2026
3
Dynamical mean-field theory of active, self-interacting heteropolymers Preprint
2026.
Repository Abstract Links BibTeX
Mean Field TheoryPolymersSoft Condensed Matter
@preprint{goychuk_gaussian_2026,
title = {Dynamical mean-field theory of active, self-interacting heteropolymers},
author = {Andriy Goychuk},
doi = {10.48550/ARXIV.2604.02085},
year = {2026},
date = {2026-01-01},
urldate = {2026-01-01},
publisher = {arXiv},
abstract = {Analytical theories of polymer dynamics typically focus on the linear response around some steady state obtained via perturbative calculations. The present study derives a dynamical, nonlinear mean-field theory that yields unified access to the evolution of conformations, contact probabilities, and fluctuations of active polymers within a single analytical framework. As in previous mean-field descriptions of passive polymers, the object of interest is the two-point correlator, which is the lowest-order relevant observable in the general Langevin equation of a polymer. In contrast, the present focus is on active polymers driven by heterogeneous monomer-level kicks and spatially correlated active flows, while allowing nonreciprocal couplings, in the presence of hydrodynamic and contact interactions. Using a Gaussian closure to truncate higher-order correlations leads to a self-consistent diffusion equation for the chain correlations. In some cases, this can be further simplified to the dynamics of pairwise squared separations in closed form. In the continuum limit, the theory reveals useful analogies to similar mean-field approximations for reaction-diffusion systems, as well as fractional diffusion in different scale-free regimes. Deriving asymptotic solutions in different parameter regimes of the continuum limit recovers the scalings of coiled, globular, and self-avoiding polymers, thus validating the theory. Applied to hydrodynamically coupled active polymers, such as chromatin, the framework predicts a sequence of crossover scalings between coiled, swollen, and hyper-compacted fractal states.},
keywords = {Mean Field Theory, Polymers, Soft Condensed Matter},
pubstate = {published},
tppubtype = {preprint}
}
Analytical theories of polymer dynamics typically focus on the linear response around some steady state obtained via perturbative calculations. The present study derives a dynamical, nonlinear mean-field theory that yields unified access to the evolution of conformations, contact probabilities, and fluctuations of active polymers within a single analytical framework. As in previous mean-field descriptions of passive polymers, the object of interest is the two-point correlator, which is the lowest-order relevant observable in the general Langevin equation of a polymer. In contrast, the present focus is on active polymers driven by heterogeneous monomer-level kicks and spatially correlated active flows, while allowing nonreciprocal couplings, in the presence of hydrodynamic and contact interactions. Using a Gaussian closure to truncate higher-order correlations leads to a self-consistent diffusion equation for the chain correlations. In some cases, this can be further simplified to the dynamics of pairwise squared separations in closed form. In the continuum limit, the theory reveals useful analogies to similar mean-field approximations for reaction-diffusion systems, as well as fractional diffusion in different scale-free regimes. Deriving asymptotic solutions in different parameter regimes of the continuum limit recovers the scalings of coiled, globular, and self-avoiding polymers, thus validating the theory. Applied to hydrodynamically coupled active polymers, such as chromatin, the framework predicts a sequence of crossover scalings between coiled, swollen, and hyper-compacted fractal states.
2025
2
RNA gradients can guide condensates toward promoters: Implications for enhancer–promoter contacts and condensate-promoter kissing Open access
David Goh*; Deepti Kannan*; Pradeep Natarajan*; Andriy Goychuk†; Arup K. Chakraborty†
* Equal contribution † Corresponding author
In: The Journal of Chemical Physics, vol. 163, iss. 10, pp. 104905, 2025, ISSN: 0021-9606, 1089-7690.
Repository Abstract Links BibTeX
Biological PhysicsBiomolecular InteractionsChromatinGene transcriptionPhase transitionsPolymersProtein-Protein-InteractionsReentrantRibonucleic AcidSimulation
@article{goh_rna_2025,
title = {RNA gradients can guide condensates toward promoters: Implications for enhancer–promoter contacts and condensate-promoter kissing},
author = {David Goh and Deepti Kannan and Pradeep Natarajan and Andriy Goychuk and Arup K. Chakraborty},
doi = {10.1063/5.0277838},
issn = {0021-9606, 1089-7690},
year = {2025},
date = {2025-09-01},
urldate = {2025-09-01},
journal = {The Journal of Chemical Physics},
volume = {163},
issue = {10},
pages = {104905},
abstract = {We study how protein condensates respond to a site of active RNA transcription (i.e., a gene promoter) due to electrostatic protein–RNA interactions. Our results indicate that condensates can show directed motion toward the promoter, driven by gradients in the RNA concentration. Analytical theory, consistent with simulations, predicts that the droplet velocity has a non-monotonic dependence on the distance to the promoter. We explore the consequences of this gradient-sensing mechanism for enhancer–promoter (E–P) communication using polymer simulations of the intervening chromatin chain. Directed motion of enhancer-bound condensates can, together with loop extrusion by cohesin, collaboratively increase the enhancer–promoter contact probability. Finally, we investigate under which conditions condensates can exhibit oscillations in their morphology and in the distance to the promoter. Oscillatory dynamics are caused by a delayed response of transcription to condensate-promoter contact and negative feedback from the accumulation of RNA at the promoter, which results in charge repulsion.},
keywords = {Biological Physics, Biomolecular Interactions, Chromatin, Gene transcription, Phase transitions, Polymers, Protein-Protein-Interactions, Reentrant, Ribonucleic Acid, Simulation},
pubstate = {published},
tppubtype = {article}
}
We study how protein condensates respond to a site of active RNA transcription (i.e., a gene promoter) due to electrostatic protein–RNA interactions. Our results indicate that condensates can show directed motion toward the promoter, driven by gradients in the RNA concentration. Analytical theory, consistent with simulations, predicts that the droplet velocity has a non-monotonic dependence on the distance to the promoter. We explore the consequences of this gradient-sensing mechanism for enhancer–promoter (E–P) communication using polymer simulations of the intervening chromatin chain. Directed motion of enhancer-bound condensates can, together with loop extrusion by cohesin, collaboratively increase the enhancer–promoter contact probability. Finally, we investigate under which conditions condensates can exhibit oscillations in their morphology and in the distance to the promoter. Oscillatory dynamics are caused by a delayed response of transcription to condensate-promoter contact and negative feedback from the accumulation of RNA at the promoter, which results in charge repulsion.
2024
1
Delayed Excitations Induce Polymer Looping and Coherent Motion Open access
Andriy Goychuk†; Deepti Kannan; Mehran Kardar†
† Corresponding author
In: Physical Review Letters, vol. 133, iss. 7, pp. 078101, 2024, ISSN: 0031-9007, 1079-7114.
Preprint Repository Abstract Links BibTeX
ChromatinLangevin EquationLiving Matter & Active MatterPolymer BehaviorPolymersWormlike Chain Model
In the press
@article{goychuk_delayed_2024,
title = {Delayed Excitations Induce Polymer Looping and Coherent Motion},
author = {Andriy Goychuk and Deepti Kannan and Mehran Kardar},
doi = {10.1103/PhysRevLett.133.078101},
issn = {0031-9007, 1079-7114},
year = {2024},
date = {2024-08-01},
urldate = {2024-08-01},
journal = {Physical Review Letters},
volume = {133},
issue = {7},
pages = {078101},
abstract = {We consider inhomogeneous polymers driven by energy-consuming active processes which encode temporal patterns of athermal kicks. We find that such temporal excitation programs, propagated by tension along the polymer, can effectively couple distinct polymer loci. Consequently, distant loci exhibit correlated motions that fold the polymer into specific conformations, as set by the local actions of the active processes and their distribution along the polymer. Interestingly, active kicks that are canceled out by a time-delayed echo can induce strong compaction of the active polymer.},
keywords = {Chromatin, Langevin Equation, Living Matter & Active Matter, Polymer Behavior, Polymers, Wormlike Chain Model},
pubstate = {published},
tppubtype = {article}
}
We consider inhomogeneous polymers driven by energy-consuming active processes which encode temporal patterns of athermal kicks. We find that such temporal excitation programs, propagated by tension along the polymer, can effectively couple distinct polymer loci. Consequently, distant loci exhibit correlated motions that fold the polymer into specific conformations, as set by the local actions of the active processes and their distribution along the polymer. Interestingly, active kicks that are canceled out by a time-delayed echo can induce strong compaction of the active polymer.