Prior studies have suggested that somatic homolog pairing in Drosophila may operate via a button mechanism between homologous loci (AlHaj Abed et al., 2019; Erceg et al., 2019; Fung et al., 1998; Gemkow et al., 1998; Rowley et al., 2019; Viets et al., 2019). In this model, discrete regions capable of pairing specifically with their corresponding homologous segments are interspersed throughout the chromosome. To quantitatively assess the feasibility of a button mechanism, we implemented a biophysical model of homologous pairing (Figure 2). Briefly, we modeled homologous chromosome arms as polymers whose dynamics are driven by short-range, attractive, specific interactions between homologous loci (buttons) to account for pairing (Materials and methods). These buttons are present at a density ρ along the chromosome and bind specifically to each other with an energy Ep. We included short-range, non-specific interactions among (peri)centromeric regions to account for the large-scale HP1-mediated clustering of centromeres (Materials and methods), which may also impact global genome organization inside nuclei (Rosin et al., 2018; Strom et al., 2017) and thus may affect pairing. As initial conditions for our simulations, we generated chromosome configurations with all centromeres at one pole of the nucleus (a ‘Rabl’ configuration; Figure 2—video 1 and 2), typical of early embryonic fly nuclei (Dernburg et al., 1996). To account for the potential steric hindrance of non-homologous chromosomes that could impede pairing, we simulated two pairs of homologous polymers. Note that other polymer models have previously been developed to study homologous pairing but mainly in a meiotic context: Nicodemi et al., 2008a; Nicodemi et al., 2008b proposed a generic model where homologous chromosomes are constrained to remain parallel and elongated and can interact via non-specific interactions, Penfold et al., 2012 investigated the role of centromeres and telomeres tethering in yeast on the inter-homolog distances but without accounting for any explicit pairing mechanisms, and Marshall and Fung, 2016 developed a glue-like model where homologous loci remain attached together when they first meet.

When we monitored the distances between homologous loci in our simulations as a function of time (Figure 2B, Figure 2—figure supplement 1), qualitatively we observed that this thermodynamic model can lead to the time-progressive pairing of homologous chromosomes (Figure 2B) and the gradual intermingling of the two homologous chromosome territories (Figure 2C). Pairing in our simulations operates via a stochastic zippering process: once random fluctuations lead to the pairing of one pair of homologous loci, the pairing of nearest-neighbor buttons is facilitated along the lengths of the homologous chromosomes in a zipper-like manner (Figure 2B). Full chromosome-wide pairing results from the progression of many zippers that ‘fire’ at random positions and times along the chromosome, as also previously predicted for meiotic homologous pairing (Marshall and Fung, 2016).

We systematically investigated the roles of button density along the genome ρ, of the strength of the pairing interaction Ep, and of the initial distance between homologous chromosomes di in dictating pairing dynamics (Figure 2D). For a given density, there is a critical value of Ep below which no large-scale pairing event occurs independently of the initial conditions (Figure 2—figure supplement 2A) since pairing imposes a huge entropic cost for the polymers and thus requires a sufficient amount of energy to be stabilized. Beyond this critical point, higher strengths of interactions and higher button densities lead to faster and stronger pairing (Figure 2D, left, center). We also find that the non-specific interactions among (peri)centromeric regions included in our model facilitate pairing, but that such interactions are not strictly necessary (Figure 2—figure supplement 2D).

The initial spatial organization of chromosomes also strongly impacts pairing efficiency. When homologous chromosomes are initially far apart, pairing is dramatically slowed and impaired (Figure 2D, right) due to the presence of the other simulated chromosomes between them (Figure 2—figure supplement 2B). We also observed that our initial chromosome configurations corresponding to a Rabl-like organization (with all centromeres at one pole of the nucleus) promotes pairing by allowing homologous buttons to start roughly aligned (Marshall and Fung, 2016; Penfold et al., 2012; Nicodemi et al., 2008b; Figure 2—figure supplement 2F). Taken together, these systematic analyses of model parameters support the view that the homologous button model is compatible with pairing.

As an alternative model, we asked whether buttons that interact non-specifically could also explain somatic pairing. We simulated the dynamics of polymers having such non-specific buttons and never observed significant chromosome-wide pairing (Figure 2—figure supplement 2C,E). These results are complementary to previous works in which we showed that the weak, non-specific interactions between epigenomic domains that drive TAD and compartment formation in Drosophila (Ghosh and Jost, 2018; Jost et al., 2014) cannot establish and maintain stable pairing by themselves (Pal et al., 2019). Thus, in addition to button density, interaction strength, and initial organization of chromosomes, a key mechanism for pairing is the specificity of preferential interactions between homologous regions.

The button model in Figure 2 makes precise predictions about pairing dynamics at single loci along the chromosome. To inform the parameters of the model and to test its predictions, it is necessary to measure pairing dynamics in real time at individual loci of a living embryo. To do so, we employed the MS2/MCP (Bertrand et al., 1998) and PP7/PCP (Chao et al., 2008) systems for labeling nascent transcripts. Here, each locus contains MS2 or PP7 loops that can be visualized with distinct colors in living embryos (Fukaya et al., 2016; Lim et al., 2018; Chen et al., 2018; Garcia et al., 2013). Specifically, we designed transgenes encoding MS2 or PP7 loops under the control of UAS (Brand and Perrimon, 1993) and integrated them at equivalent positions on homologous chromosomes (Figure 3A). Activation of transcription with GAL4 creates nascent transcripts encoding the MS2 or PP7 stem loops, each of which can be directly visualized by maternally providing fluorescently labeled MCP (MCP-mCherry) or PCP (PCP-GFP) in the embryo. The accumulation of fluorescent molecules on nascent transcripts was detected via laser-scanning confocal microscopy, providing relative three-dimensional positions of actively transcribing chromosomal loci in living Drosophila embryos (Lim et al., 2018; Chen et al., 2018).

We focused on embryos that had completed the maternal-to-zygotic transition and began to undergo gastrulation at approximately 2.5–5 hr after embryo fertilization, when pairing begins to increase substantially (Fung et al., 1998). We integrated transgenes into two genomic locations on chromosome two at polytene positions 38F and 53F, and analyzed embryos with MS2 and PP7 loops at the same positions on homologous chromosomes in order to monitor pairing (Figure 3B, top; Figure 3—video 1 and 2; Materials and methods). As a negative control, we imaged embryos in which loops were integrated at two different positions on homologous chromosomes (MS2 at position 38F and PP7 at position 53F), where we expect no pairing between transgenes (Figure 3B, middle; Figure 3—video 3). Finally, as a positive control for the spatial colocalization of MS2 and PP7 loops, we analyzed embryos where MS2 and PP7 loops were interlaced in a single transgene (Wu et al., 2014; Chen et al., 2018) on one chromosome at polytene position 38F (Figure 3B, bottom; Figure 3—video 4). For each case, we imaged multiple embryos for 30–60 min, and used custom MATLAB scripts to determine the relative 3D distances between chromosomal loci over time (Figure 3—figure supplement 1; Materials and Methods).

In embryos with both PP7 and MS2 transgenes integrated at polytene position 38F (Figure 3B, top), the majority of nuclei could be qualitatively classified into one of two categories. In ‘unpaired’ nuclei, homologous loci were typically separated by > 1 µm with large and rapid changes in inter-homolog distances (e.g. Figure 3C, blue), with a mean distance of 2.2 µm and standard deviation (SD) of 1.2 µm averaged over 30 nuclei. The measured mean distance between homologous loci was comparable within error, though systematically smaller, than the mean distance between loci in the negative control, where transgenes were integrated at non-homologous positions (Figure 3C, red, mean distance = 4.0 µm, SD = 1.3 µm, n = 21 nuclei). In contrast, in ‘paired’ nuclei, homologous loci remained consistently close to one another over time, with smaller dynamic changes in inter-homolog distance (Figure 3D, blue, mean distance = 0.4 µm, SD = 0.3 µm, n = 25 nuclei). Interestingly, while the diffraction-limited signals produced from homologous loci occasionally overlapped in paired nuclei, their average separation was systematically larger than that of the positive-control embryos carrying interlaced MS2 and PP7 loops (Figure 3D, red, mean distance = 0.2 µm, SD = 0.1 µm, n = 44 nuclei). This control measurement also constitutes a baseline for the experimental error of our quantification of inter-homolog distances (Chen et al., 2018). Our measurements thus confirmed previous observations of transgene pairing in the early embryo in which signals from paired loci maintained close association but did not completely coincide over time (Lim et al., 2018). Notably, of 38 nuclei qualitatively scored as having paired homologs, we never observed a transition back to the unpaired state over a combined imaging time of more than 8 hr. Embryos with PP7 and MS2 transgenes integrated in homologous chromosomes at polytene position 53F showed comparable dynamics of inter-homolog distances for nuclei in unpaired and paired states (Figure 3—figure supplement 2A,B). Thus, somatic homolog pairing is a highly stable state characterized by small dynamic changes in the distance between homologous loci.

Our assessment thus far has been based on a qualitative definition of pairing. In order to devise a more stringent quantitative definition of homologous pairing, we measured inter-transgene distances for homologous loci as well as for the unpaired and paired controls throughout gastrulation. We also included measurements from older embryos (~11–12 hr after fertilization) using the driver R38A04-GAL4 (Jenett et al., 2012) to express the transgenes in epidermal cells, where pairing is expected to be widespread (Fung et al., 1998; Gemkow et al., 1998). We measured the mean and SD of the inter-transgene distance for each nucleus over ~10–50 min. From these data, we established a quantitative and dynamic definition of somatic homolog pairing based on a mean distance < 1.0 µm and a corresponding standard deviation < 0.4 µm (Figure 3E, shaded region). By this definition, we considered paired 100% of nuclei that we had qualitatively scored as such, but excluded all nuclei scored as unpaired. As expected, this definition also scored 100% (15/15) of the tracked nuclei from older embryos as paired. Data for paired nuclei from early versus late embryos were in close agreement (Figure 3E, yellow), suggesting that pairing observed in early embryos is representative of pairing during later stages of development.

We next analyzed the progression of pairing through the first 6 hr of development in single embryos carrying MS2 and PP7 transgenes in homologous chromosomes at positions 38F and 53F. To accomplish this goal, we collected data for short (~10 min) intervals every 30 min from 2.5 hr to 6 hr of development, and analyzed inter-homolog distances as outlined above. We then plotted the mean of this distance as a function of its SD for each nucleus analyzed at each time point to create a dynamic assessment of somatic homolog pairing over developmental time. As expected, we detected an overall decrease in mean inter-homolog distance and its SD as development progressed (Figure 4A, Figure 3—figure supplement 2C). To directly compare our analysis to prior studies, we binned nuclei into paired and unpaired states based on their mean and SD as defined in Figure 3E and plotted the percentage of paired nuclei at each developmental time point (Figure 4B). Consistent with previous literature (Fung et al., 1998; Gemkow et al., 1998), we observed a steady increase in the proportion of paired nuclei (Figure 4B); however, by our dynamical definition of pairing, the percentage of nuclei that are paired is systematically lower at most time points than results using DNA-FISH (Figure 4—figure supplement 1). This disagreement likely reflects differences between the classic, static definition of pairing based on overlapping DNA-FISH signals in the one snapshot accessible by fixed-tissue measurements as opposed to our dynamics-based definition, which demands that loci be paired over several consecutive frames. In sum, we have demonstrated that our system captures the progression of somatic homolog pairing over developmental time, making it possible to contrast theoretical predictions and experimental measurements.

Our button model predicts that the fraction of paired loci as a function of time depends on three parameters: the initial separation between homologous chromosomes d_i, the density of buttons along the chromosome ρ, and the button–button interaction energy Ep (Figure 2D). As an initial test of our model, and to constrain the values of its parameters, we sought to compare model predictions to experimental measurements of the fraction of paired loci over developmental time.

Due to the still unknown molecular identity of the buttons, it was impossible to directly measure the button density and the button–button interaction energy. However, the initial separation between chromosomes d_i can be directly estimated using chromosome painting (Ried et al., 1998; Beliveau et al., 2012). To make this possible, we used Oligopaint probes (Beliveau et al., 2012) targeting chromosome arms 2L and 2R to perform chromosome painting on embryos ~ 130 min after fertilization, corresponding to the beginning of cell cycle 14 (Foe, 1989; Figure 4—figure supplement 2A). The resulting distribution of distances between homologous chromosome territories was well described by a simple Gaussian distribution for distances greater than 1 µm, roughly corresponding to the distance required to resolve two separate chromosome territories (Figure 4—figure supplement 2B, red line.)

We next investigated whether the button model quantitatively reproduced the pairing dynamics observed during development for reasonable values of the button density and the button–button interaction energy. We ran a series of simulations for various values of button density ρ (from 10% to 100%) and strength of interaction Ep (from −0.5k_BT to −5k_BT) starting from values for the initial distance between homologous chromosomes d_i drawn from the inferred Gaussian distribution from our Oligopaint measurements (Figure 4—figure supplement 2B, black line). For each parameter set, we monitored pairing dynamics as a function of developmental time and computed the average probability for a locus to be paired (Figure 4—figure supplement 3A, black points) using the same criterion as in Figure 3E. By minimizing a chi²-score (Figure 4—figure supplement 3B) between the predictions and the experimental pairing probability (Materials and methods), we inferred, for each button density, the strength of interaction that best fits the data (Figure 4C). Interestingly, the goodness of fit was mainly independent of button density (Figure 4—figure supplement 3C): denser buttons require less strength of interaction to reach the same best fit (black line in Figure 4C).

The inferred developmental dynamics quantitatively recapitulated the experimental observations for both investigated loci at the majority of time points analyzed (Figure 4B) for any choice of parameters given by the curve in Figure 4C. At our initial time point of 2.5 hr, we predict pairing to be slightly higher than observed for position 38F. This disagreement could reflect an underestimate of the initial distance d_i in our simulations at distances less than 1 µm, which corresponds to the resolution limit of our Oligopaint-based measurements (Figure 4—figure supplement 2B), or that homolog pairing is not yet stable early in Drosophila development (Lim et al., 2018). We also find that our simulations did not predict the large increase in pairing observed for 38F between 5.5 hr and 6 hr (Figure 4B), which may be a consequence of the proximity of 38F to the highly paired histone locus body (Hiraoka et al., 1993; Fung et al., 1998). In sum, the button model recapitulates the observed average pairing dynamics for a wide range of possible button densities coupled with interaction energies that are consistent with protein-DNA interactions.

The fit of our button model to the fraction of paired loci during development in living embryos (Figure 4B) revealed a dependency between the interaction strength Ep and the buttondensity ρ (Figure 4C). As a critical test of the model’s predictive power, we sought to go beyond averaged pairing dynamics and used the model to compute the pairing dynamics of individual loci. As can be seen qualitatively in the kymographs predicted by the model (Figure 2B, Figure 2—figure supplement 1), pairing spreads rapidly (within tens of minutes) from the buttons that constitute the initial points of contact along the chromosome. As a result, the button model predicts that homologous loci undergo a rapid transition to the paired state as the zippering mechanism of pairing progression moves across the chromosome.

To quantify the predicted pairing dynamics of homologous loci, we collected single-locus traces containing individual pairing events from our simulations (Figure 5A, top), which we defined as traces in which the inter-homolog distance drops below 0.65 µm for at least 4 min (Materials and methods). For traces corresponding to each set of simulations with various values of ρ and Ep (Figure 5B), we calculated the median dynamics of inter-homolog distances around the pairing event. Across many values of ρ and Ep, the medians of the predicted trajectories leading up to the pairing event were very similar, with inter-homolog distances decreasing rapidly from 1 to 2 µm to below 0.65 µm at an accelerating rate over the course of 10–20 min (Figure 5C–F). However, we do observe subtle differences in this pre-pairing stage: for a given button density, a stronger interaction energy Ep leads to a faster approach of the homologs (Figure 5—figure supplement 2A). The nearly independence of this first period of the pairing dynamics with respect to ρ and Ep suggests that the initial approach of homologous loci is mainly diffusion limited, while there is a slight acceleration of pairing for stronger interaction energies due to an enhanced zippering effect (Figure 5—figure supplement 2B).

In contrast to the initial pairing dynamics, varying model parameter values had a clear effect on the distance dynamics that followed the pairing event (Figure 5—figure supplement 2A). Specifically, simulations with a weak Ep led to a slow increase in inter-homolog distances as time progressed (Figure 5C, red), consistent with unstable pairing events. Conversely, simulations with a strong Ep were associated with tight pairing of homologous loci following the pairing event, with inter-homolog distances stably maintained around 130 nm, close to the spatial resolution of the model (Figure 5D, green). Notably, the values of ρ and Ep that best fit the averaged temporal evolution of the fraction of paired loci over development (Figures 4 and 5B) all led to similar predictions for the median inter-homolog distance dynamics associated with pairing events. These traces converged to a stable long-term median inter-homolog distance of ~0.5 µm (Figure 5E,F), which is nearly identical to the experimentally determined distance of ~0.44 µm between homologous loci in stably paired nuclei (compare the colored and black lines in Figure 5E,F). Our results thus suggest that the slow dynamics of the pairing probability observed during development (Figure 4) and the dynamics of inter-homolog distance after a pairing event (Figure 5) are strongly correlated.

We then compared our simulated traces to experimental observations of pairing events in nuclei of live embryos. Among the movies that we monitored, we captured 14 pairing events matching the criteria of initial large inter-homolog distances that drop below 0.65 µm for at least 4 min (Figure 5A; Figure 5—figure supplement 1; Figure 5—video 1). We aligned each of these pairing events using the same approach as with the simulated data described above and calculated the smoothed median dynamics of inter-homolog distances around the pairing event (Figure 5C–F, black lines, see also Figure 5—figure supplement 1C). The pre-pairing dynamics were fully compatible with model predictions, with a rapid decrease in inter-homolog distances over 10–20 min (Figure 5C–F, see also Figure 5—figure supplement 2C). Furthermore, the experimental post-pairing dynamics in inter-homolog distance were closely recapitulated (Figure 5F) by the predictions made using parameters that best fit the pairing probability over developmental time (Figure 5B). In sum, simulations of chromosomal behavior based on a button model with a defined set of parameters quantitatively recapitulate experimental observations of pairing events at individual loci, of stably paired homologs following a pairing event, and of the global progression of pairing dynamics over developmental time.

We modeled two pairs of homologous chromosome arms as semi-flexible self-avoiding polymers. Each chromosome consists of N = 3200 beads, with each bead containing 10 kbp and being of size b nm. The four polymers moved on a face-centered-cubic lattice of size L_x x L_y x L_z under periodic boundary conditions to account for confinement by other chromosomes. Previously, we showed that TAD and compartment formation may be quantitatively explained by epigenetic-driven interactions between loci sharing the same local chromatin state (Jost et al., 2014; Ghosh and Jost, 2018). However, such weak interactions cannot lead to global homologous pairing (Pal et al., 2019). Here, to simplify our model, we neglect these types of interactions (whose effects are mainly at the TAD scale) to focus on the effect of homolog-specific interactions. However, we do consider HP1-mediated interactions between (peri)centromeric regions that are thought to impact the global large-scale organization inside nuclei (Figure 2—figure supplement 2D; Strom et al., 2017).

Homologous pairing was modeled as contact interactions between some homologous monomers, the so-called buttons (Figure 2A). For each pair of homologous chromosomes, positions along the genome were randomly selected as buttons with a probability ρ. Each 10-kbp bead i of chromosome chr is therefore characterized by a state p_chr,i with p_chr,i = 1 if it is a button (= 0 otherwise) and p_chr,i = p_chr’,i = 1 if chr and chr’ are homologous. In addition, the first 1000 monomers of each chromosome were modeled as self-attracting centromeric and pericentromeric regions, the rest as neutral euchromatic regions. The energy of a given configuration was given by(S1)H=∑chrk∑i(1−cosθi,chr)+∑chr,chr′,i,j[Epδchr,i;chr′,jΔchr,i;chr′,jpchr,i+Ecδchr,i;chr′,jCchr,iCchr′,j],where k is the bending rigidity, θ_i,chr is the angle between the bond vectors i and i+1 of chromosome chr, δchr,i;chr',j=1 if beads i from chromosome chr and j from chr’ occupy nearest-neighbor sites (= 0 otherwise), Δchr,i;chr',j = 1 if i = j and chr and chr’ are homologous (= 0 otherwise), Cchr,i = 1 if bead i of chr is a (peri-)centromeric region, Ep < 0 is the contact energy between homologous buttons, Ec < 0 is the contact energy between centromeric beads.

The dynamics of the chains followed a simple kinetic Monte-Carlo scheme with local moves using a Metropolis criterion applied to H. The values of k (=1.5kT), b (=105 nm), Ec(=−0.1kT), L_x = L_y (=2 µm), and L_z (=4 µm) were fixed using the coarse-graining and time-mapping strategies developed in Ghosh and Jost, 2018 for a 10 nm fiber model and a volumic density = 0.009 bp/nm³ typical of Drosophila nuclei. For every set of remaining parameters (the button density ρ and the strength of pairing interaction E_p), 250 independent trajectories were simulated starting from compact, knot-free, Rabl-like initial configurations (Dernburg et al., 1996): all centromeric regions were localized at random positions at the bottom of the simulation box, the rest of the chain being confined into a cylinder of diameter ~600 nm and height ~2 µm pointing toward the top of the box (see examples in Figure 2C and Figure 2—video 1 and 2). The distance between the centers of mass of homologous chromosomes, noted as d_i, typically varied between 0.5 µm and 3 µm. Each trajectory represented ~10 h of real time. To model the developmental pairing dynamics, we ran simulations in which d_i was sampled from the distribution inferred from chromosome painting experiments (Figure 2—figure supplement 2).

To constrain model parameters, we compared the measured pairing dynamics (Figure 4B) to the model prediction. Specifically, for each parameter set, we computed a chi²-score between the predicted dynamics and experimental time points(S2)chi2=(1/5)∑t=3h5.5h[(Ppred(t)−Pexp,38F(t))2/(2σexp,38F2(t))+(Ppred(t)−Pexp,53F(t))2/(2σexp,53F2(t))],with Ppred(t) the predicted dynamics at developmental time t, Pexp,38F(t) and Pexp,53F(t) the experimental average dynamics for loci 38F and 53F at time t, respectively, and σexp,38F(t) and σexp,53F(t) their corresponding standard deviations at time t.

Flies expressing a nuclear MCP-NLS-mCherry under the control of the nanos promoter were previously described (Bothma et al., 2018). To create flies expressing PCP-NoNLS-GFP, the plasmid pCASPER4-pNOS-eGFP-PCP-ɑTub3′UTR was constructed by replacing the MCP coding region of pCASPER4-pNOS-NoNLS-eGFP-MCP-ɑTub3′UTR (Garcia et al., 2013) with the coding region of PCP (Larson et al., 2011). Transgenic lines were established via standard P-element transgenesis (Spradling and Rubin, 1982). To create flies expressing MS2 or PP7 loops under the control of UAS, we started from plasmids piB-hbP2-P2P-lacZ-MS2-24x-αTub3′UTR (Garcia et al., 2013) and piB-hbP2-P2P-lacZ-PP7-24x-αTub3′UTR, the latter of which was created by replacing the MS2 sequence of the former with the PP7 stem loop sequence (Larson et al., 2011). The hunchback P2P promoter was removed from these plasmids and replaced by 10 copies of the UAS upstream activator sequences (Brand and Perrimon, 1993) and the Drosophila Synthetic Core Promoter (DSCP) (Pfeiffer et al., 2010). Recombinase-mediated cassette exchange (Bateman et al., 2006) was then used to place each construct at two landing sites in polytene positions 38F and 53F (Bateman and Wu, 2008; Bateman et al., 2012a). Flies carrying the GAL4 driver nullo-GAL4, which drives expression in all somatic cells during the cellular blastoderm stage of cell cycle 14, were a gift from Jason Palladino and Barbara Mellone. Flies carrying the GAL4 driver R38A04-GAL4, which drives expression in epidermal cells in germband-extended embryos (Jenett et al., 2012), were acquired from the Bloomington Drosophila Stock Center. Finally, the interlaced MS2 and PP7 loops under the control of the hunchback P2 enhancer and promoter (P2P-MS2/PP7-lacZ) were based on a previously described sequence (Wu et al., 2014).

To create embryos for analysis of pairing, mothers of genotype 10XUAS-DSCP-MS2; MCP-mCherry-NLS, PCP-GFP were crossed to males of genotype nullo-GAL4, 10XUAS-DSCP-PP7. The resulting embryos are loaded with MCP-mCherry-NLS and PCP-GFP proteins due to maternal expression via the nanos promoter, and zygotic expression of nullo-GAL4 drives transcription of MS2 and PP7 loops in all somatic cells starting approximately 30 min into cell cycle 14 (cellular blastoderm). For pairing analysis, both MS2 and PP7 transgenes were in the same genomic location, either position 38F or 53F, whereas for the negative control, MS2 loops were located at 38F and PP7 loops were located at 53F. To visualize pairing at later times in development, the mothers indicated above were instead crossed to males of genotype 10XUAS-DSCP-PP7; R38A04-GAL4, where both MS2 and PP7 loops were located at position 38F. Finally, to visualize MS2 and PP7 loops derived from the same genomic location, mothers of genotype MCP-mCherry-NLS, PCP-GFP were crossed to P2P-MS2/PP7-lacZ located at position 38F.

Embryos were collected at 25°C on apple juice plates and prepared for imaging as previously described (Garcia et al., 2013). Mounted embryos were imaged using a Leica SP8 confocal microscope, with fluorescence from mCherry and eGFP collected sequentially to minimize channel crosstalk. For each movie, the imaging window was 54.3 × 54.3 µm at a resolution of 768 × 768 pixels, with slices in each z-series separated by 0.4 µm. Z-stacks were collected through either 10 or 12 µm in the z plane (26 or 31 images per stack), resulting in a time resolution of approximately 27 or 31 s per stack using a scanning speed of 800 Hz and a bidirectional scan head with no averaging. For the pairing data in Figure 3, the imaging window was centered laterally for embryos that were pre-gastrulation; for post-gastrulation embryos, the imaging window centered on a dorsal view of the embryonic head region covering mitotic domains 18 and 20 (Foe, 1989), which shows minimal movements during gastrulation and germ band extension relative to other regions of the embryo. We compared pairing levels in these cells at 6 hr of development to that of cells in a posterior abdominal segment at the same time point and found them to be nearly identical (75.0% paired, n = 16 for anterior cells vs. 73.7%, n = 19 in posterior cells according to the definition of pairing in Figure 3E), confirming that cells from different regions of the embryo are roughly equivalent for pairing dynamics at this stage. For positive-control embryos with interlaced PP7 and MS2 loops driven by the hunchback promoter, embryos were imaged during cell cycle 13 and early cell cycle 14, and the imaging window was positioned laterally as previously described (Garcia et al., 2013). To assess pairing in late-stage embryos using the R38A04-GAL4 driver, embryos were aged to approximately 11–12 hr and the imaging window was positioned laterally over an abdominal segment. For the developmental time course movies in Figure 4, imaging centered on mitotic domains 18 and 20 when these cells were in interphase. During time points when these domains were undergoing mitosis, an adjacent mitotic domain in interphase was imaged.

All images were first run through the ImageJ plug-in Trainable Weka Segmentation (Arganda-Carreras et al., 2017) and filtered with custom classifiers to generate two separate channels of 3D segmented images that isolated fluorescent spots. These segmented spots were then fitted to a Gaussian with a nonlinear least squares regression to find the 2D center. Image z-stacks were then searched for any spots tracked for three or more contiguous z-slices and the r est were discarded. Additional manual curation was employed to confirm the accuracy of segmented images and to add any spots that were missed. An initial estimate of the center of each spot was set based on the z-slice in which the spot had the greatest maximum intensity within a predefined radius from its 2D center. These initial estimates were then used to seed a 3D Gaussian fit for each spot, the center of which was used for all distance calculation. This granted us not only sub-pixel resolution in x-y but also sub-z-slice resolution, allowing for more precision in the z coordinate, which would otherwise be limited by the 0.4 µm spacing between consecutive stacked images created by confocal imaging.

Raw image z-stacks for each time frame were also maximum projected in the channel containing nuclearly localized MCP-mCherry to create 2D maps of all the nuclei in frame. These nuclear projections were then segmented and tracked in Matlab, followed by manual curation to ensure that each nucleus was consistently followed. One tracked particle lineage from each channel was then assigned a distinct nucleus based on its proximity to that nucleus in the 2D map and the particles in each channel were considered homologous chromosomes of one another. Since absolute coordinates of assigned particles were not possible to obtain due to cellular rotation and motion, all distance calculations were done with the relative coordinates of each locus from its homolog; any cellular rotation or motion was assumed to be conserved between loci in the same cell.

For the data in Figure 3, we qualitatively scored each nucleus based on the measured distances between red and green signals over the time that the signals were observed: ‘paired’ nuclei showed small distances and little variation over time and ‘unpaired’ nuclei showed larger distances and greater variation over time. Nuclei that showed a transition from large distances and variation at earlier time points to smaller distances and variation at later time points were scored as ‘pairing’ traces and were not included in Figure 3 (see Figure 5). In assessing the stability of the paired state, we included both ‘paired’ (n = 25) and ‘pairing’ (n = 13) nuclei from three embryos in the total number of nuclei (n = 38) assessed. In this analysis, we conservatively only included the observation time of ‘paired’ nuclei (> 8 hr of observation with no transition back to the unpaired state), although ‘pairing’ nuclei also remained in the paired state throughout the remaining observation time once they became paired.

In some traces, signal is temporarily lost, which could be due to either a loss of fluorescence of the MS2 or PP7 reporters caused by transcriptional bursting or due to one or both loci moving out of our imaging window. For paired loci, we randomly sampled six traces and found that only two had any missing frames, with the missing events due solely to loss of transcription (three lost frames out of 339 total tracked frames in the sampling). Therefore, missing frames do not significantly impact our measurements of paired loci. In the case of unpaired loci, where the relative movement of homologous loci is less restricted, there is a greater risk of systematically underestimating the mean distance between signals if missing frames are caused by at least one homolog moving out of the field of view. To investigate this, we randomly sampled six unpaired loci traces and found that four of the six traces had missing frames with at least one signal outside of the imaging window (54 outside-of-window frames out of 587 total tracked frames in the sampling). To probe the possible impact on the mean distance of these traces, we assumed that the distance between homologs in all the missing frames of the six sampled traces was 5 µm, corresponding to the average nucleus diameter. While it is unlikely that all our missing frames contained loci that were 5 µm apart, this approach gives us an upper bound of the possible impact of missing frames. We found a rather modest effect with an increase of the mean distance of ~12.5% (from 2.4 µm to 2.7 µm) that is unlikely to alter any of our conclusions.

To align the traces presented in Figure 5 based on a time point when the loci become paired, we manually aligned all traces that had been qualitatively assessed as ‘pairing’ traces according to several values of threshold distance and consecutive frames below that threshold. We then optimized this exploration for values that provided qualitatively good alignment of traces but that excluded as few traces as possible in order to maximize the data available for analysis. The same criteria were applied to identify and align pairing traces from simulations.

All image analysis was done using custom scripts in Matlab 2019b unless otherwise stated. These scripts can be found at https://github.com/GarciaLab/mRNADynamics/ (Garcia Lab, 2021a, copy archived at swh:1:rev:a1b5c591656cae816ed6fc4a4e447c3bd375959c, Garcia Lab, 2021b).

Embryos of genotype w¹¹¹⁸ were aged to 2–3 hr after embryo deposition, fixed, and subjected to DNA-FISH using 400 pmol of Oligopaint probes (Beliveau et al., 2012) targeting 2L and 2R (200 pmol of each probe; Rosin et al., 2018) as previously described (Bateman and Wu, 2008). Hybridized embryos were mounted in Vectashield mounting medium with DAPI (Vector Laboratories), and three-dimensional images were collected using a Leica SP8 confocal microscope. To establish initial inter-homolog distances, an image from an embryo in early interphase 14 (as judged by nuclear elongation [Fung et al., 1998]) and with high signal-to-noise ratio was analyzed using the TANGO image analysis plug-in for ImageJ (Ollion et al., 2013; Ollion et al., 2015; Belevich et al., 2016). After segmentation and assignment of each painted territory to a parent nucleus, distances between territories were measured from centroid to centroid in 3D. Since homologous chromosomes are labeled with the same color, when territories produce a continuous region of fluorescence, a distance of zero was assigned. A total of 48 nuclei were analyzed for each of 2L and 2R.