2026
3.
Andriy Goychuk
Gaussian closure and dynamical mean-field theory for self-avoiding heteropolymers Miscellaneous
2026, (Version Number: 1).
Abstract | Links | BibTeX | Tags: Mean Field Theory, Polymers, Soft Condensed Matter
@misc{goychuk_gaussian_2026,
title = {Gaussian closure and dynamical mean-field theory for self-avoiding heteropolymers},
author = {Andriy Goychuk},
url = {https://arxiv.org/abs/2604.02085},
doi = {10.48550/ARXIV.2604.02085},
year = {2026},
date = {2026-01-01},
urldate = {2026-05-29},
publisher = {arXiv},
abstract = {Analytical treatments of polymer dynamics have mostly been restricted to linear response theory around some steady state obtained via perturbative field theory. Here, I derive an analytical framework that yields unified access to the evolution of conformations, contact probabilities, and fluctuations within a dynamical mean-field theory. Starting with the Langevin equation of a hydrodynamically coupled and self-avoiding heteropolymer, the key idea is to focus on the two-point correlator as the lowest-order relevant observable. Truncating higher-order correlations via a Gaussian closure leads to a self-consistent diffusion equation for the chain correlations. The theory is validated by contrasting coiled, globular, and self-avoiding polymers within a single dynamical framework, and predicts hyper-compacted fractal states in hydrodynamically coupled active polymers such as chromatin.},
note = {Version Number: 1},
keywords = {Mean Field Theory, Polymers, Soft Condensed Matter},
pubstate = {published},
tppubtype = {misc}
}
Analytical treatments of polymer dynamics have mostly been restricted to linear response theory around some steady state obtained via perturbative field theory. Here, I derive an analytical framework that yields unified access to the evolution of conformations, contact probabilities, and fluctuations within a dynamical mean-field theory. Starting with the Langevin equation of a hydrodynamically coupled and self-avoiding heteropolymer, the key idea is to focus on the two-point correlator as the lowest-order relevant observable. Truncating higher-order correlations via a Gaussian closure leads to a self-consistent diffusion equation for the chain correlations. The theory is validated by contrasting coiled, globular, and self-avoiding polymers within a single dynamical framework, and predicts hyper-compacted fractal states in hydrodynamically coupled active polymers such as chromatin.
2025
2.
David Goh; Deepti Kannan; Pradeep Natarajan; Andriy Goychuk; Arup K. Chakraborty
RNA gradients can guide condensates toward promoters: Implications for enhancer–promoter contacts and condensate-promoter kissing Journal Article
In: The Journal of Chemical Physics, vol. 163, no. 10, pp. 104905, 2025, ISSN: 0021-9606, 1089-7690.
Abstract | Links | BibTeX | Tags: Biological Physics, Biomolecular Interactions, Chromatin, Gene transcription, Phase transitions, Polymers, Protein-Protein-Interactions, Reentrant, Ribonucleic Acid, Simulation
@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},
url = {https://pubs.aip.org/jcp/article/163/10/104905/3362007/RNA-gradients-can-guide-condensates-toward},
doi = {10.1063/5.0277838},
issn = {0021-9606, 1089-7690},
year = {2025},
date = {2025-09-01},
urldate = {2026-05-29},
journal = {The Journal of Chemical Physics},
volume = {163},
number = {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.
Andriy Goychuk; Deepti Kannan; Mehran Kardar
Delayed Excitations Induce Polymer Looping and Coherent Motion Journal Article
In: Physical Review Letters, vol. 133, no. 7, pp. 078101, 2024, ISSN: 0031-9007, 1079-7114.
Abstract | Links | BibTeX | Tags: Chromatin, Langevin Equation, Living Matter & Active Matter, Polymer Behavior, Polymers, Wormlike Chain Model
@article{goychuk_delayed_2024,
title = {Delayed Excitations Induce Polymer Looping and Coherent Motion},
author = {Andriy Goychuk and Deepti Kannan and Mehran Kardar},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.133.078101},
doi = {10.1103/PhysRevLett.133.078101},
issn = {0031-9007, 1079-7114},
year = {2024},
date = {2024-08-01},
urldate = {2026-05-29},
journal = {Physical Review Letters},
volume = {133},
number = {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.