Loop size variability and persistence over time

Nucleolus beads dynamically form loops of varying sizes. In the previous chapter we showed that dynamic looping promotes increased compaction, associativity, and substructure formation among nucleolus beads; however, we did not explicitly discuss which nucleolus beads bind with one another over the course of the simulation. Figures 7.5 & 7.4 show how often two nucleolus beads

steps does nucleolus bead ispend bound to other nucleolus beads, and what are the indices of those other nucleolus beads? Parts A and B from Figure 7.5 show a single frame from two movies that I created – using the data sets for slow and fast kinetics, respectively –, in which each frame of the movie shows the amount of time steps that a single nucleolus bead (index specified by the blue dotted line) spends bound to one of the other 360 nucleolus beads during the 15-minute simulation.

Figure 7.4: Four selected frames corresponding to the dataset for ton=0.09 and a single nucleolus.

Dynamic loop partners are shown for nucleolus beads 11, 12, 77, and 180, as indicated by the dotted blue line.

We note that dynamic looping allows for loops of differing sizes to form and that a single nucleolus bead will dynamically bind with multiple other nucleolus beads during the course of the simulation. Thus, loops truly are forming and breaking during the simulation. Furthermore, beads do not appear to preferentially form loops based on location within the chain; in other words, which two beads form a loop does not appear to be closely correlated with those beads’ indices. This behavior is also evident in the split nucleolus case (Figures 7.6 & 7.7). It is particularly noteworthy that beads dynamically bind with beads in both regions of the split nucleolus, not just their own, indicating that the two split nucleolus regions are spatially intermixing and in close proximity.

Figure 7.5: Frequency with which a given nucleolus bead forms a loop with other nucleolus beads. In the single nucleolus there are 361 total beads; here we look at nucleolus bead 77. (A)Slower kinetics, i.e. ton=90. (B)Faster kinetics, i.e. ton=0.09.

Figures 7.8 & 7.7 similarly highlight the fact that “loop size" (ie. the number of beads composing a loop) is variable, through the lens of contact maps.

Figure 7.6: Frequency with which a given nucleolus bead forms a loop with other nucleolus beads. In the split nucleolus there are 362 total beads; here we look at nucleolus bead 77. The yellow region incorporates the beads that compose region 1 of the nucleolus, the green region incorporates the beads that compose region 2 of the nucleolus. We see that bead 77 binds to beads in both nucleolus regions. Dynamic looping, ton=90.

Figure 7.7: Contact map representation of nucleolus loop binding frequency, corresponding to split nucleolus.

Figure 7.8: Contact map representation of nucleolus loop binding frequency, corresponding to single nucleolus.

Persistence of looping. In addition to learning which nucleolus beads bind to one another, I also wanted to investigate how long these dynamic loops persisted over the course of the simulation. For example, Figure 7.5 shows that nucleolus bead 77 spends 761 of 9000 time steps bound to nucleolus bead 72, but it does not provide information about the persistence of that bond – did beads 77 and 72 bind and unbind several times, or did they remain bound for all 761 time steps? Figures 7.9& 7.10 show that the magnitude of the on/off binding rates significantly influences the longevity of a dynamic crosslink. As hypothesized, slow dynamic looping enables dynamically formed loops to remain unbro- ken for a longer period of time than fast dynamic looping, in which loops are breaking and forming at almost every time step. Very interestingly, however, we see that, when viewed in conjunction with the 3D visualizations of the nucleolus shown in Figure 6.6, weak (i.e fast) dynamic looping enables sections of the genome to remain in close proximity for an extended period of time, longer

nism for phase separation, or provide a long enough period of proximity for cellular processes to occur.

Figure 7.9: Persistence of looping for nucleolus bead 115. (A) Slow dynamic looping, t_on=90 s. (B) Fast dynamic looping, ton=0.09s .

Figure 7.10: Same as Figure 7.9, just zoomed in (shorter range in x-axis). 7.2.3 3D Visualization within 3D Nucleus.

The figures in this section are snapshots of the system in time, corresponding to varying parameter choices. I include them here to help readers better visualize the nucleolus within the context of the entire nucleus. All figures (Figures 7.11, 7.12, 7.13, 7.14) are frames from movies that I created in which the beads move over time.

Figure 7.11: The nucleolus at a single point in time, when there is dynamic looping in the nucleolus with ton=90.

Figure 7.12: The nucleolus at a single point in time, when there is dynamic looping in the nucleolus with t_on=0.09.

Figure 7.13: The nucleolus at a single point in time, when the nucleolus is split into two regions. Left) Dynamic looping in the nucleolus with ton=90. Right) Dynamic looping in the nucleolus with

t_on=0.09.

Figure 7.14: The nucleolus at a single point in time, when there is dynamic looping in the nucleolus with ton=90. All 2803 beads in the system are shown as red spheres. Springs between non-nucleolus