Machine learning in molecular simulations of biomolecules

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

doi:10.7498/aps.72.20231624

Abstract

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.

Keywords:

Authors and contacts

1.
School of Physics, Nanjing University, Nanjing 210093, China
2.
Wenzhou Key Laboratory of Biophysics, Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou 325000, China

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).

FullText HTML : translate this paragraph

References

[1]	McCammon J A, Gelin B R, Karplus M 1977 Nature 267 585 Google Scholar
[2]	Schlick T, Portillo-Ledesma S 2021 Nat. Comput. Sci. 1 321 Google Scholar
[3]	Vendruscolo M, Dobson C M 2011 Curr. Biol. 21 R68 Google Scholar
[4]	Shaw D E, Maragakis P, Lindorff-Larsen K, et al. 2010 Science 330 341 Google Scholar
[5]	Zhou C Y, Jiang F, Wu Y D 2015 J. Phys. Chem. B 119 1035 Google Scholar
[6]	Zerze G H, Zheng W, Best R B, Mittal J 2019 J. Phys. Chem. Lett. 10 2227 Google 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 15959 Google Scholar
[9]	Yu I, Mori T, Ando T, Harada R, Jung J, Sugita Y, Feig M 2016 eLife 5 e19274 Google Scholar
[10]	李文飞, 张建, 王骏, 王炜 2015 物理学报 64 098701 Google Scholar Li W F, Zhang J, Wang J, Wang W 2015 Acta Phys. Sin. 64 098701 Google Scholar
[11]	Samuel A L 1959 IBM J. Res. Dev. 3 210 Google Scholar
[12]	Stigler S M 1974 Hist. Math. 1 431 Google 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 40 874 Google Scholar
[15]	Rumelhart D E, Hinton G E, Williams R J 1986 Nature 323 533 Google Scholar
[16]	Cortes C, Vapnik V 1995 Mach. Learn. 20 273 Google 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. 86 152 Google Scholar
[20]	Cai Y, Liu X, Xu X, Zhou G 2001 BMC Bioinf. 2 1 Google Scholar
[21]	Cai C, Wang W, Sun L, Chen Y 2003 Math. Biosci. 185 111 Google Scholar
[22]	Zernov V V, Balakin K V, Ivaschenko A A, Savchuk N P, Pletnev I V 2003 J. Chem. Inf. Comput. Sci. 43 2048 Google Scholar
[23]	Blank T B, Brown S D, Calhoun A W, Doren D J 1995 J. Chem. Phys. 103 4129 Google Scholar
[24]	Krizhevsky A, Sutskever I, Hinton G E 2017 Commun. ACM 60 84 Google 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 63 139 Google 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 eaaw1147 Google Scholar
[29]	Yang J, Anishchenko I, Park H, Peng Z, Ovchinnikov S, Baker D 2020 Proc. Natl. Acad. Sci. U.S.A. 117 1496 Google Scholar
[30]	Jumper J, Evans R, Pritzel A, et al. 2021 Nature 596 583 Google 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 373 871 Google Scholar
[32]	Huang B, Xu Y, Hu X, Liu Y, Liao S, Zhang J, Huang C, Hong J, Chen Q, Liu H 2022 Nature 602 523 Google 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. 2 451 Google Scholar
[34]	Köhler J, Chen Y, Krämer A, Clementi C, Noé F 2023 J. Chem. Theory Comput. 19 94216 Google 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 1089 Google Scholar
[36]	Kuhlman B, Bradley P 2019 Nat. Rev. Mol. Cell Biol. 20 681 Google Scholar
[37]	Jisna V, Jayaraj P 2021 Protein J. 40 522 Google Scholar
[38]	AlQuraishi M 2021 Curr. Opin. Chem. Biol. 65 1 Google 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 2773 Google Scholar
[40]	Huang B, Du Y, Zhang S, Li W, Wang J, Zhang J 2020 Chin. Phys. B 29 108704 Google Scholar
[41]	Zhang J, Chen D, Xia Y, et al. 2023 J. Chem. Theory Comput. 19 4338 Google Scholar
[42]	Ramanathan A, Ma H, Parvatikar A, Chennubhotla S C 2021 Curr. Opin. Struct. Biol. 66 216 Google Scholar
[43]	Noé F, Tkatchenko A, Müller K R, Clementi C 2020 Annu. Rev. Phys. Chem. 71 361 Google Scholar
[44]	Wang Y, Ribeiro J M L, Tiwary P 2020 Curr. Opin. Struct. Biol. 61 139 Google Scholar
[45]	Sambasivarao S V, Acevedo O 2009 J. Chem. Theory Comput. 5 1038 Google 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 1545 Google Scholar
[47]	Wang J, Wolf R M, Caldwell J W, Kollman P A, Case D A 2004 J. Comput. Chem. 25 528 Google Scholar
[48]	Peng X, Zhang Y, Chu H, Li Y, Zhang D, Cao L, Li G 2016 J. Chem. Theory Comput. 12 2973 Google Scholar
[49]	Liu C, Qi R, Wang Q, Piquemal J P, Ren P 2017 J. Chem. Theory Comput. 13 2751 Google 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 143001 Google Scholar
[52]	Zhang L, Han J, Wang H, Car R, Weinan E 2018 J. Chem. Phys. 149 034101 Google Scholar
[53]	Park C W, Kornbluth M, Vandermause J, Wolverton C, Kozinsky B, Mailoa J P 2021 npj Comput. Mater. 7 73 Google 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 2453 Google 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 146401 Google Scholar
[58]	Artrith N, Urban A 2016 Comput. Mater. Sci. 114 135 Google Scholar
[59]	Smith J S, Isayev O, Roitberg A E 2017 Chem. Sci. 8 3192 Google Scholar
[60]	Fan Z, Wang Y, Ying P, et al. 2022 J. Chem. Phys. 157 114801 Google Scholar
[61]	Chmiela S, Tkatchenko A, Sauceda H E, Poltavsky I, Schütt K T, Müller K R 2017 Sci. Adv. 3 e1603015 Google 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 7982 Google Scholar
[64]	Takada S, Kanada R, Tan C, Terakawa T, Li W, Kenzaki H 2015 Acc. Chem. Res. 48 3026 Google Scholar
[65]	Reith D, Pütz M, Müller-Plathe F 2003 J. Comput. Chem. 24 1624 Google Scholar
[66]	Izvekov S, Voth G A 2005 J. Phys. Chem. B 109 2469 Google Scholar
[67]	Chu J W, Ayton G, Izvekov S, Voth G 2007 Mol. Phys. 105 167 Google Scholar
[68]	Li W, Wolynes P G, Takada S 2011 Proc. Natl. Acad. Sci. U.S.A. 108 3504 Google Scholar
[69]	Gohlke H, Kiel C, Case D A 2003 J. Mol. Biol. 330 891 Google Scholar
[70]	Wang J, Olsson S, Wehmeyer C, Pérez A, Charron N E, De Fabritiis G, Noé F, Clementi C 2019 ACS Cent. Sci. 5 755 Google 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. 5 125 Google Scholar
[73]	Zhang J, Lei Y K, Yang Y I, Gao Y Q 2020 J. Chem. Phys. 153 174115 Google Scholar
[74]	Dong T, Gong T, Li W 2021 J. Phys. Chem. B 125 9490 Google Scholar
[75]	Marrink S J, Risselada H J, Yefimov S, Tieleman D P, de Vries A H 2007 J. Phys. Chem. B 111 7812 Google 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 18 382 Google Scholar
[77]	Shrake A, Rupley J A 1973 J. Mol. Biol. 79 351 Google Scholar
[78]	Torrie G M, Valleau J P 1977 J. Comput. Phys. 23 187 Google Scholar
[79]	Sugita Y, Okamoto Y 1999 Chem. Phys. Lett. 314 141 Google Scholar
[80]	Laio A, Parrinello M 2002 Proc. Natl. Acad. Sci. U.S.A. 99 12562 Google Scholar
[81]	Hamelberg D, Mongan J, McCammon J A 2004 J. Chem. Phys. 120 11919 Google Scholar
[82]	Yang L, Liu C W, Shao Q, Zhang J, Gao Y Q 2015 Acc. Chem. Res. 48 947 Google Scholar
[83]	Tribello G A, Bonomi M, Branduardi D, Camilloni C, Bussi G 2014 Comput. Phys. Commun. 185 604 Google 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 1964 Google Scholar
[86]	Chen C, Huang Y, Xiao Y 2013 J. Biomol. Struct. Dyn. 31 206 Google Scholar
[87]	Zhang J, Gong H 2020 J. Chem. Theory Comput. 16 4813 Google Scholar
[88]	Zhu W, Zhang J, Wang J, Li W, Wang W 2021 Phys. Rev. E 103 032404 Google 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 150601 Google 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 2319 Google Scholar
[93]	Lafon S, Lee A B 2006 IEEE Trans. Pattern Anal. Mach. Intell. 28 1393 Google Scholar
[94]	Das P, Moll M, Stamati H, Kavraki L E, Clementi C 2006 Proc. Natl. Acad. Sci. U.S.A. 103 9885 Google Scholar
[95]	Plaku E, Stamati H, Clementi C, Kavraki L E 2007 Proteins Struct. Funct. Bioinf. 67 897 Google Scholar
[96]	Trstanova Z, Leimkuhler B, Lelièvre T 2020 Proc. R. Soc. A 476 20190036 Google 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 17789 Google Scholar
[100]	Rydzewski J, Nowak W 2016 J. Chem. Theory Comput. 12 2110 Google Scholar
[101]	Zhou H, Wang F, Tao P 2018 J. Chem. Theory Comput. 14 5499 Google Scholar
[102]	Spiwok V, Kříž P 2020 Front. Mol. Biosci. 7 132 Google Scholar
[103]	Roweis S T, Saul L K 2000 Science 290 2323 Google 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 5591 Google 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 1452 Google Scholar
[108]	Mimitou E P, Lareau C A, Chen K Y, et al 2021 Nat. Biotechnol. 39 1246 Google 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 38 Google Scholar
[110]	Trozzi F, Wang X, Tao P 2021 J. Phys. Chem. B 125 5022 Google Scholar
[111]	Do V H, Canzar S 2021 Genome Biol. 22 130 Google 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 011052 Google 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. 4 268 Google Scholar
[115]	Barducci A, Bussi G, Parrinello M 2008 Phys. Rev. Lett. 100 020603 Google Scholar
[116]	Bonati L, Zhang Y Y, Parrinello M 2019 Proc. Natl. Acad. Sci. U.S.A. 116 17641 Google Scholar
[117]	Zhang J, Yang Y I, Noé F 2019 J. Phys. Chem. Lett. 10 5791 Google 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 8386 Google Scholar
[120]	Zhang L, Wang H, E W 2018 J. Chem. Phys. 148 12411 Google Scholar
[121]	Mardt A, Pasquali L, Wu H, Noé F 2018 Nat. Commun. 9 5 Google Scholar
[122]	Li W, Yoshii H, Hori N, Kameda T, Takada S 2010 Methods 52 106 Google Scholar
[123]	Li W, Wang J, Zhang J, Wang W 2015 Curr. Opin. Struct. Biol. 30 25 Google 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 20 Google Scholar
[127]	Huang Y P, Xia Y, Yang L, Wei J, Yang Y I, Gao Y Q 2022 Chin. J. Chem. 40 160 Google Scholar

Cited By

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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).

DownLoad: Full-Size Img PowerPoint

[1]	McCammon J A, Gelin B R, Karplus M 1977 Nature 267 585 Google Scholar
[2]	Schlick T, Portillo-Ledesma S 2021 Nat. Comput. Sci. 1 321 Google Scholar
[3]	Vendruscolo M, Dobson C M 2011 Curr. Biol. 21 R68 Google Scholar
[4]	Shaw D E, Maragakis P, Lindorff-Larsen K, et al. 2010 Science 330 341 Google Scholar
[5]	Zhou C Y, Jiang F, Wu Y D 2015 J. Phys. Chem. B 119 1035 Google Scholar
[6]	Zerze G H, Zheng W, Best R B, Mittal J 2019 J. Phys. Chem. Lett. 10 2227 Google 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 15959 Google Scholar
[9]	Yu I, Mori T, Ando T, Harada R, Jung J, Sugita Y, Feig M 2016 eLife 5 e19274 Google Scholar
[10]	李文飞, 张建, 王骏, 王炜 2015 物理学报 64 098701 Google Scholar Li W F, Zhang J, Wang J, Wang W 2015 Acta Phys. Sin. 64 098701 Google Scholar
[11]	Samuel A L 1959 IBM J. Res. Dev. 3 210 Google Scholar
[12]	Stigler S M 1974 Hist. Math. 1 431 Google 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 40 874 Google Scholar
[15]	Rumelhart D E, Hinton G E, Williams R J 1986 Nature 323 533 Google Scholar
[16]	Cortes C, Vapnik V 1995 Mach. Learn. 20 273 Google 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. 86 152 Google Scholar
[20]	Cai Y, Liu X, Xu X, Zhou G 2001 BMC Bioinf. 2 1 Google Scholar
[21]	Cai C, Wang W, Sun L, Chen Y 2003 Math. Biosci. 185 111 Google Scholar
[22]	Zernov V V, Balakin K V, Ivaschenko A A, Savchuk N P, Pletnev I V 2003 J. Chem. Inf. Comput. Sci. 43 2048 Google Scholar
[23]	Blank T B, Brown S D, Calhoun A W, Doren D J 1995 J. Chem. Phys. 103 4129 Google Scholar
[24]	Krizhevsky A, Sutskever I, Hinton G E 2017 Commun. ACM 60 84 Google 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 63 139 Google 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 eaaw1147 Google Scholar
[29]	Yang J, Anishchenko I, Park H, Peng Z, Ovchinnikov S, Baker D 2020 Proc. Natl. Acad. Sci. U.S.A. 117 1496 Google Scholar
[30]	Jumper J, Evans R, Pritzel A, et al. 2021 Nature 596 583 Google 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 373 871 Google Scholar
[32]	Huang B, Xu Y, Hu X, Liu Y, Liao S, Zhang J, Huang C, Hong J, Chen Q, Liu H 2022 Nature 602 523 Google 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. 2 451 Google Scholar
[34]	Köhler J, Chen Y, Krämer A, Clementi C, Noé F 2023 J. Chem. Theory Comput. 19 94216 Google 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 1089 Google Scholar
[36]	Kuhlman B, Bradley P 2019 Nat. Rev. Mol. Cell Biol. 20 681 Google Scholar
[37]	Jisna V, Jayaraj P 2021 Protein J. 40 522 Google Scholar
[38]	AlQuraishi M 2021 Curr. Opin. Chem. Biol. 65 1 Google 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 2773 Google Scholar
[40]	Huang B, Du Y, Zhang S, Li W, Wang J, Zhang J 2020 Chin. Phys. B 29 108704 Google Scholar
[41]	Zhang J, Chen D, Xia Y, et al. 2023 J. Chem. Theory Comput. 19 4338 Google Scholar
[42]	Ramanathan A, Ma H, Parvatikar A, Chennubhotla S C 2021 Curr. Opin. Struct. Biol. 66 216 Google Scholar
[43]	Noé F, Tkatchenko A, Müller K R, Clementi C 2020 Annu. Rev. Phys. Chem. 71 361 Google Scholar
[44]	Wang Y, Ribeiro J M L, Tiwary P 2020 Curr. Opin. Struct. Biol. 61 139 Google Scholar
[45]	Sambasivarao S V, Acevedo O 2009 J. Chem. Theory Comput. 5 1038 Google 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 1545 Google Scholar
[47]	Wang J, Wolf R M, Caldwell J W, Kollman P A, Case D A 2004 J. Comput. Chem. 25 528 Google Scholar
[48]	Peng X, Zhang Y, Chu H, Li Y, Zhang D, Cao L, Li G 2016 J. Chem. Theory Comput. 12 2973 Google Scholar
[49]	Liu C, Qi R, Wang Q, Piquemal J P, Ren P 2017 J. Chem. Theory Comput. 13 2751 Google 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 143001 Google Scholar
[52]	Zhang L, Han J, Wang H, Car R, Weinan E 2018 J. Chem. Phys. 149 034101 Google Scholar
[53]	Park C W, Kornbluth M, Vandermause J, Wolverton C, Kozinsky B, Mailoa J P 2021 npj Comput. Mater. 7 73 Google 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 2453 Google 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 146401 Google Scholar
[58]	Artrith N, Urban A 2016 Comput. Mater. Sci. 114 135 Google Scholar
[59]	Smith J S, Isayev O, Roitberg A E 2017 Chem. Sci. 8 3192 Google Scholar
[60]	Fan Z, Wang Y, Ying P, et al. 2022 J. Chem. Phys. 157 114801 Google Scholar
[61]	Chmiela S, Tkatchenko A, Sauceda H E, Poltavsky I, Schütt K T, Müller K R 2017 Sci. Adv. 3 e1603015 Google 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 7982 Google Scholar
[64]	Takada S, Kanada R, Tan C, Terakawa T, Li W, Kenzaki H 2015 Acc. Chem. Res. 48 3026 Google Scholar
[65]	Reith D, Pütz M, Müller-Plathe F 2003 J. Comput. Chem. 24 1624 Google Scholar
[66]	Izvekov S, Voth G A 2005 J. Phys. Chem. B 109 2469 Google Scholar
[67]	Chu J W, Ayton G, Izvekov S, Voth G 2007 Mol. Phys. 105 167 Google Scholar
[68]	Li W, Wolynes P G, Takada S 2011 Proc. Natl. Acad. Sci. U.S.A. 108 3504 Google Scholar
[69]	Gohlke H, Kiel C, Case D A 2003 J. Mol. Biol. 330 891 Google Scholar
[70]	Wang J, Olsson S, Wehmeyer C, Pérez A, Charron N E, De Fabritiis G, Noé F, Clementi C 2019 ACS Cent. Sci. 5 755 Google 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. 5 125 Google Scholar
[73]	Zhang J, Lei Y K, Yang Y I, Gao Y Q 2020 J. Chem. Phys. 153 174115 Google Scholar
[74]	Dong T, Gong T, Li W 2021 J. Phys. Chem. B 125 9490 Google Scholar
[75]	Marrink S J, Risselada H J, Yefimov S, Tieleman D P, de Vries A H 2007 J. Phys. Chem. B 111 7812 Google 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 18 382 Google Scholar
[77]	Shrake A, Rupley J A 1973 J. Mol. Biol. 79 351 Google Scholar
[78]	Torrie G M, Valleau J P 1977 J. Comput. Phys. 23 187 Google Scholar
[79]	Sugita Y, Okamoto Y 1999 Chem. Phys. Lett. 314 141 Google Scholar
[80]	Laio A, Parrinello M 2002 Proc. Natl. Acad. Sci. U.S.A. 99 12562 Google Scholar
[81]	Hamelberg D, Mongan J, McCammon J A 2004 J. Chem. Phys. 120 11919 Google Scholar
[82]	Yang L, Liu C W, Shao Q, Zhang J, Gao Y Q 2015 Acc. Chem. Res. 48 947 Google Scholar
[83]	Tribello G A, Bonomi M, Branduardi D, Camilloni C, Bussi G 2014 Comput. Phys. Commun. 185 604 Google 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 1964 Google Scholar
[86]	Chen C, Huang Y, Xiao Y 2013 J. Biomol. Struct. Dyn. 31 206 Google Scholar
[87]	Zhang J, Gong H 2020 J. Chem. Theory Comput. 16 4813 Google Scholar
[88]	Zhu W, Zhang J, Wang J, Li W, Wang W 2021 Phys. Rev. E 103 032404 Google 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 150601 Google 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 2319 Google Scholar
[93]	Lafon S, Lee A B 2006 IEEE Trans. Pattern Anal. Mach. Intell. 28 1393 Google Scholar
[94]	Das P, Moll M, Stamati H, Kavraki L E, Clementi C 2006 Proc. Natl. Acad. Sci. U.S.A. 103 9885 Google Scholar
[95]	Plaku E, Stamati H, Clementi C, Kavraki L E 2007 Proteins Struct. Funct. Bioinf. 67 897 Google Scholar
[96]	Trstanova Z, Leimkuhler B, Lelièvre T 2020 Proc. R. Soc. A 476 20190036 Google 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 17789 Google Scholar
[100]	Rydzewski J, Nowak W 2016 J. Chem. Theory Comput. 12 2110 Google Scholar
[101]	Zhou H, Wang F, Tao P 2018 J. Chem. Theory Comput. 14 5499 Google Scholar
[102]	Spiwok V, Kříž P 2020 Front. Mol. Biosci. 7 132 Google Scholar
[103]	Roweis S T, Saul L K 2000 Science 290 2323 Google 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 5591 Google 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 1452 Google Scholar
[108]	Mimitou E P, Lareau C A, Chen K Y, et al 2021 Nat. Biotechnol. 39 1246 Google 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 38 Google Scholar
[110]	Trozzi F, Wang X, Tao P 2021 J. Phys. Chem. B 125 5022 Google Scholar
[111]	Do V H, Canzar S 2021 Genome Biol. 22 130 Google 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 011052 Google 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. 4 268 Google Scholar
[115]	Barducci A, Bussi G, Parrinello M 2008 Phys. Rev. Lett. 100 020603 Google Scholar
[116]	Bonati L, Zhang Y Y, Parrinello M 2019 Proc. Natl. Acad. Sci. U.S.A. 116 17641 Google Scholar
[117]	Zhang J, Yang Y I, Noé F 2019 J. Phys. Chem. Lett. 10 5791 Google 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 8386 Google Scholar
[120]	Zhang L, Wang H, E W 2018 J. Chem. Phys. 148 12411 Google Scholar
[121]	Mardt A, Pasquali L, Wu H, Noé F 2018 Nat. Commun. 9 5 Google Scholar
[122]	Li W, Yoshii H, Hori N, Kameda T, Takada S 2010 Methods 52 106 Google Scholar
[123]	Li W, Wang J, Zhang J, Wang W 2015 Curr. Opin. Struct. Biol. 30 25 Google 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 20 Google Scholar
[127]	Huang Y P, Xia Y, Yang L, Wei J, Yang Y I, Gao Y Q 2022 Chin. J. Chem. 40 160 Google Scholar

[1]	Zhang Jia-Hui. Machine learning for in silico protein research. Acta Physica Sinica, 2024, 73(6): 069301. doi: 10.7498/aps.73.20231618
[2]	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
[3]	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
[4]	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
[5]	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
[6]	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
[7]	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
[8]	Zhang Jia-Wei, Yao Hong-Bo, Zhang Yuan-Zheng, Jiang Wei-Bo, Wu Yong-Hui, Zhang Ya-Ju, Ao Tian-Yong, Zheng Hai-Wu. Self-powered sensing based on triboelectric nanogenerator through machine learning and its application. Acta Physica Sinica, 2022, 71(7): 078702. doi: 10.7498/aps.71.20211632
[9]	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
[10]	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
[11]	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
[12]	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
[13]	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
[14]	Yang Zi-Xin, Gao Zhang-Ran, Sun Xiao-Fan, Cai Hong-Ling, Zhang Feng-Ming, Wu Xiao-Shan. High critical transition temperature of lead-based perovskite ferroelectric crystals: A machine learning study. Acta Physica Sinica, 2019, 68(21): 210502. doi: 10.7498/aps.68.20190942
[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

Catalog

Vol. 72, Issue 24 - 2023-12-20

Metrics

Abstract views: 1287
PDF Downloads: 121
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板