- Open Access
Critical role of the motor density and distribution on polar active polymers
Phys. Rev. Research 8, 013096 – Published 28 January, 2026
DOI: https://doi.org/10.1103/j1lq-6phk
Abstract
Polar polymer activity underlies numerous cellular processes driven by molecular motors or enzymes. Active polymers with activity on all constituent monomers display compact globular structure, while polymers with only head activity are known to result in stretched configurations. However, most biological and synthetic polymers feature activity localized in just a few sites, a scenario that significantly differs from both previous limits. In this work, we investigate how the density and distribution of motors critically influence the conformational and dynamical properties of polar active polymers. Using overdamped Langevin dynamics simulations, we show that globular conformations for high motor densities change to stretched ones for the more realistic moderate or low density of motors. Interestingly, the polymer's velocity exhibits a nonmonotonic dependence on motor density, with maximum propulsion at intermediate densities. Furthermore, the location of the first motor profoundly impacts polymer conformations; even a slight shift leads to drastic differences between coiled and stretched states. Our findings reveal that motor placement and density govern the structural transitions, characteristic timescales, and propulsion dynamics of polar active polymers, which will have numerous practical implications in the design and understanding of active synthetic and biopolymers.
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References (82)
- B. Lewin, Genes IX (Jones & Bartlett Learning, Burlington, MA, 2008), Vol. 9.
- L. Zhang, D.-A. Silva, F. Pardo-Avila, D. Wang, and X. Huang, Structural model of RNA polymerase II elongation complex with complete transcription bubble reveals NTP entry routes, PLoS Comput. Biol. 11, e1004354 (2015).
- E. P. Geiduschek and G. P. Tocchini-Valentini, Transcription by RNA polymerase III, Annu. Rev. Biochem. 57, 873 (1988).
- L. Bai, T. J. Santangelo, and M. D. Wang, Single-molecule analysis of RNA polymerase transcription, Annu. Rev. Biophys. Biomol. Struct. 35, 343 (2006).
- D. Mizuno, C. Tardin, C. F. Schmidt, and F. C. MacKintosh, Nonequilibrium mechanics of active cytoskeletal networks, Science 315, 370 (2007).
- D. Humphrey, C. Duggan, D. Saha, D. Smith, and J. Käs, Active fluidization of polymer networks through molecular motors, Nature (London) 416, 413 (2002).
- A. Yildiz, M. Tomishige, R. D. Vale, and P. R. Selvin, Kinesin walks hand-over-hand, Science 303, 676 (2004).
- C. Y. Zhou, S. L. Johnson, N. I. Gamarra, and G. J. Narlikar, Mechanisms of ATP-dependent chromatin remodeling motors, Annu. Rev. Biophys. 45, 153 (2016).
- Z. Cao and P. G. Wolynes, Motorized chain models of the ideal chromosome, Proc. Natl. Acad. Sci. USA 121, e2407077121 (2024).
- D. Needleman and Z. Dogic, Active matter at the interface between materials science and cell biology, Nat. Rev. Mater. 2, 17048 (2017).
- B. van Steensel and E. E. Furlong, The role of transcription in shaping the spatial organization of the genome, Nat. Rev. Mol. Cell Biol. 20, 327 (2019).
- K. Struhl and E. Segal, Determinants of nucleosome positioning, Nat. Struct Mol. Biol. 20, 267 (2013).
- G. Fudenberg, M. Imakaev, C. Lu, A. Goloborodko, N. Abdennur, and L. A. Mirny, Formation of chromosomal domains by loop extrusion, Cell Rep. 15, 2038 (2016).
- M. Dogterom and G. H. Koenderink, Actin–microtubule crosstalk in cell biology, Nat. Rev. Mol. Cell Biol. 20, 38 (2019).
- M. P. López, F. Huber, I. Grigoriev, M. O. Steinmetz, A. Akhmanova, G. H. Koenderink, and M. Dogterom, Actin–microtubule coordination at growing microtubule ends, Nat. Commun. 5, 4778 (2014).
- L. Bourdieu, T. Duke, M. B. Elowitz, D. A. Winkelmann, S. Leibler, and A. Libchaber, Spiral defects in motility assays: A measure of motor protein force, Phys. Rev. Lett. 75, 176 (1995).
- N. Gupta, A. Chaudhuri, and D. Chaudhuri, Morphological and dynamical properties of semiflexible filaments driven by molecular motors, Phys. Rev. E 99, 042405 (2019).
- A. Shee, N. Gupta, A. Chaudhuri, and D. Chaudhuri, A semiflexible polymer in a gliding assay: Reentrant transition, role of turnover and activity, Soft. Matter 17, 2120 (2021).
- A. Goychuk, D. Kannan, A. K. Chakraborty, and M. Kardar, Polymer folding through active processes recreates features of genome organization, Proc. Natl. Acad. Sci. USA 120, e2221726120 (2023).
- A. L. Sanborn, S. S. P. Rao, S.-C. Huang, N. C. Durand, M. H. Huntley, A. I. Jewett, I. D. Bochkov, D. Chinnappan, A. Cutkosky, J. Li, K. P. Geeting, A. Gnirke, A. Melnikov, D. McKenna, E. K. Stamenova, E. S. Lander, and E. L. Aiden, Chromatin extrusion explains key features of loop and domain formation in wild-type and engineered genomes, Proc. Natl. Acad. Sci. USA 112, E6456 (2015).
- E. Lieberman-Aiden, N. L. Van Berkum, L. Williams, M. Imakaev, T. Ragoczy, A. Telling, I. Amit, B. R. Lajoie, P. J. Sabo, M. O. Dorschner, et al., Comprehensive mapping of long-range interactions reveals folding principles of the human genome, Science 326, 289 (2009).
- D. W. Heermann, Physical nuclear organization: Loops and entropy, Curr. Opin. Cell Biol. 23, 332 (2011).
- J. Mateos-Langerak, M. Bohn, W. de Leeuw, O. Giromus, E. M. M. Manders, P. J. Verschure, M. H. G. Indemans, H. J. Gierman, D. W. Heermann, R. van Driel, and S. Goetze, Spatially confined folding of chromatin in the interphase nucleus, Proc. Natl. Acad. Sci. USA 106, 3812 (2009).
- R. K. Sachs, G. van den Engh, B. Trask, H. Yokota, and J. E. Hearst, A random-walk/giant-loop model for interphase chromosomes, Proc. Natl. Acad. Sci. USA 92, 2710 (1995).
- S. S. Rao, M. H. Huntley, N. C. Durand, E. K. Stamenova, I. D. Bochkov, J. T. Robinson, A. L. Sanborn, I. Machol, A. D. Omer, E. S. Lander, and E. L. Aiden, A 3D map of the human genome at Kilobase resolution reveals principles of chromatin looping, Cell 159, 1665 (2014).
- Q. Wen and P. A. Janmey, Polymer physics of the cytoskeleton, Curr. Opin. Solid State Mater. Sci. 15, 177 (2011).
- R. M. Robertson-Anderson, Biopolymer Networks (IOP Publishing, Bristol, UK, 2024).
- A. Agrawal, N. Ganai, S. Sengupta, and G. I. Menon, Nonequilibrium biophysical processes influence the large-scale architecture of the cell nucleus, Biophys. J. 118, 2229 (2020).
- J. Smrek, I. Chubak, C. N. Likos, and K. Kremer, Active topological glass, Nat. Commun. 11, 26 (2020).
- A. Ghosh and N. Gov, Dynamics of active semiflexible polymers, Biophys. J. 107, 1065 (2014).
- D. Osmanović and Y. Rabin, Dynamics of active rouse chains, Soft Matter 13, 963 (2017).
- S. Brahmachari, T. Markovich, F. C. MacKintosh, and J. N. Onuchic, Temporally correlated active forces drive segregation and enhanced dynamics in chromosome polymers, PRX Life 2, 033003 (2024).
- Q. MacPherson, B. Beltran, and A. J. Spakowitz, Bottom–up modeling of chromatin segregation due to epigenetic modifications, Proc. Natl. Acad. Sci. USA 115, 12739 (2018).
- M. Chiang, D. Michieletto, C. A. Brackley, N. Rattanavirotkul, H. Mohammed, D. Marenduzzo, and T. Chandra, Polymer modeling predicts chromosome reorganization in senescence, Cell Rep. 28, 3212 (2019).
- G. Shi and D. Thirumalai, From Hi-C contact map to three-dimensional organization of interphase human chromosomes, Phys. Rev. X 11, 011051 (2021).
- S. Fujishiro and M. Sasai, Generation of dynamic three-dimensional genome structure through phase separation of chromatin, Proc. Natl. Acad. Sci. USA 119, e2109838119 (2022).
- A. Kaiser, S. Babel, B. ten Hagen, C. von Ferber, and H. Löwen, How does a flexible chain of active particles swell? J. Chem. Phys. 142, 124905 (2015).
- A. Martín-Gómez, T. Eisenstecken, G. Gompper, and R. G. Winkler, Active Brownian filaments with hydrodynamic interactions: Conformations and dynamics, Soft Matter 15, 3957 (2019).
- S. K. Anand and S. P. Singh, Conformation and dynamics of a self-avoiding active flexible polymer, Phys. Rev. E 101, 030501 (2020).
- S. M. Mousavi, G. Gompper, and R. G. Winkler, Active bath-induced localization and collapse of passive semiflexible polymers, J. Chem. Phys. 155, 044902 (2021).
- V. Bianco, E. Locatelli, and P. Malgaretti, Globulelike conformation and enhanced diffusion of active polymers, Phys. Rev. Lett. 121, 217802 (2018).
- S. K. Anand and S. P. Singh, Structure and dynamics of a self-propelled semiflexible filament, Phys. Rev. E 98, 042501 (2018).
- C. A. Philipps, G. Gompper, and R. G. Winkler, Tangentially driven active polar linear polymers—an analytical study, J. Chem. Phys. 157, 194904 (2022).
- S. Kumar, R. Padinhateeri, and S. Thakur, Shear flow as a tool to distinguish microscopic activities of molecular machines in a chromatin loop, Soft Matter 20, 6500 (2024).
- A. R. Tejedor, J. Ramírez, and M. Ripoll, Progressive polymer deformation induced by polar activity and the influence of inertia, Phys. Rev. Res. 6, L032002 (2024).
- J. Oller-Iscar, A. R. Tejedor, M. Ripoll, and J. Ramírez, Computational study of active polar polymer melts: From active reptation to activity induced local alignment, Polymer 320, 128074 (2025).
- L. van Steijn, M. Fazelzadeh, and S. Jabbari-Farouji, Conformation and dynamics of wet externally actuated filaments with tangential active forces, Phys. Rev. E 110, 064504 (2024).
- R. Sinaasappel, M. Fazelzadeh, T. Hooijschuur, Q. Di, S. Jabbari-Farouji, and A. Deblais, Locomotion of active polymerlike worms in porous media, Phys. Rev. Lett. 134, 128303 (2025).
- A. Panda, R. G. Winkler, and S. P. Singh, Activity-enhanced shear thinning of flexible linear polar polymers, Phys. Rev. E 111, 055413 (2025).
- R. G. Winkler, Conformational properties of active polar semiflexible phantom polymers, J. Chem. Phys. 162, 154903 (2025).
- D. Breoni, C. Kurzthaler, B. Liebchen, H. Löwen, and S. Mandal, Giant activity-induced elasticity in entangled polymer solutions, Nat. Commun. 16, 5305 (2025).
- S. M. Mousavi, G. Gompper, and R. G. Winkler, Active Brownian ring polymers, J. Chem. Phys. 150, 064913 (2019).
- E. Locatelli, V. Bianco, and P. Malgaretti, Activity-induced collapse and arrest of active polymer rings, Phys. Rev. Lett. 126, 097801 (2021).
- S. Kumar and S. Thakur, Local polar and long-range isotropic activity assisted swelling and collapse dynamics of an active ring polymer, Macromolecules 56, 5229 (2023).
- R. G. Winkler and S. P. Singh, Active polar ring polymer in shear flow—An analytical study, J. Chem. Phys. 161, 064902 (2024).
- A. Lamura, Excluded volume effects on tangentially driven active ring polymers, Phys. Rev. E 109, 054611 (2024).
- D. Tenenbaum, K. Inlow, L. J. Friedman, A. Cai, J. Gelles, and J. Kondev, RNA Polymerase sliding on DNA can couple the transcription of nearby bacterial operons, Proc. Natl. Acad. Sci. USA 120, e2301402120 (2023).
- B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Molecular Biology of the Cell (Garland Science, New York, NY, 2002).
- R. K. Zia, J. Dong, and B. Schmittmann, Modeling translation in protein synthesis with TASEP: A tutorial and recent developments, J. Stat. Phys. 144, 405 (2011).
- V. Schaller, C. Weber, C. Semmrich, E. Frey, and A. R. Bausch, Polar patterns of driven filaments, Nature (London) 467, 73 (2010).
- A. Sciortino, L. J. Neumann, T. Krüger, I. Maryshev, T. F. Teshima, B. Wolfrum, E. Frey, and A. R. Bausch, Polarity and chirality control of an active fluid by passive nematic defects, Nat. Mater. 22, 260 (2023).
- K. R. Prathyusha, S. Henkes, and R. Sknepnek, Dynamically generated patterns in dense suspensions of active filaments, Phys. Rev. E 97, 022606 (2018).
- M. Vatin, S. Kundu, and E. Locatelli, Conformation and dynamics of partially active linear polymers, Soft Matter 20, 1892 (2024).
- R. E. Isele-Holder, J. Elgeti, and G. Gompper, Self-propelled worm-like filaments: Spontaneous spiral formation, structure, and dynamics, Soft Matter 11, 7181 (2015).
- S. Jaiswal, M. Ripoll, and S. Thakur, Diffusiophoretic Brownian dynamics: Characterization of hydrodynamic effects for an active chemoattractive polymer, Macromolecules 57, 6968 (2024).
- N. Jain and S. Thakur, Collapse dynamics of chemically active flexible polymer, Macromolecules 55, 2375 (2022).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/j1lq-6phk for further details about the simulation model, progressive deformation along the polymer contour, mean squared displacement, and supporting movies.
- S. Roca-Bonet and M. Ripoll, Self-phoretic Brownian dynamics simulations, Eur. Phys. J. E 45, 25 (2022).
- R. K. Pathria, Statistical Mechanics (Elsevier, London, UK, 2016).
- L. Qiao and R. Kapral, Control of active polymeric filaments by chemically powered nanomotors, Phys. Rev. Appl. 18, 024051 (2022).
- L. Sappl, C. N. Likos, and A. Zöttl, Polymer thermophoresis by mesoscale simulations, Macromolecules 57, 11534 (2024).
- L. Sappl, C. N. Likos, and A. Zöttl, Locally tuned hydrodynamics of active polymer chains, J. Chem. Phys. 163, 184901 (2025).
- L. Natali, L. Caprini, and F. Cecconi, How a local active force modifies the structural properties of polymers, Soft Matter 16, 2594 (2020).
- J.-X. Li, S. Wu, L.-L. Hao, Q.-L. Lei, and Y.-Q. Ma, Nonequilibrium structural and dynamic behaviors of polar active polymer controlled by head activity, Phys. Rev. Res. 5, 043064 (2023).
- S. Majumder and S. Paul, Unusual swelling and anomalous block diffusion of di- and tri-block copolymers made of active and passive monomers, J. Chem. Phys. 163, 024907 (2025).
- M. Doi, S. F. Edwards, and S. F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, Oxford, UK, 1988), Vol. 73.
- S. Paul, S. Majumder, and W. Janke, Activity mediated globule to coil transition of a flexible polymer in a poor solvent, Soft Matter 18, 6392 (2022).
- M. Foglino, E. Locatelli, C. A. Brackley, D. Michieletto, C. N. Likos, and D. Marenduzzo, Non-equilibrium effects of molecular motors on polymers, Soft Matter 15, 5995 (2019).
- S. Paul, S. Majumder, S. K. Das, and W. Janke, Effects of alignment activity on the collapse kinetics of a flexible polymer, Soft Matter 18, 1978 (2022).
- A. Zöttl and H. Stark, Emergent behavior in active colloids, J. Phys.: Condens. Matter 28, 253001 (2016).
- J. R. Howse, R. A. L. Jones, A. J. Ryan, T. Gough, R. Vafabakhsh, and R. Golestanian, Self-motile colloidal particles: From directed propulsion to random walk, Phys. Rev. Lett. 99, 048102 (2007).
- Jülich Supercomputing Centre, JURECA: Data centric and booster modules implementing the modular supercomputing architecture at Jülich supercomputing centre, J. Large Scale Res. Facil. 7, A182 (2021).