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Modeling epigenome folding: formation and dynamics of topologically associated chromatin domains.

Jost D, Carrivain P, Cavalli G, Vaillant C - Nucleic Acids Res. (2014)

Bottom Line: Remarkably, recent studies indicate that these 1D epigenomic domains tend to fold into 3D topologically associated domains forming specialized nuclear chromatin compartments.We show how experiments are fully consistent with multistable conformations where topologically associated domains of the same epigenomic state interact dynamically with each other.Our approach provides a general framework to improve our understanding of chromatin folding during cell cycle and differentiation and its relation to epigenetics.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS UMR 5672, Lyon 69007, France.

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(A) Phase diagram of the copolymer (A10B10)6 as a function of the strength of specific and non-specific interactions (in kBT unit). Insets represent typical heat maps of the probability of contacts between two monomers (in log-unit) for the different phases: coil (a), globule (b), multiphase separation (c) and multistability (d). Snapshots result from full numerical simulations of the system. (B) Contact map (left), joint-probability distribution function for the root mean squared distance (r.m.s.d.) dA between A-monomers and the r.m.s.d. dB between B-monomers (center), and typical time-evolution of dA and dB along one simulated trajectory (right), obtained from full numerical simulations for a parameter set inside the multistability region (d2 in (A)). Time is given in arbitrary simulation time-unit (see Supplementary Notes).
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Figure 2: (A) Phase diagram of the copolymer (A10B10)6 as a function of the strength of specific and non-specific interactions (in kBT unit). Insets represent typical heat maps of the probability of contacts between two monomers (in log-unit) for the different phases: coil (a), globule (b), multiphase separation (c) and multistability (d). Snapshots result from full numerical simulations of the system. (B) Contact map (left), joint-probability distribution function for the root mean squared distance (r.m.s.d.) dA between A-monomers and the r.m.s.d. dB between B-monomers (center), and typical time-evolution of dA and dB along one simulated trajectory (right), obtained from full numerical simulations for a parameter set inside the multistability region (d2 in (A)). Time is given in arbitrary simulation time-unit (see Supplementary Notes).

Mentions: To illustrate the generic effects predicted by the model, we consider, as a toy example, a chain of 120 beads with an alternation of active (A) and black (B) epigenetic domains of the same size ((A10B10)6). Figure 2 shows the richness and complexity of the observed behaviors as we vary the strengths of compaction (via Uns) and of specificity (via Us) even for such simple epigenetic sequence. The phase diagram is made of four different regions. For weak compaction and specificity, the system is in a coil phase with extended chain conformations. As we increase the compaction at weak specificity, the chain undergoes a θ-collapse transition to a globular compact phase. For strong compaction and specificity, we observe checkerboard-like contact map characteristics of microphase separated (MPS) conformations where all monomers of the same epigenetic state are densely packed into distinct 3D domains. This phase is closed to the intermingled phase observed by Jerabek and Heermann when they introduce a sinusoidal binding affinity in their dynamic loop model (30). Between the coil and MPS phases, lies a region of multistability where Equation (6) has multiple fixed points depending on the initial conditions. Theses solutions are metastable intermediate configurations between coil and MPS. For example, heat-map d1 in Figure 2 represents pearl-necklace conformations where epigenetic domains have internally collapsed but remain isolated from each other, forming topologically associated domains. The size and location of the multistability region depend on the properties of the copolymer like the number of blocks, the number of block types, or the linear organization of the blocks along the polymer. However, we qualitatively observe that the size of the region grows with the complexity of the epigenomic sequence (Supplementary Figure S4). The enlargement of the area goes often with an increase of the number of metastable states (35).


Modeling epigenome folding: formation and dynamics of topologically associated chromatin domains.

Jost D, Carrivain P, Cavalli G, Vaillant C - Nucleic Acids Res. (2014)

(A) Phase diagram of the copolymer (A10B10)6 as a function of the strength of specific and non-specific interactions (in kBT unit). Insets represent typical heat maps of the probability of contacts between two monomers (in log-unit) for the different phases: coil (a), globule (b), multiphase separation (c) and multistability (d). Snapshots result from full numerical simulations of the system. (B) Contact map (left), joint-probability distribution function for the root mean squared distance (r.m.s.d.) dA between A-monomers and the r.m.s.d. dB between B-monomers (center), and typical time-evolution of dA and dB along one simulated trajectory (right), obtained from full numerical simulations for a parameter set inside the multistability region (d2 in (A)). Time is given in arbitrary simulation time-unit (see Supplementary Notes).
© Copyright Policy - creative-commons
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4150797&req=5

Figure 2: (A) Phase diagram of the copolymer (A10B10)6 as a function of the strength of specific and non-specific interactions (in kBT unit). Insets represent typical heat maps of the probability of contacts between two monomers (in log-unit) for the different phases: coil (a), globule (b), multiphase separation (c) and multistability (d). Snapshots result from full numerical simulations of the system. (B) Contact map (left), joint-probability distribution function for the root mean squared distance (r.m.s.d.) dA between A-monomers and the r.m.s.d. dB between B-monomers (center), and typical time-evolution of dA and dB along one simulated trajectory (right), obtained from full numerical simulations for a parameter set inside the multistability region (d2 in (A)). Time is given in arbitrary simulation time-unit (see Supplementary Notes).
Mentions: To illustrate the generic effects predicted by the model, we consider, as a toy example, a chain of 120 beads with an alternation of active (A) and black (B) epigenetic domains of the same size ((A10B10)6). Figure 2 shows the richness and complexity of the observed behaviors as we vary the strengths of compaction (via Uns) and of specificity (via Us) even for such simple epigenetic sequence. The phase diagram is made of four different regions. For weak compaction and specificity, the system is in a coil phase with extended chain conformations. As we increase the compaction at weak specificity, the chain undergoes a θ-collapse transition to a globular compact phase. For strong compaction and specificity, we observe checkerboard-like contact map characteristics of microphase separated (MPS) conformations where all monomers of the same epigenetic state are densely packed into distinct 3D domains. This phase is closed to the intermingled phase observed by Jerabek and Heermann when they introduce a sinusoidal binding affinity in their dynamic loop model (30). Between the coil and MPS phases, lies a region of multistability where Equation (6) has multiple fixed points depending on the initial conditions. Theses solutions are metastable intermediate configurations between coil and MPS. For example, heat-map d1 in Figure 2 represents pearl-necklace conformations where epigenetic domains have internally collapsed but remain isolated from each other, forming topologically associated domains. The size and location of the multistability region depend on the properties of the copolymer like the number of blocks, the number of block types, or the linear organization of the blocks along the polymer. However, we qualitatively observe that the size of the region grows with the complexity of the epigenomic sequence (Supplementary Figure S4). The enlargement of the area goes often with an increase of the number of metastable states (35).

Bottom Line: Remarkably, recent studies indicate that these 1D epigenomic domains tend to fold into 3D topologically associated domains forming specialized nuclear chromatin compartments.We show how experiments are fully consistent with multistable conformations where topologically associated domains of the same epigenomic state interact dynamically with each other.Our approach provides a general framework to improve our understanding of chromatin folding during cell cycle and differentiation and its relation to epigenetics.

View Article: PubMed Central - PubMed

Affiliation: Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS UMR 5672, Lyon 69007, France.

Show MeSH
Related in: MedlinePlus