JSM Enzymology and Protein Science

Review: Elastic Network Model for Protein Structural Dynamics

Review Article | Open Access | Volume 1 | Issue 1

  • 1. SKKU Advanced Institute of Nanotechnology (SAINT), Sungkyunkwan University, South Korea
  • 2. School of Mechanical Engineering, Sungkyunkwan University, South Korea
+ Show More - Show Less
Corresponding Authors
Moon Ki Kim, SKKU Advanced Institute of Nanotechnology (SAINT), Sungkyunkwan University, Suwon 440-746, South Korea

Proteins and their complexes undergo conformational changes, which are closely related to their unique biological functions. However, it is of great challenge for both theoretical and experimental studies to resolve the protein conformational changes due to the limitations regarding the time scale, data size and computational cost. In recent years, normal mode analysis based on coarse-grained elastic network model has been proven to be suitable for the study of the collective vibration motions in macromolecules. Based on the topology of native contacts, this coarse-grained analysis can provide the global motions effectively, thus getting insights into the mechanical aspects of proteins dynamics. In this short review, the basic theory and fundamental features of elastic network models are introduced and a wide variety of examples and applications are then discussed.


Kim MH, Kim MK (2015) Review: Elastic Network Model for Protein Structural Dynamics. JSM Enzymol Protein Sci 1(1): 1001.


 Elastic network model; Normal mode analysis;  Protein dynamics


ENM: Elastic Network Model; NMA: Normal Mode Analysis; MD: Molecular Dynamics; NMR: Nuclear Magnetic Resonance; CG: Coarse-Grained; ANM: Anisotropic Network Model; MWCENM: Mass-Weighted Chemical Elastic Network Model; MWC: MonodWyman-Changeux; NMFF: Normal Mode Flexible Fitting; EM: Electron Microscopy; ENI: Elastic Network Interpolation; PNM: Plastic Network Model; AK: Adenylate Kinase; HENM: Hybrid Elastic Network Model.


In the last several decades, more than 90,000 macromolecules structures have been revealed according to the great development in biological experiments [1]. Based on these three dimensional structures, macromolecules perform various functions such as catalysis [2,3], regulation [4-6], transport [7], ligand binding [8,9], and so on. Since the relationship between molecular structure and its function is tightly involved with conformational change [10,11], several experimental and computational methods have been evolved in this field [12-16]. However, the experimental methods undergo the difficulty in direct observation of protein motions [17]. The nuclear magnetic resonance (NMR) spectroscopy is usually used to determine both the statics and dynamics of protein, but it is limited on the size of protein and also has difficulty in discrimination of fast and slow diffusion [12]. In addition, single-molecule FRET experiment is usually insufficient to completely define the conformational change with low resolution [16]. Overall, such direct experimental methods including mass spectrometry with hydrogen/deuterium exchange and single-molecule experiments using optical trapping still are not enough to reveal protein dynamics in atomic detail. As an alternative, simulations could potentially fill in some of the details [14]. Molecular dynamics (MD) simulation, based on solving the Newton’s equations of motion and getting the timedependent behaviors of proteins, is one of the most representative computational tools utilized to understand protein motions at atomic level [18,19]. Even though MD simulation has become more accurate enough to explain and predict experiment results, standard all-atom MD simulation with transferable force fields is still limited to the prediction of only an early event due to its computational burden [20]. In order to reduce the computational cost, various coarse-grained (CG) methods have been proposed by using much simplified description of potential and structure [21]. Among these CG methods, the elastic network model (ENM) with a single parameter harmonic potential has been widely used for studying global dynamics of proteins [22,23]. In this short review, we give a brief summary of ENM. An overview of the theoretical foundation and the basic features of ENMs are presented, focusing on the anisotropic network model (ANM) [24-26], and then the extensive applications of ENM are followed.

Elastic network model theory

In 1996, Tirion[22] suggested that a quadratic potential with a uniform constant for all atomic interactions would be sufficient to describe low-frequency collective motions of macromolecules. The corresponding potential is as follows:


where Ri j , , 0 Ri j , are the instantaneous and equilibrium difference between i th and j th atom, respectively, and i j , k is a spring constant between them, which equals to 1 if Ri j , is within a cutoff distance and zero otherwise. At first, Bahar and Jernigan suggested 7Å as the reliable distance cutoff value in their Guassian network model (GNM), from which one could predict the accurate B-factors compared to the experimental ones [23,27-28]. Zheng empirically proposed that the adequate cutoff distance for optimal description in ANM is 8Å [29]. However, a distance cutoff of less than 10Å could generate the mathematically unstable results in normal mode analysis (NMA) having more than six zero eigen values, which physically senses that the ENM is too sparsely modelled so that a single collective system unrealistically moves like several independent pieces. In order to overcome this problem, Jeong and his coworker [30] proposed the bond-cutoff method which determines the spring constants corresponding to the chemical interactions. This method cannot only reduce computational burden, but also generate plausible conformational changes, especially for opening motion [31]. As an example, (Figure 1)

Figure 1 Elastic network representations of for the periplasmic lysine-, arginine-, ornithine-binding protein (PDB ID: 2LAO). (a) Ribbons diagram  of target protein colored depending on secondary structures. (b) Elastic network connections between the C-alpha atoms (orange sphere). The  interactions within the cutoff distance of 11Å are illustrated as blue solid lines. (c) Example of the MWCENM. Various chemical interactions are  represented by different colored lines. Black, green, cyan, yellow, and blue lines indicate backbone, hydrogen bonds, ionic bonds, disulfide bonds,  and van der Waals interactions, respectively.

Figure 1: Elastic network representations of for the periplasmic lysine-, arginine-, ornithine-binding protein (PDB ID: 2LAO). (a) Ribbons diagram of target protein colored depending on secondary structures. (b) Elastic network connections between the C-alpha atoms (orange sphere). The interactions within the cutoff distance of 11Å are illustrated as blue solid lines. (c) Example of the MWCENM. Various chemical interactions are represented by different colored lines. Black, green, cyan, yellow, and blue lines indicate backbone, hydrogen bonds, ionic bonds, disulfide bonds, and van der Waals interactions, respectively.

shows the procedure of ENM of a protein. Once ENM is constructed, the vibrational characteristics of a target protein can be investigated by NMA [32-34]. The equation of motion is derived from the Lagrangian mechanics such that


where L = T-V. T and Vare the general kinetic energy and potential energy, respectively. δ i is the i th component of displacement vector. Substitution of these two energy terms into Eq. (1.2) yields the following equation of motion (EOM).


Where M is the global inertia matrix consisting of subdiagonal 3 by 3 matrices, Mi j , , which represent the specific mass values of each representative atom and K is the global stiffness matrix having sub-stiffness matrices, Ki j , such that



MERGEFORMAT (1.4) The full mathematical derivation of EOM is available in Ref. [35] In order to get more precise analysis, Kim et al. recently proposed a mass-weighted chemical ENM (WMCENM) that includes not only the chemical interaction but also total masses of each residue according to types of residue [31]. Substitution of δ by −1/2 M v in Eq. (1.3) yields the mass-weighted stiffness matrix as follows:



Once NMA is performed with respect to the transformed vector v in Eq. (1.5), the eigenvector set would be inversely transformed into δ by multiplication of −1/2 M . In this eigen problem, eigen values and eigenvectors of the target protein represent vibration frequencies and corresponding vibration mode shapes, respectively [36]. By combining several lowest modes, one could represent functionally collective motions of the given protein.

Applications of elastic network models

The most attractive feature of ENM is its simplicity and robustness. Despite reduced structural information of coarsegrained masses simply connected by harmonic springs, the combination of conventional normal modes forms an ortho normal basis set. Interestingly, global dynamics involving the collective motion could be represented through these several lowest frequency modes within the normal mode spectrum, thus dynamics behaviors of large systems such as ribosome [37] and virus capsids [38,39] that are hardly accessible by MD simulations could be elucidated by coarse-grained ENM with the advantage of computational efficiency. ENM based dynamics studies can provide the comprehensive description of functional motions in proteins, which is also consistent with experimental results. For example, Wang studied the functional motion of ribosome complex using the ENM [37]. The high correlation of motion between A-tRNA and P-tRNA indicates that their translocations would occur simultaneously. On the other hands, E-tRNA shows the weak correlation with other two tRNAs, which represents the independent exiting motion from E-site. In short, the comparison of several the lowest modes at each subunit provided the insight of the translocation mechanism in the ribosome. From these studies including other large protein cases, the beauty of ENM-based NMA is that lowest frequency modes involving the collective motions are sensitive only to structural (i.e. geometric) information, not chemical properties of proteins [40]. Therefore, ENM based NMA can be widely used for analyzing many biological problems.

As shown in (Figure 2),

Figure 2 Schematic models of protein-ligand binding. (a) Lock and key model. Since both ligand and protein structures are complementary, they  fit together as a lock and a key. (b) Induced fit model. When a protein binds to a ligand, conformational change occurs, leading to the additional  interaction with the ligand. (c) Pre-existing equilibrium model called MWC. Prior to the ligand-protein binding, the conformational flexibility of the  protein could yield different binding-sites for various ligands

Figure 2: Schematic models of protein-ligand binding. (a) Lock and key model. Since both ligand and protein structures are complementary, they fit together as a lock and a key. (b) Induced fit model. When a protein binds to a ligand, conformational change occurs, leading to the additional interaction with the ligand. (c) Pre-existing equilibrium model called MWC. Prior to the ligand-protein binding, the conformational flexibility of the protein could yield different binding-sites for various ligands

one of representative studies based on ENM is a molecular docking (ligand to protein and protein to protein) simulation [41-49]. For instance, Tobi and Bahar have showed that structural changes caused by relevant ligand binding are strongly correlated with intrinsic motions of proteins in their unbound state [48]. This work confirms, in selecting/ rearranging complex formation, the roles of a preexisting equilibrium called Monod-Wyman-Changeux model (MWC). Keskin recently enlarged this hypothesis into the enzymes and antibodies case [44]. Regardless of classes of proteins, the set of the lowest normal modes, although different combination with or without ligand, could cover the limited range of conformational states which are adequate for the structural change inbinding occurrence. The simulation results showed that an ensemble of similar conformations driven by intrinsic motions of native state could bind to different antigens or ligand. Despite MWC model leads to the more complicated complex combination than other two models (i.e. rigid adaptation and induced fit model), ENM could be utilized to restrict the number of candidates for molecular docking.

Another interesting application of ENM is the refinement of low-resolution structural data using the lowest-frequency normal modes [38,50-53]. Tama et al. have proposed the normal mode flexible fitting (NMFF) where the flexible fitting of highresolution structures into the low-resolution cryo-electron microscopy (cryo-EM) data is performed by deforming the structure along a few low-frequency normal modes [50,51]. This method enables us to build the feasible atomic structure and determines the most important mode for its functional motion. The similar methodology using a set of the lowest normal modes for refinement in low resolution of X-ray crystallography has been successively performed [54]. In order to improve the quality of low-frequency modes and remove the tip effect, a quite small set of collective variables were used as refinement parameter [55]. By focusing one assumption of harmonicity of protein motions in X-ray crystallography, the proposed refinement protocol results in improvements of the resolution, especially in case of large and mobile complexes at moderate resolutions [54]. Indeed, structure refinement based on ENM and NMA not only replaces the traditional homology modeling method based on sequence comparison to template, but also steps forward to the abundant practical needs such as drug designs [56].

Figure 3 Summary of various ENMs and their applications (courtesy of Ref [72])

Figure 3: Summary of various ENMs and their applications (courtesy of Ref [72])

ENM is also used for investigating the transition pathway [35, 55-59]. In case that molecular transition is accompanied by large structural change, a harmonic model presumably fails to describe it. Instead, a different class of an harmonic structure-based model called Go model has been widely used for this purpose [60]. Alternatively, an ENM-based pathway generation method called elastic network interpolation (ENI) has been introduced [35,59]. The intermediate conformations are generated by interpolating two corresponding sets of interatomic distances. This ENI overcomes the limitation of ENM-based NMA which only utilizes a harmonic potential, thus cannot describe the conformational change crossing over the energy barrier. It is also expected that ENI can be utilized as a refinement method by filling the incomplete information obtained from NMR experiment [63]. Moreover, the proposed transition pathway of ENI can act like an ensemble of MD data by capturing most of them with a span of a few lowest normal modes of each intermediate conformation [64].

The further researches have been introduced based on the free energy surface. Maragakis and karplus [65] proposed the plastic network model (PNM) in which the pathway of adenylate kinase (AK) is generated based on free energy surface. Also, the similar but more improved approach, mixed-ENM, has been proposed by solving the double-well potential function [66].

For convenience, several web servers are now available to calculate and visualize NMA results of various proteins. In ANM [25] and oGNM [67], one can similarly select either C-alpha only or all-atoms for ENM. In order to reduce the computational cost, NOMAD-Ref [68] and ElNemo [69] use the building block approximation which groups several residues into a single block. This grouping method is less effective on observation of lowest-frequency modes, but could save substantial amount of computing time. However, these coarse-graining methods would fail to address the atomic details of protein motions unless any other consideration of the rigidity of protein is provided. To overcome this limitation, cluster-NMA [70] and hybrid ENM [71] have been introduced, in which user can adjust the degrees of coarse-graining level from single atom to rigid cluster, regardless of the number of atoms that belong to a rigid cluster. More details on the complexity of various ENMs can be found elsewhere [72].

Most recently, KOSMOS has been launchedby integrating various ENM-based dynamics analysis methods including both NMA and ENI [73]. This fully automated web server cannot only provide various coarse-grained ENMs from all-atom model to rigid-cluster model, but also offer chemical information based cutoff method for better simulation accuracy.


ENM-based simulation methods have shown great success in understanding of biological functions of macromolecules based on their structural information. The fundamental philosophy of ENM is that the topological features play a dominant role in defining the global and collective motions of proteins. Hence, coarse-grained ENMs have been widely used to solve a variety of biological problems including functional motions of protein complexes, ligand binding mechanism, refinement of low resolution structural data, and transition pathway generation. Despite ENM sometimes shows the limitation owing to its modest coarse-graining [74], this robust simulation model enables us to better understand structural dynamics of target proteins at various levels.


This research was supported by the Basic Science Research Program (2011-0014584) and Pioneer Research Center Program (2012-0009579) through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology.


1. Berman HM, Westbrook J, Feng Z, Gilliland G, Bhat TN, Weissig H, et al. The Protein Data Bank. Nucleic Acids Res. 2000; 28: 235-242.

2. Hammes GG. Multiple conformational changes in enzyme catalysis. Biochemistry. 2002; 41: 8221-8228.

3. Benkovic SJ, Hammes-Schiffer S. A perspective on enzyme catalysis. Science. 2003; 301: 1196-1202.

4. Huse M, Kuriyan J. The conformational plasticity of protein kinases. Cell. 2002; 109: 275-282.

5. Doyle DA. Structural changes during ion channel gating. Trends Neurosci. 2004; 27: 298-302.

6. Swartz KJ. Towards a structural view of gating in potassium channels. Nat Rev Neurosci. 2004; 5: 905-916.

7. Quiocho FA, Ledvina PS. Atomic structure and specificity of bacterial periplasmic receptors for active transport and chemotaxis: variation of common themes. Mol Microbiol. 1996; 20: 17-25.

8. Wlodawer A, Vondrasek J. Inhibitors of HIV-1 protease: a major success of structure-assisted drug design. Annu Rev Biophys Biomol Struct. 1998; 27: 249-284.

9. Schlauderer GJ, Schulz GE. The structure of bovine mitochondrial adenylate kinase: comparison with isoenzymes in other compartments. Protein Sci. 1996; 5: 434-441.

10. Bahar I, Lezon TR, Yang LW, Eyal E. Global dynamics of proteins: bridging between structure and function. Annu Rev Biophys. 2010; 39: 23-42.

11. Karplus M, McCammon JA. Dynamics of proteins: elements and function. Annu Rev Biochem. 1983; 52: 263-300.

12. Palmer AG 3rd, Kroenke CD, Loria JP. Nuclear magnetic resonance methods for quantifying microsecond-to-millisecond motions in biological macromolecules. Methods Enzymol. 2001; 339: 204-238.

13. Lanman J, Prevelige PE Jr. High-sensitivity mass spectrometry for imaging subunit interactions: hydrogen/deuterium exchange. Curr Opin Struct Biol. 2004; 14: 181-188.

14. Karplus M, Kuriyan J. Molecular dynamics and protein function. Proc Natl Acad Sci U S A. 2005; 102: 6679-6685.

15. Lindorff-Larsen K, Best RB, Depristo MA, Dobson CM, Vendruscolo M. Simultaneous determination of protein structure and dynamics. Nature. 2005; 433: 128-132.

16. Abbondanzieri EA, Greenleaf WJ, Shaevitz JW, Landick R, Block SM. Direct observation of base-pair stepping by RNA polymerase. Nature. 2005; 438: 460-465.

17. Kondrashov DA, Cui Q, Phillips GN Jr. Optimization and evaluation of a coarse-grained model of protein motion using x-ray crystal data. Biophys J. 2006; 91: 2760-2767.

18. Levitt M. Molecular dynamics of native protein. II. Analysis and nature of motion. J Mol Biol. 1983; 168: 621-657.

19. Levitt M. Molecular dynamics of native protein. I. Computer simulation of trajectories. J Mol Biol. 1983; 168: 595-617.

20. Shaw DE, Maragakis P, Lindorff-Larsen K, Piana S, Dror RO, Eastwood MP, et al. Atomic-level characterization of the structural dynamics of proteins. Science. 2010; 330: 341-346.

21. Tozzini V. Coarse-grained models for proteins. Curr Opin Struct Biol. 2005; 15: 144-150.

22. Tirion MM. Large Amplitude Elastic Motions in Proteins from a Single-Parameter, Atomic Analysis. Phys Rev Lett. 1996; 77: 1905-1908.

23. Bahar I, Atilgan AR, Erman B. Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential. Fold Des. 1997; 2: 173-181.

24. Atilgan AR, Durell SR, Jernigan RL, Demirel MC, Keskin O, Bahar I. Anisotropy of fluctuation dynamics of proteins with an elastic network model. Biophys J. 2001; 80: 505-515.

25. Eyal E, Yang LW, Bahar I. Anisotropic network model: systematic evaluation and a new web interface. Bioinformatics. 2006; 22: 2619- 2627.

26. Tama F, Sanejouand YH. Conformational change of proteins arising from normal mode calculations. Protein Eng. 2001; 14: 1-6.

27. Haliloglu T, Bahar I, and Erman B. Gaussian dynamics of folded proteins. Phys Rev Lett. 1997; 79: 3090-3093.

28. Bahar I, Jernigan RL. Inter-residue potentials in globular proteins and the dominance of highly specific hydrophilic interactions at close separation. J Mol Biol. 1997; 266: 195-214.

29. Zheng W. A unification of the elastic network model and the Gaussian network model for optimal description of protein conformational motions and fluctuations. Biophys J. 2008; 94: 3853-3857.

30. Jeong JI, Jang Y, Kim MK. A connection rule for alpha-carbon coarse-grained elastic network models using chemical bond information. J Mol Graph Model. 2006; 24: 296-306.

31. Kim MH, Seo S, Jeong JI, Kim BJ, Liu WK, Lim BS, et al. A mass weighted chemical elastic network model elucidates closed form domain motions in proteins. Protein Sci. 2013; 22: 605-613.

32. Brooks B, Karplus M. Harmonic dynamics of proteins: normal modes and fluctuations in bovine pancreatic trypsin inhibitor. Proc Natl Acad Sci U S A. 1983; 80: 6571-6575.

33. Go N, Noguti T, Nishikawa T. Dynamics of a small globular protein in terms of low-frequency vibrational modes. Proc Natl Acad Sci U S A. 1983; 80: 3696-3700.

34. Levitt M, Sander C, Stern PS. Protein normal-mode dynamics: trypsin inhibitor, crambin, ribonuclease and lysozyme. J Mol Biol. 1985; 181: 423-447.

35. Kim MK, Chirikjian GS, Jernigan RL. Elastic models of conformational transitions in macromolecules. J Mol Graph Model. 2002; 21: 151-160.

36. Hinsen K. Analysis of domain motions by approximate normal mode calculations. Proteins. 1998; 33: 417-429. 

37. Wang Y, Rader AJ, Bahar I, Jernigan RL. Global ribosome motions revealed with elastic network model. J Struct Biol. 2004; 147: 302- 314.

38. Tama F, Brooks CL 3rd. Diversity and identity of mechanical properties of icosahedral viral capsids studied with elastic network normal mode analysis. J Mol Biol. 2005; 345: 299-314.

39. Rader AJ, Vlad DH, Bahar I. Maturation dynamics of bacteriophage HK97 capsid. Structure. 2005; 13: 413-421.

40. Petrone P, Pande VS. Can conformational change be described by only a few normal modes? Biophys J. 2006; 90: 1583-1593.

41. Lindahl E, Delarue M. Refinement of docked protein-ligand and protein-DNA structures using low frequency normal mode amplitude optimization. Nucleic Acids Res. 2005; 33: 4496-4506.

42. Ming D, Wall ME. Quantifying allosteric effects in proteins. Proteins. 2005; 59: 697-707.

43. Yang LW, Bahar I. Coupling between catalytic site and collective dynamics: a requirement for mechanochemical activity of enzymes. Structure. 2005; 13: 893-904.

44. Keskin O. Binding induced conformational changes of proteins correlate with their intrinsic fluctuations: a case study of antibodies. BMC Struct Biol. 2007; 7: 31.

45. Zheng W, Liao JC, Brooks BR, Doniach S. Toward the mechanism of dynamical couplings and translocation in hepatitis C virus NS3 helicase using elastic network model. Proteins. 2007; 67: 886-896.

46. Akten ED, Cansu S, Doruker P. A docking study using atomistic conformers generated via elastic network model for cyclosporin A/ cyclophilin A complex. J Biomol Struct Dyn. 2009; 27: 13-26.

47. Fiorucci S, Zacharias M. Binding site prediction and improved scoring during flexible protein-protein docking with ATTRACT. Proteins. 2010; 78: 3131-3139.

48. Tobi D, Bahar I. Structural changes involved in protein binding correlate with intrinsic motions of proteins in the unbound state. Proc Natl Acad Sci U S A. 2005; 102: 18908-18913.

49. Koshland DE Jr, Némethy G, Filmer D. Comparison of experimental binding data and theoretical models in proteins containing subunits. Biochemistry. 1966; 5: 365-385.

50. Tama F, Valle M, Frank J, Brooks CL 3rd. Dynamic reorganization of the functionally active ribosome explored by normal mode analysis and cryo-electron microscopy. Proc Natl Acad Sci U S A. 2003; 100: 9319-9323.

51. Tama F, Miyashita O, Brooks CL 3rd. Normal mode based flexible fitting of high-resolution structure into low-resolution experimental data from cryo-EM. J Struct Biol. 2004; 147: 315-326.

52. Hinsen K, Reuter N, Navaza J, Stokes DL, Lacapère JJ. Normal mode-based fitting of atomic structure into electron density maps: application to sarcoplasmic reticulum Ca-ATPase. Biophys J. 2005; 88: 818-827.

53. Tama F, Miyashita O, Brooks CL 3rd. Flexible multi-scale fitting of atomic structures into low-resolution electron density maps with elastic network normal mode analysis. J Mol Biol. 2004; 337: 985-999.

54. Poon BK, Chen X, Lu M, Vyas NK, Quiocho FA, Wang Q, et al. Normal mode refinement of anisotropic thermal parameters for a supramolecular complex at 3.42-A crystallographic resolution. Proc Natl Acad Sci U S A. 2007; 104: 7869-7874.

55. Lu M, Poon B, Ma J. A New Method for Coarse-Grained Elastic Normal-Mode Analysis. J Chem Theory Comput. 2006; 2: 464-471.

56. Cavasotto CN. Normal mode-based approaches in receptor ensemble docking. Methods Mol Biol. 2012; 819: 157-168.

57. Zheng W, Brooks BR. Modeling protein conformational changes by iterative fitting of distance constraints using reoriented normal modes. Biophys J. 2006; 90: 4327-4336.

58. Chu JW, Voth GA. Coarse-grained free energy functions for studying protein conformational changes: a double-well network model. Biophys J. 2007; 93: 3860-3871.

59. Franklin J, Koehl P, Doniach S, Delarue M. MinActionPath: maximum likelihood trajectory for large-scale structural transitions in a coarsegrained locally harmonic energy landscape. Nucleic Acids Res. 2007; 35: w477- w482.

60. Weiss DR, Levitt M. Can morphing methods predict intermediate structures? J Mol Biol. 2009; 385: 665-674.

61. Kim MK, Jernigan RL, Chirikjian GS. Efficient generation of feasible pathways for protein conformational transitions. Biophys J. 2002; 83: 1620-1630.

62. Taketomi H, Ueda Y, G? N. Studies on protein folding, unfolding and fluctuations by computer simulation. I. The effect of specific amino acid sequence represented by specific inter-unit interactions. Int J Pept Protein Res. 1975; 7: 445-59.

63. Kim MK. Elastic network models of biomolecular structure and dynamics. Dissertation, The Johns Hopkins University. 2004.

64. Kim MK, Li W, Shapiro BA, Chirikjian GS. A comparison between elastic network interpolation and MD simulation of 16S ribosomal RNA. J Biomol Struct Dyn. 2003; 21: 395-405.

65. Maragakis P, Karplus M. Large amplitude conformational change in proteins explored with a plastic network model: adenylate kinase. J Mol Biol. 2005; 352: 807-822.

66. Tekpinar M, Zheng W. Predicting order of conformational changes during protein conformational transitions using an interpolated elastic network model. Proteins. 2010; 78: 2469-2481.

67. Yang LW, Rader AJ, Liu X, Jursa CJ, Chen SC, Karimi HA, et al. oGNM: online computation of structural dynamics using the Gaussian Network Model. Nucleic Acids Res. 2006; 34: W24-31.

68. Lindahl E, Azuara C, Koehl P, Delarue M. NOMAD-Ref: visualization, deformation and refinement of macromolecular structures based on all-atom normal mode analysis. Nucleic Acids Res. 2006; 34: W52-56.

69. Suhre K, Sanejouand YH. ElNemo: a normal mode web server for protein movement analysis and the generation of templates for molecular replacement. Nucleic Acids Res. 2004; 32: W610-614.

70. Schuyler AD, Chirikjian GS. Efficient determination of low-frequency normal modes of large protein structures by cluster-NMA. J Mol Graph Model. 2005; 24: 46-58.

71. Kim MK, Jernigan RL, Chirikjian GS. Rigid-cluster models of conformational transitions in macromolecular machines and assemblies. Biophys J. 2005; 89: 43-55.

72. Kim MK, Jang Y, Jeong JI. Using harmonic analysis and optimization to study macromolecular dynamics. Int J Control Autom. 2006; 4: 382- 393.

73. Seo S, Kim MK. KOSMOS: a universal morph server for nucleic acids, proteins and their complexes. Nucleic Acids Res. 2012; 40: W531-536.

74. Yang L, Song G, Jernigan RL. How well can we understand large-scale protein motions using normal modes of elastic network models? Biophys J. 2007; 93: 920-929.

Kim MH, Kim MK (2015) Review: Elastic Network Model for Protein Structural Dynamics. JSM Enzymol Protein Sci 1(1): 1001

Received : 12 Jun 2014
Accepted : 07 Oct 2014
Published : 09 Oct 2014
Annals of Otolaryngology and Rhinology
ISSN : 2379-948X
Launched : 2014
JSM Schizophrenia
Launched : 2016
Journal of Nausea
Launched : 2020
JSM Internal Medicine
Launched : 2016
JSM Hepatitis
Launched : 2016
JSM Oro Facial Surgeries
ISSN : 2578-3211
Launched : 2016
Journal of Human Nutrition and Food Science
ISSN : 2333-6706
Launched : 2013
JSM Regenerative Medicine and Bioengineering
ISSN : 2379-0490
Launched : 2013
JSM Spine
ISSN : 2578-3181
Launched : 2016
Archives of Palliative Care
ISSN : 2573-1165
Launched : 2016
JSM Nutritional Disorders
ISSN : 2578-3203
Launched : 2017
Annals of Neurodegenerative Disorders
ISSN : 2476-2032
Launched : 2016
Journal of Fever
ISSN : 2641-7782
Launched : 2017
JSM Bone Marrow Research
ISSN : 2578-3351
Launched : 2016
JSM Mathematics and Statistics
ISSN : 2578-3173
Launched : 2014
Journal of Autoimmunity and Research
ISSN : 2573-1173
Launched : 2014
JSM Arthritis
ISSN : 2475-9155
Launched : 2016
JSM Head and Neck Cancer-Cases and Reviews
ISSN : 2573-1610
Launched : 2016
JSM General Surgery Cases and Images
ISSN : 2573-1564
Launched : 2016
JSM Anatomy and Physiology
ISSN : 2573-1262
Launched : 2016
JSM Dental Surgery
ISSN : 2573-1548
Launched : 2016
Annals of Emergency Surgery
ISSN : 2573-1017
Launched : 2016
Annals of Mens Health and Wellness
ISSN : 2641-7707
Launched : 2017
Journal of Preventive Medicine and Health Care
ISSN : 2576-0084
Launched : 2018
Journal of Chronic Diseases and Management
ISSN : 2573-1300
Launched : 2016
Annals of Vaccines and Immunization
ISSN : 2378-9379
Launched : 2014
JSM Heart Surgery Cases and Images
ISSN : 2578-3157
Launched : 2016
Annals of Reproductive Medicine and Treatment
ISSN : 2573-1092
Launched : 2016
JSM Brain Science
ISSN : 2573-1289
Launched : 2016
JSM Biomarkers
ISSN : 2578-3815
Launched : 2014
JSM Biology
ISSN : 2475-9392
Launched : 2016
Archives of Stem Cell and Research
ISSN : 2578-3580
Launched : 2014
Annals of Clinical and Medical Microbiology
ISSN : 2578-3629
Launched : 2014
JSM Pediatric Surgery
ISSN : 2578-3149
Launched : 2017
Journal of Memory Disorder and Rehabilitation
ISSN : 2578-319X
Launched : 2016
JSM Tropical Medicine and Research
ISSN : 2578-3165
Launched : 2016
JSM Head and Face Medicine
ISSN : 2578-3793
Launched : 2016
JSM Cardiothoracic Surgery
ISSN : 2573-1297
Launched : 2016
JSM Bone and Joint Diseases
ISSN : 2578-3351
Launched : 2017
JSM Bioavailability and Bioequivalence
ISSN : 2641-7812
Launched : 2017
JSM Atherosclerosis
ISSN : 2573-1270
Launched : 2016
Journal of Genitourinary Disorders
ISSN : 2641-7790
Launched : 2017
Journal of Fractures and Sprains
ISSN : 2578-3831
Launched : 2016
Journal of Autism and Epilepsy
ISSN : 2641-7774
Launched : 2016
Annals of Marine Biology and Research
ISSN : 2573-105X
Launched : 2014
JSM Health Education & Primary Health Care
ISSN : 2578-3777
Launched : 2016
JSM Communication Disorders
ISSN : 2578-3807
Launched : 2016
Annals of Musculoskeletal Disorders
ISSN : 2578-3599
Launched : 2016
Annals of Virology and Research
ISSN : 2573-1122
Launched : 2014
JSM Renal Medicine
ISSN : 2573-1637
Launched : 2016
Journal of Muscle Health
ISSN : 2578-3823
Launched : 2016
JSM Genetics and Genomics
ISSN : 2334-1823
Launched : 2013
JSM Anxiety and Depression
ISSN : 2475-9139
Launched : 2016
Clinical Journal of Heart Diseases
ISSN : 2641-7766
Launched : 2016
Annals of Medicinal Chemistry and Research
ISSN : 2378-9336
Launched : 2014
JSM Pain and Management
ISSN : 2578-3378
Launched : 2016
JSM Women's Health
ISSN : 2578-3696
Launched : 2016
Clinical Research in HIV or AIDS
ISSN : 2374-0094
Launched : 2013
Journal of Endocrinology, Diabetes and Obesity
ISSN : 2333-6692
Launched : 2013
Journal of Substance Abuse and Alcoholism
ISSN : 2373-9363
Launched : 2013
JSM Neurosurgery and Spine
ISSN : 2373-9479
Launched : 2013
Journal of Liver and Clinical Research
ISSN : 2379-0830
Launched : 2014
Journal of Drug Design and Research
ISSN : 2379-089X
Launched : 2014
JSM Clinical Oncology and Research
ISSN : 2373-938X
Launched : 2013
JSM Bioinformatics, Genomics and Proteomics
ISSN : 2576-1102
Launched : 2014
JSM Chemistry
ISSN : 2334-1831
Launched : 2013
Journal of Trauma and Care
ISSN : 2573-1246
Launched : 2014
JSM Surgical Oncology and Research
ISSN : 2578-3688
Launched : 2016
Annals of Food Processing and Preservation
ISSN : 2573-1033
Launched : 2016
Journal of Radiology and Radiation Therapy
ISSN : 2333-7095
Launched : 2013
JSM Physical Medicine and Rehabilitation
ISSN : 2578-3572
Launched : 2016
Annals of Clinical Pathology
ISSN : 2373-9282
Launched : 2013
Annals of Cardiovascular Diseases
ISSN : 2641-7731
Launched : 2016
Journal of Behavior
ISSN : 2576-0076
Launched : 2016
Annals of Clinical and Experimental Metabolism
ISSN : 2572-2492
Launched : 2016
Clinical Research in Infectious Diseases
ISSN : 2379-0636
Launched : 2013
JSM Microbiology
ISSN : 2333-6455
Launched : 2013
Journal of Urology and Research
ISSN : 2379-951X
Launched : 2014
Journal of Family Medicine and Community Health
ISSN : 2379-0547
Launched : 2013
Annals of Pregnancy and Care
ISSN : 2578-336X
Launched : 2017
JSM Cell and Developmental Biology
ISSN : 2379-061X
Launched : 2013
Annals of Aquaculture and Research
ISSN : 2379-0881
Launched : 2014
Clinical Research in Pulmonology
ISSN : 2333-6625
Launched : 2013
Journal of Immunology and Clinical Research
ISSN : 2333-6714
Launched : 2013
Annals of Forensic Research and Analysis
ISSN : 2378-9476
Launched : 2014
JSM Biochemistry and Molecular Biology
ISSN : 2333-7109
Launched : 2013
Annals of Breast Cancer Research
ISSN : 2641-7685
Launched : 2016
Annals of Gerontology and Geriatric Research
ISSN : 2378-9409
Launched : 2014
Journal of Sleep Medicine and Disorders
ISSN : 2379-0822
Launched : 2014
JSM Burns and Trauma
ISSN : 2475-9406
Launched : 2016
Chemical Engineering and Process Techniques
ISSN : 2333-6633
Launched : 2013
Annals of Clinical Cytology and Pathology
ISSN : 2475-9430
Launched : 2014
JSM Allergy and Asthma
ISSN : 2573-1254
Launched : 2016
Journal of Neurological Disorders and Stroke
ISSN : 2334-2307
Launched : 2013
Annals of Sports Medicine and Research
ISSN : 2379-0571
Launched : 2014
JSM Sexual Medicine
ISSN : 2578-3718
Launched : 2016
Annals of Vascular Medicine and Research
ISSN : 2378-9344
Launched : 2014
JSM Biotechnology and Biomedical Engineering
ISSN : 2333-7117
Launched : 2013
Journal of Hematology and Transfusion
ISSN : 2333-6684
Launched : 2013
JSM Environmental Science and Ecology
ISSN : 2333-7141
Launched : 2013
Journal of Cardiology and Clinical Research
ISSN : 2333-6676
Launched : 2013
JSM Nanotechnology and Nanomedicine
ISSN : 2334-1815
Launched : 2013
Journal of Ear, Nose and Throat Disorders
ISSN : 2475-9473
Launched : 2016
JSM Ophthalmology
ISSN : 2333-6447
Launched : 2013
Journal of Pharmacology and Clinical Toxicology
ISSN : 2333-7079
Launched : 2013
Annals of Psychiatry and Mental Health
ISSN : 2374-0124
Launched : 2013
Medical Journal of Obstetrics and Gynecology
ISSN : 2333-6439
Launched : 2013
Annals of Pediatrics and Child Health
ISSN : 2373-9312
Launched : 2013
JSM Clinical Pharmaceutics
ISSN : 2379-9498
Launched : 2014
JSM Foot and Ankle
ISSN : 2475-9112
Launched : 2016
JSM Alzheimer's Disease and Related Dementia
ISSN : 2378-9565
Launched : 2014
Journal of Addiction Medicine and Therapy
ISSN : 2333-665X
Launched : 2013
Journal of Veterinary Medicine and Research
ISSN : 2378-931X
Launched : 2013
Annals of Public Health and Research
ISSN : 2378-9328
Launched : 2014
Annals of Orthopedics and Rheumatology
ISSN : 2373-9290
Launched : 2013
Journal of Clinical Nephrology and Research
ISSN : 2379-0652
Launched : 2014
Annals of Community Medicine and Practice
ISSN : 2475-9465
Launched : 2014
Annals of Biometrics and Biostatistics
ISSN : 2374-0116
Launched : 2013
JSM Clinical Case Reports
ISSN : 2373-9819
Launched : 2013
Journal of Cancer Biology and Research
ISSN : 2373-9436
Launched : 2013
Journal of Surgery and Transplantation Science
ISSN : 2379-0911
Launched : 2013
Journal of Dermatology and Clinical Research
ISSN : 2373-9371
Launched : 2013
JSM Gastroenterology and Hepatology
ISSN : 2373-9487
Launched : 2013
Annals of Nursing and Practice
ISSN : 2379-9501
Launched : 2014
JSM Dentistry
ISSN : 2333-7133
Launched : 2013
Author Information X