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Mesoscale phase separation of chromatin in the nucleus

  1. Gaurav Bajpai  Is a corresponding author
  2. Daria Amiad Pavlov
  3. Dana Lorber
  4. Talila Volk
  5. Samuel Safran  Is a corresponding author
  1. Weizmann Institute of Science, Israel
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Cite this article as: eLife 2021;10:e63976 doi: 10.7554/eLife.63976

Abstract

Intact-organism imaging of Drosophila larvae reveals and quantifies chromatin-aqueous phase separation. The chromatin can be organized near the lamina layer of the nuclear envelope, conventionally fill the nucleus, be organized centrally, or as a wetting droplet. These transitions are controlled by changes in nuclear volume and the interaction of chromatin with the lamina (part of the nuclear envelope) at the nuclear periphery. Using a simple polymeric model that includes the key features of chromatin self-attraction and its binding to the lamina, we demonstrate theoretically that it is the competition of these two effects that determines the mode of chromatin distribution. The qualitative trends as well as the composition profiles obtained in our simulations compare well with the observed intact-organism imaging and quantification. Since the simulations contain only a small number of physical variables we can identify the generic mechanisms underlying the changes in the observed phase separations.

Introduction

Chromatin is a complex, linear macromolecule comprising DNA and histone proteins which in eukaryotic cells, is localized in the nucleus where it is solubilized in water, salts, and other small molecules (Cooper and Hausman, 2000; Phillips et al., 2012). In many studies, chromatin organization in interphase is homogeneous on the nuclear scale. In this ‘conventional’ picture, the chromatin and the aqueous solvent uniformly fill the nucleus as a single phase (Rosa and Shaw, 2013). Even the conventional picture accounts for phase separation similar to that of soluble AB block copolymers (Rubinstein and Colby, 2003), with regions of transcriptionally active euchromatin (A block) separated from regions of relatively inactive heterochromatin (B block); however, both are assumed to be homogeneously solubilized in the aqueous phase (Erdel and Rippe, 2018; Narlikar, 2020; Strom et al., 2017; Larson et al., 2017). For example, Hi-C experiments reveal such AB chromatin compartmentalization (Lieberman-Aiden et al., 2009) but do not provide information about their location within the nucleus.

In most previous measurements, nuclear-scale phase separation of the chromatin and the aqueous phase has not been considered. However, recent super-resolution microscopy reveals a ‘marshland’ of chromatin and aqueous phase, with a non-uniform distribution of chromatin at the submicron level (Cremer et al., 2015). Another study observed a larger scale phase separation of chromatin and the aqueous phase in early development, with the chromatin localized to the nuclear periphery (Popken et al., 2014). Both these observations did not distinguish the A and B blocks (eu and hetero chromatin) and instead identified large regions of DNA-rich chromatin separated from DNA-poor regions, presumably of the aqueous phase. More recently, we have presented (see Appendix 1—figure 1) intact-organism imaging of Drosophila larvae nuclei where the chromatin was labeled by H2B-RFP, and the nuclear envelope was labeled by Nesprin/Klar-GFP. These experiments reveal and quantify chromatin-aqueous phase separation and its control by changes in the nuclear volume and the interaction of chromatin with the lamina (part of the nuclear envelope) at the nuclear periphery (Amiad-Pavlov et al., 2020). Here, we demonstrate theoretically that it is the competition of these two effects, together with the self-attraction of the chromatin to itself that determine whether the chromatin is conventionally or peripherally distributed within the nucleus; we also show that more complex organizational modes are also possible. The model we present below that focuses on the concentration profile of chromatin (whether A or B) within the nucleus, is appropriate when the chromatin self-attraction relative to the chromatin-aqueous phase interaction, as well as the chromatin-lamina interaction are larger than the difference between the AA and BB interactions. The qualitative trends as well as the compositional profiles obtained in our simulations compare well with the observed, intact-organism imaging and quantification. Since the simulations contain only a small number of physical variables, this allows us to identify the generic mechanisms underlying the changes in the phase separation that are observed.

The physical insight obtained here focuses on the competition of two primary interactions of chromatin within the nucleus: (i) chromatin-lamina, which is attractive and tends to organize the chromatin peripherally (ii) chromatin-chromatin, that if attractive, tends to condense the chromatin and separate it from the aqueous phase. The nuclear envelope contains lamina which is a dense, fibrillar network of proteins that provide anchoring points for various proteins that bind to chromatin on one end and the lamina on the other (Ulianov et al., 2019; Kind et al., 2013; Yáñez-Cuna and van Steensel, 2017; Meister et al., 2010). These binding proteins associate with lamins that, in general, comprise two A-type (lamin A and lamin C) and two B-type (lamin B1 and lamin B2) proteins (Moir et al., 2000). However, Drosophila has only one A-type lamin (lamin C) and one B-type lamin (lamin Dm0) gene (Riemer et al., 1995; Schulze et al., 2009). A-type and B-type lamins are found at the nuclear periphery while A-type lamins are also found in the nuclear interior (Briand and Collas, 2020; Naetar et al., 2017). Those chromatin domains, which bind to the lamins are called lamina associated domains (LADs) which are similarly divided in two groups: A-LAD and B-LAD corresponding to interactions with A-type lamin and B-type lamin, respectively (van Steensel and Belmont, 2017; Briand and Collas, 2020). The anchor protein lamin B receptor (LBR) binds lamin B and acts as a tether between chromatin and the nuclear lamina (Solovei et al., 2013). Experiments performed in the absence of LBR observed a loss of peripheral LADs and an inverted architecture with LADs localized within the nuclear interior (Solovei et al., 2013; Briand and Collas, 2020). The role of lamin Dm0 in Drosophila is the same as LBR in mammalian cells (Wagner et al., 2004; Ulianov et al., 2019).

Previous models of chromatin-lamina interactions resolved euchromatin and heterochromatin domains in the context of conventional organization of chromatin (Chiang et al., 2019; Sati et al., 2020; Falk et al., 2019) where phase separation with the aqueous phase is not considered. Another model of chromatin and lamina interactions, treats chromatin as a self-avoiding polymer in good solvent and focuses on the role of lamina in the formation of chromosome territories (Maji et al., 2020). However, if chromatin were a self-avoiding polymer (with no self-attraction), its radius of gyration in aqueous solution would typically be larger than the diameter of the nucleus. Thus, under confinement, chromatin would fill the entire volume of nucleus, which is not consistent with the observation (Amiad-Pavlov et al., 2020) of peripheral or central chromatin organization. In contrast, the study presented here illustrates in an intuitive manner, how chromatin-lamina interactions control peripheral and other organizational modes that show chromatin-aqueous phase separation. The experimental observations (see Appendix 1—figure 1) of peripheral organization demonstrate the condensation of chromatin in the outer part of the nucleus, indicating the presence of chromatin self-attraction (Amiad-Pavlov et al., 2020). This motivates our model which focuses on attractive interactions within the chromatin so that it acts in the nucleus as a polymer in a relatively bad solvent. For large enough nuclear volumes and strong enough chromatin-lamina attractions, instead of filling the nucleus, the chromatin is condensed in only part of the volume near the nuclear periphery.

The model we study is generic in nature, short-ranged and does not depend on the detailed molecular origin of the chromatin self-attraction. This is an appropriate approach for understanding and predicting the nuclear-scale concentration profile of the chromatin and aqueous regions in vivo, where the identity and function of all the molecular actors are so far unknown. Nevertheless, there is ample reason to believe that such attractions are present and important in determining chromatin organization. For example, the positively charged histone tails attract negative DNA linkers and can thus promote condensation of chromatin (Gibson et al., 2019; Bajpai and Padinhateeri, 2020; Hancock, 2007). Protein condensates that interact with chromatin can also result in self-attraction. A prominent example is the phase separation of HP1 in the nucleus, which binds to the heterochromatin domains of chromatin (Strom et al., 2017; Larson et al., 2017). If one protein can bridge two or more chromatin regions that are close in physical space, but possibly far along the stretched chromatin chain, this can also result in an effective chromatin-chromatin attraction. Other nuclear proteins that interact with chromatin can play a similar role. For example, nucleoplasmic lamin A can act to ‘crosslink’ two chromatin regions in vivo (Bronshtein et al., 2016; Bronshtein et al., 2015; Stephens et al., 2017). Other studies have indeed considered chromatin to act as a polymer gel cross-linked by non-histone protein complexes (Biggs et al., 2019; Irianto et al., 2013).

In this paper, we systematically examine how the interplay between chromatin-lamina interactions, intra-chromatin interactions, and hydration affect the chromatin organization. The biological observations of different organizational modes are simulated and explained by the polymeric properties of chromatin and the competition of its bulk interactions with the surface interactions with the lamina. Different organizational modes can affect gene expression since different amounts and sections of the chromosome are exposed to the aqueous phase and the proteins and enzymes that it contains. This may be why changes in nuclear volume have been demonstrated to result in changes in gene expression (Jain et al., 2013; Thomas et al., 2002). Our simulation results also provide suggestions to experimental groups on how to vary the minimal number of parameters that will experimentally result in different modes of chromatin organization in vivo.

Model

As explained above, we are interested in the generic physical effects that determine the chromatin concentration profile at the nuclear scale. However, to predict this from computer simulations of chromatin as a self-attracting, confined polymer that is also attracted to the lamina at the nuclear periphery, we must treat a specific polymeric model. We therefore fixed the polymer monomer size, molecular weight, and persistence length, and instead varied the physical properties of the nucleus, including its volume and chromatin-lamina interactions. This was motivated by the intact-organism experiments (Amiad-Pavlov et al., 2020). Comparing the live to fixed cells showed a reduction in the nuclear volume by a factor of about three and a transition from peripheral (live) to conventional (fixed) chromatin organization. Lamin C overexpression resulted in a transition from peripheral (WT) to central (and wetting droplet) organization in the mutant (see Appendix 1—figure 1). In our simulations, we also varied the magnitude of the chromatin self-attraction to demonstrate the difference in organization of chromatin in a good solvent vs. a poor one.

Chromatin chain

For the understanding of the generic properties of interest here, we treated a single chromosome. Aqueous phase separation in case of multiple chromosomes can be mapped from our results by using the appropriate chromatin volume fraction. We were motivated by the X chromosome of Drosophila since its distribution of LAD domains is known. We therefore modeled chromatin as a polymer using a bead-spring model (Naumova et al., 2013) with N=37,333 beads. Each bead represents three nucleosomes (around 600 bp of DNA) whose diameter is denoted by σ=10 nm. Thus, our model chromosome contains about 22.4Mbp, comparable to the X chromosome. The bead-spring interactions (Eschrom) and persistence length (bending energy Ebchrom) are determined in the standard manner as detailed in Materials and methods, where it is shown that the appropriate persistence length is two beads in our representation.

In addition to the spring-bead model that accounts for the connectivity of nearest neighbor beads along the polymer chain, we include short-range interactions (both attractive and repulsive) between any two beads that are close enough in 3D space; they do not necessarily have to be ‘close’ along the chain. These, non-bonding interactions between any two beads were taken using a Lennard-Jones (LJ) potential,

(1) ELJ={4ϵi<ji,j[(σrij)12(σrij)6]when rij<rc0when rijrc

where rc refers to a cutoff distance beyond which LJ interaction is set to zero. Here rij is the distance in 3D space between ith and jth beads and ϵ is strength of potential. If there are no attractive forces between the beads (but only steric, hard-core repulsions), we truncate the LJ potential at the distance at which the repulsive force goes to zero which gives rc=21/6σ. For the case of attractive forces, of particular interest in our work, the cutoff distance is taken as rc=2.5σ. For ϵ=1kBT, the chromosome is a self-avoiding chain when rc=21/6σ and a self-attractive one when rc=2.5σ (see Appendix 2 and Appendix 2—figure 1 for scaling exponent results).

Nuclear confinement and volume

We model the nucleus to which the chromatin is localized, as spherical shell of confinement radius Rc and define a confinement potential ELJwall that accounts for the hard-core repulsion between the chromatin beads and the spherical wall. Each bead of the chromatin chain interacts with its nearest point on the wall through the potential ELJ with LJ strength 1kBT and the nuclear-chromatin cut off distance rn=21/6σ. This is the distance at which the repulsive force between the chromatin beads and the nuclear shell falls to zero. Motivated by the experiments where the nuclear volumes for live nuclei are significantly larger than those of fixed nuclei, we allow for variations of the confinement volume (with constant chromatin volume given by fixing N and the bead size). We define the parameter ϕ, as the global volume fraction of chromatin within the nucleus, with (1-ϕ), the volume fraction of the aqueous phase:

(2) ϕ=Volume of chromatin chainVolume of confinement=N×43π(σ/2)343πRc3

We varied Rc from 210 nm to 360 nm and hence ϕ from 0.1 to 0.5, where small values of ϕ model the case of chromatin in hydrated nuclei (aqueous solution) and large value of ϕ is for chromatin in dehydrated nuclei (Li et al., 2017; Maeshima et al., 2020; Pawley, 2006).

Chromatin LAD and non-LAD domains

To account for the biophysics of the bonding of the LAD domains of chromatin to the lamina, our chain comprises two types of beads in which only the LAD beads can be bonded to the lamina. The remaining non-LAD beads do not form such bonds. In order to simulate a specific system, we modeled the 22.4 Mbp regions of chromosome X (ChrX) of Drosophila where the distribution of the LAD regions is available online (Ho et al., 2014). That data indicates that 48% of the sequences are LAD with an average domain size of 90 kbp. We analyzed the data which shows an alternating pattern of LAD and non-LAD along the chromosome length (see Appendix 3—figure 1) and used these patterns in our simulations. To demonstrate that our coarse-grain model does not depend on the size of the chromosome and the locations of the LADs along the chromosome, we also used a Monte-Carlo method to randomly distribute the LAD regions along the chain (see details of method and results in Appendix 4, Appendix 4—figures 1, and Appendix 4—figures 2).

Chromatin-chromatin interactions

At the microscopic level, there are many possible interactions (e.g. electrostatic attraction between DNA and histone-tails, phase separation of the DNA binding non-histone protein HP1, and DNA crosslinking by nucleoplasmic lamin-A) which can cause chromatin self-attraction and lead to its separation from the aqueous phase. Since there may be additional bridging proteins and because even the ones we listed are not known in detail, we use a generic model for short-range chromatin-chromatin attractions. As outlined above, we model chromatin self-attraction by an attractive LJ potential (with cutoff rc=2.5σ as explained above). In the section below that considers variations of the interaction strength ϵ, we first consider the case where all beads (both LAD and non-LAD) interact with the same LJ potential. In addition, in the Appendix 7, we also consider the case in which interactions between two LAD beads are more strongly attractive compared with the interactions of two non-LAD beads or a LAD non-LAD pair. The reason for considering this more specific case, is to present an analogy for the micro phase separation of hetero and eu chromatin.

Chromatin-lamina interactions

To model the lamina that interacts with the LAD domains of the chromatin, we introduce additional beads which are localized to the confinement surface. For simplicity, we modeled the lamin beads which represent the thin, laminar shell, as static. The very short-range LAD-lamina bonding is mediated by specific proteins which we account for below. However, for the LAD regions of the chromatin to kinetically find the lamina after the initial conditions of our simulations, we include an additional, somewhat longer range attraction of the lamin and LAD beads, modeled by a relatively weak, LJ potential with ϵlm=1kBT with cutoff of rc=2.5σ (as explained above), where σ is the minimum hard-core distance between LAD and lamina beads.

The interactions of the non-LAD beads with the lamina are purely repulsive (due to their excluded volume) and to model that we use a LJ interaction with ϵln=1kBT and cutoff distance rc=21/6σ, at which point the repulsive force falls to zero. The attractive LAD-lamin attraction results in localization of the LAD near periphery compared with the non-LAD. The total, non-bonding (physical) interaction energy between lamin and chromatin (ELJlamina) is calculated from the sum of these individual LAD and non-LAD LJ interactions with lamin.

However, the most important feature of the chromatin-lamina interaction is the bonding of the LAD and the lamina via specific proteins. This depends on the availability of these proteins and the nature of their binding to the lamina. In the experiments (Amiad-Pavlov et al., 2020) that induced lamin C overexpression, there were significant changes in the chromatin organization with much less bonding of the chromatin to the lamina. Lamin overexpression has been suggested to repress the bonding activity of LBR proteins that bind the LAD domains to lamin B (Buxboim et al., 2017; Cho et al., 2017). These qualitative changes in chromatin organization as a function of the fraction of bonds that can be formed, cannot be studied using the LJ interaction which results in polymer adsorption to the lamina and not bonding, which can be restricted due to a finite number of binding sites or available binding proteins. We therefore allow for the possibility that not all LAD domains can bind to the lamina by introducing the parameter 0ψ1 which represents the fraction of the LAD domains that can bind to the lamina (for example, due to a reduction in the number of binding proteins relative to the number of LAD).

When ψ=1 all LAD can bond to the lamin beads while ψ=0 represents the situation in which no LAD-lamina bonds are possible (e.g. due to a lack of bonding proteins or bonding sites within the lamina). We allow for bond formation when a LAD bead is within a distance of r=rb=2.5σ from a lamin bead where the LJ interaction is attractive. A bond is then formed with an energy Eslamina=-kbond(rb-σ)2+kbond(r-σ)2, where we take kbond=10kBT/σ2. Thus, when the LAD-lamin distance, r is equal to rb, the bond energy is zero and when r=σ, the optimal bond energy, is attained. When the distance is either larger or smaller than σ, the energy due to the stretching of the spring is positive; at distances smaller than σ, the LJ repulsion dominates due to the excluded volume. In our model, a single LAD bead can form a maximum of one bond with a given lamin bead. The difference between the LJ interactions of the lamin and LAD and the bonding energy is seen when one considers the detachment of the lamin and LAD. For the LJ interaction, there are no energy barriers and the probabilities of all the distances between the LAD/lamin are just related to the Boltzmann factor (Blake and De Coninck, 2011) of the LJ potential. For bonding of the LAD and lamin (e.g. through the LBR protein, not explicitly considered in our model), a more general approach is used that does not require a description of all the intermediate configurations between bonding and non-bonding. LAD-lamin bonds are formed when the distance r between a LAD bead and the lamin obeys r<rb where we take rb=2.5σ. Once the bond is formed, the LAD-lamin interaction is given by a spring with an equilibrium spring length of σ and spring constant of 10kBT/σ2. The bonds can break only if r fluctuates to values greater than rb and the breaking occurs with a probability Pbreak=e-Ubond/kBT where for a situation of detailed balance, Ubond is the bond formation energy which we choose to be 10kBT. (In Appendix 5, we describe the effects of variations of the cutoff distance for bond breaking.)

Adding up all these contributions yields the total potential energy of chromatin in our model nucleus:

(3) Etot=Eschrom+Ebchrom+ELJchrom+ELJwall+ELJlamina+Eslamina

The total potential energy depends on the positions of the beads that determine their mutual interactions and those of the LAD beads with the lamina; the force on a given bead arises from the gradient of this potential energy.

Results

We now summarize the results of the Brownian dynamics simulations and discuss how conventional, peripheral and central organization of chromatin can be achieved by changing hydration (chromatin volume fraction ϕ), chromatin-lamina interactions (fraction of bonded LAD ψ), and intra-chromatin interactions (attraction strength ϵ). The simulations below demonstrate and quantify how the competition of chromatin self-attraction, hydration, and LAD-lamina attraction compete to determine the qualitatively different chromatin concentration profiles shown below. This is summarized at the end of this section in a state diagram showing the transitions between the various nuclear-scale chromatin organizational modes. The comparison with the experimental trends is addressed in the Discussion section.

Peripheral organization of chromatin

Before presenting the transitions in chromatin organization as a function of the parameters discussed above, we first discuss one important example of peripheral organization in pictorial detail. Motivated by the experiments, we tune the simulation parameters ϕ,ψ, and ϵ to the range where the equilibrium organization of the chromatin is peripheral, for example: ϕ=0.3,ψ=1,ϵ=1. In Figure 1, we present snapshots of simulations which demonstrate that for these particular values of (ϕ,ψ,ϵ) the chromatin is localized near the nuclear periphery. We next systematically vary these important physical parameters and show how the simulation results change to reveal different organizational modes of the chromatin.

Figure 1 with 1 supplement see all
Snapshots of the simulated system from different views.

This representation is generated by drawing the surfaces around the beads that represent the lamin and chromatin. The same set of pictures shown here are depicted in a different graphical representation, in terms of the beads themselves, in Figure 1—figure supplement 1. (a) Outside view: Our model, spherical nucleus is enclosed by lamin (NL) beads (green). Within the sphere, the chromatin chain of N = 37,333 beads contains two types of beads: LAD (yellow) and non-LAD (red). (b) Inside view: The sphere is cut at the equatorial plane to reveal one hemisphere, so that chromatin (red and yellow) is visible. The central region of the nucleus is devoid of chromatin for the particular conditions (ϕ=0.3,ψ=1,ϵ=1) of this simulation. (c) Cutting a slice near the equatorial plane: A slice is cut from the hemisphere, resulting in a 3D surface which has width of (1/10) of the sphere diameter. (d) 2D planar view: We show the equatorial (xy) plane view of the 3D slice and observe that the central regions contains no chromatin.

Variation of intra-chromatin attractive interactions

In our simulations, 48% of the chromatin are LAD domains (corresponding to ψ=1) which remain strongly bound to the lamina. For a chromatin volume fraction ϕ=0.3 and maximal chromatin-lamina attraction (i.e. all LAD domains can bond to the laminar, ψ=1), we varied the value of the chromatin self-attraction, ϵ, which is the same for all pairs of beads (LAD pairs, non-LAD pairs, and LAD/non-LAD pairs). The LAD-lamin interaction strength and the chromatin volume fraction were held fixed. In the left panel of Figure 2, we depict the chromatin concentrations in the equatorial, xy-plane calculated by taking the average of many frames (snapshots), while the system remained in equilibrium. The chromatin concentrations are shown with different colors where blue is chromatin-free and thus represents the aqueous phase, green represents low chromatin concentrations and red, high concentrations. When the intra-chromatin attractive interaction strength is relatively large, ϵ=1, the chromatin organization is peripheral. When the self-attraction is sufficiently small ( ϵ<1/2), the chromatin fills the entire volume, showing conventional organization. In the right hand panel of Figure 2, we plot the local volume fraction of chromatin ϕ(r), within a spherical shell as a function of the normalized radial distance r, where r=0 represents the nuclear center and r=1 represents the position of the nuclear envelope. We show the results for different values of the chromatin self-attraction. Here, ϕ(r) is the local volume fraction of chromatin; the average of ϕ(r) over the spherical volume is the global volume fraction ϕ. In the plot, we observe that for higher intra-chromatin attraction (ϵ0.75), the local volume fraction shows a peak near the nuclear periphery (r=1) and decreases to zero near the center, consistent with peripheral organization. For smaller intra-chromatin attraction (ϵ0.5), the local volume fraction has a peak near the nuclear periphery (r=1) but never decreases to zero since, in conventional organization, the chromatin fills the entire volume of the nucleus. This demonstrates the role of the chromatin self-attractions in stabilizing peripheral chromatin organization with a relatively high local volume fraction (red) of chromatin compared to the case of relatively small self-attractions where the chromatin fills the entire nucleus, with a smaller local volume fraction (green).

Variation of the chromatin concentration profile as a function of the intra-chromatin attractive interactions.

Left panel: Chromatin concentrations are shown for different intra-chromatin attraction strengths (ϵ) with a volume fraction of chromatin ϕ=0.3 and maximal LAD-lamina interactions (ψ=1). For smaller values of the attractions, the chromatin no longer shows peripheral localization, and fills the entire nucleus. This demonstrates the role of the chromatin self-attractions in stabilizing peripheral chromatin organization with a relatively high local volume fraction (red) of chromatin compared to the case of relatively small self-attractions where the chromatin fills the entire nucleus, with a smaller local volume fraction (green). Right panel: The local volume fraction profiles of chromatin for different ϵ plotted as a function of the radial distance r where r=0 is the nuclear center and r=1 is the position of the nuclear envelope. These local volume fraction profiles are obtained by averaging over the azimuthal and polar angles in thin spherical shells at distances from the nuclear center to the nuclear periphery.

Variation of the fraction of the LAD domains bound to the lamina

In our simulations, we considered the case in which not all LAD domains (in our simulations, 48% of the chromatin) can bind to the lamin beads. This was suggested by the experiments in systems where lamin C was overexpressed and may be due to a reduction in the number of lamin-binding proteins or the obscuring or burial of lamin-binding sites in the overexpressed situation (Buxboim et al., 2017). The parameter ψ represents the fraction of LAD beads that can potentially bind to the lamin. We now present the results of simulations that vary the value of ψ for fixed values of ϕ=0.3 and ϵ=1. The left hand panel of Figure 3, shows that a decrease in the value of ψ results in a transition of the chromatin organization from peripheral to central. While in the equatorial plane, this is indeed mostly central organization, the 3D structure is more complex with a ‘droplet’ of chromatin which ‘wets’ and thus contacts the bottom of the hemisphere due to the LAD-lamin attractions. This ‘wetting droplet’ configuration is discussed in more detail and shown in Appendix 5 and Appendix 5—figure 1, where its kinetic features are also explored. A similar progression is observed for a small chromatin volume fraction, ϕ=0.1, and shown in Figure 3—figure supplement 1. In the right hand panel of Figure 3, the local chromatin volume fraction shows a peak near the nuclar periphery (r=1) for ψ=1 while for ψ=0.1 the peak of the local volume fraction is shifted toward the center (r=0).

Figure 3 with 1 supplement see all
Variation of the chromatin concentration profile as a function of the fraction of LAD domains bound to the lamina.

Left panel: Variation in the fraction ψ of LAD beads that can bond to the lamin, associated domains relative to its maximal value of ψ=1, where 48% of the chromatin consists of LAD domains that can bind to the lamin. The values of the chromatin volume fraction ϕ=0.3 and chromatin self-interaction strength, ϵ=1 are fixed. Those LAD domains (a fraction, 1-ψ) not bound to the lamin are not necessarily found near the periphery of the nucleus and are mixed with the non-LAD chromatin. For small values of ψ, the chromatin is no longer peripherally localized but fills the nucleus more uniformly (but see the discussion of the ‘wetting droplet’ in Appendix 5 and Appendix 5—figure 1), since there are relatively few LAD-lamin bonds to localize the chromatin at the nuclear periphery. Right panel: The local volume fraction profiles of chromatin as a function of the radial distance r, where r=0 is the nuclear center and r=1 is the location of the nuclear envelope.

Effect of hydration (variation of chromatin volume fraction) of the nucleus

In the experiments, the volume of live Drosophila larva nuclei had an average value of 1183um3, while fixed nuclei had an average volume of 381um3, with corresponding changes in the chromatin organization from peripheral to conventional. This motivated our simulation study of the effect of changes in the relative fractions of the chromatin on chromatin organization, by changing the parameter ϕ. For relatively high chromatin volume fractions (ϕ=0.5), chromatin fills the entire volume of nucleus and shows conventional organization; there is no phase separation of chromatin and aqueous phase due to the overabundance of chromatin in the system (left panel of Figure 4). As we decrease the volume fraction of chromatin, the organization shows a transition from conventional to one that is more peripheral. In this case, there is sufficient aqueous phase so that phase separation is possible.

Variation of the chromatin concentration profile as a function of the chromatin volume fraction.

Left panel: Chromatin concentrations are shown for different volume fractions of chromatin, ϕRight panel: The local volume fraction profiles show peripheral organization for ϕ=0.3 and ϕ=0.1 but not for ϕ=0.5. This demonstrates the transition from peripheral to conventional chromatin organization as the nucleus is dehydrated and ϕ is increased.

Transitions from peripheral to uniform to central localization of chromatin

In the results shown above, we see how chromatin organization changes when we change ϕ,ψ and ϵ. Here, we summarize the transitions of chromatin organization from peripheral to central or from peripheral to uniform via a state diagram. We did many simulations (total 84 simulations) for different values of the parameters (ϕ,ψ,ϵ) and calculated local volume fraction profiles for these ranges. From the plots of local volume fraction, we classified the chromatin organization as peripheral, central (which can include the wetting droplet configurations discussed in Appendix 5 and Appendix 5—figure 1) or conventional. In Figure 5, we present the state diagram showing the transitions in chromatin organization by variations of the chromatin volume fraction, fraction of LAD that can bond to the lamin, and the intra-chromatin attraction strength (ϕ,ψ,ϵ). These results show how this minimal set of coarse-grained, simulation parameters (ϕ,ψ,ϵ) already determines a rich variety of chromatin organization in the nucleus.

State diagrams showing the transition from peripheral to uniform to central localization of chromatin.

(a) For a fixed value of ψ=1 (maximally bonded LAD), we calculated the local volume fraction obtained from simulations with different pairs (24 pairs) of the chromatin volume fraction and self-attraction (ϕ,ϵ) where 0.1ϕ0.5 and 0.25ϵ1. For each pair of (ϕ,ϵ), we used the plots of the local volume fraction to determine the chromatin organization mode. In the graph, the blue line shows the transition between conventional (uniformly distributed) chromatin organization, and peripheral organization. (b) For a fixed value of the chromatin self-attraction ϵ=1kBT, we calculated the local volume fraction obtained from simulations with different pairs (60 pairs) of the chromatin volume fraction and fraction of LAD that can bond to the lamina (ϕ,ψ) where 0.1ϕ0.5 and 0.1ψ1. The blue line shows the transition from central (and wetting drop) to peripheral chromatin organization. In figures (a) and (b), the bars are the simulation results while the line is a guide to the eye.

Discussion

We have shown here that the observed transitions in nuclear-scale chromatin organization in eukaryotic cells can be understood from the physics of a simple polymer model. The comparison of the theoretical and experimental trends indicates that these transitions are due to competition of polymer entropy, self-attraction of the chromatin and the chromatin-lamina attraction. By varying the values of the three generic parameters (ϕ,ϵ,ψ) that respectively control these effects, our simulations demonstrated the transitions between peripheral, central and conventional organization of chromatin as seen in the experiments.

For example, peripheral organization of chromatin was observed in our simulations when: (i) The radius of confinement within the nucleus is greater than radius of gyration of chromatin (Rc>Rg where Rg is for the self-attractive case), which is relevant for relatively small volume fractions of chromatin (ϕ=0.3). (ii) Chromatin must be self-attractive for its localization on the nuclear periphery, which occurs for significant chromatin self-attraction (ϵ=1);. (iii) Chromatin-lamina interactions are strong, as in the simulations for the case where all (or most) of the LADs can bond to the lamina (ψ=1) (see Figure 1).

Starting with these parameter values that resulted in peripheral organization, we then varied ϕ,ψ,ϵ to determine from our simulations, the transitions from peripheral to central to conventional, by varying one parameter at a time. We found transitions from peripheral to conventional when the self-attraction and volume fractions were decreased: 0.25ϵ1 and 0.1ϕ0.5 (see Figure 2 and Figure 4). We also found transitions from peripheral to central by reducing the chromatin-lamina interactions (0ψ1) (see Figure 3). We plotted the state diagrams for these transitions in Figure 5. These qualitatively track the observed experimental trends, for example, peripheral to conventional chromatin organization when the cell is dehydrated so that the chromatin volume fraction is increased. In Appendix 1 and Appendix 5, we discuss in more detail the comparison of the simulations and the experimental images that are published elsewhere (Amiad-Pavlov et al., 2020). In Appendix 6 and Appendix 6—figure 1, we calculated contact map from our simulation results (whose snapshots are shown in Appendix 1—figure 1a) and compared the contact maps of peripheral, conventional and central organization. The results show that chromatin in peripheral organization is condensed in a manner similar to conventional organization but is more condensed compared with central (Appendix 6—figure 1a and (b)) organization. We have also shown that lamins prevent chromosomes from mixing and help chromosomes remain in well-defined regions (analogous to territories) (see Appendix 6—figure 1c). We have also shown that like conventional, peripheral chromatin is also organized in a fractal manner (see Appendix 6—figure 1d).

An interesting experimental feature observed in the peripheral organization of chromatin, is that euchromatin (active chromatin, typically associated with non-LAD) and heterochromatin (inactive chromatin, typically associated with LAD) regions do not separate in the radial directions, but are separated in the perpendicular (angular) direction (see Figure 6c). Our simulations show that this can be the case even if the self-attraction of LAD and non-LAD are the same; this corresponds to the limit of negligibly small differences in heterochromatin/euchromatin interactions relative to their interactions with the aqueous phase and with the lamina. In this case, the angular separation originates in the stronger binding of the LAD domains to the lamina. We observed the angular separation of LAD and non-LAD in our simulations, when we allowed both the LAD and the non-LAD to have LJ attractions to the lamina (arising from physical interactions such as van der Waals) but allow only the LAD to additionally forms biochemical bonds with the lamina (Biophysically, this corresponds to bonds formed via proteins such as BAF). The angular alternation of LAD and non-LAD on the nuclear periphery occurs when only a fraction of the LAD can bind to the lamina (e.g., due to a limited number of binding proteins or sites) corresponding to ψ=0.5, and for ϕ=0.1, and ϵ=0.5, (see Figure 6b). These values of our simulation parameters also correspond to the experimental conditions. Small volume fractions of chromatin (ϕ=0.1) correspond experimentally to large (hydrated) Drosophila nuclei (Amiad-Pavlov et al., 2020). We note that for these simulations a somewhat smaller self-attraction, ϵ=0.5, shows the angular separation of LAD and non-LAD chromatin as seen in the experiments, whereas for ϵ=1, we find a homogeneous peripheral distribution with mostly LAD domains near the lamina, similar to Figure 6a. Although the qualitative trends in the simulations and experiments are indeed similar, it would be interesting for new experiments to more quantitatively test our predicted transitions in the state diagram of Figure 5. For example, in vitro experiments could control the amount of dehydration (changing the chromosome fraction ϕ with fixed chromosome mass) by spreading cells on surfaces (Guo et al., 2017; Adar and Safran, 2020).

Angular separation of LAD and non-LAD chromatin.

(a) Simulation snapshot for parameter values ψ=1, ϕ=0.1, and ϵ=0.5, shows peripheral organization with LAD near lamina and non-LADs separated from LADs in the radial direction. (b) Simulation snapshot for parameter values ψ=0.5, ϕ=0.1, and ϵ=0.5, shows peripheral organization with alternating LAD and non-LAD regions in the angular direction at the nuclear periphery. (c) Experimentally labeled H3K9ac (euchromatin/most of non-LAD/green) and His2B (chromatin/LAD and non-LAD/red) in muscle nuclei of intact Drosophila larvae, shows heterochromatin (associated with LAD) by dark red color and euchromatin (associated with non-LAD) by merging the red and green colors in peripheral organization. Both the experiments and simulations show an angular distribution of LAD and non-LAD as opposed to a radial distribution.

To focus on the essential physics of chromatin self-attraction vs. chromatin-lamina interactions, we have simplified the chromatin self-attractions to be the same for the euchromatin (EC) and heterochromatin (HC) domains. This is appropriate when the chromatin-aqueous phase interaction and the lamin-chromatin interaction are larger than the differences in the interactions of euchromatin and heterochromatin. Our model is the minimal one required to understand how the chromatin separates from the aqueous phase in peripheral and central organization. Although, previous models explicitly accounted for different interactions of euchromatin and heterochromatin domains, they did not consider the various types of nuclear-scale chromatin/aqueous phase/laminar organization and typically focused only on conventional chromatin organization. In addition, in the Appendix 7, we have discussed simulation results that show coexistence (micro phase separation) of more condensed and less condensed regions of chromatin due to different self-attractions of the LAD and non-LAD regions. This is analogous to the observed differences in concentration of chromatin in heterochromatin and euchromatin. Those results also show that peripheral organization cannot be achieved if difference in interaction of the LAD and non-LAD regions is too large. This justifies the original model presented in the main text in which differences in the self-attraction of the LAD and non-LAD regions are neglected, as a first approximation. But at the next order of approximation where we include differences in the self-attraction of different chromatin regions, the simulations show micro phase separation.

Materials and methods

Modeling the stretching energy and bending energy of the chromatin chain

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The stretching energy of the chromatin chain is calculated as:

(4) Eschrom=iks(ri2a)2

where 𝐫i is the distance between ith and (i+1)th beads. ks and 2a are respectively, the spring constant and equilibrium distance between two neighboring beads.

The chromosome has a persistence length of 2 beads (1.2 kb) which is based on a previous estimate (Marko and Siggia, 1997) of a persistence length of 1–2 kb for interphase chromatin. Since the bending energy determines the persistence length, this estimate allows us to write the bending energy of chromosome as:

(5) Ebchrom=ikb(1cosθi)

where θi is the relative angle between two neighboring beads, kb is bending stiffness which is taken as lpkBT/σ. Here lp is persistence length, σ is diameter of the bead, kB is Boltzmann constant, and T is absolute temperature.

Langevin dynamics

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The system is simulated calculating the Brownian dynamics of the chromatin beads in which the aqueous solvent is treated implicitly by the average frictional force it exerts on the moving beads and by the deviations from this average, represented by a stochastic force. For the use in computer simulations, the discrete time (Doyle and Underhill, 2005; Plimpton, 1995) equation of motion of the beads in this model is given by the Langevin equation:

(6) 𝐫i(t+Δt)=𝐫i(t)-Δtγm𝐫iEtot(t)+6kBTΔtγm𝝃i(t)

where m is bead mass, Δt is the time-step, γ is damping contact (related to the friction of the beads with the aqueous solvent) and 𝝃 is the stochastic force (thermal noise applied by the implicit aqueous solvent to each bead) and has the standard statistical properties used in Brownian dynamics simulations of equilibrium systems (Doyle and Underhill, 2005). The LAMMPS package is used for our calculations (Plimpton, 1995).

Initial conditions and equilibration

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Our initial condition has the chromatin chain comprising both LAD and non-LAD domains (that are many beads long) that are mixed along the chain as indicated by the sequence data (Ho et al., 2014). The center of mass of the chain is initially at the center of the nucleus and the dynamics are determined by the numerical solution of the stochastic Langevin equation that in general, includes the forces that arise from the interactions of the chromatin beads with themselves and the LAD domains with the lamina, plus the stochastic forces due to the implicit solvent. Initially, we include only the excluded volume chromatin-chromatin interactions, LAD-lamin attractions with LJ interactions and allow a fraction ψ of LAD domains within a distance rb of the lamina to create/break bonds with lamin beads, via the spring model, allowing for both bond creation and breaking dynamics. After equilibration, we changed the chromatin-chromatin interactions to allow for self-attraction and let the system re-equilibrate, again using the LAMMPS package (Plimpton, 1995). The parameter values used in the simulations are summarized in Table 1.

Simulation parameters

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Table 1
Parameter values used in the simulations.
ParameterDescriptionReduced unitSI unit
kBTThermal energy1.04.1 × 10−21J
mBead mass1.010−21 kg
σLJ size parameter1.010 nm
ϵLJ energy parameter1.0kBT4.1 × 10−21J
rcContact distance2.5σ25 nm
ksSpring constant100kBT/σ20.41 Jm−2
lpPersistence length2.0σ20 nm
kbBending stiffness2.0kBT8.2 × 10−21J
τDamping time1.0×(3πησ3/KBT)2 µs
ΔtTime step0.01τ20 ns

Experiment’s details

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Experimental documentation techniques, sample sizes etc. are described in our experimental paper (Amiad-Pavlov et al., 2020).

Appendix 1

Comparison of the simulations with the experimental images

Appendix 1—figure 1
Comparison of the simulations with the experimental images.

(a) Snapshots of simulations for chromatin-chromatin attractions ϵ=0.5. For relatively small volume fraction of chromatin (ϕ=0.1) and relatively high chromatin-lamina binding interactions (ψ=0.5), the simulation shows peripheral organization of chromatin. For ϕ=0.1 (small) and ψ=0.1 (small), we obtain central organization of chromatin (see Appendix 5 on the wetting droplet). For ϕ=0.3 (high) and ψ=1 (high), the simulations show conventional organization of chromatin, where the entire nucleus is filled. (b) Different organization of chromatin obtained in the experiments: peripheral, central and conventional are seen in experiments in the control, lamin A/C overexpression and fixed nuclei respectively (Amiad-Pavlov et al., 2020).

Appendix 2

Unconfined chromatin chains: self-avoiding and self-attractive

Here, we demonstrate that in the absence of confinement, the chromatin chain of our simulation model obeys the known scaling behavior of long polymer chains in both the self-avoiding (good solvent) and self-attractive (poor solvent) scenarios. Self-avoiding chains are modeled by cutting off the LJ potential when the force goes to zero. As defined in the main text, this occurs for the cutoff rc=21/6=1.1225. Self-attracting chains are modeled by including the attractive region of the LJ potential and the cutoff is set at rc=2.5. For a persistence length of two beads and a and LJ potential strength of ϵ=1kBT, we simulated self-avoiding chromatin chains of N=100,200,500, and 1000 beads and self-attracting chains for additional values of N up to 100,000 as shown in the figure (see Appendix 2—figure 1). To obtain the power law scaling from our simulations, we calculated the radius of gyration Rg for these various values of N and write.

(7) Rg=lp2Npν

where lp is persistence length, Np is number of persistence length (Np=N/lp), and ν is the scaling exponent. For the self-avoiding case, a good fit is found with ν=0.59 and for the self-attracting case, ν1/3 as expected (Rubinstein and Colby, 2003) from the theory of unconfined chains.

Appendix 2—figure 1
Scaling behavior of unconfined chromatin chains in good and poor solvent.

(a) LJ potential as a function of the distance between two beads, with snapshot of simulations of chromatin chain having 500 beads. Snapshots show unconfined, self-avoiding chromatin in good solvent conditions for a cutoff distance rc=21/6=1.1225 (green) and self-attractive chromatin in poor solvent conditions, for a cutoff distance rc=2.5. (b) Radius of gyration Rg vs. the number of beads N is calculated from the simulations of unconfined chromatin chain having N=100,100,000 beads (green and red dots). The green and red lines are guides to the eye. They can be fit with the power laws shown, demonstrating the polymeric scaling in the unconfined case for both good and poor solvent conditions.

Appendix 3

Analysis of LADs sequence data of Drosophila

Appendix 3—figure 1
Analysis of LADs sequence data of Drosophila.

(a) Mean cluster length of LAD for different chromosomes of Drosophila (Ho et al., 2014). (b) Length distribution of LAD for different Drosophila chromosomes. In both subfigures (a) and (b), the vertical bars represent the standard deviation (SD). (c) An alternating distribution of LAD (violet) and non-LAD (white) along the 22.4 Mbp regions of chromosome X (ChrX). (d) Same LAD distribution used in our coarse-grain model with a chromatin chain of 37,333 beads. From the sequence data it is clear, LAD regions in Drosophila consist of 150 beads, and not single ones.

Appendix 4

Alternate simulations for random LAD sequences

To demonstrate that our simulation results do not depend on any specific LAD sequence data, we also generated LAD distributions using a Monte-Carlo method. We considered two cases for LAD binding to lamin: (i) Randomly distributed as single beads, (ii) Exponentially distributed cluster with a mean of 150 beads. (i) LAD randomly distributed as single beads: In this method, we considered a fraction f of LAD beads within the chromatin chain that can bond to the lamin and distributed these randomly along the chain as single beads. (ii) LAD are exponentially distributed in clusters: In this method, we used basic knowledge of the experimental sequence data for Drosophila that indicates that LAD are distributed along the chromatin chain in an exponential manner, in regions with a mean length of 150 beads. From this distribution, we used Monte-Carlo method to generate LAD regions along the chromatin chain. We first generated LAD clusters for a fraction f of chromatin beads from an exponential distribution with a mean length 150 beads. We then arranged these clusters in descending order (m1>m2>m3. where m1,m2,m3 are the number of beads in each cluster). Using a Monte-Carlo method, we first randomly choose a position (1N where N is the total number of beads in the chain) for the cluster of size m1. Next, we choose a position for the cluster of m2 LAD beads, making sure that it does not overlap with the first cluster of m1 beads. After placing the m1 and m2 clusters in the chromatin chain,the m3 cluster can be placed between these two only if there is enough space between the two cluster to fit m3 beads. We repeat the process until the sum of all the clusters is equal to Nf (m1+m2+.=Nf).

Appendix 4—figure 1
Alternate simulations for random LAD sequences.

(a) Schematic diagram describing our coarse-grained model of chromatin-lamina interactions. Two cases for LAD binding to lamin: (i) Randomly distributed as single beads, (ii) Exponentially distributed cluster (many beads). Chromatin concentrations and local chromatin volume fraction profiles for ϕ=0.3 and ϵ=1 are shown when LAD binds to lamin as a (b) single bead (c) cluster.

Local volume fraction profiles of LAD, non-LAD, and lamin beads

Appendix 4—figure 2
Local volume fraction profiles of LAD, non-LAD, and lamin beads.

For ϕ=0.3,ϵ=1,f=0.5, the local volume fraction profiles of LAD, non-LAD and lamin beads are shown. The graph shows the location of each of these bead types in the spherical volume where r=0 is the sphere center and r=1 is the sphere surface.

Appendix 5

Central organization and wetting droplet

From simulations of the chromatin for small values of ψ (fraction of LAD which can bond to the lamin), we found a central organization of chromatin with several ‘arms’ (see ‘arms’ in Appendix 5—figure 1a) that contact the lamina. This occurred when the unbinding probability (related to the bond breaking as explained below) was relatively small and is thus a kinetic effect. Nevertheless, the experiments indicate such configuration. Since each LAD domain is rather large (150 beads and not a single ‘monomer’ of the chain), once it binds to the lamina, unbinding – which must involve the near-simultaneous detachment from the lamina of all 150 beads – occurs with low probability. These conditions resulted in the ‘arms’ that resembled the experiment (see Appendix 5—figure 1b). Different LAD domains will randomly contact the lamina at different positions, resulting in several ‘arms’. If we greatly increase probability of unbinding, then even if an entire arm randomly binds, it can unbind and the system can reach the equilibrium of an approximately wetting droplet that contacts the lamina in one region and not via many ‘arms’. Thus, this is a matter of time scales and the irreversibility of the LAD-lamin binding that determines whether the chromatin in the weak-binding limit, shows central localization with several bound ‘arms’ or whether it equilibrates to the wetting droplet. We recall that these effects refer to LAD-lamin binding as opposed to the physical chromatin-chromatin attractions, since LAD-lamin attractions are mediated by specific binding proteins. In Appendix 5—figure 1a, we show 3D snapshots of simulations for ψ=0.1,ϕ=0.1,ϵ=1. All the configurations show central organization of chromatin. The difference between the first two from the left is in the detachment kinetics of the LAD domains; we control this by varying the distance rb between the LAD and the lamin at which the bond between them (biophysically mediated via BAF and other proteins not explicitly included in our simulation) breaks; that is, the spring energy representing the bond, abruptly goes to zero when the bond is stretched to a distance larger than rb. In the ‘wetting droplet’ configuration (second from left) we take rb=1.1225, so that bond breaking happens much more easily than in the simulations (first from left) that show several ‘arms’ where rb=2.5 and the LAD-lamin distance can fluctuate over a larger range and still remain bonded. Thus, for rb=1.1225, the chromatin equilibrates into a ‘wetting droplet’ with the relatively simple geometry shown here with no ‘arms’ that are ‘stuck’ to the lamina. The third picture from the left shows the chromatin localization in the center with neither ‘arms’ nor ‘wetting droplet’ configurations for the case where no bonds are formed between the LAD and the lamin. The center of mass of the chromatin can be found anywhere within the nuclear volume.

Appendix 5—figure 1
Wetting droplet and central chromatin organization for relatively weak LAD-lamina interactions.

(a) 3D snapshots of simulations showing central organization of chromatin with/without ‘arms’ as well as the wetting droplet. (b) Experiments also suggest central organization of chromatin with/without ‘arms’ as well as the wetting droplet for the case of Lamin A/C overexpression (Amiad-Pavlov et al., 2020).

Appendix 6

Comparison of chromatin contacts in peripheral, central, and conventional organization

In Hi-C experiments, cells are fixed by formaldehyde which has been reported (Li et al., 2017; Maeshima et al., 2020) to lead to cell shrinkage; thus, the cell and nuclear volume of fixed cells can be considerably smaller than those of live, intact cells (by a factor of up to three in our experiments) (Amiad-Pavlov et al., 2020). It is thus of biological interest to compare the chromatin contact maps for cells with different chromatin volume fractions. Contact maps, as typically measured in Hi-C experiments, quantify the contacts between pairs of chromatin regions in cells. In the simulations presented here, we compare the contact properties of chromatin in nuclei with different volume fractions of chromatin, that correspond to fixed (conventional organization) and live (peripheral/central organization) cells. We calculated the contact map from the simulations whose snapshots are shown in Appendix 1—figure 1a. We define contact between two beads of chromatin chain when their distance is 1.5σ. In Appendix 6—figure 1a, we compare the contact maps of central (ψ=0.1,ϵ=0.5,ϕ=0.1) and peripheral (ψ=0.5,ϵ=0.5,ϕ=0.1) organization of chromatin at 50 kbp resolution. We conclude that the map of central chromatin has more distal contacts (color) compare to peripheral chromatin. We know from previous studies that condensed chromatin shows less distal contact compared with open chromatin in nucleus (Naumova et al., 2013). This means that in our model, the peripheral chromatin corresponds to a more condensed state compared with central organization. Next, in Appendix 6—figure 1b, we compare the contact maps of conventional (ψ=1,ϵ=0.5,ϕ=0.3) and peripheral (ψ=0.5,ϵ=0.5,ϕ=0.1) chromatin. Our result show that both peripheral and conventional are in a relatively condensed state compared with central organization. To understand how chromosomes mix with time, we mark our long chromatin chain of 22Mpb with 2Mbp regions. We define contacts within these 2 Mbp chromatin regions as local contacts and contacts between the different 2 Mbp chromatin regions as distal contacts (Chiang et al., 2019). If we roughly think of each marked section as a separate chromosome, local contact may correspond to contact within a chromosome and distal contact may correspond to contact between chromosomes. We then calculated the open chromatin index (OCI) which is simply equal to ratio of the averaged sum (over all segments) of distal contact and averaged sum of local contact. In Appendix 6—figure 1c, we show the OCI for central, peripheral and conventional chromatin. The OCI increases with time for central chromatin and relatively quickly saturates to a constant value for conventional and peripheral. Our result shows that these different regions (roughly corresponding to different chromosomes) do not mix when their interaction with the lamin is high (ψ0.5) and remain in their original regions (analogous to territories) within the nucleus. To understand the nature of this packaging, we computed the contact probability (P(s)) along the length (s) of our model of chromosome X. This shows a power law decay with P(s)s-1, corresponding to a fractal globule where the various segments have not mixed (Mirny, 2011). In Appendix 6—figure 1d, each of the various chromatin organizations shows fractal globule behavior. However, since the OCI of central chromatin (pre-wetting droplet) increases with time, its fractal globule nature may evolve into equilibrium globule after a much longer time. Such dynamics are outside the scope of this paper.

Appendix 6—figure 1
Comparison of chromatin contacts in peripheral, central, and conventional organization.

(a,b) Contact maps from simulations, of different 50-kbp bins, for different chromatin organization. The color scheme varies from black to white, representing high to low contact counts (log(Pij)). (a) Comparison of contact map of central (lower diagonal) and peripheral (upper diagonal) chromatin organization. (b) Comparison of contact map of conventional (lower diagonal) and peripheral (upper diagonal) chromatin organization. (c) Open chromatin index (OCI) plotted with respect to time (simulation frames) for central, peripheral, and conventional organization chromatin. (d) Contact probability as a function of contour distance for central, peripheral, and conventional organization chromatin, calculated from the simulations (dots). The red line is a guide to the eye indicating a power-law behavior, which suggests the fractal globule packing nature.

Appendix 7

Phase separation of euchromatin-like and heterochromatin-like regions in conventional chromatin packing within the nucleus

In our previous results, we considered the case where the self-attractions of the LAD and non-LAD beads were identical; the only difference between them was that only the LAD were attracted (bonded) to the lamin. We studied the changes in the chromatin organization as we reduced the fraction of bonds between LADs and lamina (ψ), which, for small enough ψ, results in a transition from peripheral to central (wetting droplet) organization. Here, we consider the effects of a difference in the self-attraction of the LAD and non-LAD beads with each other as a model of the different self-attractions within heterochromatin and euchromatin. However, we realize that there are other aspects of hetero and euchromatin, such as their different post-translational modifications that are not explicitly included here. We modelled the non-LAD beads as a self-avoiding (polymer in good solvent) and the LAD beads as a self-attracting (polymer in poor solvent). Due to the self-avoiding non-LAD regions, the chromatin fills the entire nucleus and shows conventional organization (see Appendix 7—figure 1). We now change the bonding interactions between the LAD and lamina beads via a reduction in the parameter ψ. Appendix 7—figure 1 shows phase separation of the non-LAD and LAD regions for different values of ψ. The snapshots of the simulations (see Appendix 7—figure 1a) indicate that for ψ=1, the LAD beads (yellow) are distributed in the periphery and separated from the non-LAD (red). For ψ=0.5, we can see mixing of the LAD and non-LAD beads. When ψ=0, all the LAD beads are distributed in the center but due to the different self-attractions used in the simulations discussed in this section, are phase separated from the non-LAD beads. In Appendix 7—figure 1b, we show the chromatin concentration profile where high chromatin concentration is represented by red, low concentration by green and aqueous phase by blue. These demonstrate the existence of A/B like compartments that may correspond to the non-uniform distribution of chromatin in different cells (Falk et al., 2019). The central panel of Appendix 7—figure 1b which shows a more uniform filling of the nucleus by the non-LAD beads may correspond to the patchy ‘marshland’ measured for chromatin in aqueous phase Cremer et al., 2015. The results in this section show that different chromatin packing concentrations can be obtained by a combination of different attractions and LAD lamin attraction. While not a complete model of hetero and eu chromatin, they do have certain features in common with the different packings commonly associated with these two chromatin types.

Appendix 7—figure 1
Phase separation of euchromatin-like and heterochromatin-like regions in conventional chromatin.

(a) Snapshots of simulations for different ψ are shown. In figure, LAD beads (yellow) are self attractive chain whereas non-LAD beads (red) are self-avoiding. This modeling results in a stronger separation of the two types of beads into spatially distinct regions. (b) Chromatin concentrations for different ψ are shown. High (red) and low (green) concentrations of chromatin with aqueous phase (blue) shows A/B compartments like (non-uniform) distribution of chromatin. (c) Local volume fraction of the LAD beads shows peripheral organization of those regions for ψ=1, a uniform distribution for ψ=0.5 and central organization for ψ=0.

Data availability

All data generated or analysed during this study are included in the manuscript and supporting files. Source data files are available on zenodo using the following link: https://zenodo.org/record/4772105.

The following data sets were generated
    1. Bajpai G
    2. Amiad Pavlov D
    3. Lorber D
    4. Volk T
    5. Safran S
    (2021) Zenodo
    ID 4772105. Mesoscale phase separation of chromatin in the nucleus.

References

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    A molecular approach
    In: Cooper G. M, editors. The Cell. Sunderland: Sinauer Associates. pp. 603–604.
  2. Book
    1. Doyle PS
    2. Underhill PT
    (2005) Brownian Dynamics Simulations of Polymers and Soft Matter Dordrecht
    In: Yip S, editors. Handbook of Materials Modeling. Netherlands: Springer. pp. 2619–2630.
    https://doi.org/10.1007/978-1-4020-3286-8_140
  3. Book
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    Polymer Physics
    New York: Oxford university press.

Decision letter

  1. Karsten Kruse
    Reviewing Editor; University of Geneva, Switzerland
  2. K VijayRaghavan
    Senior Editor; National Centre for Biological Sciences, Tata Institute of Fundamental Research, India
  3. Helmut Schiessel
    Reviewer

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

The authors study theoretically chromatin distribution in the nucleus. This is a very well-written study that identifies the physical variables underlying observed nuclear phase separation. It is of broad interest for understanding chromatin organization.

Decision letter after peer review:

Thank you for submitting your article "Mesoscale phase separation of chromatin in the nucleus" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by K VijayRaghavan as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Helmut Schiessel (Reviewer #2).

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

As the editors have judged that your manuscript is of interest, but as described below there are some doubts on whether your work goes sufficiently beyond your Ref.[12] of the manuscript to merit publication in eLife.

You study theoretically the effect of nuclear volume and the interaction of chromatin with the lamina on the distribution of chromatin within the nucleus using a simple polymer model. In your model, you also consider self-attraction of the chromatin. You find that depending on the relative strength of these effects, the chromatin is either homogeneously distributed within the nucleus or is localized peripherally. An intermediate state with the chromatin "partially wetting" the nuclear lamina is also observed. These states of chromatin distribution were also observed in Drosophila nuclei. This is a very well-written study that presents. The most important finding being that of the effect of the solvent quality on phase separation. However, the fact that the configuration of a spherically confined polymer can steered in the manner shown by directly manipulating the relative self-interaction versus the affinity of (parts of) the chain to the boundary is not really surprising. Also it is not clear, whether the difference between eu- and heterochromatin can indeed be neglected in this context.

If you decide to submit a revised version to eLife, please, make sure to comment in particular on why you think that the results presented here and that go beyond Ref.[12] merit publication in eLife rather than a more physics oriented journal like Soft Matter.

Essential revisions:

1. Why do you need a second potential in addition to the LJ potential after bond formation between an LAD bead and a lamina bead?

2. Are the effects of fixation well described by changing the chromatin volume fraction alone?

3. The paragraph on page 8 about bond formation is a little difficult to follow. Could you clarify the probability for bond breaking Pbreak}. One would expect to find in the exponent the difference between the elastic energy at σ and at rb.

4. Earlier work in C. elegans (e.g. Meister P et al. Genes Dev. (2010)) seems to suggest that the specific affinity of heterochromatin to the lamina is important to understand the global structure of the nucleus. The authors definitely appear aware of this issue, by explicitly stating that their model holds whenever the generic interactions between chromosome and lamins are more important than the e.g. eu/hetero cross-interactions. However, in the discussion they appear to want to have it both ways in the end, by appealing (without further references) to a correlation between the occurrence of LAD domains and the eu/hetero nature of regions of the chromosome. Could you clarify this issue?

https://doi.org/10.7554/eLife.63976.sa1

Author response

You study theoretically the effect of nuclear volume and the interaction of chromatin with the lamina on the distribution of chromatin within the nucleus using a simple polymer model. In your model, you also consider self-attraction of the chromatin. You find that depending on the relative strength of these effects, the chromatin is either homogeneously distributed within the nucleus or is localized peripherally. An intermediate state with the chromatin "partially wetting" the nuclear lamina is also observed. These states of chromatin distribution were also observed in Drosophila nuclei. This is a very well-written study that presents. The most important finding being that of the effect of the solvent quality on phase separation.

We thank the reviewers for their positive approach regarding our article; we are also grateful to the reviewers for their insightful comments and questions that have helped us to improve the manuscript. Below we address the reviewers’ concerns in detail. Based on the referee comments, we have done new simulations and have revised the manuscript to address all the concerns. The changes in the manuscript have been marked in red in the revised manuscript.

However, the fact that the configuration of a spherically confined polymer can steered in the manner shown by directly manipulating the relative self-interaction versus the affinity of (parts of) the chain to the boundary is not really surprising.

We believe that our paper is important for biologists because it presents a new paradigm that the chromatin can be (depending on hydration) phase separated in the nucleus. This is the first time that, to our knowledge, chromatin phase separation is discussed based on experimental data. That is why we submitted the paper to eLife and not to a physics journal, proper. The observations, model simulations and explanations change the biological paradigm and show that the competition of the surface and bulk interactions, can indeed be fine-tuned to lead to the transitions between peripheral, conventional and central (wetting droplet) organization. Our paper provides the conceptual and modeling basis for these transitions which are indeed observed in the experiments as we discuss in the paper.

Moreover, we present a guide for further experiments that can map the global state diagram showing the transitions between conventional, peripheral and central (wetting droplet) organization of chromatin. An additional interesting observation, simulation result and explanation involves the wetting droplet (in equilibrium, as shown in Appendix 5–figure 1) as well as the non-equilibrium droplet with arm-like extensions that are kinetically “stuck” to the lamin layer (also shown in Appendix 5–figure 1); these are not commonly used in biology or biophysics. In our simulations in Appendix 5, we show that these different situations are kinetically determined.

Because chromatin organization can have profound effects on gene expression (see just below for the text we inserted in the paper), it is important to explain these effects and quantify them for biologists and biophysics even though some of the qualitative properties may not surprise experts in polymer physics, per se. That is precisely the reason we are submitting to eLife. In light of the referee comment, we have further explained the novelty and importance of the paper on page 3 of the Introduction where we added the following text: “In this paper we systematically examine how the interplay between chromatinlamina interactions, intra-chromatin interactions, and hydration affect the chromatin organization. […] Our simulation results also provide suggestions to experimental groups on how to vary the minimal number of parameters that will experimentally result in different modes of chromatin organization in vivo.”

Also it is not clear, whether the difference between eu- and heterochromatin can indeed be neglected in this context.

We justify our use of the same self-attractions of eu and hetero chromatin, as a first approximation only, from the experiments themselves. The experimental figure of the peripheral organization shown in Figure 6(c), indicates that both heterochromatin and euchromatin are found in the peripheral part of the nucleus. They both separate from the aqueous phase in the center. This suggests that the chromatin attractions driving this phase separation are to a first approximation, similar for heterochromatin and euchromatin. Of course to the next approximation, the self-attraction of heterochromatin and of euchromatin differ and that is why the experiments imaged alternating regions of heterochromatin and euchromatin along the angular direction in the nuclear periphery (see Figure 6(c)). Our simulations show that this can indeed be the case when the LAD interactions with the lamin are larger than the smaller differences between the self-attraction of euchromatin vs. heterochromatin (see Figure 6(b)). We explained this in the paper on page 10 of the Discussion part.

Based on the referee comments, we have added new simulation results to the paper that do take into account different self-attraction for the LAD compared to the self-attraction of the non LAD regions. Note that we are aware that there are other differences between heterochromatin and euchromatin such as histone modifications. These new simulations are not meant to replicate hetero and euchromatin in detail, but rather to show that micro phase separation within the chromatin (as opposed to chromatin/aqueous phase separation) can occur even for different self-attractions of the LAD and non-LAD regions. This is analogous to eu and heterochromatin whose detailed study is outside the scope of our paper. We have done this in the limiting case that the attractions of the LAD regions (as an analogy of heterochromatin) are larger than the non LAD regions (as an analogy of euchromatin). In Appendix 7, motivated by previous models, we considered the non-LAD regions as polymers in good solvent and the LAD regions as polymers in poor solvent [3]. These new simulation results show phase separation of the LAD and nonLAD regions for the relatively high volume fraction regime where the overall chromatin is conventionally packed and not phase separated from the aqueous phase (see the new Appendix 7 and Appendix 7–figure 1 in revised manuscript). Our new results also demonstrate that peripheral organization cannot be achieved if the difference in interactions of the self-attractions of the LAD and non-LAD is large. This justifies our original model as presented in the main text in which differences in the self-attraction of the LAD and non-LAD are neglected to a first approximation. The primary effect is then phase separation of chromatin from the aqueous phase as observed. Our new simulations demonstrate that the largest interactions are the chromatin-chromatin self-attractions and that the differences in those attractions due to other modifications (such as LAD and non-LAD) are secondary.

We have referred to these new results of Appendix 7, in the main text on page 5, where we added the following text:

“In addition, in the Appendix 7, we also consider the case in which interactions between two LAD beads are more strongly attractive compared with the interactions of two nonLAD beads or a LAD non-LAD pair. […] But at the next order of approximation where we include differences in the self-attraction of different chromatin regions, the simulations show micro phase separation.”

If you decide to submit a revised version to eLife, please, make sure to comment in particular on why you think that the results presented here and that go beyond Ref.[12] merit publication in eLife rather than a more physics oriented journal like Soft Matter.

We believe that paper is important for biologists because it presents a new paradigm that the chromatin can (depending on hydration) phase separate from the aqueous phase in the nucleus. To our knowledge, this the first time that chromatin phase separation is analyzed using simulations and discussed physically in comparison with experimental data. This evidence changes the biological paradigm and shows that the competition between the surface (lamin) and bulk chromatin interaction can indeed be fine tuned in both simulations and experiments to result in transitions between peripheral, conventional and central organization. Those transitions are indeed observed in the experiments as we discuss. Moreover, we present a guide to further experiments that can map the global state diagram of conventional, peripheral and central (wetting droplet) organization of chromatin. Because the organization can have profound effects on gene expression, it is important to explain these effects and quantify them for biologists and biophysicists even though the qualitative polymer properties may not surprise experts in polymer physics. That is precisely the reason we are submitting to eLife.

Based on the referee remarks we have further highlighted the biological implications of our results in a manner that relates to experiment. We have now included the results of additional calculations that relate our predictions of phase separation to the Hi-C contact maps of chromatin, which are of great interest to biologists. In particular, to relate the new paradigms of chromatin organization to the contact maps, we calculated those contact maps from our simulation results and compared the maps of peripheral, conventional and central organization (see Appendix 6 and Appendix 6–figure 1 in revised manuscript). Our new results show that chromatin in peripheral organization is condensed (in the sense of Hi-C maps) in a manner that is comparable to conventional organization but is more condensed (in the Hi-C sense) than central organization (Appendix 6–figure 1(a) and (b)). We have also shown that the lamin attraction prevents peripherally organized chromosomes from mixing and help chromosomes remain in well-define regions (analogous to territories) (see Appendix 6–figure 1(c)). We have also shown that similar to conventional organization, peripheral chromatin is also organized in a fractal globule fashion (see Appendix 6–figure 1(d)).

We have summarized the new results on the Hi-C contact map (presented in detail in the new Appendix 6) and how they impact the various chromatin concentration profiles in the main paper of the paper on page 10, where we added the following text:

“In Appendix 6 and Appendix 6–figure 1 we calculated contact map from our simulation results (whose snapshots are shown in Appendix 1–figure 1(a)) and compared the contact maps of peripheral, conventional and central organization. […] We have also shown that like conventional, peripheral chromatin is also organized in a fractal manner (see Appendix 6–figure 1(d)).”

Essential revisions:

1. Why do you need a second potential in addition to the LJ potential after bond formation between an LAD bead and a lamina bead?

We used harmonic potential in addition to the LJ potential for following reasons:

i. The short-range LJ attraction (ϵ = 1kBT, rc = 2.5σ) was not strong enough to have localize LAD beads in the periphery. Even for cases where the LJ simulation parameters are larger (but still reasonable) and should favor peripheral organization, this potential was not enough to localize in periphery. That is accomplished by a more specific bonding model which introduces a strong energy penalty for changing the bond length. The main difference with the LJ interaction (which causes “polymer adsorption” but not bonding) is that once a bond is formed, there can be a strong energy penalty for changing the bond length (see below for the discussion of bond breaking).

ii. The LAD regions are initially uniformly distributed within the nucleus. The LJ attraction allow the LAD regions to kinetically become localized at the periphery where the bond formation further stabilizes their connection to the lamin. Biologically, the anchor protein lamin B receptor (LBR) binds lamin B and acts as a tether between chromatin and the nuclear lamina. To mimic LBR protein binding, we used a bonding potential between lamin and some fraction of the LAD beads. We restricted only a fraction, ψ, of the LAD beads to bind to simulate the finite fraction of binding sites or binding proteins; those were changed by the experiments in which lamin A/C were overexpressed. The use of bonding and the restriction of the number of binding sites/proteins allows us to predict how the chromatin concentration profile changes as a function of the fraction ψ of bonds that can be formed (e.g., experimentally caused by the finite number of LBR proteins or available lamin binding sites). This corresponds to the experiments on overexpression of Lam A/C (see Appendix 1–figure 1). These qualitative changes in chromatin organization as a function of the fraction of bonds that can be formed, cannot be studied using the LJ interaction which results in polymer adsorption to the lamina but not bonding, which can be limited due to the bonding restrictions.

iii. In our model, the bond between lamin and LAD is dynamic and can break (see below for a discussion of the breaking probability). Also, a single LAD bead can form a maximum of one bond with a given lamin bead. So, to simulate the transition from peripheral to central, we need only change the breaking bond properties of the LAD and lamin (see Appendix 5 and Appendix 5–figure 1 in revised manuscript).

In light of the referee comment, we have further explained the importance of bonding potential in the paper on page 5 of the Model where we added the following text:

“These qualitative changes in chromatin organization as a function of the fraction of bonds that can be formed, cannot be studied using the LJ interaction which results in polymer adsorption to the lamina and not bonding, which can be restricted due to a finite number of binding sites or available binding proteins.”

2. Are the effects of fixation well described by changing the chromatin volume fraction alone?

It has been reported that tissue fixation can cause a reduction in both the cellular and nuclear volumes due to dehydration of the cell [4–6]. For example, in Hi-C experiments, cells are fixed by formaldehyde. It has been reported the fixation of cells with formaldehyde leads to cell shrinkage and the cell volume of fixed cells can be significantly smaller than the cell volume of living cells [7,8]. Also, our experiments measured the volume of live Drosophila larva nuclei as having an average value of 1183µm3, while fixed nuclei had an average volume of 381µm3 [9].

3. The paragraph on page 8 about bond formation is a little difficult to follow. Could you clarify the probability for bond breaking Pbreak. One would expect to find in the exponent the difference between the elastic energy at σ and at rb.

We apologize for the confusion. The bond breaking kinetics are parameterized in a general manner by Pbreakthat does not require a detailed formulation of the interaction potential responsible for bonding, other than its curvature near the minimum, as we now explain here and in the revised text:

i. In Langevin simulations, per se, only forces are relevant.

ii. In the bond model the relevant force is due to a spring (bond) that is formed whenr (which is LAD-lamin distance) is less than or equal to rb≡ 2.5σ. Changes in the LAD lamin distance results in a spring-like force that restores the bond to its optimal length of r = σ with a spring constant of 10kBT/σ2.

iii. The bond stabilization energy i.e. energy when r = σ enters only indirectly since the bond breaking probability (and not a detailed bond potential) is used by the LAMMPS software. (We have appropriately modified the original discussion in the paper; see below.)

iv. Two parameters enter to describe bond breaking in LAMMPS.

a. Pbreak: Probability that over many time steps the bond will stochastically break.

b. rb: Bond breaking only occurs if r (the LAD-lamin distance) obeys r > rb. That means, when r is too small, bond breaking does not occur and the bond distance fluctuates due to the competition of thee thermal forces and the spring.

v. These two features allow us to describe bond formation and bond breaking withoutincluding a detailed attractive potential that describes how the bond is formed with all intermediate configurations.

vi. We have therefore taken Pbreak = eUbond/kBTwhere we set Ubond = 10kBT. This represents a fairly long-lived bond. We took rb = 2.5σ. For bonds whose formation/breaking is given by detailed balance, Ubondis the energy gained upon formation of the bond (relative to the unbonded state). In Appendix 5 where we show the wetting droplet, we have compared a value of rb = 1.1225σ where the unbonding is fast so that the equilibrium wetting droplet (Appendix 5–figure 1(a)) is obtained. For rb = 2.5σ, the unbonding is slow and the system remains “stuck” in the non-equilibrium state with many arms as show in Appendix 5–figure 1(a).

In light of the referee comment, we have further explained the probability for bond breaking Pbreak in the paper on page 5 of the Model section where we added the following text: “The difference between the LJ interactions of the lamin and LAD and the bonding energy is seen when one considers the detachment of the lamin and LAD. […] (In Appendix 5, we describe the effects of variations of the cutoff distance for bond breaking.) ”

4. Earlier work in C. elegans (e.g. Meister P et al. Genes Dev. (2010)) seems to suggest that the specific affinity of heterochromatin to the lamina is important to understand the global structure of the nucleus. The authors definitely appear aware of this issue, by explicitly stating that their model holds whenever the generic interactions between chromosome and lamins are more important than the e.g. eu/hetero cross-interactions. However, in the discussion they appear to want to have it both ways in the end, by appealing (without further references) to a correlation between the occurrence of LAD domains and the eu/hetero nature of regions of the chromosome. Could you clarify this issue?

First, we thank to referee for the reference [11]; we have now added this to the revised manuscript. In the revised manuscript (and in our comments to the referees and the paper revisions noted above), we have now clarified that the simulations relate to LAD and non-LAD regions of chromatin. These is no modeling of hetero and euchromatin as relates to histone modifications. However, in the new Appendix 5 we now present a study of a system where the attractions of the LAD and non-LAD beads are different.

This results in micro phase separation of those regions and is analogous to micro phase separation associated with eu and heterochromatin.

In the peripheral organization, the experiment image in Figure 6(c) shows that both heterochromatin and euchromatin are found in the peripheral part of the nucleus. They both separate from the aqueous phase in the center. This suggests that the chromatin attractions driving this phase separation are to a first approximation, similar for heterochromatin and euchromatin as we assumed in the main text. Of course in the next order of approximation, the self-attraction of heterochromatin and of euchromatin differ and that is why the experiments imaged alternating regions of heterochromatin and euchromatin along the angular direction in the nuclear periphery (see Figure 6(c)). In Discussion part, based on our simulation results (see Figure 6(b)), we suggest that this can be the case when LJ attraction between LAD-lamin and nonLAD-lamin are same but LAD-lamin also have bonding attraction.

References:

1. Jain N, Iyer KV, Kumar A, Shivashankar G (2013) Cell geometric constraints induce modular gene-expression patterns via redistribution of hdac3 regulated by actomyosin contractility. Proceedings of the National Academy of Sciences 110:11349–11354.

2. Thomas CH, Collier JH, Sfeir CS, Healy KE (2002) Engineering gene expression and protein synthesis by modulation of nuclear shape. Proceedings of the National Academy of Sciences 99:1972–1977.

3. Chiang M, et al. (2019) Polymer Modeling Predicts Chromosome Reorganization in Senescence. Cell Reports 28:3212–3223.e6.

4. Xie K, Yang Y, Jiang H (2018) Controlling cellular volume via mechanical and physical properties of substrate. Biophysical journal 114:675–687.

5. Windner SE, Manhart A, Brown A, Mogilner A, Baylies MK (2019) Nuclear scaling is coordinated among individual nuclei in multinucleated muscle fibers. Developmental cell 49:48–62.

6. Pawley J (2006) Handbook of biological confocal microscopy (Springer Science and Business Media) Vol. 236.

7. Li Y, et al. (2017) The effects of chemical fixation on the cellular nanostructure. Experimental cell research 358:253–259.

8. Maeshima K, Tamura S, Hansen JC, Itoh Y (2020) Fluid-like chromatin: Toward understanding the real chromatin organization present in the cell. Current opinion in cell biology 64:77–89.

9. Amiad-Pavlov D, Lorber D, Bajpai G, Safran S, Volk T (2020) Live imaging of chromatin distribution in muscle nuclei reveals novel principles of nuclear architecture and chromatin compartmentalization. bioRxiv.

10. Blake T, De Coninck J (2011) Dynamics of wetting and Kramers’ theory. The European Physical Journal Special Topics 197:249–264.

11. Meister P, Towbin BD, Pike BL, Ponti A, Gasser SM (2010) The spatial dynamics of tissue-specific promoters during C. elegans development. Genes and development 24:766–782.

https://doi.org/10.7554/eLife.63976.sa2

Article and author information

Author details

  1. Gaurav Bajpai

    Weizmann Institute of Science, Rehovot, Israel
    Present address
    Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot, Israel
    Contribution
    Conceptualization, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing
    For correspondence
    gaurav.bajpai@weizmann.ac.il
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-3875-4599
  2. Daria Amiad Pavlov

    Weizmann Institute of Science, Rehovot, Israel
    Present address
    Department of Molecular Genetics, Weizmann Institute of Science, Rehovot, Israel
    Contribution
    Conceptualization, Validation, Investigation, Writing - review and editing, Performed and analyzed the experiments
    Competing interests
    No competing interests declared
  3. Dana Lorber

    Weizmann Institute of Science, Rehovot, Israel
    Present address
    Department of Molecular Genetics, Weizmann Institute of Science, Rehovot, Israel
    Contribution
    Conceptualization, Validation, Investigation, Writing - review and editing, Performed and analyzed the experiments
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-0635-8703
  4. Talila Volk

    Weizmann Institute of Science, Rehovot, Israel
    Contribution
    Conceptualization, Validation, Investigation, Writing - review and editing, Performed and analyzed the experiments
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-3800-2621
  5. Samuel Safran

    Weizmann Institute of Science, Rehovot, Israel
    Contribution
    Conceptualization, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing
    For correspondence
    sam.safran@weizmann.ac.il
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-0798-1492

Funding

Perlman Family Foundation

  • Samuel Safran

Volkswagen Foundation

  • Samuel Safran

United States - Israel Binational Science Foundation

  • Samuel Safran

Weizmann Institute of Science (Weizmann Curie Research Grant 2021)

  • Talila Volk
  • Samuel Safran

Weizmann Institute of Science (Weizmann-Krenter-Katz Grant Program 2019)

  • Talila Volk
  • Samuel Safran

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

SAS and TV are grateful for the support of the Kretner-Katz Foundation and the Weizmann-Curie grant, and SAS for the support of Perlman family foundation, the US-Israel Binational Science Foundation, and the Volkswagen Foundation for their support. We thank D Deviri, Omar Adame-Arana, Phil Pincus, and Michael Rubinstein for useful discussions.

Senior Editor

  1. K VijayRaghavan, National Centre for Biological Sciences, Tata Institute of Fundamental Research, India

Reviewing Editor

  1. Karsten Kruse, University of Geneva, Switzerland

Reviewer

  1. Helmut Schiessel

Publication history

  1. Received: October 13, 2020
  2. Accepted: April 30, 2021
  3. Accepted Manuscript published: May 4, 2021 (version 1)
  4. Version of Record published: May 21, 2021 (version 2)
  5. Version of Record updated: May 26, 2021 (version 3)

Copyright

© 2021, Bajpai et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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