Dynamics of networks in a viscoelastic and active environment

Grimm, J.P.; Dolgushev, Maxim

doi:10.1039/c7sm02050c

Cited by 9 publications

(2 citation statements)

References 50 publications

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“…Therefore, once the interaction matrix

is given, we can calculate and simulate the dynamics and conformations of the polymer model in thermal equilibrium. The positive values of the matrix

stand for elastic forces between two monomers, and the model formally resembles the Gaussian network model ( 27 , 28 , 29 ). Mathematically, although a negative value of the matrix

can make the polymer system unstable, the positive semidefiniteness of the Laplacian matrix of

is a necessary and sufficient condition for the stability of the polymer network model ( 25 ).…”

Section: Methodsmentioning

confidence: 99%

Microrheology for Hi-C Data Reveals the Spectrum of the Dynamic 3D Genome Organization

Shinkai

Sugawara

Miura

et al. 2020

Biophysical Journal

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The one-dimensional information of genomic DNA is hierarchically packed inside the eukaryotic cell nucleus and organized in a three-dimensional (3D) space. Genome-wide chromosome conformation capture (Hi-C) methods have uncovered the 3D genome organization and revealed multiscale chromatin domains of compartments and topologically associating domains (TADs). Moreover, single-nucleosome live-cell imaging experiments have revealed the dynamic organization of chromatin domains caused by stochastic thermal fluctuations. However, the mechanism underlying the dynamic regulation of such hierarchical and structural chromatin units within the microscale thermal medium remains unclear. Microrheology is a way to measure dynamic viscoelastic properties coupling between thermal microenvironment and mechanical response. Here, we propose a new, to our knowledge, microrheology for Hi-C data to analyze the dynamic compliance property as a measure of rigidness and flexibility of genomic regions along with the time evolution. Our method allows the conversion of an Hi-C matrix into the spectrum of the dynamic rheological property along the genomic coordinate of a single chromosome. To demonstrate the power of the technique, we analyzed Hi-C data during the neural differentiation of mouse embryonic stem cells. We found that TAD boundaries behave as more rigid nodes than the intra-TAD regions. The spectrum clearly shows the dynamic viscoelasticity of chromatin domain formation at different timescales. Furthermore, we characterized the appearance of synchronous and liquid-like intercompartment interactions in differentiated cells. Together, our microrheology data derived from Hi-C data provide physical insights into the dynamics of the 3D genome organization.

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“…Therefore, once the interaction matrix

is given, we can calculate and simulate the dynamics and conformations of the polymer model in thermal equilibrium. The positive values of the matrix

stand for elastic forces between two monomers, and the model formally resembles the Gaussian network model ( 27 , 28 , 29 ). Mathematically, although a negative value of the matrix

can make the polymer system unstable, the positive semidefiniteness of the Laplacian matrix of

is a necessary and sufficient condition for the stability of the polymer network model ( 25 ).…”

Section: Methodsmentioning

confidence: 99%

Microrheology for Hi-C Data Reveals the Spectrum of the Dynamic 3D Genome Organization

Shinkai

Sugawara

Miura

et al. 2020

Biophysical Journal

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show abstract

“…Therefore, the physical interactions of all pairs can be described as an N × N matrix K = K i j . The positive values of K stand for elastic forces between two monomers, and the model formally resembles the Gaussian network model (27)(28)(29). Here, the negative values are acceptable as repulsive forces in the polymer network model.…”

Section: Theory Of Microrheology To Convert Hi-c Data Into Complex Comentioning

confidence: 99%

Microrheology for Hi-C Data Reveals the Spectrum of the Dynamic 3D Genome Organization

Shinkai

Sugawara

Miura

et al. 2019

Preprint

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The 1-dimensional information of genomic DNA is hierarchically packed inside the eukaryotic cell nucleus and organized in 3-dimensional (3D) space. Genome-wide chromosome conformation capture (Hi-C) methods have uncovered the 3D genome organization and revealed multiscale chromatin domains of compartments and topologically associating domains (TADs). Moreover, single-nucleosome live-cell imaging experiments have revealed the dynamic organization of chromatin domains caused by stochastic thermal fluctuations. However, the mechanism underlying the dynamic regulation of such hierarchical and structural chromatin units within the micro-scale thermal medium remains unclear. Microrheology is a way to measure dynamic viscoelastic properties coupling between thermal microenvironment and mechanical response. Here, we propose, to our knowledge, a new microrheology for Hi-C data to analyze the compliance property as a barometer of rigidness and flexibility of genomic regions along with the time evolution. Our method allows conversion of a Hi-C matrix into the spectrum of the rheological property along the genomic coordinate of a single chromosome. To demonstrate the technique, we analyzed Hi-C data during the neural differentiation of mouse embryonic stem cells. We found that TAD boundaries behave as more rigid nodes than the intra-TAD region. The spectrum clearly shows the rheological property of the dynamic chromatin domain formations at an individual time scale. Furthermore, we characterized the appearance of synchronous and liquid-like inter-compartment interactions in differentiated cells. Together, our microrheology provides physical insights revealing the dynamic 3D genome organization from Hi-C data. SIGNIFICANCE Genomic DNA is hierarchically packed inside the eukaryotic cell nucleus, and the genome organization in 3D contributes to proper genome functions at the multiscale chromatin domains. Although thermal fluctuations inevitably drive movements of the genome molecules in the micro-scale cell environment, there is no method, as yet, to quantify such dynamic 3D genome organization of hierarchical and structural chromatin units. Here, we describe a method to calculate rheological properties as barometers of flexibility and liquid-like behavior of genomic regions. We show that biologically relevant boundaries between chromatin domains are more rigid than the inside at a particular time scale. Our method allows interpretation of static and population-averaged genome conformation data as dynamic and hierarchical 3D genome picture.

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Viscoelastic active diffusion governed by nonequilibrium fractional Langevin equations: Underdamped dynamics and ergodicity breaking

Joo,

Jeon

2023

Chaos, Solitons & Fractals

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Dynamics of networks in a viscoelastic and active environment

Cited by 9 publications

References 50 publications

Microrheology for Hi-C Data Reveals the Spectrum of the Dynamic 3D Genome Organization

Microrheology for Hi-C Data Reveals the Spectrum of the Dynamic 3D Genome Organization

Microrheology for Hi-C Data Reveals the Spectrum of the Dynamic 3D Genome Organization

Viscoelastic active diffusion governed by nonequilibrium fractional Langevin equations: Underdamped dynamics and ergodicity breaking

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