Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Machine learning in molecular simulations of biomolecules

Guan Xing-Yue Huang Heng-Yan Peng Hua-Qi Liu Yan-Hang Li Wen-Fei Wang Wei

Citation:

Machine learning in molecular simulations of biomolecules

Guan Xing-Yue, Huang Heng-Yan, Peng Hua-Qi, Liu Yan-Hang, Li Wen-Fei, Wang Wei
PDF
HTML
Get Citation
  • Molecular simulation has already become a powerful tool for studying life principles at a molecular level. The past 50-year researches show that molecular simulation has been able to quantitatively characterize the kinetic and thermodynamic properties of complex molecular processes, such as protein folding and conformational changes. In recent years, the application of machine learning algorithms represented by deep learning has further promoted the development of molecular simulation. This work reviews machine learning methods in biomolecular simulation, focusing on the important progress made by machine learning algorithms in improving the accuracy of molecular force fields, the efficiency of molecular simulation conformation sampling, and also the processing of high-dimensional simulation data. The future researches to further overcome the bottleneck of accuracy and efficiency of molecular simulation, expand the scope of molecular simulation, and realize the integration of computational simulation and experimental based on machine learning technique is prospected.
      Corresponding author: Li Wen-Fei, wfli@nju.edu.cn ; Wang Wei, wangwei@nju.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11974173).
    [1]

    McCammon J A, Gelin B R, Karplus M 1977 Nature 267 585Google Scholar

    [2]

    Schlick T, Portillo-Ledesma S 2021 Nat. Comput. Sci. 1 321Google Scholar

    [3]

    Vendruscolo M, Dobson C M 2011 Curr. Biol. 21 R68Google Scholar

    [4]

    Shaw D E, Maragakis P, Lindorff-Larsen K, et al. 2010 Science 330 341Google Scholar

    [5]

    Zhou C Y, Jiang F, Wu Y D 2015 J. Phys. Chem. B 119 1035Google Scholar

    [6]

    Zerze G H, Zheng W, Best R B, Mittal J 2019 J. Phys. Chem. Lett. 10 2227Google Scholar

    [7]

    Robustelli P, Piana S, Shaw D E 2018 Proc. Natl. Acad. Sci. U.S.A. 115 E4758

    [8]

    Perilla J R, Schulten K 2017 Nat. Commun. 8 15959Google Scholar

    [9]

    Yu I, Mori T, Ando T, Harada R, Jung J, Sugita Y, Feig M 2016 eLife 5 e19274Google Scholar

    [10]

    李文飞, 张建, 王骏, 王炜 2015 64 098701Google Scholar

    Li W F, Zhang J, Wang J, Wang W 2015 Acta Phys. Sin. 64 098701Google Scholar

    [11]

    Samuel A L 1959 IBM J. Res. Dev. 3 210Google Scholar

    [12]

    Stigler S M 1974 Hist. Math. 1 431Google Scholar

    [13]

    Fix E, Hodges J L 1951 Discriminatory Analysis, Nonparametric Discrimination: Consistency Properties (Randolph Field, Texas: USAF School of Aviation Medicine) Tech. Rep. 4

    [14]

    Breiman L, Friedman J H, Olshen R A, Stone C J 1984 Biometrics 40 874Google Scholar

    [15]

    Rumelhart D E, Hinton G E, Williams R J 1986 Nature 323 533Google Scholar

    [16]

    Cortes C, Vapnik V 1995 Mach. Learn. 20 273Google Scholar

    [17]

    Ho T K 1995 Proceedings of 3rd International Conference on Document Analysis and Recognition Montreal, QC, Canada, August 14–16, 1995 p278

    [18]

    Freund Y, Schapire R E 1996 Proceedings of the Thirteenth International Conference on International Conference on Machine Learning San Francisco, CA, USA, July 1996 p148

    [19]

    Holley L, Karplus M 1989 Proc. Natl. Acad. Sci. U.S.A. 86 152Google Scholar

    [20]

    Cai Y, Liu X, Xu X, Zhou G 2001 BMC Bioinf. 2 1Google Scholar

    [21]

    Cai C, Wang W, Sun L, Chen Y 2003 Math. Biosci. 185 111Google Scholar

    [22]

    Zernov V V, Balakin K V, Ivaschenko A A, Savchuk N P, Pletnev I V 2003 J. Chem. Inf. Comput. Sci. 43 2048Google Scholar

    [23]

    Blank T B, Brown S D, Calhoun A W, Doren D J 1995 J. Chem. Phys. 103 4129Google Scholar

    [24]

    Krizhevsky A, Sutskever I, Hinton G E 2017 Commun. ACM 60 84Google Scholar

    [25]

    He K, Zhang X, Ren S, Sun J 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Las Vegas, NV, USA, June 27–30, 2016 p770

    [26]

    Goodfellow I, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y 2020 Commun. ACM 63 139Google Scholar

    [27]

    Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez A N, Kaiser L, Polosukhin I 2017 Proceedings of the 31st International Conference on Neural Information Processing Systems New York, USA, December 4–9, 2017 p6000

    [28]

    Noé F, Olsson S, Köhler J, Wu H 2019 Science 365 eaaw1147Google Scholar

    [29]

    Yang J, Anishchenko I, Park H, Peng Z, Ovchinnikov S, Baker D 2020 Proc. Natl. Acad. Sci. U.S.A. 117 1496Google Scholar

    [30]

    Jumper J, Evans R, Pritzel A, et al. 2021 Nature 596 583Google Scholar

    [31]

    Baek M, DiMaio F, Anishchenko I, Dauparas J, Ovchinnikov S, Lee G R, Wang J, Cong Q, Kinch L N, Schaeffer R D, Millán C, Park H, Adams C, Glassman C R, DeGiovanni A, Pereira J H, Rodrigues A V, Van Dijk A A, Ebrecht A C, Opperman D J, Sagmeister T, Buhlheller C, Pavkov-Keller T, Rathinaswamy M K, Dalwadi U, Yip C K, Burke J E, Garcia K C, Grishin N V, Adams P D, Read R J, Baker D 2021 Science 373 871Google Scholar

    [32]

    Huang B, Xu Y, Hu X, Liu Y, Liao S, Zhang J, Huang C, Hong J, Chen Q, Liu H 2022 Nature 602 523Google Scholar

    [33]

    Liu Y, Zhang L, Wang W, Zhu M, Wang C, Li F, Zhang J, Li H, Chen Q, Liu H 2022 Nat. Comput. Sci. 2 451Google Scholar

    [34]

    Köhler J, Chen Y, Krämer A, Clementi C, Noé F 2023 J. Chem. Theory Comput. 19 94216Google Scholar

    [35]

    Watson J L, Juergens D, Bennett N R, Trippe B L, Yim J, Eisenach H E, Ahern W, Borst A J, Ragotte R J, Milles L F, Wicky B I M, Hanikel N, Pellock S J, Courbet A, Sheffler W, Wang J, Venkatesh P, Sappington I, Torres S V, Lauko A, Bortoli V D, Mathieu E, Ovchinnikov S, Barzilay R, Jaakkola T S, DiMaio F, Baek M, Baker D 2023 Nature 620 1089Google Scholar

    [36]

    Kuhlman B, Bradley P 2019 Nat. Rev. Mol. Cell Biol. 20 681Google Scholar

    [37]

    Jisna V, Jayaraj P 2021 Protein J. 40 522Google Scholar

    [38]

    AlQuraishi M 2021 Curr. Opin. Chem. Biol. 65 1Google Scholar

    [39]

    Xu Y, Verma D, Sheridan R P, Liaw A, Ma J, Marshall N M, McIntosh J, Sherer E C, Svetnik V, Johnston J M 2020 J. Chem. Inf. Model. 60 2773Google Scholar

    [40]

    Huang B, Du Y, Zhang S, Li W, Wang J, Zhang J 2020 Chin. Phys. B 29 108704Google Scholar

    [41]

    Zhang J, Chen D, Xia Y, et al. 2023 J. Chem. Theory Comput. 19 4338Google Scholar

    [42]

    Ramanathan A, Ma H, Parvatikar A, Chennubhotla S C 2021 Curr. Opin. Struct. Biol. 66 216Google Scholar

    [43]

    Noé F, Tkatchenko A, Müller K R, Clementi C 2020 Annu. Rev. Phys. Chem. 71 361Google Scholar

    [44]

    Wang Y, Ribeiro J M L, Tiwary P 2020 Curr. Opin. Struct. Biol. 61 139Google Scholar

    [45]

    Sambasivarao S V, Acevedo O 2009 J. Chem. Theory Comput. 5 1038Google Scholar

    [46]

    Brooks B R, Brooks Ⅲ C L, Mackerell Jr. A D, Nilsson L, Petrella R J, Roux B, Won Y, Archontis G, Bartels C, Boresch S, Caflisch A, Caves L, Cui Q, Dinner A R, Feig M, Fischer S, Gao J, Hodoscek M, Im W, Kuczera K, Lazaridis T, Ma J, Ovchinnikov V, Paci E, Pastor R W, Post C B, Pu J Z, Schaefer M, Tidor B, Venable R M, Woodcock H L, Wu X, Yang W, York D M, Karplus M 2009 J. Comput. Chem. 30 1545Google Scholar

    [47]

    Wang J, Wolf R M, Caldwell J W, Kollman P A, Case D A 2004 J. Comput. Chem. 25 528Google Scholar

    [48]

    Peng X, Zhang Y, Chu H, Li Y, Zhang D, Cao L, Li G 2016 J. Chem. Theory Comput. 12 2973Google Scholar

    [49]

    Liu C, Qi R, Wang Q, Piquemal J P, Ren P 2017 J. Chem. Theory Comput. 13 2751Google Scholar

    [50]

    Schütt K T, Kindermans P J, Sauceda H E, Chmiela S, Tkatchenko A, Müller K R 2017 Proceedings of the 31st International Conference on Neural Information Processing Systems New York, USA, December 4–9, 2017 p992

    [51]

    Zhang L, Han J, Wang H, Car R, Weinan E 2018 Phys. Rev. Lett. 120 143001Google Scholar

    [52]

    Zhang L, Han J, Wang H, Car R, Weinan E 2018 J. Chem. Phys. 149 034101Google Scholar

    [53]

    Park C W, Kornbluth M, Vandermause J, Wolverton C, Kozinsky B, Mailoa J P 2021 npj Comput. Mater. 7 73Google Scholar

    [54]

    batznerzner S, Musaelian A, Sun L, Geiger M, Mailoa J P, Kornbluth M, Molinari N, Smidt T E, Kozinsky B 2022 Nat. Commun. 13 2453Google Scholar

    [55]

    Wang Y, Li S, He X, Li M, Wang Z, Zheng N, Shao B, Wang T, Liu T Y 2022 arXiv: 2210.16518 [cs.LG

    [56]

    Zhang L F, Han J Q, Wang H, Saidi W, Car R, E W H 2018 Advances in Neural Information Processing Systems Montreal, Canada, Decembe 3–8, 2018 p4441

    [57]

    Behler J, Parrinello M 2007 Phys. Rev. Lett. 98 146401Google Scholar

    [58]

    Artrith N, Urban A 2016 Comput. Mater. Sci. 114 135Google Scholar

    [59]

    Smith J S, Isayev O, Roitberg A E 2017 Chem. Sci. 8 3192Google Scholar

    [60]

    Fan Z, Wang Y, Ying P, et al. 2022 J. Chem. Phys. 157 114801Google Scholar

    [61]

    Chmiela S, Tkatchenko A, Sauceda H E, Poltavsky I, Schütt K T, Müller K R 2017 Sci. Adv. 3 e1603015Google Scholar

    [62]

    Gilmer N M P, Schoenholz S S, Riley P F, Vinyals O, Dahl G E 2017 Proceedings of the 34th International Conference on Machine Learning Sydney, Australia, August 6–11, 2017 p1263

    [63]

    Wang X, Xu Y, Zheng H, Yu K 2021 J. Phys. Chem. Lett. 12 7982Google Scholar

    [64]

    Takada S, Kanada R, Tan C, Terakawa T, Li W, Kenzaki H 2015 Acc. Chem. Res. 48 3026Google Scholar

    [65]

    Reith D, Pütz M, Müller-Plathe F 2003 J. Comput. Chem. 24 1624Google Scholar

    [66]

    Izvekov S, Voth G A 2005 J. Phys. Chem. B 109 2469Google Scholar

    [67]

    Chu J W, Ayton G, Izvekov S, Voth G 2007 Mol. Phys. 105 167Google Scholar

    [68]

    Li W, Wolynes P G, Takada S 2011 Proc. Natl. Acad. Sci. U.S.A. 108 3504Google Scholar

    [69]

    Gohlke H, Kiel C, Case D A 2003 J. Mol. Biol. 330 891Google Scholar

    [70]

    Wang J, Olsson S, Wehmeyer C, Pérez A, Charron N E, De Fabritiis G, Noé F, Clementi C 2019 ACS Cent. Sci. 5 755Google Scholar

    [71]

    Arts M, Satorras V G, Huang C W, Zuegner D, Federici M, Clementi C, Noé F, Pinsler R, van den Berg R 2023 arXiv: 2302.00600 [cs.LG

    [72]

    Wang W, Gómez-Bombarelli R 2019 Npj Comput. Mater. 5 125Google Scholar

    [73]

    Zhang J, Lei Y K, Yang Y I, Gao Y Q 2020 J. Chem. Phys. 153 174115Google Scholar

    [74]

    Dong T, Gong T, Li W 2021 J. Phys. Chem. B 125 9490Google Scholar

    [75]

    Marrink S J, Risselada H J, Yefimov S, Tieleman D P, de Vries A H 2007 J. Phys. Chem. B 111 7812Google Scholar

    [76]

    Souza P C T, Alessandri R, Barnoud J, Thallmair S, Faustino I, Grünewald F, Patmanidis I, Abdizadeh H, Bruininks B M H, Wassenaar T A, Kroon P C, Melcr J, Nieto V, Corradi V, Khan H M, Domański J, Javanainen M, Martinez-Seara H, Reuter N, Best R B, Vattulainen I, Monticelli L, Periole1 X, Tieleman D P, de Vries A H, Marrink S J 2021 Nat. Methods 18 382Google Scholar

    [77]

    Shrake A, Rupley J A 1973 J. Mol. Biol. 79 351Google Scholar

    [78]

    Torrie G M, Valleau J P 1977 J. Comput. Phys. 23 187Google Scholar

    [79]

    Sugita Y, Okamoto Y 1999 Chem. Phys. Lett. 314 141Google Scholar

    [80]

    Laio A, Parrinello M 2002 Proc. Natl. Acad. Sci. U.S.A. 99 12562Google Scholar

    [81]

    Hamelberg D, Mongan J, McCammon J A 2004 J. Chem. Phys. 120 11919Google Scholar

    [82]

    Yang L, Liu C W, Shao Q, Zhang J, Gao Y Q 2015 Acc. Chem. Res. 48 947Google Scholar

    [83]

    Tribello G A, Bonomi M, Branduardi D, Camilloni C, Bussi G 2014 Comput. Phys. Commun. 185 604Google Scholar

    [84]

    E W, Ren W, Vanden-Eijnden E 2002 Phys. Rev. B 66 052301

    [85]

    Dellago C, Bolhuis P G, Csajka F S, Chandler D 1998 J. Chem. Phys. 108 1964Google Scholar

    [86]

    Chen C, Huang Y, Xiao Y 2013 J. Biomol. Struct. Dyn. 31 206Google Scholar

    [87]

    Zhang J, Gong H 2020 J. Chem. Theory Comput. 16 4813Google Scholar

    [88]

    Zhu W, Zhang J, Wang J, Li W, Wang W 2021 Phys. Rev. E 103 032404Google Scholar

    [89]

    Zheng S, He J, Liu C, et al. 2023 arXiv: 2306.05445 [physics.chem-ph

    [90]

    Schneider E, Dai L, Topper R Q, Drechsel-Grau C, Tuckerman M E 2017 Phys. Rev. Lett. 119 150601Google Scholar

    [91]

    Jolliffe I T 2002 Principal Component Analysis for Special Types of Data (New York: Springer) pp338–372

    [92]

    Tenenbaum J B, de Silva V, Langford J C 2000 Science 290 2319Google Scholar

    [93]

    Lafon S, Lee A B 2006 IEEE Trans. Pattern Anal. Mach. Intell. 28 1393Google Scholar

    [94]

    Das P, Moll M, Stamati H, Kavraki L E, Clementi C 2006 Proc. Natl. Acad. Sci. U.S.A. 103 9885Google Scholar

    [95]

    Plaku E, Stamati H, Clementi C, Kavraki L E 2007 Proteins Struct. Funct. Bioinf. 67 897Google Scholar

    [96]

    Trstanova Z, Leimkuhler B, Lelièvre T 2020 Proc. R. Soc. A 476 20190036Google Scholar

    [97]

    van der Maaten L, Hinton G 2008 J. Mach. Learn. Res. 9 2579

    [98]

    Hinton G, Roweis S 2002 Proceedings of the 15th International Conference on Neural Information Processing Systems Vancouver, British Columbia, Canada, December 9–14, 2002 p857

    [99]

    Li W, Terakawa T, Wang W, Takada S 2012 Proc. Natl. Acad. Sci. U.S.A. 109 17789Google Scholar

    [100]

    Rydzewski J, Nowak W 2016 J. Chem. Theory Comput. 12 2110Google Scholar

    [101]

    Zhou H, Wang F, Tao P 2018 J. Chem. Theory Comput. 14 5499Google Scholar

    [102]

    Spiwok V, Kříž P 2020 Front. Mol. Biosci. 7 132Google Scholar

    [103]

    Roweis S T, Saul L K 2000 Science 290 2323Google Scholar

    [104]

    Belkin M, Niyogi P 2001 Proceedings of the 14th International Conference on Neural Information Processing Systems: Natural and Synthetic Vancouver, British Columbia, Canada, December 3–8, 2001 p585

    [105]

    Donoho D L, Grimes C 2003 Proc. Natl. Acad. Sci. U.S.A. 100 5591Google Scholar

    [106]

    McInnes L, Healy J, Melville J 2018 arXiv: 1802.03426 [stat.ML

    [107]

    Chen S, Lake B B, Zhang K 2019 Nat. Biotechnol. 37 1452Google Scholar

    [108]

    Mimitou E P, Lareau C A, Chen K Y, et al 2021 Nat. Biotechnol. 39 1246Google Scholar

    [109]

    Becht E, McInnes L, Healy J, Dutertre C A, Kwok I W, Ng L G, Ginhoux F, Newell E W 2019 Nat. Biotechnol. 37 38Google Scholar

    [110]

    Trozzi F, Wang X, Tao P 2021 J. Phys. Chem. B 125 5022Google Scholar

    [111]

    Do V H, Canzar S 2021 Genome Biol. 22 130Google Scholar

    [112]

    Kingma D P, Welling M 2013 arXiv:1312.6114 [stat.ML

    [113]

    Ramaswamy V K, Musson S C, Willcocks C G, Degiacomi M T 2021 Phys. Rev. X 11 011052Google Scholar

    [114]

    Gómez-Bombarelli R, Wei J N, Duvenaud D, Hernández-Lobatznero J M, Sánchez-Lengeling B, Sheberla D, Aguilera-Iparraguirre J, Hirzel T D, Adams R P, Aspuru-Guzik A 2018 ACS Cent. Sci. 4 268Google Scholar

    [115]

    Barducci A, Bussi G, Parrinello M 2008 Phys. Rev. Lett. 100 020603Google Scholar

    [116]

    Bonati L, Zhang Y Y, Parrinello M 2019 Proc. Natl. Acad. Sci. U.S.A. 116 17641Google Scholar

    [117]

    Zhang J, Yang Y I, Noé F 2019 J. Phys. Chem. Lett. 10 5791Google Scholar

    [118]

    Rezende D J, Mohamed S 2015 Proceedings of the 32nd International Conference on International Conference on Machine Learning 37 1530

    [119]

    Shamsi Z, Cheng K J, Shukla D 2018 J. Phys. Chem. B 122 8386Google Scholar

    [120]

    Zhang L, Wang H, E W 2018 J. Chem. Phys. 148 12411Google Scholar

    [121]

    Mardt A, Pasquali L, Wu H, Noé F 2018 Nat. Commun. 9 5Google Scholar

    [122]

    Li W, Yoshii H, Hori N, Kameda T, Takada S 2010 Methods 52 106Google Scholar

    [123]

    Li W, Wang J, Zhang J, Wang W 2015 Curr. Opin. Struct. Biol. 30 25Google Scholar

    [124]

    Li G H 2023 Chemical Theory and Multiscale Simulation in Biomolecules: From Principles to Case Studies (1st Ed.) (Elsevier

    [125]

    Meier J, Rao R, Verkuil R, Liu J, Sercu T, Rives A 2021 Language Models Enable Zero-shot Prediction of the Effects of Mutations on Protein Function (35th Conference on Neural Information Processing Systems (NeurIPS 2021)

    [126]

    Wang D, Wang Y, Chang J, Zhang L, Wang H, E W 2021 Nat. Comput. Sci. 2 20Google Scholar

    [127]

    Huang Y P, Xia Y, Yang L, Wei J, Yang Y I, Gao Y Q 2022 Chin. J. Chem. 40 160Google Scholar

  • 图 1  每年结合生物分子模拟与机器学习的文献数目随年份的变化, 数据来源于Scopus

    Figure 1.  Number of publications with the key words “molecular simulations” and “machine learning” published per year as a function of years. Data were taken from Scopus.

    图 2  神经网络用于生物分子构象能量面及力场的拟合

    Figure 2.  Schematic diagram for representing the biomolecular force field by a neural network.

    图 3  基于粗粒化结构的蛋白残基溶剂可及性表面积(SASA)计算. 左图: 蛋白分子(protein G, PDB code:1pgb)的全原子结构图与粗粒化结构图; 右图: 使用DeepCGSA由粗粒化结构计算得到的SASA与参考值的对比. 其中参考值使用Shrake-Rupley算法由全原子结构计算得到[77]. DeepCGSA能够基于粗粒化结构给出接近参考值的SASA计算结果

    Figure 3.  SASA estimation based on coarse-grained protein structure. Left: All-atom structure and coarse-grained structure of protein G (PDB code: 1 pgb). Right: Correlation plot between the SASA values from DeepCGSA based on one-bead coarse-grained structure and the reference values by Shrake-Rupley algorithm based on all-atom structure. The DeepCGSA can well reproduce the SASA values based on coarse-grained structure.

    图 4  用PCA (左)、t-SNE (中)和UMAP(右)对蛋白分子Protein G的基于粗粒化分子动力学的模拟轨迹[99] 降维效果对比. 蓝色到红色对应表征蛋白折叠程度的Q值; Q = 1 (红色)为完全折叠结构, Q = 0 (蓝色)为完全解折叠结构

    Figure 4.  Projection of the sampled snapshots of the coarse-grained molecular dynamics simulations for protein G [99] along the reaction coordinates constructed by PCA (left), t-SNE (middle), and UMAP (right), respectively. t-SNE and UMAP perform better than PCA in distinguishing the folded and unfolded structures. Colors from blue to red represent the structures with increasing folding extent: blue, fully unfolded; red, fully folded.

    图 5  不同生成模型的网络架构. 从左至右分别对应变分自编码器、生成对抗网络与标准化流. 即便目标同为生成符合某种分布的数据, 三种网络使用了不同的架构与方法. 变分自编码器将数据降维至低维空间后, 在低维空间采样并再次变换至高维空间; 生成对抗网络则通过生成器与分类器之间的互相对抗而使生成器生成的结果符合目标分布; 标准化流则是在目标分布与简单易采样的分布 (如高斯分布) 之间建立直接且可逆的映射

    Figure 5.  Network architecture of different generative models: Variational autoencoder (VAE, left), generative adversarial network (GAN, middle), and normalizing flow (NF, right). Three networks have different architectures. VAE first reduces data to a low-dimensional space, samples in the low-dimensional space, and then transforms back to a high-dimensional space. GAN generates target distribution by combining a generator and the discriminator. Normalizing flow model establishes a direct and reversible mapping between the target distribution and a simple and easy-to-sample distribution (such as Gaussian distribution).

    Baidu
  • [1]

    McCammon J A, Gelin B R, Karplus M 1977 Nature 267 585Google Scholar

    [2]

    Schlick T, Portillo-Ledesma S 2021 Nat. Comput. Sci. 1 321Google Scholar

    [3]

    Vendruscolo M, Dobson C M 2011 Curr. Biol. 21 R68Google Scholar

    [4]

    Shaw D E, Maragakis P, Lindorff-Larsen K, et al. 2010 Science 330 341Google Scholar

    [5]

    Zhou C Y, Jiang F, Wu Y D 2015 J. Phys. Chem. B 119 1035Google Scholar

    [6]

    Zerze G H, Zheng W, Best R B, Mittal J 2019 J. Phys. Chem. Lett. 10 2227Google Scholar

    [7]

    Robustelli P, Piana S, Shaw D E 2018 Proc. Natl. Acad. Sci. U.S.A. 115 E4758

    [8]

    Perilla J R, Schulten K 2017 Nat. Commun. 8 15959Google Scholar

    [9]

    Yu I, Mori T, Ando T, Harada R, Jung J, Sugita Y, Feig M 2016 eLife 5 e19274Google Scholar

    [10]

    李文飞, 张建, 王骏, 王炜 2015 64 098701Google Scholar

    Li W F, Zhang J, Wang J, Wang W 2015 Acta Phys. Sin. 64 098701Google Scholar

    [11]

    Samuel A L 1959 IBM J. Res. Dev. 3 210Google Scholar

    [12]

    Stigler S M 1974 Hist. Math. 1 431Google Scholar

    [13]

    Fix E, Hodges J L 1951 Discriminatory Analysis, Nonparametric Discrimination: Consistency Properties (Randolph Field, Texas: USAF School of Aviation Medicine) Tech. Rep. 4

    [14]

    Breiman L, Friedman J H, Olshen R A, Stone C J 1984 Biometrics 40 874Google Scholar

    [15]

    Rumelhart D E, Hinton G E, Williams R J 1986 Nature 323 533Google Scholar

    [16]

    Cortes C, Vapnik V 1995 Mach. Learn. 20 273Google Scholar

    [17]

    Ho T K 1995 Proceedings of 3rd International Conference on Document Analysis and Recognition Montreal, QC, Canada, August 14–16, 1995 p278

    [18]

    Freund Y, Schapire R E 1996 Proceedings of the Thirteenth International Conference on International Conference on Machine Learning San Francisco, CA, USA, July 1996 p148

    [19]

    Holley L, Karplus M 1989 Proc. Natl. Acad. Sci. U.S.A. 86 152Google Scholar

    [20]

    Cai Y, Liu X, Xu X, Zhou G 2001 BMC Bioinf. 2 1Google Scholar

    [21]

    Cai C, Wang W, Sun L, Chen Y 2003 Math. Biosci. 185 111Google Scholar

    [22]

    Zernov V V, Balakin K V, Ivaschenko A A, Savchuk N P, Pletnev I V 2003 J. Chem. Inf. Comput. Sci. 43 2048Google Scholar

    [23]

    Blank T B, Brown S D, Calhoun A W, Doren D J 1995 J. Chem. Phys. 103 4129Google Scholar

    [24]

    Krizhevsky A, Sutskever I, Hinton G E 2017 Commun. ACM 60 84Google Scholar

    [25]

    He K, Zhang X, Ren S, Sun J 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Las Vegas, NV, USA, June 27–30, 2016 p770

    [26]

    Goodfellow I, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y 2020 Commun. ACM 63 139Google Scholar

    [27]

    Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez A N, Kaiser L, Polosukhin I 2017 Proceedings of the 31st International Conference on Neural Information Processing Systems New York, USA, December 4–9, 2017 p6000

    [28]

    Noé F, Olsson S, Köhler J, Wu H 2019 Science 365 eaaw1147Google Scholar

    [29]

    Yang J, Anishchenko I, Park H, Peng Z, Ovchinnikov S, Baker D 2020 Proc. Natl. Acad. Sci. U.S.A. 117 1496Google Scholar

    [30]

    Jumper J, Evans R, Pritzel A, et al. 2021 Nature 596 583Google Scholar

    [31]

    Baek M, DiMaio F, Anishchenko I, Dauparas J, Ovchinnikov S, Lee G R, Wang J, Cong Q, Kinch L N, Schaeffer R D, Millán C, Park H, Adams C, Glassman C R, DeGiovanni A, Pereira J H, Rodrigues A V, Van Dijk A A, Ebrecht A C, Opperman D J, Sagmeister T, Buhlheller C, Pavkov-Keller T, Rathinaswamy M K, Dalwadi U, Yip C K, Burke J E, Garcia K C, Grishin N V, Adams P D, Read R J, Baker D 2021 Science 373 871Google Scholar

    [32]

    Huang B, Xu Y, Hu X, Liu Y, Liao S, Zhang J, Huang C, Hong J, Chen Q, Liu H 2022 Nature 602 523Google Scholar

    [33]

    Liu Y, Zhang L, Wang W, Zhu M, Wang C, Li F, Zhang J, Li H, Chen Q, Liu H 2022 Nat. Comput. Sci. 2 451Google Scholar

    [34]

    Köhler J, Chen Y, Krämer A, Clementi C, Noé F 2023 J. Chem. Theory Comput. 19 94216Google Scholar

    [35]

    Watson J L, Juergens D, Bennett N R, Trippe B L, Yim J, Eisenach H E, Ahern W, Borst A J, Ragotte R J, Milles L F, Wicky B I M, Hanikel N, Pellock S J, Courbet A, Sheffler W, Wang J, Venkatesh P, Sappington I, Torres S V, Lauko A, Bortoli V D, Mathieu E, Ovchinnikov S, Barzilay R, Jaakkola T S, DiMaio F, Baek M, Baker D 2023 Nature 620 1089Google Scholar

    [36]

    Kuhlman B, Bradley P 2019 Nat. Rev. Mol. Cell Biol. 20 681Google Scholar

    [37]

    Jisna V, Jayaraj P 2021 Protein J. 40 522Google Scholar

    [38]

    AlQuraishi M 2021 Curr. Opin. Chem. Biol. 65 1Google Scholar

    [39]

    Xu Y, Verma D, Sheridan R P, Liaw A, Ma J, Marshall N M, McIntosh J, Sherer E C, Svetnik V, Johnston J M 2020 J. Chem. Inf. Model. 60 2773Google Scholar

    [40]

    Huang B, Du Y, Zhang S, Li W, Wang J, Zhang J 2020 Chin. Phys. B 29 108704Google Scholar

    [41]

    Zhang J, Chen D, Xia Y, et al. 2023 J. Chem. Theory Comput. 19 4338Google Scholar

    [42]

    Ramanathan A, Ma H, Parvatikar A, Chennubhotla S C 2021 Curr. Opin. Struct. Biol. 66 216Google Scholar

    [43]

    Noé F, Tkatchenko A, Müller K R, Clementi C 2020 Annu. Rev. Phys. Chem. 71 361Google Scholar

    [44]

    Wang Y, Ribeiro J M L, Tiwary P 2020 Curr. Opin. Struct. Biol. 61 139Google Scholar

    [45]

    Sambasivarao S V, Acevedo O 2009 J. Chem. Theory Comput. 5 1038Google Scholar

    [46]

    Brooks B R, Brooks Ⅲ C L, Mackerell Jr. A D, Nilsson L, Petrella R J, Roux B, Won Y, Archontis G, Bartels C, Boresch S, Caflisch A, Caves L, Cui Q, Dinner A R, Feig M, Fischer S, Gao J, Hodoscek M, Im W, Kuczera K, Lazaridis T, Ma J, Ovchinnikov V, Paci E, Pastor R W, Post C B, Pu J Z, Schaefer M, Tidor B, Venable R M, Woodcock H L, Wu X, Yang W, York D M, Karplus M 2009 J. Comput. Chem. 30 1545Google Scholar

    [47]

    Wang J, Wolf R M, Caldwell J W, Kollman P A, Case D A 2004 J. Comput. Chem. 25 528Google Scholar

    [48]

    Peng X, Zhang Y, Chu H, Li Y, Zhang D, Cao L, Li G 2016 J. Chem. Theory Comput. 12 2973Google Scholar

    [49]

    Liu C, Qi R, Wang Q, Piquemal J P, Ren P 2017 J. Chem. Theory Comput. 13 2751Google Scholar

    [50]

    Schütt K T, Kindermans P J, Sauceda H E, Chmiela S, Tkatchenko A, Müller K R 2017 Proceedings of the 31st International Conference on Neural Information Processing Systems New York, USA, December 4–9, 2017 p992

    [51]

    Zhang L, Han J, Wang H, Car R, Weinan E 2018 Phys. Rev. Lett. 120 143001Google Scholar

    [52]

    Zhang L, Han J, Wang H, Car R, Weinan E 2018 J. Chem. Phys. 149 034101Google Scholar

    [53]

    Park C W, Kornbluth M, Vandermause J, Wolverton C, Kozinsky B, Mailoa J P 2021 npj Comput. Mater. 7 73Google Scholar

    [54]

    batznerzner S, Musaelian A, Sun L, Geiger M, Mailoa J P, Kornbluth M, Molinari N, Smidt T E, Kozinsky B 2022 Nat. Commun. 13 2453Google Scholar

    [55]

    Wang Y, Li S, He X, Li M, Wang Z, Zheng N, Shao B, Wang T, Liu T Y 2022 arXiv: 2210.16518 [cs.LG

    [56]

    Zhang L F, Han J Q, Wang H, Saidi W, Car R, E W H 2018 Advances in Neural Information Processing Systems Montreal, Canada, Decembe 3–8, 2018 p4441

    [57]

    Behler J, Parrinello M 2007 Phys. Rev. Lett. 98 146401Google Scholar

    [58]

    Artrith N, Urban A 2016 Comput. Mater. Sci. 114 135Google Scholar

    [59]

    Smith J S, Isayev O, Roitberg A E 2017 Chem. Sci. 8 3192Google Scholar

    [60]

    Fan Z, Wang Y, Ying P, et al. 2022 J. Chem. Phys. 157 114801Google Scholar

    [61]

    Chmiela S, Tkatchenko A, Sauceda H E, Poltavsky I, Schütt K T, Müller K R 2017 Sci. Adv. 3 e1603015Google Scholar

    [62]

    Gilmer N M P, Schoenholz S S, Riley P F, Vinyals O, Dahl G E 2017 Proceedings of the 34th International Conference on Machine Learning Sydney, Australia, August 6–11, 2017 p1263

    [63]

    Wang X, Xu Y, Zheng H, Yu K 2021 J. Phys. Chem. Lett. 12 7982Google Scholar

    [64]

    Takada S, Kanada R, Tan C, Terakawa T, Li W, Kenzaki H 2015 Acc. Chem. Res. 48 3026Google Scholar

    [65]

    Reith D, Pütz M, Müller-Plathe F 2003 J. Comput. Chem. 24 1624Google Scholar

    [66]

    Izvekov S, Voth G A 2005 J. Phys. Chem. B 109 2469Google Scholar

    [67]

    Chu J W, Ayton G, Izvekov S, Voth G 2007 Mol. Phys. 105 167Google Scholar

    [68]

    Li W, Wolynes P G, Takada S 2011 Proc. Natl. Acad. Sci. U.S.A. 108 3504Google Scholar

    [69]

    Gohlke H, Kiel C, Case D A 2003 J. Mol. Biol. 330 891Google Scholar

    [70]

    Wang J, Olsson S, Wehmeyer C, Pérez A, Charron N E, De Fabritiis G, Noé F, Clementi C 2019 ACS Cent. Sci. 5 755Google Scholar

    [71]

    Arts M, Satorras V G, Huang C W, Zuegner D, Federici M, Clementi C, Noé F, Pinsler R, van den Berg R 2023 arXiv: 2302.00600 [cs.LG

    [72]

    Wang W, Gómez-Bombarelli R 2019 Npj Comput. Mater. 5 125Google Scholar

    [73]

    Zhang J, Lei Y K, Yang Y I, Gao Y Q 2020 J. Chem. Phys. 153 174115Google Scholar

    [74]

    Dong T, Gong T, Li W 2021 J. Phys. Chem. B 125 9490Google Scholar

    [75]

    Marrink S J, Risselada H J, Yefimov S, Tieleman D P, de Vries A H 2007 J. Phys. Chem. B 111 7812Google Scholar

    [76]

    Souza P C T, Alessandri R, Barnoud J, Thallmair S, Faustino I, Grünewald F, Patmanidis I, Abdizadeh H, Bruininks B M H, Wassenaar T A, Kroon P C, Melcr J, Nieto V, Corradi V, Khan H M, Domański J, Javanainen M, Martinez-Seara H, Reuter N, Best R B, Vattulainen I, Monticelli L, Periole1 X, Tieleman D P, de Vries A H, Marrink S J 2021 Nat. Methods 18 382Google Scholar

    [77]

    Shrake A, Rupley J A 1973 J. Mol. Biol. 79 351Google Scholar

    [78]

    Torrie G M, Valleau J P 1977 J. Comput. Phys. 23 187Google Scholar

    [79]

    Sugita Y, Okamoto Y 1999 Chem. Phys. Lett. 314 141Google Scholar

    [80]

    Laio A, Parrinello M 2002 Proc. Natl. Acad. Sci. U.S.A. 99 12562Google Scholar

    [81]

    Hamelberg D, Mongan J, McCammon J A 2004 J. Chem. Phys. 120 11919Google Scholar

    [82]

    Yang L, Liu C W, Shao Q, Zhang J, Gao Y Q 2015 Acc. Chem. Res. 48 947Google Scholar

    [83]

    Tribello G A, Bonomi M, Branduardi D, Camilloni C, Bussi G 2014 Comput. Phys. Commun. 185 604Google Scholar

    [84]

    E W, Ren W, Vanden-Eijnden E 2002 Phys. Rev. B 66 052301

    [85]

    Dellago C, Bolhuis P G, Csajka F S, Chandler D 1998 J. Chem. Phys. 108 1964Google Scholar

    [86]

    Chen C, Huang Y, Xiao Y 2013 J. Biomol. Struct. Dyn. 31 206Google Scholar

    [87]

    Zhang J, Gong H 2020 J. Chem. Theory Comput. 16 4813Google Scholar

    [88]

    Zhu W, Zhang J, Wang J, Li W, Wang W 2021 Phys. Rev. E 103 032404Google Scholar

    [89]

    Zheng S, He J, Liu C, et al. 2023 arXiv: 2306.05445 [physics.chem-ph

    [90]

    Schneider E, Dai L, Topper R Q, Drechsel-Grau C, Tuckerman M E 2017 Phys. Rev. Lett. 119 150601Google Scholar

    [91]

    Jolliffe I T 2002 Principal Component Analysis for Special Types of Data (New York: Springer) pp338–372

    [92]

    Tenenbaum J B, de Silva V, Langford J C 2000 Science 290 2319Google Scholar

    [93]

    Lafon S, Lee A B 2006 IEEE Trans. Pattern Anal. Mach. Intell. 28 1393Google Scholar

    [94]

    Das P, Moll M, Stamati H, Kavraki L E, Clementi C 2006 Proc. Natl. Acad. Sci. U.S.A. 103 9885Google Scholar

    [95]

    Plaku E, Stamati H, Clementi C, Kavraki L E 2007 Proteins Struct. Funct. Bioinf. 67 897Google Scholar

    [96]

    Trstanova Z, Leimkuhler B, Lelièvre T 2020 Proc. R. Soc. A 476 20190036Google Scholar

    [97]

    van der Maaten L, Hinton G 2008 J. Mach. Learn. Res. 9 2579

    [98]

    Hinton G, Roweis S 2002 Proceedings of the 15th International Conference on Neural Information Processing Systems Vancouver, British Columbia, Canada, December 9–14, 2002 p857

    [99]

    Li W, Terakawa T, Wang W, Takada S 2012 Proc. Natl. Acad. Sci. U.S.A. 109 17789Google Scholar

    [100]

    Rydzewski J, Nowak W 2016 J. Chem. Theory Comput. 12 2110Google Scholar

    [101]

    Zhou H, Wang F, Tao P 2018 J. Chem. Theory Comput. 14 5499Google Scholar

    [102]

    Spiwok V, Kříž P 2020 Front. Mol. Biosci. 7 132Google Scholar

    [103]

    Roweis S T, Saul L K 2000 Science 290 2323Google Scholar

    [104]

    Belkin M, Niyogi P 2001 Proceedings of the 14th International Conference on Neural Information Processing Systems: Natural and Synthetic Vancouver, British Columbia, Canada, December 3–8, 2001 p585

    [105]

    Donoho D L, Grimes C 2003 Proc. Natl. Acad. Sci. U.S.A. 100 5591Google Scholar

    [106]

    McInnes L, Healy J, Melville J 2018 arXiv: 1802.03426 [stat.ML

    [107]

    Chen S, Lake B B, Zhang K 2019 Nat. Biotechnol. 37 1452Google Scholar

    [108]

    Mimitou E P, Lareau C A, Chen K Y, et al 2021 Nat. Biotechnol. 39 1246Google Scholar

    [109]

    Becht E, McInnes L, Healy J, Dutertre C A, Kwok I W, Ng L G, Ginhoux F, Newell E W 2019 Nat. Biotechnol. 37 38Google Scholar

    [110]

    Trozzi F, Wang X, Tao P 2021 J. Phys. Chem. B 125 5022Google Scholar

    [111]

    Do V H, Canzar S 2021 Genome Biol. 22 130Google Scholar

    [112]

    Kingma D P, Welling M 2013 arXiv:1312.6114 [stat.ML

    [113]

    Ramaswamy V K, Musson S C, Willcocks C G, Degiacomi M T 2021 Phys. Rev. X 11 011052Google Scholar

    [114]

    Gómez-Bombarelli R, Wei J N, Duvenaud D, Hernández-Lobatznero J M, Sánchez-Lengeling B, Sheberla D, Aguilera-Iparraguirre J, Hirzel T D, Adams R P, Aspuru-Guzik A 2018 ACS Cent. Sci. 4 268Google Scholar

    [115]

    Barducci A, Bussi G, Parrinello M 2008 Phys. Rev. Lett. 100 020603Google Scholar

    [116]

    Bonati L, Zhang Y Y, Parrinello M 2019 Proc. Natl. Acad. Sci. U.S.A. 116 17641Google Scholar

    [117]

    Zhang J, Yang Y I, Noé F 2019 J. Phys. Chem. Lett. 10 5791Google Scholar

    [118]

    Rezende D J, Mohamed S 2015 Proceedings of the 32nd International Conference on International Conference on Machine Learning 37 1530

    [119]

    Shamsi Z, Cheng K J, Shukla D 2018 J. Phys. Chem. B 122 8386Google Scholar

    [120]

    Zhang L, Wang H, E W 2018 J. Chem. Phys. 148 12411Google Scholar

    [121]

    Mardt A, Pasquali L, Wu H, Noé F 2018 Nat. Commun. 9 5Google Scholar

    [122]

    Li W, Yoshii H, Hori N, Kameda T, Takada S 2010 Methods 52 106Google Scholar

    [123]

    Li W, Wang J, Zhang J, Wang W 2015 Curr. Opin. Struct. Biol. 30 25Google Scholar

    [124]

    Li G H 2023 Chemical Theory and Multiscale Simulation in Biomolecules: From Principles to Case Studies (1st Ed.) (Elsevier

    [125]

    Meier J, Rao R, Verkuil R, Liu J, Sercu T, Rives A 2021 Language Models Enable Zero-shot Prediction of the Effects of Mutations on Protein Function (35th Conference on Neural Information Processing Systems (NeurIPS 2021)

    [126]

    Wang D, Wang Y, Chang J, Zhang L, Wang H, E W 2021 Nat. Comput. Sci. 2 20Google Scholar

    [127]

    Huang Y P, Xia Y, Yang L, Wei J, Yang Y I, Gao Y Q 2022 Chin. J. Chem. 40 160Google Scholar

  • [1] Zhang Xu, Ding Jin-Min, Hou Chen-Yang, Zhao Yi-Ming, Liu Hong-Wei, Liang Sheng. Machine learning based laser homogenization method. Acta Physica Sinica, 2024, 73(16): 164205. doi: 10.7498/aps.73.20240747
    [2] Zhang Jia-Hui. Machine learning for in silico protein research. Acta Physica Sinica, 2024, 73(6): 069301. doi: 10.7498/aps.73.20231618
    [3] Zhang Xue-Song, Fan Zhen-Zhong, Tong Qi-Lei, Fu Yuan-Feng. Analysis of nanobubble collapse process by molecular simulation method. Acta Physica Sinica, 2024, 73(20): 204701. doi: 10.7498/aps.73.20241105
    [4] Ouyang Xin-Jian, Zhang Yan-Xing, Wang Zhi-Long, Zhang Feng, Chen Wei-Jia, Zhuang Yuan, Jie Xiao, Liu Lai-Jun, Wang Da-Wei. Modeling ferroelectric phase transitions with graph convolutional neural networks. Acta Physica Sinica, 2024, 73(8): 086301. doi: 10.7498/aps.73.20240156
    [5] Guo Wei-Chen, Ai Bao-Quan, He Liang. Reveal flocking phase transition of self-propelled active particles by machine learning regression uncertainty. Acta Physica Sinica, 2023, 72(20): 200701. doi: 10.7498/aps.72.20230896
    [6] Yang Jian-Yu, Xi Kun, Zhu Li-Zhe. Transition state searching for complex biomolecules: Algorithms and machine learning. Acta Physica Sinica, 2023, 72(24): 248701. doi: 10.7498/aps.72.20231319
    [7] Liu Ye, Niu He-Ran, Li Bing-Bing, Ma Xin-Hua, Cui Shu-Wang. Application of machine learning in cosmic ray particle identification. Acta Physica Sinica, 2023, 72(14): 140202. doi: 10.7498/aps.72.20230334
    [8] Zhang Yi-Fan, Ren Wei, Wang Wei-Li, Ding Shu-Jian, Li Nan, Chang Liang, Zhou Qian. Machine learning combined with solid solution strengthening model for predicting hardness of high entropy alloys. Acta Physica Sinica, 2023, 72(18): 180701. doi: 10.7498/aps.72.20230646
    [9] Luo Qi-Rui, Shen Yi-Fan, Luo Meng-Bo. Computer simulation and machine learning of polymer collapse and critical adsorption phase transitions. Acta Physica Sinica, 2023, 72(24): 240502. doi: 10.7498/aps.72.20231058
    [10] Chen Jing-Jing, Qiu Xiao-Lin, Li Ke, Zhou Dan, Yuan Jun-Jun. Mechanical performance analysis of nanocrystalline CoNiCrFeMn high entropy alloy: atomic simulation method. Acta Physica Sinica, 2022, 71(19): 199601. doi: 10.7498/aps.71.20220733
    [11] Ai Fei, Liu Zhi-Bing, Zhang Yuan-Tao. Numerical study of discharge characteristics of atmospheric dielectric barrier discharges by integrating machine learning. Acta Physica Sinica, 2022, 71(24): 245201. doi: 10.7498/aps.71.20221555
    [12] Lin Jian, Ye Meng, Zhu Jia-Wei, Li Xiao-Peng. Machine learning assisted quantum adiabatic algorithm design. Acta Physica Sinica, 2021, 70(14): 140306. doi: 10.7498/aps.70.20210831
    [13] Chen Jiang-Zhi, Yang Chen-Wen, Ren Jie. Machine learning based on wave and diffusion physical systems. Acta Physica Sinica, 2021, 70(14): 144204. doi: 10.7498/aps.70.20210879
    [14] Liu Wu, Zhu Cheng-Wan, Li Hao-Tian, Zhao Su-Ling, Qiao Bo, Xu Zheng, Song Dan-Dan. Optimization of Ga content gradient in Cu(In,Ga)Se2 solar cells through machine learning and device simulation. Acta Physica Sinica, 2021, 70(23): 238802. doi: 10.7498/aps.70.20211234
    [15] Liang Yi-Ran, Liang Qing. Molecular simulation of interaction between charged nanoparticles and phase-separated biomembranes containning charged lipids. Acta Physica Sinica, 2019, 68(2): 028701. doi: 10.7498/aps.68.20181891
    [16] Cheng Yun, Li Jie, Jia Ming, Tang Yi-Wei, Du Shuang-Long, Ai Li-Hua, Yin Bao-Hua, Ai Liang. Application status and future of multi-scale numerical models for lithium ion battery. Acta Physica Sinica, 2015, 64(21): 210202. doi: 10.7498/aps.64.210202
    [17] Li Wen-Fei, Zhang Jian, Wang Jun, Wang Wei. Multiscale theory and computational method for biomolecule simulations. Acta Physica Sinica, 2015, 64(9): 098701. doi: 10.7498/aps.64.098701
    [18] Xiang Hui, Liu Da-Huan, Yang Qing-Yuan, Mi Jian-Guo, Zhong Chong-Li. Effect of framework flexibility on diffusion of short alkanes in metal-organic framework. Acta Physica Sinica, 2011, 60(9): 093602. doi: 10.7498/aps.60.093602
    [19] Wang Dong-Yi, Xue Chun-Yu, Zhong Chong-Li. A molecular simulation of diffusion mechanism of n-alkanes in copper(Ⅱ) benzene-1,3,5-tricarboxylate metal-organic framework. Acta Physica Sinica, 2009, 58(8): 5552-5559. doi: 10.7498/aps.58.5552
    [20] Xu Jing. Molecular dynamics modelling of adsorption of HEDP on calcite surface. Acta Physica Sinica, 2006, 55(3): 1107-1112. doi: 10.7498/aps.55.1107
Metrics
  • Abstract views:  3308
  • PDF Downloads:  197
  • Cited By: 0
Publishing process
  • Received Date:  08 October 2023
  • Accepted Date:  01 November 2023
  • Available Online:  09 November 2023
  • Published Online:  20 December 2023

/

返回文章
返回
Baidu
map