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PreprintCited by 21Nuclear Structure and FunctionGenomics and Chromatin DynamicsProtein Structure and Dynamics

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Nucleus size and its effect on the chromatin structure in living cells

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Efremov, Artem K., Hovan, Ladislav, Yan, Jie·2021·Biophysical Journal
DOI 10.1101/2021.07.27.453925PMC PMC9675033

Preprint — published as 10.1016/j.bpj.2022.09.019 · Paper page

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Abstract

DNA-architectural proteins play a major role in organization of chromosomal DNA in living cells by packaging it into chromatin, whose spatial conformation is determined by an intricate interplay between the DNA-binding properties of architectural proteins and physical constraints applied to the DNA by a tight nuclear space. Yet, the exact effects of the cell nucleus size on DNA-protein interactions and chromatin structure currently remain obscure. Furthermore, there is even no clear understanding of molecular mechanisms responsible for the nucleus size regulation in living cells. To find answers to these questions, we developed a general theoretical framework based on a combination of polymer field theory and transfer-matrix calculations, which showed that the nucleus size is mainly determined by the difference between the surface tensions of the nuclear envelope and the endoplasmic reticulum membrane as well as the osmotic pressure exerted by cytosolic macromolecules on the nucleus. In addition, the model demonstrated that the cell nucleus functions as a piezoelectric element, changing its electrostatic potential in a size-dependent manner. This effect has been found to have a profound impact on stability of nucleosomes, revealing a previously unknown link between the nucleus size and chromatin structure. Overall, our study provides new insights into the molecular mechanisms responsible for regulation of the cell nucleus size, as well as the potential role of nuclear organization in shaping the cell response to environmental cues. SIGNIFICANCE STATEMENT: The cell nucleus plays a central role in the life of eukaryotic cells, providing the highest level of control of intracellular processes. Depending on the stage of the cell cycle and / or surrounding environment, the size of the cell nucleus may undergo changes that are believed to cause chromatin reorganization, affecting gene transcription. At present, however, there is no clear understanding of the molecular mechanisms that may be responsible for such regulation, whose exact effect on chromatin structure remains unclear. In this study, by developing an advanced computational approach, we explore these issues from a physical perspective, revealing previously unknown mechanisms contributing to organization of the cell nucleus and chromatin.

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Figure 1 Semiflexible polymer model of chromosomal DNA packaging in the nucleus of a eukaryotic cell. (a) Main protein complexes involved in histone transportation and nucleosome formation. In the model, nucleosomes assemble on DNA from H2A ⋅ H2B and H3⋅ H4 histone dimers, which are transported by histone-binding chaperones schematically indicated as c1 and c2 in the figure. Specifically, by picking up newly synthesized histone dimers in the cell cytoplasm, chaperones switch from an unloaded state (c1 u or c2 u) to a histone-bound state (c1 b or c2 b, respectively). Then, by moving through NPCs, chaperones enter the cell nucleus, where they can deposit histone dimers onto the chromosomal DNA via nucleosome assembly. In addition to histone-binding chaperones, NPCs also allow free diffusion of ions and small metabolites between the cell nucleus and cytosol, helping to maintain the stability of the ionic microenvironment in the nucleoplasm. The bottom part of (a) shows the summary chemical equation of nucleosome assembly, which proceeds in several substeps detailed in (50, 51, 52, 53). (b) Conformations of chromosomes. In the model, conformations of chromosomes are described by triplets of unit vectors, (x^(u)(su), y^(u)(su), z^(u)(su)), u=1,…,Q, with each triplet indicating the orientation of the respective (uth) DNA molecule with reference to the fixed coordinate system, (x0, y0, z0), at a point corresponding to the arc length su∈[0, Lu] along the DNA. Here, Lu is the length of the u^th DNA molecule. (c) Discretized polymer model of DNA. To calculate the partition function, each DNA polymer was represented by a polygonal chain comprised of small straight segments, each of which was treated as a rigid body with an attached local Cartesian coordinate frame, (xj, yj, zj), representing the DNA segment orientation in space with respect to the fixed global coordinate system, (x0, y0, z0).
Figure 1 Semiflexible polymer model of chromosomal DNA packaging in the nucleus of a eukaryotic cell. (a) Main protein complexes involved in histone transportation and nucleosome formation. In the model, nucleosomes assemble on DNA from H2A ⋅ H2B and H3⋅ H4 histone dimers, which are transported by histone-binding chaperones schematically indicated as c1 and c2 in the figure. Specifically, by picking up newly synthesized histone dimers in the cell cytoplasm, chaperones switch from an unloaded state (c1 u or c2 u) to a histone-bound state (c1 b or c2 b, respectively). Then, by moving through NPCs, chaperones enter the cell nucleus, where they can deposit histone dimers onto the chromosomal DNA via nucleosome assembly. In addition to histone-binding chaperones, NPCs also allow free diffusion of ions and small metabolites between the cell nucleus and cytosol, helping to maintain the stability of the ionic microenvironment in the nucleoplasm. The bottom part of (a) shows the summary chemical equation of nucleosome assembly, which proceeds in several substeps detailed in (50, 51, 52, 53). (b) Conformations of chromosomes. In the model, conformations of chromosomes are described by triplets of unit vectors, (x^(u)(su), y^(u)(su), z^(u)(su)), u=1,…,Q, with each triplet indicating the orientation of the respective (uth) DNA molecule with reference to the fixed coordinate system, (x0, y0, z0), at a point corresponding to the arc length su∈[0, Lu] along the DNA. Here, Lu is the length of the u^th DNA molecule. (c) Discretized polymer model of DNA. To calculate the partition function, each DNA polymer was represented by a polygonal chain comprised of small straight segments, each of which was treated as a rigid body with an attached local Cartesian coordinate frame, (xj, yj, zj), representing the DNA segment orientation in space with respect to the fixed global coordinate system, (x0, y0, z0).CC BY · PubMed Central
Figure 2 DNA packaging in viral particles. (a) Schematic picture of DNA packaging in a viral particle. Due to the tight capsid space, DNA adopts a coil-like conformation (78, 79, 80, 81, 82). (b) Energy contributions made by DNA (blue curve) and ions (red curve) into the total free energy of a viral particle (black curve) as functions of the capsid size. Data points shown in the graph are the results of transfer-matrix calculations; whereas lines indicate smoothing spline interpolation. Solid curves correspond to the case of a viral DNA that has the bending and twisting persistence lengths corresponding to those of B-DNA: A=50 nm (75,76) and C=95 nm (86, 87, 88), respectively; whereas dashed curves demonstrate results obtained for a freely moving joint polymer chain of the same length but with zero bending and twisting elasticities between the polymer segments. All energy values are shown in the graph up to a nonessential additive constant. (c) Electrostatic and volume-exclusion DNA interaction energies per single DNA basepair as functions of the capsid size. The curves are calculated using Eq. L28 from Online Appendix L. (d and e) Spatial distribution and volume-averaged value of the electrostatic potential in viral particles of different sizes. Each data point shown in (e) corresponds to a curve from (d). The solid line in (e) demonstrates the smoothing spline interpolation of the data points. (f) Pressure generated by DNA and ions on the walls of a viral particle at different capsid sizes. The curves are calculated based on the data shown in (b). The green rectangle indicates the area corresponding to the experimentally measured range in λ-phage particles (83,84). (g and h) The average correlation function between a pair of unit vectors tangent to the DNA backbone and the root mean-square distance (RMSD) between two points located on the DNA as functions of the genomic distance along the DNA. In all computations, the DNA length was 14 μm, which corresponds to the size of EMBL3 λ-phage genome of 41.5 kbp (83). The size of DNA segments in the discretized polymer model was b=3.4 nm.
Figure 2 DNA packaging in viral particles. (a) Schematic picture of DNA packaging in a viral particle. Due to the tight capsid space, DNA adopts a coil-like conformation (78, 79, 80, 81, 82). (b) Energy contributions made by DNA (blue curve) and ions (red curve) into the total free energy of a viral particle (black curve) as functions of the capsid size. Data points shown in the graph are the results of transfer-matrix calculations; whereas lines indicate smoothing spline interpolation. Solid curves correspond to the case of a viral DNA that has the bending and twisting persistence lengths corresponding to those of B-DNA: A=50 nm (75,76) and C=95 nm (86, 87, 88), respectively; whereas dashed curves demonstrate results obtained for a freely moving joint polymer chain of the same length but with zero bending and twisting elasticities between the polymer segments. All energy values are shown in the graph up to a nonessential additive constant. (c) Electrostatic and volume-exclusion DNA interaction energies per single DNA basepair as functions of the capsid size. The curves are calculated using Eq. L28 from Online Appendix L. (d and e) Spatial distribution and volume-averaged value of the electrostatic potential in viral particles of different sizes. Each data point shown in (e) corresponds to a curve from (d). The solid line in (e) demonstrates the smoothing spline interpolation of the data points. (f) Pressure generated by DNA and ions on the walls of a viral particle at different capsid sizes. The curves are calculated based on the data shown in (b). The green rectangle indicates the area corresponding to the experimentally measured range in λ-phage particles (83,84). (g and h) The average correlation function between a pair of unit vectors tangent to the DNA backbone and the root mean-square distance (RMSD) between two points located on the DNA as functions of the genomic distance along the DNA. In all computations, the DNA length was 14 μm, which corresponds to the size of EMBL3 λ-phage genome of 41.5 kbp (83). The size of DNA segments in the discretized polymer model was b=3.4 nm.CC BY · PubMed Central
Figure 3 Cell nucleus size regulation. (a) Schematic picture of cellular components exerting pressure on the NE. In general, the nucleus size is determined by mechanical equilibrium between the pressures created by DNA (pDNA), ions (pions) and macromolecules (pmacro). In addition, it has been previously suggested that the NE and ER may be involved in a tug-of-war with each other over the shared lipid membrane (1), which can be described in terms of pNE and pER pressures associated with the surface tensions of the NE and ER membrane. (b) Pressures exerted on the NE by DNA, ions, macromolecules, and the surface tensions of the NE and ER membrane as functions of the nucleus size. The yellow curve, which represents the osmotic pressure created by cytosolic macromolecules, is plotted for the case of nmacro=10¹⁰ molecules. The magenta curve demonstrates the net pressure, pNE+pER, generated by Δσ=20 mN/m difference in the surface tensions of the NE and ER membrane; whereas the green dashed curve indicates the equilibrium value of the net pressure, pNE+pER=−pDNA−pions−pmacro (Eq. 10). In the calculations, the total length of DNA was set equal to 2.1 m, which corresponds to the size of the human genome of ∼6.2 Gbp (62). The size of DNA segments in the discretized polymer model was b=3.4 nm. (c) Relative contributions of different cell components to the total positive/negative pressure acting on the NE calculated based on the data shown in (b). Results displayed in (a) and (b) were obtained in the case of a cell with the total volume of Vcell=8000μm3. Smaller cells (Vcell=4000μm3) demonstrate very similar behavior (see Fig. S1). (d) Correlation between the nucleus and cell volumes. Solid curves indicate fitting of experimental data from (19,20,22,25) either to the full model described by Eq. 10 or to the reduced model described by Eq. 11. In the former case, the fitting was done by varying a single model parameter—the difference between the surface tensions of the NE and ER membrane, Δσ; whereas, in the latter case, the linear fitting of the Δσ/ζ ratio shown in (e) was used as an input to Eq. 12. The inset displays a large-scale view of the fitting of the experimental data from (19). (e) Δσ/ζ ratio as a function of the nucleus size. Data points show the values calculated using Eq. 11 based on experimental data presented in (d). Solid lines indicate linear fitting of the data points. The inset demonstrates a large-scale view of the fitting of the data points obtained based on (19).
Figure 3 Cell nucleus size regulation. (a) Schematic picture of cellular components exerting pressure on the NE. In general, the nucleus size is determined by mechanical equilibrium between the pressures created by DNA (pDNA), ions (pions) and macromolecules (pmacro). In addition, it has been previously suggested that the NE and ER may be involved in a tug-of-war with each other over the shared lipid membrane (1), which can be described in terms of pNE and pER pressures associated with the surface tensions of the NE and ER membrane. (b) Pressures exerted on the NE by DNA, ions, macromolecules, and the surface tensions of the NE and ER membrane as functions of the nucleus size. The yellow curve, which represents the osmotic pressure created by cytosolic macromolecules, is plotted for the case of nmacro=10¹⁰ molecules. The magenta curve demonstrates the net pressure, pNE+pER, generated by Δσ=20 mN/m difference in the surface tensions of the NE and ER membrane; whereas the green dashed curve indicates the equilibrium value of the net pressure, pNE+pER=−pDNA−pions−pmacro (Eq. 10). In the calculations, the total length of DNA was set equal to 2.1 m, which corresponds to the size of the human genome of ∼6.2 Gbp (62). The size of DNA segments in the discretized polymer model was b=3.4 nm. (c) Relative contributions of different cell components to the total positive/negative pressure acting on the NE calculated based on the data shown in (b). Results displayed in (a) and (b) were obtained in the case of a cell with the total volume of Vcell=8000μm3. Smaller cells (Vcell=4000μm3) demonstrate very similar behavior (see Fig. S1). (d) Correlation between the nucleus and cell volumes. Solid curves indicate fitting of experimental data from (19,20,22,25) either to the full model described by Eq. 10 or to the reduced model described by Eq. 11. In the former case, the fitting was done by varying a single model parameter—the difference between the surface tensions of the NE and ER membrane, Δσ; whereas, in the latter case, the linear fitting of the Δσ/ζ ratio shown in (e) was used as an input to Eq. 12. The inset displays a large-scale view of the fitting of the experimental data from (19). (e) Δσ/ζ ratio as a function of the nucleus size. Data points show the values calculated using Eq. 11 based on experimental data presented in (d). Solid lines indicate linear fitting of the data points. The inset demonstrates a large-scale view of the fitting of the data points obtained based on (19).CC BY · PubMed Central
Figure 4 Nuclear electrostatic potential and nucleosome stability as functions of the nucleus size. (a) Distribution of the electrostatic potential in nuclei of different sizes. The plot shows results obtained for a cell with the total volume of Vcell=8000μm3. In smaller cells (Vcell=4000μm3), the nuclear electrostatic potential exhibits a similar distribution (see Fig. S2). (b) Volume-averaged value of the electrostatic potential in nuclei of different sizes. Data points indicate values calculated based on the curves shown in (a) and Fig. S2; whereas solid lines demonstrate smoothing spline interpolation. (c) Occupancy fraction of chromosomal DNA by nucleosomes as a function of the nucleus size. Data points represent results of transfer-matrix calculations; whereas solid lines show smoothing spline interpolation. (d and e) Force-extension and force-DNA occupancy fraction curves obtained by mechanical stretching of a small fragment of chromosomal DNA in nuclei of different sizes. Solid curves in (d) and (e), except for control curves 1 and 2, demonstrate results of transfer-matrix calculations performed for a cell with the total volume of Vcell=8000μm3 (see also Fig. S3 for the Vcell=4000μm3 case). Dashed curves in (d) indicate force-extension curves calculated for an isolated DNA fragment at different values of the binding free energy of histone octamers to DNA in the absence of the nuclear electrostatic potential (49). Control curve 1 shows the result of transfer-matrix calculations in the absence of electrostatic interactions for an infinitely large cell nucleus; whereas control curve 2 depicts transfer-matrix calculations for in vitro experiments performed in ATP-depleted and diluted Xenopus egg extract (49,98). (f) Binding free energy of histone octamers to DNA as a function of the cell nucleus size. The data points were calculated based on the force-extension curves from (d) and Fig. S3a, as specified in the main text. Solid curves indicate prediction of the binding free energy of histone octamers by Eq. 13.
Figure 4 Nuclear electrostatic potential and nucleosome stability as functions of the nucleus size. (a) Distribution of the electrostatic potential in nuclei of different sizes. The plot shows results obtained for a cell with the total volume of Vcell=8000μm3. In smaller cells (Vcell=4000μm3), the nuclear electrostatic potential exhibits a similar distribution (see Fig. S2). (b) Volume-averaged value of the electrostatic potential in nuclei of different sizes. Data points indicate values calculated based on the curves shown in (a) and Fig. S2; whereas solid lines demonstrate smoothing spline interpolation. (c) Occupancy fraction of chromosomal DNA by nucleosomes as a function of the nucleus size. Data points represent results of transfer-matrix calculations; whereas solid lines show smoothing spline interpolation. (d and e) Force-extension and force-DNA occupancy fraction curves obtained by mechanical stretching of a small fragment of chromosomal DNA in nuclei of different sizes. Solid curves in (d) and (e), except for control curves 1 and 2, demonstrate results of transfer-matrix calculations performed for a cell with the total volume of Vcell=8000μm3 (see also Fig. S3 for the Vcell=4000μm3 case). Dashed curves in (d) indicate force-extension curves calculated for an isolated DNA fragment at different values of the binding free energy of histone octamers to DNA in the absence of the nuclear electrostatic potential (49). Control curve 1 shows the result of transfer-matrix calculations in the absence of electrostatic interactions for an infinitely large cell nucleus; whereas control curve 2 depicts transfer-matrix calculations for in vitro experiments performed in ATP-depleted and diluted Xenopus egg extract (49,98). (f) Binding free energy of histone octamers to DNA as a function of the cell nucleus size. The data points were calculated based on the force-extension curves from (d) and Fig. S3a, as specified in the main text. Solid curves indicate prediction of the binding free energy of histone octamers by Eq. 13.CC BY · PubMed Central
Figure 5 Effect of the electrical charge of chaperones on the binding free energy of histone octamers to DNA. The plot demonstrates the results of calculations based on Eq. 13, performed for various electrical charges of histone-binding chaperones. For the sake of simplicity, it was assumed in the calculations that H2A ⋅ H2B-binding chaperones (c1), as well as H3 ⋅ H4-binding chaperones (c2), have the same electrical charges: qc1u=qc2u. The dashed curve shown in the graph indicates the model prediction based on the electrical charges of the chaperones estimated from the nucleocytoplasmic distribution of chaperone-transported histone dimers in HeLa cells (see Online Appendix A).
Figure 5 Effect of the electrical charge of chaperones on the binding free energy of histone octamers to DNA. The plot demonstrates the results of calculations based on Eq. 13, performed for various electrical charges of histone-binding chaperones. For the sake of simplicity, it was assumed in the calculations that H2A ⋅ H2B-binding chaperones (c1), as well as H3 ⋅ H4-binding chaperones (c2), have the same electrical charges: qc1u=qc2u. The dashed curve shown in the graph indicates the model prediction based on the electrical charges of the chaperones estimated from the nucleocytoplasmic distribution of chaperone-transported histone dimers in HeLa cells (see Online Appendix A).CC BY · PubMed Central

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Metadata

Authors
Efremov, A. K., Hovan, L., & Yan, J.
Affiliations
  • National University of Singapore (SG)
  • University of Geneva (CH)
Corresponding author
Efremov, Artem K.
ORCID
Venue
Biophysical Journal
Publisher
openRxiv
Published
2021-07-27
Volume
121
Issue
21
Pages
4189-4204
ISSN
0006-3495 (ISSN-L)
DOI
10.1101/2021.07.27.453925
PMC
PMC9675033
OpenAlex
W4296799747
Cited by
21
References
1
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FWCI
1.39
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • Biophysical Journal (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
Funders
  • National Research Foundation
  • National Research Foundation Singapore
  • Ministry of Education - Singapore
  • Mechanobiology Institute, Singapore
  • Shenzhen Bay Laboratory
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Nuclear Structure and Function
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Genomics and Chromatin Dynamics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
Keywords
nuclear size, nucleosome stability, chromatin structure, endoplasmic reticulum membrane, osmotic pressure, piezoelectric properties, polymer field theory, nuclear organization
MeSH terms
Cell Nucleus, Chromatin, DNA, Nucleosomes, Cell Nucleus Size

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

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