Please wait a minute...
Chin. Phys. B, 2020, Vol. 29(10): 108706    DOI: 10.1088/1674-1056/abad24
Special Issue: SPECIAL TOPIC — Modeling and simulations for the structures and functions of proteins and nucleic acids
Topical Review—Modeling and simulations for the structures and functions of proteins and nucleic acids Prev   Next  

Find slow dynamic modes via analyzing molecular dynamics simulation trajectories

Chuanbiao Zhang(张传彪)1 and Xin Zhou(周昕)2,
1 College of Physics and Electronic Engineering, Heze University, Heze 274015, China
2 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China

It is a central issue to find the slow dynamic modes of biological macromolecules via analyzing the large-scale data of molecular dynamics simulation (MD). While the MD data are high-dimensional time-successive series involving all-atomic details and sub-picosecond time resolution, a few collective variables which characterizing the motions in longer than nanoseconds are needed to be chosen for an intuitive understanding of the dynamics of the system. The trajectory map (TM) was presented in our previous works to provide an efficient method to find the low-dimensional slow dynamic collective-motion modes from high-dimensional time series. In this paper, we present a more straight understanding about the principle of TM via the slow-mode linear space of the conformational probability distribution functions of MD trajectories and more clearly discuss the relation between the TM and the current other similar methods in finding slow modes.

Keywords:  molecular dynamics simulation      slow modes      trajectory map  
Received:  18 June 2020      Revised:  27 July 2020      Published:  05 October 2020
PACS:  87.15.A- (Theory, modeling, and computer simulation)  
  02.70.Ns (Molecular dynamics and particle methods)  
  82.20.Wt (Computational modeling; simulation)  
Corresponding Authors:  Corresponding author. E-mail:   
About author: 
†Corresponding author. E-mail:
* Project supported by the National Natural Science Foundation of China (Grant No. 11904086).

Cite this article: 

Chuanbiao Zhang(张传彪) and Xin Zhou(周昕)† Find slow dynamic modes via analyzing molecular dynamics simulation trajectories 2020 Chin. Phys. B 29 108706

Fig. 1.  

(a) Time evolution of the RMSD of the Trp-cage to its native structure, the slow variables B1 and B2 obtained in the TM. Red line is time-window-smoothed one (Δ t = 200 ns). (b) Eigenvalue of the variance–covariance matrix of the trajectory-mapped points. The inset is the contribution of each basis function to the slow variables B1 and B2. (c) The free-energy landscape (in units of kBT) in the slow-variable space (B1, B2).

Fig. 2.  

Time-ordered similarity matrix of the MD trajectory. The similarity between two samples C(t2, t1) = B(t2) ⋅ B(t1). (b) The time-rearranged similarity matrix, suggesting three metastable states. (c) Kinetic transition network. Numbers near the arrows are the corresponding transition rates. The population of each state in the 208-μs MD trajectory is listed in bracket (which approaches to the equilibrium one, in consistent with the fact the folding and unfolding transitions occur more than ten times during the MD simulation). Residue TRP6 and PRO17 are shown in blue, GLY11 in red.

Piana S, Lindorff-Larsen K, Shaw D E 2012 Proc. Natl. Acad. Sci. USA 109 17845 DOI: 10.1073/pnas.1201811109
Lyulin S V, Gurtovenko A A, Larin S V, Nazarychev V M, Lyulin A V 2013 Macromolecules 46 6357 DOI: 10.1021/ma4011632
Lane T J, Shukla D, Kyle A B, Vijay S P 2013 Curr. Opin. Struct. Biol. 23 58 DOI: 10.1016/
Jain A K 2008 Machine Learning and Knowledge Discovery Berlin, Heidelberg Springer 3 4 DOI: 10.1007/978-3-540-87479-9_3
Schubert E, Sander J, Ester M, Kriegel H P, Xu X 2017 ACM Trans. Database Syst. 42 19 DOI: 10.1145/3068335
Alex R, Laio A 2014 Science 344 1492
Hotelling H 1933 J. Educ. Psychol. 24 417 DOI: 10.1037/h0071325
Hyvrinen A, Oja E 2000 Neural Netw. 13 411 DOI: 10.1016/S0893-6080(00)00026-5
Schwantes C R, Pande V S 2013 J. Chem. Theory. Comput. 9 2000 DOI: 10.1021/ct300878a
Tenenbaum J B, de Silva V, Langford J C 2000 Science 290 2319
Nadler B, Lafon S, Coifman R R, Kevrekidis I G 2006 Appl. Comput. Harmon. Anal. 21 113 DOI: 10.1016/j.acha.2005.07.004
Shea J E, Brooks C L 2001 Ann. Rev. Phys. Chem. 52 499 DOI: 10.1146/annurev.physchem.52.1.499
Mu Y G, Nguyen P H, Stock G 2005 Proteins 58 45 DOI: 10.1002/prot.20310
Sims G E, Choi I G, Kim S H 2005 Proc. Natl. Acad. Sci. USA 102 618
Rao F, Karplus M 2010 Proc. Natl. Acad. Sci. USA 107 9152
Das P, Moll M, Stamati H, Kavraki L E, Clementi C 2006 Proc. Natl. Acad. Sci. USA 103 9885
Nadler B, Lafon S, Coifman R R, Kevrekidis I G 2006 Appl. Comput. Harmon. Anal. 21 113 DOI: 10.1016/j.acha.2005.07.004
Krivov S V, Karplus M 2004 Proc. Natl. Acad. Sci. USA 101 14766
Maisuradze G G, Liwo A, Scheraga H A 2009 Phys. Rev. Lett. 102 238102 DOI: 10.1103/PhysRevLett.102.238102
Torda A E, Gunsteren W F 1994 J. Comput. Chem. 15 1331 DOI: 10.1002/jcc.540151203
Shao J Y, Tanner S W, Thompson N, Cheatham T E 2007 J. Chem. Theory. Comput. 3 2312 DOI: 10.1021/ct700119m
Deuflhard P, Huisinga W, Fischer A, Schutte C 2000 Linear Algebra Appl. 315 39 DOI: 10.1016/S0024-3795(00)00095-1
Deuflhard P, Weber M 2005 Numer Linear Algebra Appl. 398 161 DOI: 10.1016/j.laa.2004.10.026
Gfeller D, De Los Rios P, Caflisch A, Rao F 2007 Proc. Natl. Acad. Sci. USA 104 1817 DOI: 10.1073/pnas.0608099104
Noe F, Horenko I, Schutte C, Smith J C 2007 J. Chem. Phys. 126 155102 DOI: 10.1063/1.2714539
Chodera J D, Singhal N, Pande V S, Dill K A, Swope W C 2007 J. Chem. Phys. 126 155101 DOI: 10.1063/1.2714538
Bowman G R, Pande V S 2010 Proc. Natl. Acad. Sci. USA 107 10890
Bowman G R, Meng L, Huang X 2013 J. Chem. Phys. 139 121905 DOI: 10.1063/1.4812768
Weber J K, Jack R L, Pande V S 2013 J. Am. Chem. Soc. 135 5501 DOI: 10.1021/ja4002663
Pande V S, Beauchamp K, Bowman G R 2010 Methods 52 99 DOI: 10.1016/j.ymeth.2010.06.002
Deng N J, Dai W, Levy R M 2013 J. Phys. Chem. B 117 12787 DOI: 10.1021/jp401962k
Naritomi Y, Fuchigami S 2011 J. Chem. Phys. 134 065101 DOI: 10.1063/1.3554380
Nuske F, Keller B G, Perez-Hernandez G, Mey A S J S, Noe F 2014 J. Chem. Theory. Comput. 10 1739 DOI: 10.1021/ct4009156
Gong L C, Zhou X 2010 J. Phys. Chem. B 114 10266 DOI: 10.1021/jp100737g
Gong L C, Zhou X 2009 Phys. Rev. E 80 026707 DOI: 10.1103/PhysRevE.80.026707
Zhang C B, Li M, Zhou X 2015 Chin. Phys. B 24 120202 DOI: 10.1088/1674-1056/24/12/120202
Gong L C, Zhou X, Ouyang Z C 2015 PloS One 10 e0125932 DOI: 10.1371/journal.pone.0125932
Zhang C B, Yu J, Zhou X 2017 J. Phys. Chem. B 121 4678 DOI: 10.1021/acs.jpcb.7b00664
Zhang C B, Ye F F, Li M, Zhou X 2019 Sci. China: Phys. Mech. 62 067012 DOI: 10.1007/s11433-018-9313-1
Zhang C B, Xu S, Zhou X 2019 Phys. Rev. E 100 033301 DOI: 10.1103/PhysRevE.100.033301
Neidigh J W, Fesinmeyer R M, Andersen N H 2002 Nat. Struct. Biol. 9 425
Bipasha B, Lin J C, Williams V D, Kummler P, Neidigh J W, Andersen N H 2008 Protein Eng. Des. Sel. 21 171 DOI: 10.1093/protein/gzm082
Lindorff-Larsen K, Piana S, Dror R O, Shaw D E 2011 Science 334 517
Day R, Paschek D, Garcia A E 2010 Proteins 78 1889 DOI: 10.1002/prot.22702
Spiwok V, Oborsky P, Pazurikova J, Krenek A, Kralova B 2015 J. Chem. Phys. 142 115101 DOI: 10.1063/1.4914828
Kim S B, Dsilva C J, Kevrekidis I G, Debenedetti P G 2015 J. Chem. Phys. 142 085101 DOI: 10.1063/1.4913322
Andryushchenko V A, Chekmarev S F 2016 Eur. Biophys. J. 45 229 DOI: 10.1007/s00249-015-1089-7
Zang T W, Yu L L, Zhang C, Ma J P 2014 J. Chem. Phys. 141 044113 DOI: 10.1063/1.4890038
Zhan L X, Chen J Z Y, Liu W K 2007 Proteins 66 436 DOI: 10.1002/prot.21157
Huang X H, Hagen M, Kim B, Friesner R A, Zhou R H, Berne B J 2007 J. Phys. Chem. B 111 5405 DOI: 10.1021/jp068826w
Pitera J W, Swope W C 2003 Proc. Natl. Acad. Sci. USA 100 7587 DOI: 10.1073/pnas.1330954100
Hornak V, Abel R, Okur A, Strockbine B, Roitberg A, Simmerling C 2006 Proteins 65 712 DOI: 10.1002/prot.21123
Lai Z Z, Preketes N K, Mukamel S, Wang J 2013 J. Phys. Chem. B 117 4661 DOI: 10.1021/jp309122b
Abaskharon R M, Culik R M, Woolley G A, Gai F 2015 J. Phys. Chem. Lett. 6 521 DOI: 10.1021/jz502654q
Andryushchenko V A, Chekmarev S F 2016 Eur. Biophys. J. 45 229 DOI: 10.1007/s00249-015-1089-7
Piana S, Lindorff-Larsen K, Shaw D E 2011 Biophys. J. 100 L47 DOI: 10.1016/j.bpj.2011.03.051
Jorgensen W L, Chandrasekhar J, Madura J D, Impey R W, Klein M L 1983 J. Chem. Phys. 79 926 DOI: 10.1063/1.445869
MacKerell A D, Bashford D, Bellott M et al. 1998 J. Phys. Chem. B 102 3586 DOI: 10.1021/jp973084f
Altis A, Otten M, Nguyen P H, Hegger R, Stock G 2008 J. Chem. Phys. 128 245102 DOI: 10.1063/1.2945165
Laio A, Gervasio F L 2008 Rep. Prog. Phys. 71 126601 DOI: 10.1088/0034-4885/71/12/126601
Torrie G M, Valleau J P 1977 J. Comput. Phys. 23 187
Allen R J, Valeriani C, Wolde P R 2009 J. Phys.: Condens. Matter 21 463102 DOI: 10.1088/0953-8984/21/46/463102/meta
[1] Tolman length of simple droplet: Theoretical study and molecular dynamics simulation
Shu-Wen Cui(崔树稳), Jiu-An Wei(魏久安), Qiang Li(李强), Wei-Wei Liu(刘伟伟), Ping Qian(钱萍), and Xiao Song Wang(王小松). Chin. Phys. B, 2021, 30(1): 016801.
[2] Size effect of He clusters on the interactions with self-interstitial tungsten atoms at different temperatures
Jinlong Wang(王金龙), Wenqiang Dang(党文强), Daping Liu(刘大平), Zhichao Guo(郭志超). Chin. Phys. B, 2020, 29(9): 093101.
[3] Oscillation of S5 helix under different temperatures in determination of the open probability of TRPV1 channel
Tie Li(李铁), Jun-Wei Li(李军委), Chun-Li Pang(庞春丽), Hailong An(安海龙), Yi-Zhao Geng(耿轶钊), Jing-Qin Wang(王景芹). Chin. Phys. B, 2020, 29(9): 098701.
[4] Different potential of mean force of two-state protein GB1 and downhill protein gpW revealed by molecular dynamics simulation
Xiaofeng Zhang(张晓峰), Zilong Guo(郭子龙), Ping Yu(余平), Qiushi Li(李秋实), Xin Zhou(周昕), Hu Chen(陈虎). Chin. Phys. B, 2020, 29(7): 078701.
[5] Balancing strength and plasticity of dual-phase amorphous/crystalline nanostructured Mg alloys
Jia-Yi Wang(王佳怡), Hai-Yang Song(宋海洋), Min-Rong An(安敏荣), Qiong Deng(邓琼), Yu-Long Li(李玉龙). Chin. Phys. B, 2020, 29(6): 066201.
[6] Anisotropic plasticity of nanocrystalline Ti: A molecular dynamics simulation
Minrong An(安敏荣), Mengjia Su(宿梦嘉), Qiong Deng(邓琼), Haiyang Song(宋海洋), Chen Wang(王晨), Yu Shang(尚玉). Chin. Phys. B, 2020, 29(4): 046201.
[7] Molecular dynamics simulation of thermal conductivity of silicone rubber
Wenxue Xu(徐文雪), Yanyan Wu(吴雁艳), Yuan Zhu(祝渊), Xin-Gang Liang(梁新刚). Chin. Phys. B, 2020, 29(4): 046601.
[8] Fractional variant of Stokes-Einstein relation in aqueous ionic solutions under external static electric fields
Gan Ren(任淦), Shikai Tian(田时开). Chin. Phys. B, 2020, 29(3): 036101.
[9] Structural and dynamical mechanisms of a naturally occurring variant of the human prion protein in preventing prion conversion
Yiming Tang(唐一鸣), Yifei Yao(姚逸飞), and Guanghong Wei(韦广红)†. Chin. Phys. B, 2020, 29(10): 108710.
[10] Density functional calculations of efficient H2 separation from impurity gases (H2, N2, H2O, CO, Cl2, and CH4) via bilayer g-C3N4 membrane
Yuan Guo(郭源), Chunmei Tang(唐春梅), Xinbo Wang(王鑫波), Cheng Wang(王成), Ling Fu(付玲). Chin. Phys. B, 2019, 28(4): 048102.
[11] Alkyl group functionalization-induced phonon thermal conductivity attenuation in graphene nanoribbons
Caiyun Wang(王彩云), Shuang Lu(鲁爽), Xiaodong Yu(于晓东), Haipeng Li(李海鹏). Chin. Phys. B, 2019, 28(1): 016501.
[12] Approximate expression of Young's equation and molecular dynamics simulation for its applicability
Shu-Wen Cui(崔树稳), Jiu-An Wei(魏久安), Wei-Wei Liu(刘伟伟), Ru-Zeng Zhu(朱如曾), Qian Ping(钱萍). Chin. Phys. B, 2019, 28(1): 016801.
[13] Potentials of classical force fields for interactions between Na+ and carbon nanotubes
De-Yuan Li(李德远), Guo-Sheng Shi(石国升), Feng Hong(洪峰), Hai-Ping Fang(方海平). Chin. Phys. B, 2018, 27(9): 098801.
[14] Molecular dynamics simulations on the dynamics of two-dimensional rounded squares
Zhang-lin Hou(侯章林), Ying Ju(句颖), Yi-wu Zong(宗奕吾), Fang-fu Ye(叶方富), Kun Zhao(赵坤). Chin. Phys. B, 2018, 27(8): 088203.
[15] A simulation study of water property changes using geometrical alteration in SPC/E
Ming-Ru Li(李明儒), Nan Zhang(张楠), Feng-Shou Zhang(张丰收). Chin. Phys. B, 2018, 27(8): 083103.
No Suggested Reading articles found!