Analyzing Conformational Transition Pathways in Semi-flexible Polymer Chains with Deep Learning

Wan-Chen Zhao; Hai-Yang Huo; Zhong-Yuan Lu; Zhao-Yan Sun

doi:10.1007/s10118-025-3451-2

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Analyzing Conformational Transition Pathways in Semi-flexible Polymer Chains with Deep Learning

RESEARCH ARTICLE | Updated：2025-12-03

- Analyzing Conformational Transition Pathways in Semi-flexible Polymer Chains with Deep Learning
- Chinese Journal of Polymer Science Vol. 43, Issue 12, Pages: 2201-2212(2025)
- Affiliations：
  
  a.State Key Laboratory of Polymer Science and Technology, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China
  b.State Key Laboratory of Supramolecular Structure and Materials, College of Chemistry, Jilin University, Changchun 130012, China
  c.School of Applied Chemistry and Engineering, University of Science and Technology of China, Hefei 230026, China
- Author bio：
  
  luzhu@jlu.edu.cn (Z.Y.L.)
  zysun@ciac.ac.cn (Z.Y.S.)
- Funds：
- DOI：10.1007/s10118-025-3451-2
  CLC：
- Received：01 August 2025，
  
  Accepted：09 September 2025，
  
  Online First：19 November 2025，
  
  Published：15 December 2025
- Accepted：
Scan QR Code
Zhao, W. C.; Huo, H. Y.; Lu, Z. Y.; Sun, Z. Y. Analyzing conformational transition pathways in semi-flexible polymer chains with deep learning. Chinese J. Polym. Sci. 2025, 43, 2201–2212

Wan-Chen Zhao, Hai-Yang Huo, Zhong-Yuan Lu, et al. Analyzing Conformational Transition Pathways in Semi-flexible Polymer Chains with Deep Learning[J]. Chinese Journal of Polymer Science, 2025, 43(12): 2201-2212.
Zhao, W. C.; Huo, H. Y.; Lu, Z. Y.; Sun, Z. Y. Analyzing conformational transition pathways in semi-flexible polymer chains with deep learning. Chinese J. Polym. Sci. 2025, 43, 2201–2212 DOI： 10.1007/s10118-025-3451-2.

Wan-Chen Zhao, Hai-Yang Huo, Zhong-Yuan Lu, et al. Analyzing Conformational Transition Pathways in Semi-flexible Polymer Chains with Deep Learning[J]. Chinese Journal of Polymer Science, 2025, 43(12): 2201-2212. DOI： 10.1007/s10118-025-3451-2.

摘要

We developed a self-supervised learning framework that integrates a PST-transformer with physics-informed contrastive learning

enabling the automated extraction and clustering of polymer conformational evolution features. Based on conformation transition data generated from coarse-grained molecular dynamics simulations

the framework successfully identified five representative unfolding pathways of semiflexible polymer chains during heating.

Abstract

Polymers often exhibit multi-state conformational transitions with multiple pathways as temperature varies. However

characterizing the inherent features of these pathways is hindered by the lack of physical characterizations that can distinguish various transition pathways between complex and disordered states. In this work

we introduced a machine-learning framework based on spatiotemporal point-cloud neural networks to identify and analyze conformational transition pathways in polymer chains. As a case study

we applied this framework to the temperature-induced unfolding of a single semi-flexible polymer chain

simulated

via

coarse-grained molecular dynamics. We first combined spatiotemporal point cloud neural networks and contrastive

learning to extract features of conformational evolution

and then we employed unsupervised learning methods to cluster distinct transition pathways and unfolding trajectories. Our results reveal that

with increasing temperature

semi-flexible polymer chains exhibit five distinct unfolding pathways: rigid rod

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random coil; small toroid

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large toroid

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hairpin

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random coil; rod bundle

$$ \to $$

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hairpin

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random coil; hairpin

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random coil; and tailed structure

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random coil. We further calculated the structural order parameters of those typical conformations with distinct transition pathways

we distincted five transition mechanisms

including the strai

ghtening of rigid rods

tightening of small rings

expansion of hairpin ends

symmetrization of rod bundles

and retraction of tailed structures. These findings demonstrate that our framework presents a promising data-driven approach for analyzing complex conformational transitions in disordered polymers

which might be potentially extendable to other heterogeneous systems like intrinsically disordered proteins.

关键词

Keywords

references

Nakano, T.; Okamoto, Y. Synthetic helical polymers: conformation and function. Chem. Rev. 2001 , 101 , 4013−4038..

[Wang, Z. G. 50th Anniversary perspective: polymer conformation-a pedagogical review. Macromolecules 2017, 50 , 9073-9114..

[Bovey, A. Chain structure and conformation of macromolecules, Academic Press , New York, 1982 , p.1-17.

Stockmay er, W. Problems of the statistical thermodynamics of dilute polymer solutions. Macromol. Chem. Phys. 1960 , 35 , 54−74..

Tiktopulo, E.; Bychkova, V.; Ricka, J.; Ptitsyn, O. Cooperativity of the coil-globule transition in a homopolymer: Microcalorimetric study of poly( N -isopropylacrylamide). Macromolecules 1994 , 27 , 2879−2882..

Chu, B.; Ying, Q.; Grosberg, A. Y. Two-stage kinetics of single-chain collapse. Polystyrene in cyclohexane. Macromolecules 1995 , 28 , 180−189..

Zhang, G.; Wu, C. Reentrant coil-to-globule-to-coil transition of a single linear homopolymer chain in a water/methanol mixture. Phys. Rev. Lett. 2001 , 86 , 822−825..

Picarra, S.; Duhamel, J.; Fedorov, A.; Martinho, J. Coil-globule transition of pyrene-labeled polystyrene in cyclohexane: determination of polymer chain radii by fluorescence. J. Phys. Chem. B 2004 , 108 , 12009−12015..

Gao, Y.; Yang, J.; Ding, Y.; Ye, X. Effect of urea on phase transition of poly( N -isopropylacrylamide) inv estigated by differential scanning calorimetry. J. Phys. Chem. B 2014 , 118 , 9460−9466..

Chan, H. S.; Dill, K. A. Compact polymers. Macromolecules 1989 , 22 , 4559−4573..

Kamata, K.; Araki, T.; Tanaka, H. Hydrodynamic selection of the kinetic pathway of a polymer coil-globule transition. Phys. Rev. Lett. 2009 , 102 , 108303..

Taylor, M. P.; Ye, Y.; Adhikari, S. R. Conformation of a flexible polymer in explicit solvent: accurate solvation potentials for Lennard-Jones chains. J. Chem. Phys. 2015 , 143 , 204901..

Flory, P.; Mark, J.; Abe, A. Random-coil configurations of vinyl polymer chains. The influence of stereoregularity on the average dimensions. J. Am. Chem. Soc. 1966 , 88 , 639−650..

[Su, W. F. Principles of polymer design and synthesis, Springer, New York, 2013 , p. 89.

Haque, F. M.; Grayson, S. M. The synthesis, properties and potential applications of cyclic polymers. Nat. Chem. 2020 , 12 , 433−444..

Leigh, T.; Fernandez-Trillo, P. Helical polymers for biological and medical applications. Nat. Rev. Chem. 2020 , 4 , 291−310..

[Helfand, E. Dynamics of conformational transitions in polymers. Science 1984 , 9 , 647−650..

Helfand, E. Theory of the kinetics of conformational transitions in polymers. J. Chem. Phys. 1971 , 54 , 4651−4661..

[Khokhlov, A. R.; Starodubtzev, S. G.; Vasilevskaya, V. V., Conformational transitions in polymer gels: theory and experiment, Springer, New York, 2005 , p.123-171.

Vasilevskaya, V. V.; Khalatur, P. G.; Khokhlov, A. R. Conformational polymorphism of amphiphilic polymers in a poor solvent. Macromolecules 2003 , 36 , 10103−10111..

Caruso, M. M.; Davis, D. A.; Shen, Q.; Odom, S. A.; Sottos, N. R.; White, S. R.; Moore, J. S. Mechanically-induced chemical changes in polymeric materials. Chem. Rev. 2009 , 109 , 5755−5798..

Kumar, S.; Li, M. S. Biomolecules under mechanical force. Phys. Rep. 2010 , 486 , 1−74..

Huser, T.; Yan, M.; Rothberg, L. J. Single chain spectroscopy of conformational dependence of conjugated polymer photophysics. Proc. Natl. Acad. Sci. 2000 , 97 , 11187−11191..

Santoso, Y.; Joyce, C. M.; Potapova, O.; Le Reste, L.; Hohlbein, J.; Torella, J. P.; Grindley, N. D.; Kapanidis, A. N. Conformational transitions in DNA polymerase I revealed by single-molecule FRET. Proc. Natl. Acad. Sci. 2010 , 107 , 715−720..

Vacha, M.; Habuchi, S. Conformation and physics of polymer chains: a single-molecule perspective. Npg. Asia. Mater. 2010 , 2 , 134−142..

Bolinger, J. C.; Traub, M. C.; Brazard, J .; Adachi, T.; Barbara, P. F.; Vanden Bout, D. A. Conformation and energy transfer in single conjugated polymers. Acc. Chem. Res. 2012 , 45 , 1992−2001..

Duan, X.; Shi, A. C.; An, L. Formation of ionomer microparticles via polyelectrolyte complexation. Macromolecules 2021 , 54 , 9053−9062..

Forrey, C.; Douglas, J. F.; Gilson, M. K. The fundamental role of flexibility on the strength of molecular binding. Soft Matter 2012 , 8 , 6385−6392..

Stukan, M.; Ivanov, V.; Grosberg, A. Y.; Paul, W.; Binder, K. Chain length dependence of the state diagram of a single stiff-chain macromolecule: theory and Monte Carlo simulation. J. Chem. Phys. 2003 , 118 , 3392−3400..

Hoang, T. X.; Giacometti, A.; Podgornik, R.; Nguyen, N. T.; Banavar, J. R.; Maritan,A. From toroidal to rod-like condensates of semiflexible polymers. J. Chem. Phys. 2014 , 140 , 064902.

Zhang, X.; Bao, L.; Wu, Y. Y.; Zhu, X. L.; Tan, Z. J. Radial distribution function of semiflexible oligomers with stretching fl exibility. J. Chem. Phys. 2017 , 147 , 054901..

Vilfan, I. D.; Conwell, C. C.; Sarkar, T.; Hud, N. V. Time study of DNA condensate morphology: implications regarding the nucleation, growth, and equilibrium populations of toroids and rods. Biochemistry 2006 , 45 , 8174−8183..

Maurstad, G.; Stokke, B. T. Toroids of stiff polyelectrolytes. Curr. Opin. Colloid Interface Sci. 2005 , 10 , 16−21..

Hud, N. V.; Vilfan, I. D. Toroidal DNA condensates: unraveling the fine structure and the role of nucleation in determining size. Annu. Rev. Biophys. Biomol. Struct. 2005 , 34 , 295−318..

Nguyen, N. T.; Ngo, A. T.; Hoang, T. X. Energetic preference and topological constraint effects on the formation of DNA twisted toroidal bundles. J. Chem. Phys. 2023 , 158 , 114904..

Li, Y.; Chen, X.; Tong, C.; Li, L.; Qin, C.; Zhang, M.; Zhao, Y.; Chen, Q.; Wang, Y. Double-helix duality: rods bow, toroids wow in the nuclease arena. J. Phys. Chem. Lett. 2025 , 16 , 3 874−3878..

Wu, J.; Cheng, C.; Liu, G.; Zhang, P.; Chen, T. The folding pathways and thermodynamics of semiflexible polymers. J. Chem. Phys. 2018 , 148 , 184901..

Chu, W. T.; Yan, Z.; Chu, X.; Zheng, X.; Liu, Z.; Xu, L.; Zhang, K.; Wang, J. Physics of biomolecular recognition and conformational dynamics. Rep. Prog. Phys. 2021 , 84 , 126601..

Cheng, Y. Single-particle cryo-EM—how did it get here and where will it go. Science 2018 , 361 , 876−880..

Elf, J.; Barkefors, I. Single-molecule kinetics in living cells. Annu. Rev. Biochem. 2019 , 88 , 635−659..

Weiss, S. Measuring conformational dynamics of biomolecules by single molecule fluorescence spectroscopy. Nat. Struct. Biol. 2000 , 7 , 724−729..

Ivetac, A.; Andrew McCammon, J. Molecular recognition in the case of flexible targets. Curr. Pharm. Des. 2011 , 17 , 1663−1671..

Lu, Q.; Wang, J. Single molecule conformational dynamics of adenylate kinase: energy landscape, structural correlations, and transition state ensembles. J. Am. Chem. Soc. 2008 , 130 , 4772−4783..

Frauenfelder, H.; Sligar, S. G.; Wolynes, P. G. The energy landscapes and motions of proteins. Science 1991 , 254 , 1598−1603..

Bryngelson, J. D.; Wolynes, P. G. Spin glasses and the statistical mechanics of protein folding. Proc. Natl. Acad. Sci. 1987 , 84 , 7524−7528..

Onuchic, J. N.; Luthey-Schulten, Z.; Wolynes, P. G. Theory of protein folding: the energy landscape perspective. Annu. Rev. Phys. Chem. 1997 , 48 , 545−600..

Wang, J.; Verkhivker, G. M. Energy landscape theory, funnels, specificity, and optimal criterion format of biomolecular binding. Phys. Rev. Lett. 2003 , 90 , 188101..

Wang, J.; Xu, L.; Wang, E. Optimal specificity and function for flexible biomolecular recognition. Biophys. J. 2007 , 92 , 109−111..

Onuchic, J. N.; Wolynes, P. G. Theory of protein folding. Curr. Opin. Struct. Biol. 2004 , 14 , 70−75..

Chu, X.; Gan, L.; Wang, E.; Wang, J. Quantifying the topography of the intrinsic energy landscape of flexible biomolecular recognition. Proc. Natl. Acad. Sci. 2013 , 110 , 2342−2351..

Chu, X.; Wang, J. Specificity and affinity quantification of flexible recognition from underlying energy landscape topography. PLoS Comput. Biol. 2014 , 10 , 1003782..

Lobanov, M. Y.; Bogatyreva, N.; Galzitskaya, O. Radius of gyration as an indicator of protein structure compactness. Mol. Biol. 2008 , 42 , 623−628..

[Lai, W.-J. C.; Kayedkhordeh, M.; Cornell, E. V.; Farah, E.; Bellaousov, S.; Rietmeijer, R.; Salsi, E.; Mathews, D. H.; Ermolenko, D. N. mRNAs and lncRNAs intrinsically form seconda ry structures with short end-to-end distances. Nat. Commun . 2018, 9 , 4328..

Valle, F.; Favre, M.; De Los Rios, P.; Rosa, A.; Dietler, G. Scaling exponents and probability distributions of DNA end-to-end distance. Phys. Rev. Lett. 2005 , 95 , 158105..

Zhang, W.; Chen, S. J. Analyzing the biopolymer folding rates and pathways using kinetic cluster method. J. Chem. Phys. 2003 , 119 , 8716−8729..

Tao, L.; Varshney, V.; Li, Y. Benchmarking machine learning models for polymer informatics: an example of glass transition temperature. J. Chem. Inf. Model. 2021 , 61 , 5395−5413..

Sha, W.; Li, Y.; Tang, S.; Tian, J.; Zhao, Y.; Guo, Y.; Zhang, W.; Zhang, X.; Lu, S.; Cao, Y. C. Machine learning in polymer informatics. InfoMat 2021 , 3 , 353−361..

Rahman, A.; Deshpande, P.; Radue, M. S.; Odegard, G. M.; Gowtham, S.; Ghosh, S.; Spear, A. D. A machine learning framework for predicting the shear strength of carbon nanotube-polymer interfaces based on molecular dynamics simulation data. Compos. Sci. Technol 2021 , 207 , 108627..

Yoshida, K.; Kanematsu, Y.; Rocabado, D. S. R.; Ishimoto, T. Modelling the dynamic physical properties of vulcanised polymer models by molecular dynamics simulations and machine learning. Comput. Mater. Sci 2023 , 221 , 112081..

Wang, F. T.; Liu, X.; Cheng, J. Water structures and anisotropic dynamics at Pt(211)/water interface revealed by machine learning molecular dynamics. Mater. Futures 2024 , 3 , 041001..

[Shi, W.; Rajkumar, R. Point-gnn: graph neural network for 3D object detection in a point cloud, arXiv. 2020, 2003.01251 ..

[Liu, Y.; Fan, B.; Xiang, S.; Pan, C. Relation-shape convolutional neural network for point cloud analysis. arXiv . 2019 , 1904.07601 ..

Li, Z.; Jiang, M.; Wang, S.; Zhang, S. Deep learning methods for molecular representation and property prediction. Drug Discov. Today 2022 , 27 , 103373..

Braghetto, A.; Kundu, S.; Baiesi, M.; Orlandini, E. Machine learning understands knotted polymers. Macromolecules 2023 , 56 , 2899−2909..

Ge, W.; De Silva, R.; Fan, Y.; Sisson, S. A.; Stenzel, M. H. Machine learning in polymer research. Adv. Mater. 2025 , 37 , 2413695..

Vandans, O.; Yang, K.; Wu, Z.; Dai, L. Identifying knot types of polymer conformations by machine learning. Phys. Rev. E 2020 , 101 , 022502..

Sun, L. W.; Li, H.; Zhang, X. Q.; Gao, H. B.; Luo, M. B. Identifying conformation states of polymer through unsupervised machine learning. Chinese J. Polym. Sci. 2020 , 38 , 1403−1408..

Bejagam, K. K.; An, Y.; Singh, S.; Deshmukh, S. A. Machine-learning enabled new insights into the coil-to-globule transition of thermosensitive polymers using a coarse-grained model. J. Phys. Chem. Lett. 2018 , 9 , 6480−6488..

[Bhattacharya, D.; Patra, T. K. dPOLY: Deep learning of polymer phases and phase transition. Macromolecules 2021, 54 , 3065-3074..

Weeks, J. D.; Chandler, D.; Andersen, H. C. Role of repulsive forces in determining the equilibrium structure of simple liquids. J. Chem. Phys. 1971 , 54 , 5237−5247..

Kremer, K.; Grest, G. S. Dynamics of entangled linear polymer melts: A molecular-dynamics simulation. J. Chem. Phys. 1990 , 92 , 5057−5086..

[Zhu, Y. L.; Liu, H.; Li, Z. W.; Qian, H. J.; Milano, G.; Lu, Z. Y., GALAMOST: GPU-accelerated large-scale molecular simulation toolkit. Wiley Online Library, 2013 .

Zhu, Y. L.; Pan, D.; Li, Z. W.; Liu, H.; Qian, H. J.; Zhao, Y.; Lu, Z. Y.; Sun, Z. Y. Employing multi-GPU power for molecular dynamics simulation: an extension of GALAMOST. Mol. Phys. 2018 , 116 , 1065−1077..

Fan, H.; Yang, Y.; Kankanhalli, M. Point spatio-temporal transformer networks for point cloud vid eo modeling. Ieee. T. Pattern. Anal. 2022 , 45 , 2181−2192..

[Voita, E.; Talbot, D.; Moiseev, F.; Sennrich, R.; Titov, I. Analyzing multi-head self-attention: specialized heads do the heavy lifting, the rest can be pruned. arXiv . 2019, 1905.09418 ..

[Chen, T.; Kornblith, S.; Norouzi, M.; Hinton, G. A simple framework for contrastive learning of visual representations. arXiv . 2020 , 2002.05709 ..

Abdi, H.; Williams, L. J. Principal component analysis. Wiley Interdiscip. Rev. 2010 , 2 , 433−459..

[Reynolds, D., Gaussian mixture models. In Encyclopedia of biometrics , Springer, 2015 ; pp. 827-832..

Maaten, L. v. d.; Hinton, G. Visualizing data using t-SNE. J. Mach. Learn. Res. 2008 , 9 , 2579−2605..

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