Rotation of sex combs in Drosophila melanogaster requires precise and coordinated spatio-temporal dynamics from forces generated by epithelial cells
[['Morphogenesis concerns the development of forms in organisms .', 'It is a major theme in biology not only because of its importance in its own right , but also because of its essential relationship and interactions with biological evolution .', 'Darwin pointed out that the adult form of an organism depends on its developmental trajectory .', 'Hence , if heredity is important in determining the adult form , it must exert its influence during development [1] .', 'As with many natural phenomena , physical processes involving morphogenesis inherently span many hierarchical levels of biological organization and time scales , in that events from one level ( e . g . genetic level ) can alter events at another level ( e . g . cellular level ) .', 'A central research topic in evo-devo is to understand how those hierarchical levels integrate leading to evolution [2–4] .', 'One example of morphogenesis that lends itself to exploring physical processes at genetic , cellular and tissue levels through time is the formation of a morphological feature called the sex comb ( SC ) in species of the Drosophilidae family ( Fig 1A ) [5–7] .', 'Existence of SCs is a male-specific trait of many species of flies .', 'The phylogenetic relationships of these species have been studied showing that SCs have evolved independently several times [8–10] .', 'In D . melanogaster , the SC is a linear , almost vertical arrangement of modified bristles on the first-tarsal segment of their forelegs .', 'During development , SCs of D . melanogaster were imputed to rotate from a horizontal to an almost vertical position ( Fig 1B ) [11] and this has been corroborated using modern genetic and microscopical tools [6 , 12–14] .', 'In related experiments , Malagón [15] had initial evidence that the major force driving SC rotation was provided by cell expansion distal to ( below ) the SC , and that the cells proximal to ( above ) the SC passively responded by diminishing in area and disappearing from the epithelium .', 'However , not all species of flies with vertical , linear SCs develop them through rotation .', 'Some species utilize different bristles which are already in a vertical position and merely have to come together to form a vertical column .', 'Indeed some species with vertical SCs on more than one segment use a different method on each segment [8] .', 'Drosophila SCs display spectacular developmental and morphological variations during evolution .', 'Some examples include comb shape ( Fig 1E ) , comb length ( Fig 1F ) , number of combs per tarsal segment , tooth size and pigmentation .', 'Possibly , the most interesting comb feature involves its orientation [9] , which constantly changes between three positions relative to joint: transverse , diagonal , and vertical ( Fig 1D ) .', 'Malagon and Larsen [16] suggest that genetic perturbations in D . melanogaster can easily phenocopy changes in comb variation .', 'Thus , the SC system provides a rich developmental and evolutionary phenomenology with which to explore the strategies and tactics involved in morphogenesis and its evolution .', 'Understanding the dynamics of cell behaviours and the mechanical constraints underlying SC morphogenesis represents an important step towards linking the genetics of cellular behaviours which occur during development to their evolution over time .', 'Combined use of different approaches is essential for further progress in evolutionary-developmental biology .', 'We previously used a combination of developmental and experimental approaches and showed the role of developmental constraints and interaction between development and selection in the rotation and evolution of SCs in D . melanogaster [6] .', 'Here , we use a combination of computational modelling ( cellular Potts model , or CPM , [17] ) with experimental evidence to investigate and quantify the spatio-temporal dynamics and interplay of various mechanical characteristics of cells critical for the proper rotation of SCs in D . melanogaster .', 'Although computational modelling or a hybrid computational-experimental approach has been used successfully to describe various cellular processes , including examples in morphogenesis [18–26] , to our best knowledge this work represents the first hybrid approach used to explore the cellular dynamics driving SC morphogenesis .', 'Furthermore , we emphasize that in addition to replicating experimental results in our simulations , we have generated quantitative and falsifiable hypotheses which can guide future experiments , thus showing the synergy between experiments and computational modelling in generating novel insights in broad areas of biology .'], ['In this section we show via simulation how the initial spatial arrangement of distal cells is critical for proper SC rotation .', 'Fig 2A and 2B show snapshots of two SC rotation simulations .', 'These two examples share identical initial spatial cell configurations .', 'Importantly , under this specific initial cell configuration , every distal cell has an initial cell size roughly equal to each other ( when t = 0 mcs , top panels of Fig 2A and 2B ) .', 'Moreover , a t a r g e t t e r m ( Eq 5 ) is set to be equal for every distal cell in each simulation of Fig 2A and 2B .', 'The only difference in parameter setup between Fig 2A and 2B is that a t a r g e t t e r m of distal cells of Fig 2A is smaller than that of Fig 2B .', '( a t a r g e t t e r m ( c = E P 1 ) = a t a r g e t t e r m ( c = E P 2 ) = 13 pixels in Fig 2A , while a t a r g e t t e r m ( c = E P 1 ) = a t a r g e t t e r m ( c = E P 2 ) = 20 pixels in Fig 2B .', ') Taken together , expansion rates of distal cells are different across simulations ( and with Fig 2B having a higher expansion rate than Fig 2A ) , even though the expansion rates are roughly uniform across distal cells within a simulation .', 'It is clear that proper rotation is unlikely to occur with such uniform expansion rates of distal cells , as evidenced by the severe curvature of ( Fig 2A ) or broken ( Fig 2B ) SC at the end of rotation .', 'These rotation defects are not rescued by a blanket change in expansion rates of distal epithelial cells ( SC rotations in both Fig 2A and 2B are defective ) .', 'The curvatures of the rotated SCs suggest that uniformity of expansion rate across epithelial cells causes unequal rotation along the length of the SC , with the base end receiving more rotation than the tip end .', 'To restore proper rotation , distal cells have to be arranged in a manner that provides more rotation to the SC tip .', 'One way to achieve this is to make the initial sizes inhomogeneous across distal cells , with the distal epithelial cells having smaller initial sizes closer to the tip end of the SC ( top panel of Fig 2C ) .', 'When coupled with similar a t a r g e t t e r m values ( Table', '2 ) across distal cells , this inhomogeneous spatial arrangement of epithelial cells creates a differential push which largely maintains the shape of the SC during the entire rotation , therefore increasing the likelihood of proper SC rotation ( Fig 2C ) .', 'Even though we have shown only three examples , the above phenomenon is robust in all simulations .', 'In fact , we are unable to produce a normally straight and vertical SC in any simulation with initial spatial cell configurations and a t a r g e t t e r m values that represent uniform expansion rates across distal epithelial cells .', 'Proper SC rotations can only occur in simulations with inhomogeneous distal epithelial cell expansion rates in the manner as in Fig 2C .', 'We thus deduce that such inhomogeneous expansion rates amongst distal epithelial cells , brought about by the inhomogeneous initial spatial cell configuration , must be a critical biological mechanism underlying proper SC rotation .', 'Having established that the initial spatial configuration of epithelial cells is crucial for proper SC rotation , we now investigate the dependence of SC orientation on the expansion parameters of epithelial cells .', 'Fig 3A , 3B and 3C show respectively three representative SC simulations in which we obtain increasing final rotation angles α ( definition in Fig 3E ) while controlling expansion rates of distal cells .', 'In each of the three simulations , we start with the common initial condition ( top panel of Fig', '3 ) where the starting areas of distal cells are different , with the larger cells concentrated towards the base ( pivot point ) of the SC and the smaller cells concentrated towards the SC “tip” .', 'This common initial condition used here is identical to the one used in Fig 2C .', 'To obtain different final rotated SC angles α , we control the expansion characteristics by using different values of a t a r g e t t e r m for distal cells in each of the three representative simulations .', 'We set smaller values of a t a r g e t t e r m to obtain a smaller α , and vice versa .', 'Specifically , we set a t a r g e t t e r m ( c = E P 1 ) = 6 .', '5 and a t a r g e t t e r m ( c = E P 2 ) = 5 in Fig 3A; a t a r g e t t e r m ( c = E P 1 ) = 9 and a t a r g e t t e r m ( c = E P 2 ) = 7 in Fig 3B .', 'In Fig 3C , the default values of a t a r g e t t e r m are used ( Table 2 ) .', 'Spatially inhomogeneous distal cell expansion is observed in each of these three simulations from the summary statistics Fig 3D .', 'Specifically , in each of these three simulations , the magenta distal cells EP2 ( closer to the SC “tip” ) expand the most and the blue distal cells EP1 ( closer to the base pivot point ) expand the least .', 'As discussed in Fig 2C , such spatially inhomogeneous and differential expansion in distal epithelial cells is critical for providing the appropriate amount of push across the length of SC , so that it is still well-formed and intact towards the end of the rotation .', 'We illustrate here that the degree of the inhomogeneity determines the final SC rotation angle α .', 'An SC rotation with a higher angle α requires a higher spatial inhomogeneity of expansion between distal cells at each of the extreme ends of SC , as one readily observes from the summary statistics that the spatial inhomogeneity in distal cell expansion is highest in Fig 3C but lowest in Fig 3A .', 'Do we find spatial heterogeneity during distal cell expansion as predicted from our simulations ?', 'To test this , we performed in vivo experiments with ♀wt , ♂babPR72 and ♂wt ( Fig 4 ) .', 'SC rotation is absent from ♀wt , while rotation is partial in ectopic heterozygous babPR72 mutants with sex comb on the second tarsal segment t2 .', 'Although five pupae were measured for each of ♀wt , ♂babPR72 and ♂wt for statistical analyses ( Table A in S1 Text ) , we only display images taken at the start and at the end of the rotation of the same representative pupa for each of ♀wt , ♂babPR72 and ♂wt respectively .', 'Following our conventions , we label the distal cells closer to the SC base as “EP1” ( blue ) , the distal cells closer to the SC tip as “EP2” ( magenta ) .', 'The line separating EP1 and EP2 cells is located at the half length mark of the SC on every image on which area analysis was performed .', 'Three observations are clear from Fig 4:', '1 ) In rotating sex combs studied ( ♂wt and ♂babPR72 ) , average initial apical area ( obtained by dividing the coloured area with the number of cells in the area ) of EP2 ( magenta ) is smaller than that of EP1 ( blue ) , showing the spatial inhomogeneity of initial apical areas amongst distal cells ( median P r ( E P 2 I n i t i a l E P 1 I n i t i a l < 1 ) = 1 .', '00 with P r ( E P 2 I n i t i a l E P 1 I n i t i a l < 1 ) > 0 .', '5 at least 99 . 98% of times for ♂wt; median P r ( E P 2 I n i t i a l E P 1 I n i t i a l < 1 ) = 0 .', '99 with P r ( E P 2 I n i t i a l E P 1 I n i t i a l < 1 ) > 0 .', '5 at least 99 . 98% of the times for ♂babPR72 ) , while spatial inhomogeneity of distal cell areas is not apparent in ♀wt .', '( Median P r ( E P 2 I n i t i a l E P 1 I n i t i a l < 1 ) ∼ 0 .', '54 with P r ( E P 2 I n i t i a l E P 1 I n i t i a l < 1 ) > 0 .', '5 approximately 65% of times–S1 Text , Table B in S1 Text and Figure A in S1 Text ) .', '2 ) In rotating sex combs studied ( ♂wt and ♂babPR72 ) , EP2 on average expands at a faster rate ( defined as final area initial area × 1 time taken ) than EP1 , providing a differential push to the SC during rotation ( median Pr ( Cinhomogeneity > 1 ) = 1 . 00 with Pr ( Cinhomogeneity > 1 ) > 0 . 5 at least 99 . 98% of the times for ♂wt , median Pr ( Cinhomogeneity > 1 ) = 1 . 00 with Pr ( Cinhomogeneity > 1 ) > 0 . 5 at least 99 . 98% of times for ♂babPR72–Table B in S1 Text and Figure A in S1 Text ) , and', '3 ) how much EP2 expands faster on average than EP1 is related to α , with a higher α correlated with a greater disparity in expansion rates between EP2 and EP1 ( median Pr ( ΔCinhomogeneity ( ♂wt , ♀wt ) > 0 ) = 1 . 00 with Pr ( ΔCinhomogeneity ( ♂wt , ♀wt ) > 0 ) > 0 . 5 at least 99 . 98% of the times; median Pr ( ΔCinhomogeneity ( ♂wt , ♂babPR72 ) > 0 ) = 0 . 70 with Pr ( ΔCinhomogeneity ( ♂wt , ♂babPR72 ) > 0 ) > 0 . 5 90% of the times; median Pr ( ΔCinhomogeneity ( ♂babPR72 , ♀wt ) > 0 ) = 0 . 99 with Pr ( ΔCinhomogeneity ( ♂babPR72 , ♀wt ) > 0 ) > 0 . 5 at least 99 . 98% of the times–Figure A in S1 Text and Table B in S1 Text ) , further buttressing the differential push claim in simulations .', '( Pr means probability . Please see , for example [30–32] , for Monte Carlo simulations and bootstrapping method for statistical analyses . )', 'Next , we investigate the dependence of SC rotation on the length of the SC and the adhesion between successive SC teeth .', 'To quantify SC rotation , we have already introduced α in the previous section and used it in Fig 3 to describe how much SCs rotate .', 'We now introduce ABASCT , angle between adjacent sex comb teeth , which is useful to quantify the departure of rotated SCs from linearity .', 'In Fig 5A , we illustrate the standard deviation ( SD ) of ABASCT is related to SC shape variation .', 'β1 , β2 , β3 and β4 are respectively the angles between SC teeth 1 and 2 , 2 and 3 , 3 and 4 , and 4 and 5 of example SC1 .', 'The SD of these angles is a measure of curvature of SCs .', 'An almost straight SC , SC2 , has a lower ABASCT SD value , but an SC that is highly non-linear , such as SC3 , has a relatively large ABASCT SD value .', 'We emphasize that ABASCT SD and α measure separate properties of the SC .', 'For example , SC2 and SC3 have identical α but distinct ABASCT SDs .', 'Hitherto we have mostly discussed how spatial properties of distal epithelial cells may help proper SC rotation .', 'However , even with inhomogeneous spatial patterning of distal cells , the rotated simulated SCs suffer from a decreasing intact ratio as the length of SC is increased ( Fig 6A ) .', 'In particular , the intact ratio of 11-tooth SCs drops considerably across virtually all examined SC adhesion parameters when compared with the shorter 9-tooth SCs .', 'In this section we explore whether introducing temporal dynamics to the expansion of distal epithelial cells , in addition to spatial patterning , could improve the breaking statistics of rotated SCs .', 'We perform additional simulations in which the blue distal cells ( EP1 ) expand later in the simulations , while keeping everything else identical .', 'There are 3 × 36 = 108 additional sets of simulations , which cover 3 magnitudes of delayed expansion of EP1 cells ( 40 , 120 and 200 mcs ) .', 'Visual examination of the aggregate statistics suggests that these extra simulations share similar α and ABASCT SD distributions with the regular , non-delayed simulations ( Figure G in S1 Text and Figure H in S1 Text ) .', 'However , comparison of intact ratios between the delayed and non-delayed simulations ( Fig 8A ) shows that while there is no apparent improvement on intact ratios for shorter 5 , 7 , 9-tooth SCs , there is a consistent improvement for 11-tooth SCs across almost all SC adhesion parameters ( Table D in S1 Text ) .', 'In fact , with an appropriate delay parameter ( ∼ 120 mcs ) , intact ratios of 11-tooth SC approach that of a 9-tooth one .', 'Too high a delay parameter ( > 150 mcs ) does not make intact ratios higher .', 'On the contrary , it causes compression of cells at the centre of the distal region , a phenomenon not readily observed in experiments .', 'Fig 8B shows two examples of 11-tooth SC simulations in which a delayed expansion of EP1 affects the final outcome of the SC , with the one having a delayed expansion of EP1 enjoying an intact SC while the non-delayed simulation has a broken rotated SC .', 'To determine whether such a temporal delay exists in experiments , we collect data on the time course of growth of distal cells in each of our short , wildtype and long SC examples ( Fig 9 ) .', 'The percentage growth in area of these cells ( as compared to the start of measurement at either 22 or 23 hours AP ) is then fitted with logistic functions to determine the time lag between the expansion phase of distal epithelial cells in different areas .', 'The results of curve fitting suggest that , in our long SC example ( Fig 9C ) , there is a delay in the expansion phase of distal epithelial cells closer to the base of the SC relative to the distal epithelial cells closer to the SC tip , with the start of expansion phase of magenta cells ( closer to the SC tip ) at 23 . 27 hours ( 22 . 25-24 . 28 hours 95% CI ) , while that of blue cells ( closer to the SC base ) is 27 . 42 hours ( 26 . 34-28 . 51 hours 95% CI ) .', 'In the wildtype example ( Fig 9B ) , however , there is no statistically significant difference between the start of the expansion phase of the selected magenta and blue cells .', 'Our experimental results provide evidence that longer SCs may take advantage of the time delay to achieve proper rotations .', 'We emphasize that even though delayed expansion of blue coloured cells is also detected in our short SC example ( Fig 9A ) , it does not represent an inconsistency between modelling and experiments because delayed expansion of EP1 ( blue ) cells does not statistically affect the intact ratio of shorter SCs ( Fig 8A ) .'], ['SC rotation in D . melanogaster involves a complex pattern of cell behaviours ( such as cell proliferation , shape change and movement ) [15 , 27 , 34 , 35] .', 'However , how these multiple cellular processes contribute to SC morphogenesis has remained elusive .', 'We wished to understand how the temporal and spatial properties of each cell behaviour contribute to normal comb rotation .', 'Although this would be experimentally impractical , it is possible to explore these properties computationally by simulating the effects of varying cell behaviours .', 'From extensive simulations , we deduce that proper rotation of the SC depends on precise spatio-temporal dynamics of distal cells .', 'The initial spatial cell size distribution in the distal epithelium was found to be important to minimize SC bending and malformation .', 'In particular , distal cells closer to the SC base ( pivot point ) have larger initial apical areas than cells farther away from the base .', 'Such inhomogeneity in initial apical areas of distal cells translates into a differential push across the length of SC as the cells expand , ensuring proper SC rotation in simulations .', 'In addition to spatial distribution , a temporal component was also discovered in our simulations , when delay in expansion of distal cells closer to SC base relative to cells closer to the SC tip reduces incidence of long SC breaking during rotation .', 'These simulations are not only useful in showing that cell behaviours distal to the rotating comb are likely sufficient to provide the motive force for comb rotation , they also suggest relationships of which importance was not previously realized .', 'In fact , having found in simulations of the spatio-temporal dynamics of the distal cells predicted to be crucial for proper SC rotations , we were able to go back to the original data in the 4D movies and confirm that this was indeed occurring biologically .', 'Not only did the simulations produce testable hypotheses concerning developmental mechanisms in the model species D . melanogaster they also suggested hypotheses concerning how changes in developmental processes might produce different SC patterns during fly evolution .', 'For instance , changes in rotation angle might be due to changes in expansion of distal cells ( Fig 4 ) .', 'Our work also suggests potential avenues for these changes and which paths might be forbidden .', 'As an example , rotation of long SCs in our simulations are more difficult because increasing comb length generates multiple problems for movement including comb breaking , atypical alignment , among others ( Fig 6 ) .', 'These results are consistent with the differing strategies to achieve SC morphogenesis taken up by multiple Drosophila species with long SCs .', 'Most of the SCs from these species lack rotation , appearing already in a vertical position early in the developmental process [6 , 9 , 13] .', 'Furthermore , other species with long rotating SCs such as Drosophila guanche display frequent broken and misaligned bristles [6] , consistent with our simulations .', 'From our biological Drosophila experiments , we observed a relatively consistent linear shape ( quantified by ABASCT SDs , [8 , 13 , 27] ) of rotating SCs amongst Drosophila species , yet the orientation of SCs ( i . e . α ) has a larger variation [13] .', 'On the other hand , we have discovered from our simulations that SC shape is primarily ( though not exclusively ) governed by the initial inhomogeneity of distal cell sizes ( Fig 2 ) , while SC orientation can be controlled by the subsequent rate of expansion of these cells ( Fig 3 ) .', 'Therefore , if these two phenotypes ( shape and orientation of SCs ) follow distinct evolutionary trajectories , our simulation results suggest that there may be signatures left by evolution on the two corresponding governing cellular characteristics ( initial inhomogeneity in distal cell sizes and subsequent expansion of these cells , respectively ) .', 'In other words , a canalized SC shape implies a conserved spatial inhomogeneity in initial distal cell areas , but variation in SC orientation implies diversity in subsequent expansion rates of these cells .', 'Preliminary evidence from Fig 4 suggests this is indeed the case .', 'Summary statistics Fig 4D and subsequent statistical analyses in particular from Figure A in S1 Text show an approximate , albeit imperfect conserved existence of inhomogeneity of initial distal cell areas across the male fly genotype examples ( both wildtype and mutant ) , which exhibit different SC orientations but similar SC shapes .', 'It is primarily the variation in the subsequent expansion of epithelial cells between the fly genotypes that determines the SC orientation .', 'Our results suggest the possibility of separate molecular mechanisms , which are born out of evolution and are continuously modified by it , underlying these two cell characteristics .', 'In addition , our results raise the question of whether Drosophila species using developmental mechanisms other than rotation also canalize their SC shape while exhibiting higher variation in comb orientation .', 'There are several shortcomings in this first work to study SC rotation in silico which warrant future improvements .', 'First , although we attempt to replicate as close to experimental results as possible , αs in our simulations generally have slightly lower values than expected for normal rotation .', 'Our results thus suggest that other cellular processes may also contribute to SC rotation .', 'For example , joint formation is not included in our simulations yet previous studies have pointed out that it affects the basal part of SC [13] and constitutes the male-specific movement of sensillum campaniforme [15] .', 'Effects of joint formation on SC rotation can be studied using photo-activated lines that can disrupt development precisely [36 , 37] .', 'We also did not systematically investigate the possibility of the “pulling” effect from proximal cells during SC rotation .', 'A primary reason we focused on the distal , not proximal cells is that even without significant contraction in apical areas in the proximal region , proper SC rotation could still occur [15] .', 'There is also an absence of experimental observation of any initial spatial arrangement of proximal cells similar to , but opposite in direction of , distal cells .', 'The apparent absence of such spatial arrangement means that proximal cells are unlikely to exert a coordinated pulling force similar to the pushing force of distal cells during SC rotation .', 'Moreover , we did not observe from experiments a clear spatial or temporal sequence in which proximal cells extrude from the epithelium , meaning that it is more likely that the proximal cells were passively “squeezed” due to external pressure rather than actively contracting generating a pulling force .', 'Nevertheless , for future considerations it would be desirable to quantify the effects ( if any ) of proximal cells in next iterations of simulation models .', 'Currently , although cell extrusion is included in our simulations , its effects are not examined thoroughly .', 'While cell extrusion is shown to be the consequence of cell crowding rather than a major driving force of development [38 , 39] , future simulations could better quantify its effects above the SC and test whether it buffers comb shape .', 'From the simulation perspective , the parameters used here are chosen to reproduce SC dynamics as observed in experiments .', 'A consequence of such an approach is that these parameters may not correspond to the mechanical characteristics of actual SC or epithelial cells .', 'In theory , mechanical characteristics of cells are related to the spatial derivatives of the Hamiltonian Heff used in CPM .', 'However , the exact correspondence is usually complicated and may depend on the specific topology of the cellular systems studied .', 'Although there have been attempts to perform CPM simulations with parameters based on matching the terms of Heff and the mechanical characteristics of cells [40] , the majority of simulation examples in the literature use our approach of choosing parameters based on the correct reproduction of observed cellular behaviours [41] .', 'We expect the major conclusions established in this work should be largely independent of the specific parameters used in the simulation model , so long as those parameters also demonstrate observed cellular behaviours .', 'For example , it would be extremely difficult to imagine something as fundamental as the spatio-temporal properties of distal cells not to hold if another set of more “realistic” parameters were used for simulations , in particular when these previously unnoticed spatio-temporal properties are themselves demonstrated in experiments ( Figs 4 and 9 ) .', 'Future simulations could address this issue by further refining the parameters so as to reflect the actual mechanical characteristics of cells .', 'In addition , some of the cells in the simulations have a very small initial lattice size ( ≤ 5 pixels ) .', 'This could potentially create issues when the stochastic effects of the simulations become large .', 'For example , these small cells could disappear due to stochastic effects early in the simulations with no chance to expand .', 'To check whether our simulation results are scalable in size , we performed some sample simulations with identical cell arrangements but with a resolution 4 times as much ( i . e . 228 × 168 pixels in the sample simulations vs . 114 × 84 pixels–Figure I in S1 Text ) .', 'We discovered that SCs were able to properly rotate just as in the original simulations .', 'Thus , although some anomalous effects could be present in the simulated cells in the original simulations due to their smaller grid sizes , these are likely not severe enough to have impacted the conclusions of this work .', 'In the area analysis of Fig 4 and Table A in S1 Text , we classified distal cells by a demarcation line drawn at the halfway length mark of the SC on every confocal image where area analysis was performed .', 'The demarcation line is horizontal for 30° ≤ α ≤ 90° but perpendicular to the SC for α < 30° .', 'Any distal cell above the line ( closer to SC tip ) was defined as EP2 and any distal cell below it ( closer to the SC base ) EP1 .', 'Such an approximate method of classifying distal cells in experiment could be problematic because movement of cells during SC rotation means that some of the distal cells may have different classifications at the start and at the end of SC rotation .', 'To ensure that our classification method is robust , we have performed individual cell tracking on a sample fly leg ( Figure J in S1 Text ) .', 'The advantage of individual cell tracking is that the cell labels ( whether the cells are defined as EP1 or EP2 ) are consistent throughout the entire area analysis .', 'We obtained identical conclusions with individual cell tracking as with our original method , thus showing that our approximate method of cell classification does not significantly affect the conclusions established in this work .', 'Separately , a certain degree of cell compression was observed along the EP1/EP2 boundary in the simulations of Fig 3A and 3B , while no such simulation artefact was observed in Fig 3C .', 'Cell compression occurs in some simulations because of the inhomogeneous expansion rates amongst the distal cells due to their different initial areas , terminal target areas and timing of expansion .', 'Therefore , some EP1 or EP2 cells are receiving more pushing forces than others , causing compression .', 'In particular , the imbalance in pressure along the EP1/EP2 boundary is more acute in Fig 3A and 3B simply because we reduced the expansion of magenta EP2 cells in Fig 3A and 3B ( as compared to Fig 3C ) , but we did not reduce as much expansion for the blue EP1 cells .', 'We believe that such cell compression can be further mitigated by fine-tuning initial distal cell area configurations , terminal target areas and λ parameters .', 'As well as expansion , distal cells were observed experimentally to elongate along the y or the ordinate axis during SC rotation .', 'While we have included cell polarization ( ϵ in Table 2 ) in our model , it remains an interesting question the extent of distal cell polarization contributes to SC rotation .', 'Although we have not systematically examined the issue from a simulation standpoint , in the early model development we ran limited sets of simulations in which distal cell expansion was isotropic ( i . e . cell polarization was absent ) , we noticed that simulated SCs could still properly rotate but the rotation angle ( α ) was generally smaller by 10-15° as compared to simulations with cell polarization .', 'More extensive simulations are required to fully elucidate the relationship between cell polarization and SC rotation .', 'Finally , during the measurement of temporal changes in apical areas of distal cells ( Fig 9 ) , we noticed that in addition to the primary growth pattern following logistic function ( fitted curves of Fig 9A , 9B and 9C ) , there also exists oscillatory behaviours for several of the cell samples measured , in particular the ones in Fig 9A and 9C .', 'Although actin-myosin binding dynamics are thought to be responsible for similar oscillatory behaviours with a much shorter time scale [42] , we remain agnostic about the possible mechanisms for cell area oscillations in our case because of their long periods ( up to a few hours ) .', 'Future experiments are required to answer the open question about the mechanism underlying these oscillations and whether such oscillatory behaviours contribute to SC rotation .'], ['Unless otherwise specified , simulations were performed in sets .', 'A set consists of 48 independent simulations .', 'These 48 simulations share identical parameters and initial cell configurations , but differ in the seed for pseudo random number generation ( Knuth’s subtractive method , [31 , 51] ) which affects the selection of pixels for attempted flips .', 'Since these simulations can be regarded as multiple numerical experiments under the same parameters , we can extract attributes from these outputs and perform analyses to determine how different parameters affect outputs in a statistical manner .', 'In other sections we have
['Introduction', 'Results', 'Discussion', 'Materials and Methods']
['The morphogenesis of sex combs ( SCs ) , a male trait in many species of fruit flies , is an excellent system in which to study the cell biology , genetics and evolution of a trait .', 'In Drosophila melanogaster , where the incipient SC rotates from horizontal to a vertical position , three signal comb properties have been documented: length , final angle and shape ( linearity ) .', 'During SC rotation , in which many cellular processes are occurring both spatially and temporally , it is difficult to distinguish which processes are crucial for which attributes of the comb .', 'We have used a novel approach combining simulations and experiments to uncover the spatio-temporal dynamics underlying SC rotation .', 'Our results indicate that', '1 ) the final SC shape is primarily controlled by the inhomogeneity of initial cell size in cells close to the immature comb ,', '2 ) the final angle is primarily controlled by later cell expansion and', '3 ) a temporal sequence of cell expansion mitigates the malformations generally associated with longer rotated SCs .', 'Overall , our work has linked together the morphological diversity of SCs and the cellular dynamics behind such diversity , thus providing important insights on how evolution may affect SC development via the behaviours of surrounding epithelial cells .']
['The sex comb ( SC ) is a series of modified bristles on the male forelegs of many species of fruit flies .', 'The size , position and shape of these sex combs vary drastically across different fly species .', 'Therefore , SCs are a model system which illustrates the interaction between evolution and organism development influencing phenotypic features .', 'In this work , we use a combined simulation-experimental approach to study the cellular processes involved in the rotation of developing SCs in common fruit flies ( D . melanogaster ) .', 'Our results indicate that despite the appearance of a complicated set of motions of surrounding cells associated with SC rotation , the final SC attributes only depend on a few selected parameters .', 'We showed that changes in the timing and extent of cell size increase in distal cells altered the extent of SC rotation and breakage .', 'Furthermore , these changes were sufficient to account for the observed variations in SC rotation between different fly species .', 'Thus , our computational model has given us important insights on how evolution may use various cellular processes as a means to manifest the diversity of SCs across different fly species .']
['invertebrates', 'medicine and health sciences', 'statistics', 'animals', 'epithelial cells', 'simulation and modeling', 'animal models', 'developmental biology', 'drosophila melanogaster', 'model organisms', 'mathematics', 'experimental organism systems', 'morphogenesis', 'drosophila', 'digestive system', 'research and analysis methods', 'dentition', 'animal cells', 'animal studies', 'digestive physiology', 'mathematical and statistical techniques', 'biological tissue', 'monte carlo method', 'head', 'insects', 'arthropoda', 'teeth', 'eukaryota', 'cell biology', 'anatomy', 'physiology', 'jaw', 'epithelium', 'biology and life sciences', 'cellular types', 'physical sciences', 'evolutionary biology', 'statistical methods', 'organisms', 'evolutionary developmental biology']