3D Cell Neighbour Dynamics in Growing Pseudostratified Epithelia
Abstract
During morphogenesis, epithelial sheets remodel into complex geometries. How cells dynamically organize their contact with neighbouring cells in these tightly packed tissues is poorly understood. We have used lightsheet microscopy of growing mouse embryonic lung explants, threedimensional cell segmentation, and physical theory to unravel the principles behind 3D cell organization in growing pseudostratified epithelia. We find that cells have highly irregular 3D shapes and exhibit numerous neighbour intercalations along the apicalbasal axis as well as over time. Despite the fluidic nature, the cell packing configurations follow fundamental relationships previously described for apical epithelial layers, i.e., Euler’s formula, Lewis’ law, and AboavWeaire’s law, at all times and across the entire tissue thickness. This arrangement minimizes the lateral cellcell surface energy for a given crosssectional area variability, generated primarily by the distribution and movement of nuclei. We conclude that the complex 3D cell organization in growing epithelia emerges from simple physical principles.
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Author Response:
Evaluation Summary:
The authors measure the threedimensional organization within an epithelial cell monolayer and find that cell neighbors change frequently along the apicobasal axis. Stateoftheart image analysis convincingly justifies correlation, though not causation, between epithelial cell packing and nuclear position. With some stronger theoretical arguments to back up the claims made, this paper will be of interest to scientists studying tissue mechanics and packing of cells in epithelial tissues.
As we emphasize also in the title of this paper, we can explain the observed 3D cell neighbour relationships with a minimisation of the lateral cellcell surface contact energy. It is important to distinguish this from questions regarding the 3D cell shape, which we do not address. The confusion easily arises …
Author Response:
Evaluation Summary:
The authors measure the threedimensional organization within an epithelial cell monolayer and find that cell neighbors change frequently along the apicobasal axis. Stateoftheart image analysis convincingly justifies correlation, though not causation, between epithelial cell packing and nuclear position. With some stronger theoretical arguments to back up the claims made, this paper will be of interest to scientists studying tissue mechanics and packing of cells in epithelial tissues.
As we emphasize also in the title of this paper, we can explain the observed 3D cell neighbour relationships with a minimisation of the lateral cellcell surface contact energy. It is important to distinguish this from questions regarding the 3D cell shape, which we do not address. The confusion easily arises because our theory explains the polygon type and thus the shape of crosssectional areas, but not their size. The size of the different crosssectional areas, however, defines the overall 3D shape of the cell.
We show that, where present, the nuclear crosssectional area is only slightly smaller than that of the cell, and the two measures correlate strongly (r = 0.94, Figure 5g). Referees 1 & 3 comment that this does not imply that the nucleus affects the crosssectional area of the cell. We beg to differ here. The measured nuclear volumes are too large to allow a spherical nucleus to fit into a cylindrical cell of the measured height (as we now show explicitly in the new Figure 5h). Accordingly, to fit into the cell, the nucleus has to deform. Nuclei respond to external forces with anisotropic shape changes (Haase et al., 2016; Neelam et al., 2016), which is consistent with the elliptical nuclear shapes that we observe (Figure 5d). However, there is a limit to how much the stiff nucleus can deform (Lammerding, 2011; Shah et al., 2021), necessarily resulting in a local widening of the cell where the nucleus is present. Cell sections without nucleus typically have smaller crosssectional areas, leading to a higher frequency of small crosssections in cells compared to nuclei. We have added these additional explanations and references to the manuscript to strengthen the argument.
Nuclei in pseudostratified epithelia are well known to move continuously during the cell cycle, a phenomenon referred to as interkinetic nuclear migration (IKNM). The moving nuclei will continuously change the crosssectional areas. In the live microscopy, the nuclei are not visible as we lack a live reporter for the nuclei. But given the strong correlation between the crosssectional areas between nucleus and cell along the entire apicalbasal axis and independent of the nuclear position and thus cell cycle phase (Figure 5g), and given the measured crosssectional size of the nuclei, we believe that it is a safe inference that the nuclei are located at the wide parts of the cells, and these wide parts move during the cell cycle (Figure 8), consistent with IKNM.
In summary, we defined the physical principle behind the 3D cell neighbour relationships, and our data strongly suggest that the shape and movement of the nucleus is a key driver of the cell shape changes that translate into neighbour changes, both along the apicalbasal axis and over time. Future work is required to unravel the physical determinants of the 3D shape of the epithelial cells and their nuclei.
Reviewer #1 (Public Review):
The authors aim at characterizing the cellular organization in epithelial sheets by reconstructing the shape of lung epithelial cells from light sheet microscopy images. The find that in each imaging plane, the organization follows the laws of Lewis and AboaveWeaire, which describe the organization of the apical surface of tightly packed cell monolayers, but that the organization can differ substantially between different planes. Equivalently, the authors observe frequent cell neighbor exchanges as the imaging plane moves from the basal to the apical side. The authors achieve a very good reconstruction of static and dynamic monolayers. The finding of frequent neighbor exchanges as one moves along the apicobasal axis can potentially change our image of epithelial monolayers, which so far mostly considers these cells to have the shape of prisms and frusta to which socalled scutoids have recently been added.
The quantification of the packing uses the same methods as for cell packing in two dimensions and underlying mechanism proposed by the authors neglects contributions from the dimension along the apicobasal axis. The authors reasoning behind the observed AboaveWeaire's and Lewis' laws utilizes the same arguments as for the cell packing in apical layers. The differences between the cellular organization in different layers is ascribed to the position of the nuclei along the apicobasal axis. Here, the authors take correlations for causes and this discussion is missing any threedimensional elements (except for the nucleus position). Explicitly, the authors state that the origin of the observed laws is a minimization of the lateral cellcell surface energy in each plane. However, the cells are oblivious to the planes and the analysis should include the cellcell interaction energy of the whole cell surface. Furthermore, the nucleus with its stiffness against deformations would need to be included in this analysis. Finally, according to the authors, the changing nucleus position along the apicobasal axis is at the origin of the neighbor exchanges. Apart from a correlation, there is no data supporting this claim.
This assessment appears to reflect a misunderstanding. We are not analysing the determinants of the 3D cell shape, but of the 3D cell neighbour relationships. The confusion easily arises because our theory explains the polygon type and thus the shape of crosssectional areas, but not their size. The size of the different crosssectional areas, however, defines the overall 3D shape of the cell.
We show that the observed cell neighbour arrangements minimise the total cell perimeter in each plane for the observed area distribution in that plane. Integrating over the entire apicalbasal axis, this then minimises the lateral cellcell contact surface energy for the given distribution of cell volumes along the apicalbasal axis.
Here, it is important to emphasize that we are NOT saying that the 3D cell geometry itself minimises the overall cellcell contact surface energy. If that was the case, we would expect spherical cells, or if the height was enforced, cylindrical cells, or if also cellcell adhesion was enforced, hexagonal honeycomb structures of equallysized cells. However, because of active processes, including cell growth and division, cell volumes differ, and the stiff, moving nucleus (in conjunction with other cellular forces) further enforces irregular cell shapes. For those irregular cell shapes, the particular neighbour arrangements minimise the lateral surface energy.
We can consider each plane separately, because experiments show that epithelia return to a mechanical equilibrium on a timescale of minutes, if not faster. Accordingly, we can expect that the packing reflects a mechanical equilibrium. The balance of forces must then hold in any cutting plane. That’s why AboavWeaire's and Lewis’ laws hold in each plane, and we can consider planes separately.
Reviewer #2 (Public Review):
Through detailed analysis of growing mouse embryonic lung explants, these authors investigate the statistical and physical relationships underlying threedimensional cell organization in pseudostratified epithelial tissues. The authors find that tissue curvature plays a minor role in their tissue of interest, but that cell crosssectional area and neighbour statistics conform to previously proposed geometrical 'laws' and can be explained with a minimisation of lateral cellcell contact surface energy, which in turn follows from nuclear packing and dynamics. Overall, this work constitutes a significant investigation into the drivers of complex threedimensional cell shapes and tissue structures, the primary aims appear to be largely supported by the data provided, and the work should be of interest to many in developmental biology.
Thank you.
Reviewer #3 (Public Review):
Gómez et al. study cellular packing in epithelial tissues. The authors dissect how 2D cell packing statistics change along the apicobasal axis by examining different crosssections parallel to the epithelial surface. They obtain 3D exvivo data, both fixed and live, from the developing mouse pseudostratified lung epithelium, which they analyze using 3D cell segmentation. They compare these experimental data to known topological invariants (Euler characteristic), existing phenomenological relations (AboavWeaire law, Lewis' law), and phenomenological relations by the authors (quadratic cell area scaling, dependence of hexagon fraction on cell area variability), which they had proposed in an earlier paper (Kokic et al., 2019).
The authors moreover discuss changes in the 2D cell neighbor relations that occur in the lung epithelium along the apicobasal axis, which they call T1L transitions ("lateral" T1 transitions). Recent work had already discussed such T1L transitions and proposed that they can be induced by epithelial curvature. The authors of the current manuscript first tested this existing hypothesis on their experimental data on both tubular parts and tips of the developing mouse bronchioles, and they conclude that curvature cannot explain the T1L transitions they observe. However, they demonstrate that the T1L transitions in their data are strongly correlated with variations in the crosssectional cell area and the nucleus positions in the pseudostratified epithelium.
 This paper will be of interest for anybody working on cell packing in tissues and the mechanics of epithelia. In the past, 2D cellular packing arrangements in epithelia have most often been studied at the apical side only, because of technical limitations. Using stateoftheart imaging and image analysis techniques, this manuscript goes a step further and studies how the 2D cellular packing changes along the apicobasal axis. The only other papers that I am aware of that have started to address this question are GómezGálvez et al., Nat. Comm., 2018, which the authors cite, and Rupprecht et al., MBoC, 2017, which first discussed apicobasal changes in cell neighbor relations as far as I know. Hence, being among the first papers to address this question, the current manuscript would be of interest to the community.
Thank you. We are now citing Rupprecht et al., MBoC, 2017 in the revised version. We apologise to the authors for the oversight of not including this paper in the original version.
 A major conclusion that T1L transitions are correlated with changes in the crosssectional cell area and the nucleus positions are well supported by the data. While the authors seem to claim causation here, this is not backed by the experimental data presented.
Reviewer 1 had similar concerns, and we have expanded our statement in the section “Changes in crosssectional area as a result of interkinetic nuclear migration (IKNM)” to read: "Where present, the nuclear crosssectional areas are only slightly smaller than those of the entire cell, and the crosssectional areas of the cell and the nucleus are strongly correlated (r = 0.94, Figure 5g). The strong correlation can be accounted for by the opposing actions of cells and nuclei in the columnar epithelium. The nuclear volumes are too large to allow for a spherical nucleus to fit into a cylindrical cell of the measured height (Figure 5h). Accordingly, to fit into the cell, the nucleus necessarily has to deform. Nuclei respond to external forces with anisotropic shape changes (Haase et al., 2016; Neelam et al., 2016), which is consistent with the elliptical nuclear shapes that we observe (Figure 5d). However, there is a limit to how much the stiff nucleus can deform (Lammerding, 2011; Shah et al., 2021), resulting in a local widening of the cell where the nucleus is present. Cell sections without nucleus typically have smaller crosssectional areas, thereby leading to a higher frequency of small crosssections in cells compared to nuclei." While we, of course, agree that correlation does not imply causation, we believe that our various data taken together strongly indicate that anything but causation is unlikely.
 The topological and phenomenological relations discussed seem to be reflected by the data. However, estimations of uncertainties would be required to better judge this point (e.g. in Fig. 2 e,f).
AboavWeaire’s and Lewis’ laws are phenomenological and hold only approximately. Deviations of the actual data from the lines are therefore expected. We have described these two relationships and how much they deviate from the original simple straight lines in much detail in earlier publications [Vetter et al., bioRxiv 2019; Kokic et al., bioRxiv 2019]. In Fig. 2e,f, we plot the phenomenological relationships only for reference; the data is not expected to approach them exactly with shrinking uncertainty bounds. Nevertheless, we agree that error estimates help judge the statistical significance with which we find the data to deviate from the simple phenomenological laws. We have added error bars (SEM) to all data points in Fig 2f. In Fig 2e, they are omitted because they are smaller than the symbols.
 In lines 165197, the authors discuss in how far the observed numbers of T1L transitions per cell can be consistent with curvatureinduced transitions as discussed earlier (e.g. GómezGálvez et al.). To this end, they also use theoretical predictions derived in the Supplemental Material (SM). Unfortunately, there appear to be several problems with the derivation in the SM.
We thank the referee for their careful checking of our theory, which allowed us to improve the quality of the supplementary material. We are resolving all points below.
a) Most importantly, in Eq. S5, epsilon is derived for the situation displayed in Fig. S1b. However, after a T1L transition on the blue line, the formula will qualitatively change (e.g. the "1+" should go from the numerator to the denominator, and the meaning on n changes as the cells abutting the blue line are now the other two cells). Hence, computing the derivative in Eq. S6 to see how epsilon changes during a T1 transition seems highly problematic.
The particular aspect addressed here appears to be a misunderstanding. Our theory relates the foldchange of tissue curvature between two consecutive T1L transitions to the local neighbor number n that the cell has in between them. Thus, between two radii R1 and R2 where two consecutive T1L transitions occur, n is constant. The derivative dɛ/dn is to be interpreted as the infinitesimal continuation of the difference in aspect ratio between (regular) polygons that differ by one edge. This corresponds to the region between two T1L transitions. The misunderstanding might have originated from us not mentioning this perspective clearly enough in the SM text. In the revised version of the SM, we have expanded the discussion by adding a new paragraph (last paragraph on p.2), and by rephrasing the text relating to the corresponding equations.
b) The angle integral, first formula on the second page of the SM, appears to evaluate to exactly zero, which is different from what the authors obtain.
Thank you for spotting this. Indeed, we have been imprecise at this point in the derivation. As our theory quantifies the curvature change between T1L transition irrespective of their sign, we meant to average the absolute value of dɛ/dr over all possible orientations. Doing this then yields the nonzero integral value as we had it in the original SM. The integrand in the angle integral was missing the magnitude bars. We have fixed this in the revised version, carrying through the absolute value in the entire derivation after the integration. The consequence of this correction is that the final equation that we arrive at (now Eq. S9 in the SM) is now symmetric with respect to R1 <> R2, as it, of course, should be. The blue curve that we plotted in Fig. 3g of the main article, and with it our conclusion regarding the impact of curvature, are unaffected by this correction.
Unfortunately, these two points cast strong doubt on the predicted formula in Eq. S8, Fig. S2, blue curve in Fig. 3g. As a consequence, the conclusions drawn in lines 165197 of the main text are not sufficiently convincing.
 The authors compare to predictions from their earlier preprint (Kokic et al., 2019), where they say that Lewis' law is replaced by a quadratic dependency of cell area on cell neighbor number when the cell area fluctuations become large. However, it is not clear whether this transition between linear and quadratic prediction is smooth or discontinuous. Moreover, the magnitude of cell area fluctuations where the transition is expected to occur seems unclear. In these aspects, the theoretical prediction seems elusive, which makes it harder to critically compare it to the experimental data.
As we showed in our previous preprint (Kokic et al., 2019) using simulations, the transition is continuous until the cell area variability is high enough to support the quadratic relationship. Accordingly, the individual apical samples only approximate the linear Lewis’ law (Figure 1h). Figure 1k shows by how little the apical area variability has to increase to support a quadratic relationship (comparison between black points and all other points).
Minor comments / potential sources of confusion for readers:
 There seems to be a typo in Eq. (2). What is likely meant is m_n = 5 + 8/n.
Thanks for spotting the typo  we have corrected this.
 It is unclear how the "T1L transitions per cell" are counted (e.g. when talking about "up to 14 cell neighbour changes per cell" on line 154, in lines 165197, or in Figs. 3d, 8b). Do the authors refer to the number of T1L transitions divided by the number of cells, or the average number of times a cell is involved in a T1L transition? The latter number should be at least four times the former, because at least four cells are typically involved in a single T1L transition. The caption to Fig. 3d suggests that the former is meant, while lines 304307 in the discussion suggest the latter is meant.
T1L transitions per cell refers to the number of times a single cell is changing a neighbour relationship along the apicalbasal axis. We analysed this for each cell in the epithelium individually, and in Figure 3d, we report the fraction of cells with n neighbour changes along their apicalbasal axis. A neighbour change for a cell will, of course, also imply a neighbour change for neighbouring cells, which is counted when analysing that particular neighbouring cell.
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Evaluation Summary:
The authors measure the threedimensional organization within an epithelial cell monolayer and find that cell neighbors change frequently along the apicobasal axis. Stateoftheart image analysis convincingly justifies correlation, though not causation, between epithelial cell packing and nuclear position. With some stronger theoretical arguments to back up the claims made, this paper will be of interest to scientists studying tissue mechanics and packing of cells in epithelial tissues.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)
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Reviewer #1 (Public Review):
The authors aim at characterizing the cellular organization in epithelial sheets by reconstructing the shape of lung epithelial cells from light sheet microscopy images. The find that in each imaging plane, the organization follows the laws of Lewis and AboaveWeaire, which describe the organization of the apical surface of tightly packed cell monolayers, but that the organization can differ substantially between different planes. Equivalently, the authors observe frequent cell neighbor exchanges as the imaging plane moves from the basal to the apical side. The authors achieve a very good reconstruction of static and dynamic monolayers. The finding of frequent neighbor exchanges as one moves along the apicobasal axis can potentially change our image of epithelial monolayers, which so far mostly considers …
Reviewer #1 (Public Review):
The authors aim at characterizing the cellular organization in epithelial sheets by reconstructing the shape of lung epithelial cells from light sheet microscopy images. The find that in each imaging plane, the organization follows the laws of Lewis and AboaveWeaire, which describe the organization of the apical surface of tightly packed cell monolayers, but that the organization can differ substantially between different planes. Equivalently, the authors observe frequent cell neighbor exchanges as the imaging plane moves from the basal to the apical side. The authors achieve a very good reconstruction of static and dynamic monolayers. The finding of frequent neighbor exchanges as one moves along the apicobasal axis can potentially change our image of epithelial monolayers, which so far mostly considers these cells to have the shape of prisms and frusta to which socalled scutoids have recently been added.
The quantification of the packing uses the same methods as for cell packing in two dimensions and underlying mechanism proposed by the authors neglects contributions from the dimension along the apicobasal axis. The authors reasoning behind the observed AboaveWeaire's and Lewis' laws utilizes the same arguments as for the cell packing in apical layers. The differences between the cellular organization in different layers is ascribed to the position of the nuclei along the apicobasal axis. Here, the authors take correlations for causes and this discussion is missing any threedimensional elements (except for the nucleus position). Explicitly, the authors state that the origin of the observed laws is a minimization of the lateral cellcell surface energy in each plane. However, the cells are oblivious to the planes and the analysis should include the cellcell interaction energy of the whole cell surface. Furthermore, the nucleus with its stiffness against deformations would need to be included in this analysis. Finally, according to the authors, the changing nucleus position along the apicobasal axis is at the origin of the neighbor exchanges. Apart from a correlation, there is no data supporting this claim.
Was this evaluation helpful? 
Reviewer #2 (Public Review):
Through detailed analysis of growing mouse embryonic lung explants, these authors investigate the statistical and physical relationships underlying threedimensional cell organization in pseudostratified epithelial tissues. The authors find that tissue curvature plays a minor role in their tissue of interest, but that cell crosssectional area and neighbour statistics conform to previously proposed geometrical 'laws' and can be explained with a minimisation of lateral cellcell contact surface energy, which in turn follows from nuclear packing and dynamics. Overall, this work constitutes a significant investigation into the drivers of complex threedimensional cell shapes and tissue structures, the primary aims appear to be largely supported by the data provided, and the work should be of interest to many in …
Reviewer #2 (Public Review):
Through detailed analysis of growing mouse embryonic lung explants, these authors investigate the statistical and physical relationships underlying threedimensional cell organization in pseudostratified epithelial tissues. The authors find that tissue curvature plays a minor role in their tissue of interest, but that cell crosssectional area and neighbour statistics conform to previously proposed geometrical 'laws' and can be explained with a minimisation of lateral cellcell contact surface energy, which in turn follows from nuclear packing and dynamics. Overall, this work constitutes a significant investigation into the drivers of complex threedimensional cell shapes and tissue structures, the primary aims appear to be largely supported by the data provided, and the work should be of interest to many in developmental biology.
Was this evaluation helpful? 
Reviewer #3 (Public Review):
Gómez et al. study cellular packing in epithelial tissues. The authors dissect how 2D cell packing statistics change along the apicobasal axis by examining different crosssections parallel to the epithelial surface. They obtain 3D exvivo data, both fixed and live, from the developing mouse pseudostratified lung epithelium, which they analyze using 3D cell segmentation. They compare these experimental data to known topological invariants (Euler characteristic), existing phenomenological relations (AboavWeaire law, Lewis' law), and phenomenological relations by the authors (quadratic cell area scaling, dependence of hexagon fraction on cell area variability), which they had proposed in an earlier paper (Kokic et al., 2019).
The authors moreover discuss changes in the 2D cell neighbor relations that occur …
Reviewer #3 (Public Review):
Gómez et al. study cellular packing in epithelial tissues. The authors dissect how 2D cell packing statistics change along the apicobasal axis by examining different crosssections parallel to the epithelial surface. They obtain 3D exvivo data, both fixed and live, from the developing mouse pseudostratified lung epithelium, which they analyze using 3D cell segmentation. They compare these experimental data to known topological invariants (Euler characteristic), existing phenomenological relations (AboavWeaire law, Lewis' law), and phenomenological relations by the authors (quadratic cell area scaling, dependence of hexagon fraction on cell area variability), which they had proposed in an earlier paper (Kokic et al., 2019).
The authors moreover discuss changes in the 2D cell neighbor relations that occur in the lung epithelium along the apicobasal axis, which they call T1L transitions ("lateral" T1 transitions). Recent work had already discussed such T1L transitions and proposed that they can be induced by epithelial curvature. The authors of the current manuscript first tested this existing hypothesis on their experimental data on both tubular parts and tips of the developing mouse bronchioles, and they conclude that curvature cannot explain the T1L transitions they observe. However, they demonstrate that the T1L transitions in their data are strongly correlated with variations in the crosssectional cell area and the nucleus positions in the pseudostratified epithelium.
1. This paper will be of interest for anybody working on cell packing in tissues and the mechanics of epithelia. In the past, 2D cellular packing arrangements in epithelia have most often been studied at the apical side only, because of technical limitations. Using stateoftheart imaging and image analysis techniques, this manuscript goes a step further and studies how the 2D cellular packing changes along the apicobasal axis. The only other papers that I am aware of that have started to address this question are GómezGálvez et al., Nat. Comm., 2018, which the authors cite, and Rupprecht et al., MBoC, 2017, which first discussed apicobasal changes in cell neighbor relations as far as I know. Hence, being among the first papers to address this question, the current manuscript would be of interest to the community.
2. A major conclusion that T1L transitions are correlated with changes in the crosssectional cell area and the nucleus positions are well supported by the data. While the authors seem to claim causation here, this is not backed by the experimental data presented.
3. The topological and phenomenological relations discussed seem to be reflected by the data. However, estimations of uncertainties would be required to better judge this point (e.g. in Fig. 2 e,f).
4. In lines 165197, the authors discuss in how far the observed numbers of T1L transitions per cell can be consistent with curvatureinduced transitions as discussed earlier (e.g. GómezGálvez et al.). To this end, they also use theoretical predictions derived in the Supplemental Material (SM). Unfortunately, there appear to be several problems with the derivation in the SM.
a) Most importantly, in Eq. S5, epsilon is derived for the situation displayed in Fig. S1b. However, after a T1L transition on the blue line, the formula will qualitatively change (e.g. the "1+" should go from the numerator to the denominator, and the meaning on n changes as the cells abutting the blue line are now the other two cells). Hence, computing the derivative in Eq. S6 to see how epsilon changes during a T1 transition seems highly problematic.
b) The angle integral, first formula on the second page of the SM, appears to evaluate to exactly zero, which is different from what the authors obtain.
Unfortunately, these two points cast strong doubt on the predicted formula in Eq. S8, Fig. S2, blue curve in Fig. 3g. As a consequence, the conclusions drawn in lines 165197 of the main text are not sufficiently convincing.
5. The authors compare to predictions from their earlier preprint (Kokic et al., 2019), where they say that Lewis' law is replaced by a quadratic dependency of cell area on cell neighbor number when the cell area fluctuations become large. However, it is not clear whether this transition between linear and quadratic prediction is smooth or discontinuous. Moreover, the magnitude of cell area fluctuations where the transition is expected to occur seems unclear. In these aspects, the theoretical prediction seems elusive, which makes it harder to critically compare it to the experimental data.
Minor comments / potential sources of confusion for readers:
6. There seems to be a typo in Eq. (2). What is likely meant is m_n = 5 + 8/n.
7. It is unclear how the "T1L transitions per cell" are counted (e.g. when talking about "up to 14 cell neighbour changes per cell" on line 154, in lines 165197, or in Figs. 3d, 8b). Do the authors refer to the number of T1L transitions divided by the number of cells, or the average number of times a cell is involved in a T1L transition? The latter number should be at least four times the former, because at least four cells are typically involved in a single T1L transition. The caption to Fig. 3d suggests that the former is meant, while lines 304307 in the discussion suggest the latter is meant.
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