Despite the modern advances in the available computational resources, the length and time scales of the physical systems that can be studied in full atomic detail, via molecular simulations, are still limited. To overcome such limitations, coarse-grained (CG) models have been developed to reduce the dimensionality of the physical system under study. However, to study such systems at the atomic level, it is necessary to re-introduce the atomistic details into the CG description. Such an ill-posed mathematical problem is typically treated via numerical algorithms, which need to balance accuracy, efficiency, and general applicability. Here, we introduce an efficient and versatile method for backmapping multi-component CG macromolecules of arbitrary microstructures. By utilizing deep learning algorithms, we train a convolutional neural network to learn structural correlations between polymer configurations at the atomistic and their corresponding CG descriptions, obtained from atomistic simulations. The trained model is then utilized to get predictions of atomistic structures from input CG configurations. As an illustrative example, we apply the convolutional neural network to polybutadiene copolymers of various microstructures, in which each monomer microstructure (i.e., cis-1,4, trans-1,4, and vinyl-1,2) is represented as a different CG particle type. The proposed methodology is transferable over molecular weight and various microstructures. Moreover, starting from a specific single CG configuration with a given microstructure, we show that by modifying its chemistry (i.e., CG particle types), we are able to obtain a set of well equilibrated polymer configurations of different microstructures (chemistry) than the one of the original CG configuration.
REFERENCES
1.
G. S.
Ayton
, W. G.
Noid
, and G. A.
Voth
, “Multiscale modeling of biomolecular systems: In serial and in parallel
,” Curr. Opin. Struct. Biol.
17
(2
), 192
–198
(2007
).2.
T.
Murtola
, A.
Bunker
, I.
Vattulainen
, M.
Deserno
, and M.
Karttunen
, “Multiscale modeling of emergent materials: Biological and soft matter
,” Phys. Chem. Chem. Phys.
11
, 1869
–1892
(2009
).3.
4.
V. A.
Harmandaris
, V. G.
Mavrantzas
, D. N.
Theodorou
, M.
Kröger
, J.
Ramírez
, H. C.
Öttinger
, and D.
Vlassopoulos
, “Crossover from the rouse to the entangled polymer melt regime: Signals from long, detailed atomistic molecular dynamics simulations, supported by rheological experiments
,” Macromolecules
36
(4
), 1376
–1387
(2003
).5.
M.
Kotelyanskii
and D. N.
Theodorou
, Simulation Methods for Polymers
(CRC Press
, 2004
).6.
W. G.
Noid
, J.-W.
Chu
, G. S.
Ayton
, V.
Krishna
, S.
Izvekov
, G. A.
Voth
, A.
Das
, and H. C.
Andersen
, “The multiscale coarse-graining method. I. A Rigorous bridge between atomistic and coarse-grained models
,” J. Chem. Phys.
128
(24
), 244114
(2008
).7.
G. A.
Voth
, Coarse-Graining of Condensed Phase and Biomolecular Systems
(CRC Press
, 2008
).8.
V. A.
Harmandaris
, D.
Reith
, N. F. A.
van der Vegt
, and K.
Kremer
, “Comparison between coarse-graining models for polymer systems: Two mapping schemes for polystyrene
,” Macromol. Chem. Phys.
208
(19-20
), 2109
–2120
(2007
).9.
V. A.
Harmandaris
, N. P.
Adhikari
, N. F. A.
van der Vegt
, and K.
Kremer
, “Hierarchical modeling of polystyrene: From atomistic to coarse-grained simulations
,” Macromolecules
39
(19
), 6708
–6719
(2006
).10.
V. A.
Harmandaris
and K.
Kremer
, “Predicting polymer dynamics at multiple length and time scales
,” Soft Matter
5
, 3920
–3926
(2009
).11.
S. J.
Marrink
, H. J.
Risselada
, S.
Yefimov
, D. P.
Tieleman
, and A. H.
de Vries
, “The MARTINI force field: Coarse grained model for biomolecular simulations
,” J. Phys. Chem. B
111
(27
), 7812
–7824
(2007
).12.
R.
Potestio
, C.
Peter
, and K.
Kremer
, “Computer simulations of soft matter: Linking the scales
,” Entropy
16
(8
), 4199
–4245
(2014
).13.
W. G.
Noid
, “Perspective: Coarse-grained models for biomolecular systems
,” J. Chem. Phys.
139
(9
), 090901
(2013
).14.
E.
Brini
, E. A.
Algaer
, P.
Ganguly
, C.
Li
, F.
Rodríguez-Ropero
, and N. F. A.
van der Vegt
, “Systematic coarse-graining methods for soft matter simulations—A review
,” Soft Matter
9
, 2108
–2119
(2013
).15.
S.
Izvekov
and G. A.
Voth
, “Multiscale coarse graining of liquid-state systems
,” J. Chem. Phys.
123
(13
), 134105
(2005
).16.
W.
Tschöp
, K.
Kremer
, J.
Batoulis
, T.
Bürger
, and O.
Hahn
, “Simulation of polymer melts. I. Coarse-graining procedure for polycarbonates
,” Acta Polym.
49
(2-3
), 61
–74
(1998
).17.
F.
Müller-Plathe
, “Coarse-graining in polymer simulation: From the atomistic to the mesoscopic scale and back
,” ChemPhysChem
3
(9
), 754
–769
(2002
).18.
R. L. C.
Akkermans
and W. J.
Briels
, “Coarse-grained interactions in polymer melts: A variational approach
,” J. Chem. Phys.
115
(13
), 6210
–6219
(2001
).19.
V. A.
Harmandaris
and K.
Kremer
, “Dynamics of polystyrene melts through hierarchical multiscale simulations
,” Macromolecules
42
(3
), 791
–802
(2009
).20.
K.
Johnston
and V.
Harmandaris
, “Hierarchical simulations of hybrid polymer–solid materials
,” Soft Matter
9
, 6696
–6710
(2013
).21.
L.
Lu
, S.
Izvekov
, A.
Das
, H. C.
Andersen
, and G. A.
Voth
, “Efficient, regularized, and scalable algorithms for multiscale coarse-graining
,” J. Chem. Theory Comput.
6
(3
), 954
–965
(2010
).22.
J. F.
Rudzinski
and W. G.
Noid
, “Coarse-graining entropy, forces, and structures
,” J. Chem. Phys.
135
(21
), 214101
(2011
).23.
I.
Bilionis
and N.
Zabaras
, “A stochastic optimization approach to coarse-graining using a relative-entropy framework
,” J. Chem. Phys.
138
(4
), 044313
(2013
).24.
A. P.
Lyubartsev
and A.
Laaksonen
, On the Reduction of Molecular Degrees of Freedom in Computer Simulations
(Springer
, Berlin, Heidelberg
, 2004
), pp. 219
–244
.25.
D.
Fritz
, V. A.
Harmandaris
, K.
Kremer
, and N. F. A.
van der Vegt
, “Coarse grained polymer melts based on isolated atomistic chains: Simulation of polystyrene of different tacticities
,” Macromolecules
42
(19
), 7579
–7588
(2009
).26.
J.
Zhao
, S.
Nagao
, and Z.
Zhang
, “Thermomechanical properties dependence on chain length in bulk polyethylene: Coarse-grained molecular dynamics simulations
,” J. Mater. Res.
25
(3
), 537
–544
(2010
).27.
N.
Shahidi
, A.
Chazirakis
, V.
Harmandaris
, and M.
Doxastakis
, “Coarse-graining of polyisoprene melts using inverse Monte Carlo and local density potentials
,” J. Chem. Phys.
152
(12
), 124902
(2020
).28.
W.
Li
, P. K.
Jana
, A. F.
Behbahani
, G.
Kritikos
, L.
Schneider
, P.
Polińska
, C.
Burkhart
, V. A.
Harmandaris
, M.
Müller
, and M.
Doxastakis
, “Dynamics of long entangled polyisoprene melts via multiscale modeling
,” Macromolecules
54
(18
), 8693
–8713
(2021
).29.
L.
Yelash
, M.
Müller
, W.
Paul
, and K.
Binder
, “How well can coarse-grained models of real polymers describe their structure? The case of polybutadiene
,” J. Chem. Theory Comput.
2
(3
), 588
–597
(2006
).30.
A. F.
Behbahani
, L.
Schneider
, A.
Rissanou
, A.
Chazirakis
, P.
Bačová
, P. K.
Jana
, W.
Li
, M.
Doxastakis
, P.
Polińska
, C.
Burkhart
et al, “Dynamics and rheology of polymer melts via hierarchical atomistic, coarse-grained, and slip-spring simulations
,” Macromolecules
54
(6
), 2740
–2762
(2021
).31.
V.
Harmandaris
and M.
Doxastakis
, “Molecular dynamics of polyisoprene/polystyrene oligomer blends: The role of self-concentration and fluctuations on blend dynamics
,” J. Chem. Phys.
139
(3
), 034904
(2013
).32.
Y. N.
Pandey
, A.
Brayton
, C.
Burkhart
, G. J.
Papakonstantopoulos
, and M.
Doxastakis
, “Multiscale modeling of polyisoprene on graphite
,” J. Chem. Phys.
140
(5
), 054908
(2014
).33.
L.-J.
Chen
, H.-J.
Qian
, Z.-Y.
Lu
, Z.-S.
Li
, and C.-C.
Sun
, “An automatic coarse-graining and fine-graining simulation method: Application on polyethylene
,” J. Phys. Chem. B
110
(47
), 24093
–24100
(2006
).34.
G.
Santangelo
, A.
Di Matteo
, F.
Müller-Plathe
, and G.
Milano
, “From mesoscale back to atomistic models: A fast reverse-mapping procedure for vinyl polymer chains
,” J. Phys. Chem. B
111
(11
), 2765
–2773
(2007
).35.
A. J.
Rzepiela
, L. V.
Schäfer
, N.
Goga
, H. J.
Risselada
, A. H.
de Vries
, and S. J.
Marrink
, “Reconstruction of atomistic details from coarse-grained structures
,” J. Comput. Chem.
31
(6
), 1333
–1343
(2010
).36.
J.
Krajniak
, S.
Pandiyan
, E.
Nies
, and G.
Samaey
, “Generic adaptive resolution method for reverse mapping of polymers from coarse-grained to atomistic descriptions
,” J. Chem. Theory Comput.
12
(11
), 5549
–5562
(2016
).37.
G.
Zhang
, A.
Chazirakis
, V. A.
Harmandaris
, T.
Stuehn
, K. C.
Daoulas
, and K.
Kremer
, “Hierarchical modelling of polystyrene melts: From soft blobs to atomistic resolution
,” Soft Matter
15
, 289
–302
(2019
).38.
T.
Spyriouni
, C.
Tzoumanekas
, D.
Theodorou
, F.
Müller-Plathe
, and G.
Milano
, “Coarse-grained and reverse-mapped united-atom simulations of long-chain atactic polystyrene melts: Structure, thermodynamic properties, chain conformation, and entanglements
,” Macromolecules
40
(10
), 3876
–3885
(2007
).39.
A.
Ghanbari
, M. C.
Böhm
, and F.
Müller-Plathe
, “A simple reverse mapping procedure for coarse-grained polymer models with rigid side groups
,” Macromolecules
44
(13
), 5520
–5526
(2011
).40.
T. A.
Wassenaar
, K.
Pluhackova
, R. A.
Böckmann
, S. J.
Marrink
, and D. P.
Tieleman
, “Going backward: A flexible geometric approach to reverse transformation from coarse grained to atomistic models
,” J. Chem. Theory Comput.
10
(2
), 676
–690
(2014
).41.
J.
Krajniak
, Z.
Zhang
, S.
Pandiyan
, E.
Nies
, and G.
Samaey
, “Reverse mapping method for complex polymer systems
,” J. Comput. Chem.
39
(11
), 648
–664
(2018
).42.
J.
Peng
, C.
Yuan
, R.
Ma
, and Z.
Zhang
, “Backmapping from multiresolution coarse-grained models to atomic structures of large biomolecules by restrained molecular dynamics simulations using Bayesian inference
,” J. Chem. Theory Comput.
15
(5
), 3344
–3353
(2019
).43.
L. E.
Lombardi
, M. A.
Martí
, and L.
Capece
, “CG2AA: Backmapping protein coarse-grained structures
,” Bioinformatics
32
(8
), 1235
–1237
(2015
).44.
M. R.
Machado
and S.
Pantano
, “SIRAH tools: Mapping, backmapping and visualization of coarse-grained models
,” Bioinformatics
32
(10
), 1568
–1570
(2016
).45.
A. E.
Badaczewska-Dawid
, A.
Kolinski
, and S.
Kmiecik
, “Computational reconstruction of atomistic protein structures from coarse-grained models
,” Comput. Struct. Biotechnol. J.
18
, 162
–176
(2020
).46.
O. N.
Vickery
and P. J.
Stansfeld
, “CG2AT2: An enhanced fragment-based approach for serial multi-scale molecular dynamics simulations
,” J. Chem. Theory Comput.
17
(10
), 6472
–6482
(2021
).47.
W.
Li
, C.
Burkhart
, P.
Polińska
, V.
Harmandaris
, and M.
Doxastakis
, “Backmapping coarse-grained macromolecules: An efficient and versatile machine learning approach
,” J. Chem. Phys.
153
(4
), 041101
(2020
).48.
K. A.
Louison
, I. L.
Dryden
, and C. A.
Laughton
, “GLIMPS: A machine learning approach to resolution transformation for multiscale modeling
,” J. Chem. Theory Comput.
17
(12
), 7930
–7937
(2021
).49.
W.
Wang
and R.
Gómez-Bombarelli
, “Coarse-graining auto-encoders for molecular dynamics
,” npj Comput. Mater.
5
(1
), 125
(2019
).50.
M.
Stieffenhofer
, T.
Bereau
, and M.
Wand
, “Adversarial reverse mapping of condensed-phase molecular structures: Chemical transferability
,” APL Mater.
9
(3
), 031107
(2021
).51.
E.
Kalligiannaki
, V.
Harmandaris
, M. A.
Katsoulakis
, and P.
Plecháč
, “The geometry of generalized force matching and related information metrics in coarse-graining of molecular systems
,” J. Chem. Phys.
143
(8
), 084105
(2015
).52.
E.
Kalligiannaki
, A.
Chazirakis
, A.
Tsourtis
, M. A.
Katsoulakis
, P.
Plecháč
, and V. A.
Harmandaris
, “Parametrizing coarse grained models for molecular systems at equilibrium
,” Eur. Phys. J. Spec. Topics
225
(8
), 1347
–1372
(2016
).53.
A. F.
Behbahani
, A.
Rissanou
, G.
Kritikos
, M.
Doxastakis
, C.
Burkhart
, P.
Polińska
, and V. A.
Harmandaris
, “Conformations and dynamics of polymer chains in cis and trans polybutadiene/silica nanocomposites through atomistic simulations: From the unentangled to the entangled regime
,” Macromolecules
53
(15
), 6173
–6189
(2020
).54.
A.
Rissanou
, A.
Chazirakis
, P.
Polinska
, C.
Burkhart
, M.
Doxastakis
, and V.
Harmandaris
, “Polybutadiene copolymers via atomistic and systematic coarse-grained simulations
,” Macromolecules
55
(1
), 224
–240
(2022
).55.
M.
Abadi
, A.
Agarwal
, P.
Barham
, E.
Brevdo
, Z.
Chen
et al, “TensorFlow: Large-scale machine learning on heterogeneous systems
,” arXiv:1603.04467 (2016
).56.
57.
E.
Christofi
and V.
Harmandaris
(2022
) "CNN-BackMap-CG
," Github. https://github.com/SimEA-ERA/CNN-BackMap-CG© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.