752Accesses
3Citations
7Altmetric
Abstract
Macromolecular assemblies such as protein complexes and protein/RNA condensates are involved in most fundamental cellular processes. The arrangement of subunits within these nano-assemblies is critical for their biological function and is determined by the topology of physical contacts within and between the subunits forming the complex. Describing the spatial arrangement of these interactions is of central importance to understand their functional and stability consequences. In this concept article, we propose a circuit topology-based formalism to define the topology of a complex consisting of linear polymeric chains with inter- and intrachain interactions. We apply our method to a system of model polymer chains as well as protein assemblies. We show that circuit topology can categorize different forms of chain assemblies. Our multi-chain circuit topology should aid analysis and predictions of mechanistic and evolutionary principles in the design of macromolecular assemblies.

Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Alberti, S.; Hyman, A. A. Biomolecular condensates at the nexus of cellular stress, protein aggregation disease and ageing.Nat. Rev. Mol. Cell Biol.2021,22, 196–213.
Marx, V. Cell biology befriends soft matter physics.Nat. Methods2020,17, 567–570.
Virnau, P.; Mirny, L. A.; Kardar, M. Intricate knots in proteins: Function and evolution.PLoS Comput. Biol.2006,2 e122.
Mashaghi, A.; van Wijk, R. J.; Tans, S. J. Circuit topology of proteins and nucleic acids.Structure2014,22, 1227–1237.
Golovnev, A.; Mashaghi, A. Generalized circuit topology of folded linear chains.iScience2020,23, 101492.
Mugler, A.; Tans, S. J.; Mashaghi, A. Circuit topology of self-interacting chains: Implications for folding and unfolding dynamics.Phys. Chem. Chem. Phys.2014,16, 22537–22544.
Scalvini, B.; Sheikhhassani, V.; Mashaghi, A. Topological principles of protein folding.Phys. Chem. Chem. Phys.2021,23, 21316–21328.
Heidari, M.; Schiessel, H.; Mashaghi, A. Circuit topology analysis of polymer folding reactions.ACS Cent. Sci.2020,6, 839–847.
Schullian, O.; Woodard, J.; Tirandaz, A.; Mashaghi, A. A circuit topology approach to categorizing changes in biomolecular structure.Front. Phys.2020,8, 5.
Levy, E. D.; Pereira-Leal, J. B.; Chothia, C.; Teichmann, S. A. 3D complex: A structural classification of protein complexes.PLoS Comput. Biol.2006,2, e155.
Ozawa, Y.; Saito, R.; Fujimori, S.; Kashima, H.; Ishizaka, M.; Yanagawa, H.; Miyamoto-Sato, E.; Tomita, M. Protein complex prediction via verifying and reconstructing the topology of domain-domain interactions.BMC Bioinformatics2010,11, 350.
Mashaghi, A. R.; Ramezanpour, A.; Karimipour, V. Investigation of a protein complex network.Eur. Phys. J. B2004,41, 113–121.
Gutmanas, A.; Alhroub, Y.; Battle, G. M.; Berrisford, J. M.; Bochet, E.; Conroy, M. J.; Dana, J. M.; Montecelo, M. A. F.; van Ginkel, G. et al. PDBe: Protein data bank in Europe.Nucleic Acids Res.2014,42, D285–D291.
Kopp, J.; Schwede, T. The SWISS-MODEL Repository: New features and functionalities.Nucleic Acids Res.2006,34, D315–D318.
Bruce, J. E.In vivo protein complex topologies: Sights through a cross-linking lens.Proteomics2012,12, 1565–1575.
Politis, A.; Schmidt, C.; Tjioe, E.; Sandercock, A. M.; Lasker, K.; Gordiyenko, Y.; Russel, D.; Sali, A.; Robinson, C. V. Topological models of heteromeric protein assemblies from mass spectrometry: Application to the yeast eIF3:eIF5 complex.Chem. Biol.2015,22, 117–128.
Zheng, C. X.; Yang, L.; Hoopmann, M. R.; Eng, J. K.; Tang, X. T.; Weisbrod, C. R.; Bruce, J. E. Cross-linking measurements ofin vivo protein complex topologies.Mol. Cell. Proteomics2011,10, M110.006841.
Kremer, K.; Grest, G. S. Dynamics of entangled linear polymer melts: A molecular-dynamics simulation.J. Chem. Phys.1990,92, 5057–5086.
Plimpton, S. Fast parallel algorithms for short-range molecular dynamics.J. Comput. Phys.1995,117, 1–19.
Alexander-Katz, A.; Schneider, M. F.; Schneider, S. W.; Wixforth, A.; Netz, R. R. Shear-flow-induced unfolding of polymeric globules.Phys. Rev. Lett.2006,97, 138101.
Heidari, M.; Satarifard, V.; Mashaghi, A. Mapping a single-molecule folding process onto a topological space.Phys. Chem. Chem. Phys.2019,21, 20338–20345.
de Gennes, P. G.Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, 1979.
Mirny, L. A. The fractal globule as a model of chromatin architecture in the cell.Chromosome Res.2011,19, 37–51.
Onsager, L. The effects of shape on the interaction of colloidal particles.Ann. N. Y. Acad. Sci.1949,51, 627–659.
Bolhuis, P.; Frenkel, D. Tracing the phase boundaries of hard spherocylinders.J. Chem. Phys.1997,106, 666–687.
Shundyak, K.; van Roij, R. van der Schoot, P. Theory of the isotropic-nematic transition in dispersions of compressible rods.Phys. Rev. E2006,74, 021710.
Meldal, B. H. M.; Bye-A-jee, H.; Gajdoš, L.; Hammerová, Z.; Horáčková, A.; Melicher, F.; Perfetto, L.; Pokorný, D.; Lopez, M. R.; Türková, A. et al. Complex Portal 2018: Extended content and enhanced visualization tools for macromolecular complexes.Nucleic Acids Res.2019,47, D550–D558.
RCSB PDB.RCSB PDB [Online].https://www.rcsb.org/search (accessed Feb 1, 2022).
Sartori, P.; Leibler, S. Lessons from equilibrium statistical physics regarding the assembly of protein complexes.Proc. Natl. Acad. Sci. USA2020,117, 114–120.
Larson, A. G.; Elnatan, D.; Keenen, M. M.; Trnka, M. J.; Johnston, J. B.; Burlingame, A. L.; Agard, D. A.; Redding, S.; Narlikar, G. J. Liquid droplet formation by HP1α suggests a role for phase separation in heterochromatin.Nature2017,547, 236–240.
Gibson, B. A.; Doolittle, L. K.; Schneider, M. W. G.; Jensen, L. E.; Gamarra, N.; Henry, L.; Gerlich, D. W.; Redding, S.; Rosen, M. K. Organization of chromatin by intrinsic and regulated phase separation.Cell2019,179, 470–484.
Kilic, S.; Lezaja, A.; Gatti, M.; Bianco, E.; Michelena, J.; Imhof, R.; Altmeyer, M. Phase separation of 53BP1 determines liquid-like behavior of DNA repair compartments.EMBO J.2019,38, e101379.
Chong, S. S.; Dugast-Darzacq, C.; Liu, Z.; Dong, P.; Dailey, G. M.; Cattoglio, C.; Heckert, A.; Banala, S.; Lavis, L.; Darzacq, X. et al. Imaging dynamic and selective low-complexity domain interactions that control gene transcription.Science2018,361, eaar2555.
Cho, W. K.; Spille, J. H.; Hecht, M.; Lee, C.; Li, C.; Grube, V.; Cisse, I. I. Mediator and RNA polymerase II clusters associate in transcription-dependent condensates.Science2018,361, 412–415.
Parker, W. M.; Bell, M.; Mir, M.; Kao, J. A.; Darzacq, X.; Botchan, M. R.; Berger, J. M. A new class of disordered elements controls DNA replication through initiator self-assembly.eLife2019,8, e48562.
Scholl, D.; Deniz, A. A. Conformational freedom and topological confinement of proteins in biomolecular condensates.J. Mol. Biol.2022,434, 167348.
Shank, E. A.; Cecconi, C.; Dill, J. W.; Marqusee, S.; Bustamante, C. The folding cooperativity of a protein is controlled by its chain topology.Nature2010,465, 637–640.
Baker, D. A surprising simplicity to protein folding.Nature2000,405, 39–42.
Koga, N.; Tatsumi-Koga, R.; Liu, G. H.; Xiao, R.; Acton, T. B.; Montelione, G. T.; Baker, D. Principles for designing ideal protein structures.Nature2012,491, 222–227.
Ong, C. T.; Corces, V. G. CTCF: An architectural protein bridging genome topology and function.Nat. Rev. Genet.2014,15, 234–246.
Rapp, M.; Granseth, E.; Seppälä, S.; von Heijne, G. Identification and evolution of dual-topology membrane proteins.Nat. Struct. Mol. Biol.2006,13, 112–116.
Peisajovich, S. G.; Rockah, L.; Tawfik, D. S. Evolution of new protein topologies through multistep gene rearrangements.Nat. Genet.2006,38, 168–174.
Sato, P. M.; Yoganathan, K.; Jung, J. H.; Peisajovich, S. G. The robustness of a signaling complex to domain rearrangements facilitates network evolution.PLoS Biol.2014,12, e1002012.
de Souza, N. An expanded human interactome.Nat. Methods2015,12, 107.
Rolland, T.; Taşan, M.; Charloteaux, B.; Pevzner, S. J.; Zhong, Q.; Sahni, N.; Yi, S.; Lemmens, I.; Fontanillo, C.; Mosca, R. et al. A proteome-scale map of the human interactome network.Cell2014,159, 1212–1226.
Boisvert, F. M.; van Koningsbruggen, S.; Navascués, J.; Lamond, A. I. The multifunctional nucleolus.Nat. Rev. Mol. Cell Biol.2007,8, 574–585.
Nepusz, T.; Yu, H. Y.; Paccanaro, A. Detecting overlapping protein complexes in protein-protein interaction networks.Nat. Methods2012,9, 471–472.
Spirin, V.; Mirny, L. A. Protein complexes and functional modules in molecular networks.Proc. Natl. Acad. Sci. USA2003,100, 12123–12128.
Ganser, L. R.; Myong, S. Methods to study phase-separated condensates and the underlying molecular interactions.Trends Biochem. Sci.2020,45, 1004–1005.
Cao, J.; Gong, H.; Xie, L.; Li, Y.; Zhang, N.; Tian, W.; Zhang, R.; Zhou, J.; Wang, T.; Zhai, Y. et al. Super-assembled carbon nanofibers decorated with dual catalytically active sites as bifunctional oxygen catalysts for rechargeable Zn-air batteries.Mater. Today Energy2021,20, 100682.
Lapenta, F.; Aupič, J.; Strmšek, Ž.; Jerala, R. Coiled coil protein origami: From modular design principles towards biotechnological applications.Chem. Soc. Rev.2018,47, 3530–3542.
Kočar, V.; Schreck, J. S.; Čeru, S.; Gradišar, H.; Bašić, N.; Pisanski, T.; Doye, J. P. K.; Jerala, R. Design principles for rapid folding of knotted DNA nanostructures.Nat. Commun.2016,7, 10803.
Acknowledgements
The authors thank Martin Karplus (Harvard University), Arjen Jakobi (Delft University of Technology), and Alexandre Dawid (University Grenoble Alpes) for helpful discussions and critical reading of the manuscript.
Author information
Authors and Affiliations
Medical Systems Biophysics and Bioengineering, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, Leiden, 2333CC, the Netherlands
Maziar Heidari, Duane Moes, Otto Schullian, Barbara Scalvini & Alireza Mashaghi
Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, Berlin, 14195, Germany
Otto Schullian
Harvard Medical School, Harvard University, 25 Shattuck St, Boston, MA, 02115, USA
Alireza Mashaghi
- Maziar Heidari
You can also search for this author inPubMed Google Scholar
- Duane Moes
You can also search for this author inPubMed Google Scholar
- Otto Schullian
You can also search for this author inPubMed Google Scholar
- Barbara Scalvini
You can also search for this author inPubMed Google Scholar
- Alireza Mashaghi
You can also search for this author inPubMed Google Scholar
Corresponding author
Correspondence toAlireza Mashaghi.
Electronic supplementary material
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visithttp://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Heidari, M., Moes, D., Schullian, O.et al. A topology framework for macromolecular complexes and condensates.Nano Res.15, 9809–9817 (2022). https://doi.org/10.1007/s12274-022-4355-x
Received:
Revised:
Accepted:
Published:
Issue Date:
Share this article
Anyone you share the following link with will be able to read this content:
Sorry, a shareable link is not currently available for this article.
Provided by the Springer Nature SharedIt content-sharing initiative