2025
7
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.
2023
6
Polymer folding through active processes recreates features of genome organization
Andriy Goychuk*; Deepti Kannan*; Arup K. Chakraborty†; Mehran Kardar†
* Equal contribution † Corresponding author
In: Proceedings of the National Academy of Sciences, vol. 120, no. 20, pp. e2221726120, 2023, ISSN: 0027-8424, 1091-6490.
Repository Abstract Links BibTeX
Active ProcessesAnalytical TheoryGenome OrganizationPolymer MechanicsSimulationStochastic Processes
@article{goychuk_polymer_2023,
title = {Polymer folding through active processes recreates features of genome organization},
author = {Andriy Goychuk and Deepti Kannan and Arup K. Chakraborty and Mehran Kardar},
doi = {10.1073/pnas.2221726120},
issn = {0027-8424, 1091-6490},
year = {2023},
date = {2023-05-01},
urldate = {2023-05-01},
journal = {Proceedings of the National Academy of Sciences},
volume = {120},
number = {20},
pages = {e2221726120},
abstract = {From proteins to chromosomes, polymers fold into specific conformations that control their biological function. Polymer folding has long been studied with equilibrium thermodynamics, yet intracellular organization and regulation involve energy-consuming, active processes. Signatures of activity have been measured in the context of chromatin motion, which shows spatial correlations and enhanced subdiffusion only in the presence of adenosine triphosphate. Moreover, chromatin motion varies with genomic coordinate, pointing toward a heterogeneous pattern of active processes along the sequence. How do such patterns of activity affect the conformation of a polymer such as chromatin? We address this question by combining analytical theory and simulations to study a polymer subjected to sequence-dependent correlated active forces. Our analysis shows that a local increase in activity (larger active forces) can cause the polymer backbone to bend and expand, while less active segments straighten out and condense. Our simulations further predict that modest activity differences can drive compartmentalization of the polymer consistent with the patterns observed in chromosome conformation capture experiments. Moreover, segments of the polymer that show correlated active (sub)diffusion attract each other through effective long-ranged harmonic interactions, whereas anticorrelations lead to effective repulsions. Thus, our theory offers nonequilibrium mechanisms for forming genomic compartments, which cannot be distinguished from affinity-based folding using structural data alone. As a first step toward exploring whether active mechanisms contribute to shaping genome conformations, we discuss a data-driven approach.},
keywords = {Active Processes, Analytical Theory, Genome Organization, Polymer Mechanics, Simulation, Stochastic Processes},
pubstate = {published},
tppubtype = {article}
}
From proteins to chromosomes, polymers fold into specific conformations that control their biological function. Polymer folding has long been studied with equilibrium thermodynamics, yet intracellular organization and regulation involve energy-consuming, active processes. Signatures of activity have been measured in the context of chromatin motion, which shows spatial correlations and enhanced subdiffusion only in the presence of adenosine triphosphate. Moreover, chromatin motion varies with genomic coordinate, pointing toward a heterogeneous pattern of active processes along the sequence. How do such patterns of activity affect the conformation of a polymer such as chromatin? We address this question by combining analytical theory and simulations to study a polymer subjected to sequence-dependent correlated active forces. Our analysis shows that a local increase in activity (larger active forces) can cause the polymer backbone to bend and expand, while less active segments straighten out and condense. Our simulations further predict that modest activity differences can drive compartmentalization of the polymer consistent with the patterns observed in chromosome conformation capture experiments. Moreover, segments of the polymer that show correlated active (sub)diffusion attract each other through effective long-ranged harmonic interactions, whereas anticorrelations lead to effective repulsions. Thus, our theory offers nonequilibrium mechanisms for forming genomic compartments, which cannot be distinguished from affinity-based folding using structural data alone. As a first step toward exploring whether active mechanisms contribute to shaping genome conformations, we discuss a data-driven approach.
5
Enzyme-Enriched Condensates Show Self-Propulsion, Positioning, and Coexistence Open access
Leonardo Demarchi*; Andriy Goychuk†*; Ivan Maryshev; Erwin Frey†
* Equal contribution † Corresponding author
In: Physical Review Letters, vol. 130, no. 12, pp. 128401, 2023, ISSN: 0031-9007, 1079-7114.
Repository Abstract Links BibTeX
Analytical TheoryBiomolecular DynamicsEnzymesLiquid-Liquid Phase TransitionNonequilibrium SystemsPattern FormationProtein-Protein InteractionsSimulationTraveling Waves
In the press
@article{demarchi_enzyme-enriched_2023,
title = {Enzyme-Enriched Condensates Show Self-Propulsion, Positioning, and Coexistence},
author = {Leonardo Demarchi and Andriy Goychuk and Ivan Maryshev and Erwin Frey},
doi = {10.1103/PhysRevLett.130.128401},
issn = {0031-9007, 1079-7114},
year = {2023},
date = {2023-03-01},
urldate = {2023-03-01},
journal = {Physical Review Letters},
volume = {130},
number = {12},
pages = {128401},
abstract = {Enzyme-enriched condensates can organize the spatial distribution of their substrates by catalyzing nonequilibrium reactions. Conversely, an inhomogeneous substrate distribution induces enzyme fluxes through substrate-enzyme interactions. We find that condensates move toward the center of a confining domain when this feedback is weak. Above a feedback threshold, they exhibit self-propulsion, leading to oscillatory dynamics. Moreover, catalysis-driven enzyme fluxes can lead to interrupted coarsening, resulting in equidistant condensate positioning, and to condensate division.},
keywords = {Analytical Theory, Biomolecular Dynamics, Enzymes, Liquid-Liquid Phase Transition, Nonequilibrium Systems, Pattern Formation, Protein-Protein Interactions, Simulation, Traveling Waves},
pubstate = {published},
tppubtype = {article}
}
Enzyme-enriched condensates can organize the spatial distribution of their substrates by catalyzing nonequilibrium reactions. Conversely, an inhomogeneous substrate distribution induces enzyme fluxes through substrate-enzyme interactions. We find that condensates move toward the center of a confining domain when this feedback is weak. Above a feedback threshold, they exhibit self-propulsion, leading to oscillatory dynamics. Moreover, catalysis-driven enzyme fluxes can lead to interrupted coarsening, resulting in equidistant condensate positioning, and to condensate division.
2021
4
Tissue flow through pores: a computational study Preprint
Felix Kempf; Andriy Goychuk; Erwin Frey
2021.
Cell MigrationCell PolarizationCellular Potts ModelCollective DynamicsConfined MigrationSimulation
@preprint{kempf_tissue_2021,
title = {Tissue flow through pores: a computational study},
author = {Felix Kempf and Andriy Goychuk and Erwin Frey},
url = {http://biorxiv.org/lookup/doi/10.1101/2021.03.25.436985},
doi = {10.1101/2021.03.25.436985},
year = {2021},
date = {2021-03-01},
urldate = {2021-03-01},
publisher = {Biophysics},
abstract = {Cell migration is of major importance for the understanding of phenomena such as morphogenesis, cancer metastasis, or wound healing. In many of these situations cells are under external confinement. In this work we show by means of computer simulations with a Cellular Potts Model (CPM) that the presence of a bottleneck in an otherwise straight channel has a major influence on the internal organisation of an invading cellular monolayer and the motion of individual cells therein. Comparable to a glass or viscoelastic material, the cell sheet is found to exhibit features of both classical solids and classical fluids. The local ordering on average corresponds to a regular hexagonal lattice, while the relative motion of cells is unbounded. Compared to an unconstricted channel, we observe that a bottleneck perturbs the formation of regular hexagonal arrangements in the epithelial sheet and leads to pile-ups and backflow of cells near the entrance to the constriction, which also affects the overall invasion speed. The scale of these various phenomena depends on the dimensions of the different channel parts, as well as the shape of the funnel domain that connects wider to narrower regions.},
keywords = {Cell Migration, Cell Polarization, Cellular Potts Model, Collective Dynamics, Confined Migration, Simulation},
pubstate = {published},
tppubtype = {preprint}
}
Cell migration is of major importance for the understanding of phenomena such as morphogenesis, cancer metastasis, or wound healing. In many of these situations cells are under external confinement. In this work we show by means of computer simulations with a Cellular Potts Model (CPM) that the presence of a bottleneck in an otherwise straight channel has a major influence on the internal organisation of an invading cellular monolayer and the motion of individual cells therein. Comparable to a glass or viscoelastic material, the cell sheet is found to exhibit features of both classical solids and classical fluids. The local ordering on average corresponds to a regular hexagonal lattice, while the relative motion of cells is unbounded. Compared to an unconstricted channel, we observe that a bottleneck perturbs the formation of regular hexagonal arrangements in the epithelial sheet and leads to pile-ups and backflow of cells near the entrance to the constriction, which also affects the overall invasion speed. The scale of these various phenomena depends on the dimensions of the different channel parts, as well as the shape of the funnel domain that connects wider to narrower regions.
2020
3
Quasi-periodic migration of single cells on short microlanes
Fang Zhou; Sophia A. Schaffer; Christoph Schreiber; Felix J. Segerer; Andriy Goychuk; Erwin Frey; Joachim O. Rädler
In: PLOS ONE, vol. 15, no. 4, pp. e0230679, 2020, ISSN: 1932-6203.
Actin PolymerizationActinsCell MigrationCellular Potts ModelCytoskeletonDepolarizationDirected Cell MigrationSimulationTransfectionVelocity
@article{zhou_quasi-periodic_2020,
title = {Quasi-periodic migration of single cells on short microlanes},
author = {Fang Zhou and Sophia A. Schaffer and Christoph Schreiber and Felix J. Segerer and Andriy Goychuk and Erwin Frey and Joachim O. Rädler},
editor = {Jordi Garcia-Ojalvo},
url = {https://dx.plos.org/10.1371/journal.pone.0230679},
doi = {10.1371/journal.pone.0230679},
issn = {1932-6203},
year = {2020},
date = {2020-04-01},
urldate = {2026-05-29},
journal = {PLOS ONE},
volume = {15},
number = {4},
pages = {e0230679},
abstract = {Cell migration on microlanes represents a suitable and simple platform for the exploration of the molecular mechanisms underlying cell cytoskeleton dynamics. Here, we report on the quasi-periodic movement of cells confined in stripe-shaped microlanes. We observe persistent polarized cell shapes and directed pole-to-pole motion within the microlanes. Cells depolarize at one end of a given microlane, followed by delayed repolarization towards the opposite end. We analyze cell motility via the spatial velocity distribution, the velocity frequency spectrum and the reversal time as a measure for depolarization and spontaneous repolarization of cells at the microlane ends. The frequent encounters of a boundary in the stripe geometry provides a robust framework for quantitative investigations of the cytoskeleton protrusion and repolarization dynamics. In a first advance to rigorously test physical models of cell migration, we find that the statistics of the cell migration is recapitulated by a Cellular Potts model with a minimal description of cytoskeleton dynamics. Using LifeAct-GFP transfected cells and microlanes with differently shaped ends, we show that the local deformation of the leading cell edge in response to the tip geometry can locally either amplify or quench actin polymerization, while leaving the average reversal times unaffected.},
keywords = {Actin Polymerization, Actins, Cell Migration, Cellular Potts Model, Cytoskeleton, Depolarization, Directed Cell Migration, Simulation, Transfection, Velocity},
pubstate = {published},
tppubtype = {article}
}
Cell migration on microlanes represents a suitable and simple platform for the exploration of the molecular mechanisms underlying cell cytoskeleton dynamics. Here, we report on the quasi-periodic movement of cells confined in stripe-shaped microlanes. We observe persistent polarized cell shapes and directed pole-to-pole motion within the microlanes. Cells depolarize at one end of a given microlane, followed by delayed repolarization towards the opposite end. We analyze cell motility via the spatial velocity distribution, the velocity frequency spectrum and the reversal time as a measure for depolarization and spontaneous repolarization of cells at the microlane ends. The frequent encounters of a boundary in the stripe geometry provides a robust framework for quantitative investigations of the cytoskeleton protrusion and repolarization dynamics. In a first advance to rigorously test physical models of cell migration, we find that the statistics of the cell migration is recapitulated by a Cellular Potts model with a minimal description of cytoskeleton dynamics. Using LifeAct-GFP transfected cells and microlanes with differently shaped ends, we show that the local deformation of the leading cell edge in response to the tip geometry can locally either amplify or quench actin polymerization, while leaving the average reversal times unaffected.
2019
2
Bridging the gap between single-cell migration and collective dynamics Open access
Florian Thüroff*; Andriy Goychuk*; Matthias Reiter; Erwin Frey
* Equal contribution
In: eLife, vol. 8, pp. e46842, 2019, ISSN: 2050-084X.
Cell MigrationCell PolarizationCellular Potts ModelCollective DynamicsSimulationWound Healing
@article{thuroff_bridging_2019,
title = {Bridging the gap between single-cell migration and collective dynamics},
author = {Florian Thüroff and Andriy Goychuk and Matthias Reiter and Erwin Frey},
doi = {10.7554/eLife.46842},
issn = {2050-084X},
year = {2019},
date = {2019-12-01},
urldate = {2019-12-01},
journal = {eLife},
volume = {8},
pages = {e46842},
abstract = {Motivated by the wealth of experimental data recently available, we present a cellular-automaton-based modeling framework focussing on high-level cell functions and their concerted effect on cellular migration patterns. Specifically, we formulate a coarse-grained description of cell polarity through self-regulated actin organization and its response to mechanical cues. Furthermore, we address the impact of cell adhesion on collective migration in cell cohorts. The model faithfully reproduces typical cell shapes and movements down to the level of single cells, yet allows for the efficient simulation of confluent tissues. In confined circular geometries, we find that specific properties of individual cells (polarizability; contractility) influence the emerging collective motion of small cell cohorts. Finally, we study the properties of expanding cellular monolayers (front morphology; stress and velocity distributions) at the level of extended tissues.},
keywords = {Cell Migration, Cell Polarization, Cellular Potts Model, Collective Dynamics, Simulation, Wound Healing},
pubstate = {published},
tppubtype = {article}
}
Motivated by the wealth of experimental data recently available, we present a cellular-automaton-based modeling framework focussing on high-level cell functions and their concerted effect on cellular migration patterns. Specifically, we formulate a coarse-grained description of cell polarity through self-regulated actin organization and its response to mechanical cues. Furthermore, we address the impact of cell adhesion on collective migration in cell cohorts. The model faithfully reproduces typical cell shapes and movements down to the level of single cells, yet allows for the efficient simulation of confluent tissues. In confined circular geometries, we find that specific properties of individual cells (polarizability; contractility) influence the emerging collective motion of small cell cohorts. Finally, we study the properties of expanding cellular monolayers (front morphology; stress and velocity distributions) at the level of extended tissues.
2018
1
Morphology and Motility of Cells on Soft Substrates Preprint
Andriy Goychuk; David B. Brückner; Andrew W. Holle; Joachim P. Spatz; Chase P. Broedersz; Erwin Frey
2018, (Version Number: 2).
Biological PhysicsCell BehaviorCell MigrationCell PolarizationCellular Potts ModelMechanobiologySimulationTraction Force
@preprint{goychuk_morphology_2018,
title = {Morphology and Motility of Cells on Soft Substrates},
author = {Andriy Goychuk and David B. Brückner and Andrew W. Holle and Joachim P. Spatz and Chase P. Broedersz and Erwin Frey},
url = {https://arxiv.org/abs/1808.00314},
doi = {10.48550/ARXIV.1808.00314},
year = {2018},
date = {2018-01-01},
urldate = {2018-01-01},
publisher = {arXiv},
abstract = {Recent experiments suggest that the interplay between cells and the mechanics of their substrate gives rise to a diversity of morphological and migrational behaviors. Here, we develop a Cellular Potts Model of polarizing cells on a visco-elastic substrate. We compare our model with experiments on endothelial cells plated on polyacrylamide hydrogels to constrain model parameters and test predictions. Our analysis reveals that morphology and migratory behavior are determined by an intricate interplay between cellular polarization and substrate strain gradients generated by traction forces exerted by cells (self-haptotaxis).},
note = {Version Number: 2},
keywords = {Biological Physics, Cell Behavior, Cell Migration, Cell Polarization, Cellular Potts Model, Mechanobiology, Simulation, Traction Force},
pubstate = {published},
tppubtype = {preprint}
}
Recent experiments suggest that the interplay between cells and the mechanics of their substrate gives rise to a diversity of morphological and migrational behaviors. Here, we develop a Cellular Potts Model of polarizing cells on a visco-elastic substrate. We compare our model with experiments on endothelial cells plated on polyacrylamide hydrogels to constrain model parameters and test predictions. Our analysis reveals that morphology and migratory behavior are determined by an intricate interplay between cellular polarization and substrate strain gradients generated by traction forces exerted by cells (self-haptotaxis).