. © 2014 Wiley Periodicals, Inc.