Mechanical positioning of multiple nuclei in muscle cells
[['One of the fundamental challenges of cell biology is to define principles of spatial organization of the cell [1] , and , in particular , to unravel the mechanisms that control the position , size , and shape of organelles .', 'The nucleus is the principal organelle and organizational center of eukaryotic cells .', 'In textbooks , it is typically depicted in the middle of the cell; however , the nucleus’ actual position , ( as in the apical/basal position in developing neuroepithelia [2] ) , depends on the cell’s migratory state , cell cycle stage , and differentiation status [3] .', 'Proper nuclear position is vital for many cell functions , including spatially correct cell division and the direction of cell migration [3] .', 'Multinucleation is one mechanism adopted by cells to generate and sustain large cell sizes .', 'Muscle cells are one of the largest cell types , which are formed by fusion of mononucleated myoblasts and contain up to several tens ( invertebrates ) to several hundred ( vertebrates ) nuclei .', 'Myonuclei are typically positioned at the cell’s periphery , and are distributed to maximize internuclear distance .', 'However , in muscles undergoing repair , they are found towards the cell center , and in muscle diseases known as Centronuclear Myopathies , myonuclei are also found to be mispositioned [4 , 5] .', 'It has been argued [6] , that correct positioning of myonuclei is not only an indicator , but also a cause of muscle diseases .', 'A possible mechanism is provided by the Myonuclear Domain Hypothesis [7 , 8] , which suggests that each nucleus caters for a particular domain of the cell by making the gene products locally needed .', 'Mispositioned nuclei would consequently not be able to guarantee the correct supply of products to their cytoplasmic domains , affecting muscle function .', 'In this work , we focus on nuclear positioning mechanisms in multinucleated muscle fibers .', 'Drosophila is a good in vivo model system for investigating muscle development , growth , and homeostasis [9–11] , due to the simplicity of its muscle pattern , the ease of genetic manipulation , and the homology of relevant genes and processes to mammalian muscle .', 'Nuclei in newly fused Drosophila embryonic muscle cells undergo an orchestrated series of movements , best described in lateral transverse muscles: after fusion of the myoblasts , the resulting muscle cell is thought to disassemble its centrosomes and redistribute γ-tubulin around each nuclear envelope .', 'The myonuclei initially form a cluster close to the cell center .', 'The cluster splits into two subclusters that then migrate towards the opposing cell poles .', 'Subsequently both clusters break apart , and the nuclei spread out evenly along the cell long axis [12 , 13] .', 'As the nuclei spread in the muscle cell , sarcomeres , the fundamental contractile units in muscle , form into myofibrils within each cell , and , at the end of embryogenesis , the nuclei become positioned along the long axis of the cell at its periphery , thereby maximizing internuclear distance .', 'During the subsequent larval stages of development , the muscle cells grow 20-40 fold over the course of 5 days without the addition of new myonuclei [14] .', 'Nevertheless , the myonuclei remain appropriately positioned along the cell , although the mechanisms that are responsible for this are not clear .', 'While the actomyosin network may be involved in nuclear positioning [15] , microtubules ( MTs ) , MAPs ( MT Associated Proteins ) , and MT-based motors , such as kinesin and dynein , have been shown to play a major role [12 , 16–18] .', 'As examples , in embryos in which MTs are severed in the muscle cell , the central cluster does not split; in many motor mutants , nuclear spreading in the muscle cell is perturbed [19] .', 'However , the precise mechanisms controlling myonuclear positioning remain poorly understood .', 'Modeling has proven to be very useful in complementing cell biological methods in problems of positioning with , for example , the mitotic spindle [20 , 21] .', 'Mathematical modeling focused on multinucleated cells and nuclear positioning is in its infancy .', 'Simple conceptual models of nuclei repelling each other were used in [22] and [23] to show that such models can explain regular distribution of nuclei in muscle cells and in the Drosophila blastoderm syncytium .', 'Detailed mechanical simulations were done in [24] to understand multiple nuclear movements in multinucleate fungus Ashbya gossypii .', 'Here , we use computational modeling to understand the mechanisms regulating nuclear positioning in Drosophila larva muscle cells .', 'We hypothesize that nuclear positioning is a result of a MT-motor based force balance .', 'Rather than assuming the nature of this force balance , we screened multiple computer-generated forces by comparing the spatial nuclear patterns that they predict to quantitative microscopy data from biological specimens .', 'We then simulated a detailed agent-based model to confirm the predictions of the screen .', 'One model explains all biological data , including many subtle patterns of multi-nuclear positioning .', 'Based on this model we propose that myonuclei are positioned by establishing a force balance via MT-mediated repulsion .'], ['We have focused on data obtained from Ventral Longitudinal ( VL ) muscles VL3 and VL4 of Drosophila 3rd instar larvae ( Fig 1A–1C ) .', 'The 200 analyzed muscle cells ( 103 VL3 and 97 VL4 cells ) contained between 6 and 23 nuclei ( VL3: 15 . 3 ± 2 . 9 , VL4: 9 . 3 ± 1 . 6 ) .', 'Representative confocal microscopy images of fixed samples with fluorescently labeled muscle cells ( actin ) , myonuclei ( lamin , Hoechst ) and microtubules ( alpha-tubulin ) are shown in Fig 1A–1C .', 'We used cells from three control genetic backgrounds ( w1118 , Dmef2-GAL4;UAS-2xEGFP , Dmef2-GAL4;UAS-GFP RNAi ) .', 'VL muscles are flat rectangular cells with nuclei located on one cell side .', 'We employed the following terminology: cell length is the dimension along the long axis of the cell ( y-direction ) , cell width is the dimension along the short axis of the cellular rectangle ( x-direction ) ( Fig 1B ) .', 'We referred to the edge of the z-projection of the cell as the cell boundary , and distinguished between cell sides ( long segments of the rectangular shape ) and cell poles ( short segments of the rectangle ) .', 'We defined the subcellular localization of nuclei and measured several geometric parameters relevant to nuclear positioning , including nuclear numbers , shapes , nearest neighbor distances , and distances to the cell boundary , and used statistical tools to analyze the data .', 'The following features of VL muscle cells and nuclei informed our modeling:', '1 ) Both cell types share a similar length ( VL3: 499 . 2 ± 57 . 7μm , VL4: 491 . 8 ± 57 . 1μm ) , but VL4 cells’ width is significantly smaller ( VL3: 80 . 4 ± 17 . 5μm , VL4: 51 . 7 ± 11 . 3μm ) .', '2 ) Nuclei are not randomly positioned .', 'We simulated random nuclear positioning by generating random and independently uniformly distributed x- and y-coordinates of the nuclear centers in rectangular domains .', 'Analyzing the experimentally measured nearest-neighbor distances between the nuclei showed that the arrangement is not random ( Fig 1E ) ; rather , there is a characteristic distance between the neighboring nuclei .', '3 ) Along the long axis of the cell , nuclei are relatively evenly spread , with a slight increase of the nuclear density near the cell poles ( Fig 1F , lower row ) .', '4 ) Along the short axis of the cell , nuclei tend to form a single file ( SF ) near the cell center in narrower VL4 cells , whereas in wider VL3 cells , nuclei are typically found in a double file ( DF ) arrangement ( Fig 1F , upper row ) .', 'In fact , the average nuclear x-position within each cell is a function of the cell width ( Fig 1G ) : the nuclear x-position increases with increasing cell width , irrespective of the cell type .', 'Thus , nuclei in a wide VL4 cell have the same position as those of a VL3 cell of equal width .', '5 ) VL3 and VL4 nuclei have the shape of flat ellipsoidal discs with their long axis oriented along the cell’s long axis ( Fig 1B and 1D ) .', '6 ) Microtubules ( MTs ) anchored at the nuclear envelopes form asters around each nuceus ( Fig 1C ) .', 'When MT organization is disrupted , nuclei have been shown to be mispositioned [25] , suggesting that MTs exert forces on the nuclei , and that the resulting force balance is the key to the nuclear positioning .', 'One general approach to modeling movements of cell organelles generated by MT-motor forces is “interacting particle modeling” .', 'After assuming or calculating a mean MT-motor force between material objects in the cell as a function of distance between the objects , one can solve equations of motion for the interacting objects via position-dependent force laws .', 'This leads to solving a system of ordinary differential equations ( ODEs ) , the number of which is equal to the number of the objects [22 , 23 , 26 , 27] .', 'Such models can be simulated rapidly such that many different internuclear force types can be screened .', 'Another approach is to avoid assumptions and approximations and to formulate a “detailed agent-based model” , which involves solving numerically equations of elasticity theory for each MT , together with equations of motions for motors and objects to which MTs and/or motors are anchored [24] .', 'This leads to solving a large system of partial differential equations ( PDEs ) , or a gigantic ODE system , which is much more difficult and computationally expensive than the first approach .', 'While this approach provides more detailed predictions , many motors are involved in the force balance [19] , and it is not clear which combination of the motors generates the force in this context .', 'Further , mechanical characteristics of most of these motors are unknown .', 'In principle , one could use all possible motor combinations [28] , but the long computation times and high dimensionality of the model parameter space makes parameter scans of the detailed stochastic model impossible [29] .', 'In this work , we systematically combine the two approaches to suggest mechanisms of nuclear positioning .', 'We begin by screening various forces using interacting particle modeling and determine which model can be responsible for not only qualitative features of the observed spatial patterns , but also explain quantitatively all the subtle geometry of the nuclear positioning .', 'Such an unbiased and systematic computational screen was needed for a few reasons .', 'First , there are multiple simple and intuitive models that predict roughly uniform nuclear distribution , and choosing between them by a traditional thinking process is vulnerable to psychological biases .', 'Second , spatial patterns generated by simple forces may be highly complex , counterintuitive , and non-robust [30] .', 'After this screen , we used learned force characteristics to inform a detailed agent-based stochastic model with explicit simulations of individual MTs to confirm the lessons from the screening .', 'The screen of the interacting particle models resulted in a single model that fits the data best .', 'According to this model , the nuclei repell each other and the cell boundaries with the long-range forces that decrease with distance .', 'This strongly suggested that pushing of MTs , either by polymerization , or by kinesin-generated force on the MT plus ends , establishes nuclear positioning: the number of growing MT ends decreases with the distance from the nucleus , and we expect a repulsive force decreasing with distance in this simple scenario .', 'To test this model in a concrete molecular context and confirm the assumptions A3-5 that underline the usage of deterministic , isotropic , and distance-dependent forces in the interacting particle model ( Sec Force-balance and force-screening ) , we turned to a detailed agent-based simulation of microtubule-generated mechanics of the multi-nuclear cell .', 'Such a model allowed examination of whether stochastic effects are negligible , and whether MT bending and resulting elastic forces result in unforeseen effects .', 'We choose to use the microscopic , stochastic simulation tool Cytosim [24 , 33] , which has been successfully applied to a wide range of cell biological problems [34–36] .', 'Using Cytosim , we simulated hundreds of MTs per nucleus , which are distributed uniformly around the nuclear circumference , cantilevered in the nuclear envelope and grow in a radially symmetric way .', 'Individual MTs are treated as elastic rods , with the length of each MT characterized by the stochastic dynamic instability process [29] , whereby each MT undergoes repeated stochastic cycles of growth , catastrophe , shortening and rescue .', 'Contact of a growing MT end with a neighboring nucleus or cell boundary results in MT bending , which generates an elastic pushing force .', 'While pushing forces do not decrease the growth rate of MTs , catastrophy rates can increase to a maximum of 0 . 02 per second ( see Tab 2 ) , resulting in relatively brief , but typically more than 50s long , force generation events .', 'Similar force events would be observed in stochastic simulations of forces exerted by a kinesin plus-end motor .', 'Thus we did not include explicit molecular descriptions of kinesins in these simulations .', 'The sum of pushing forces from all MTs constitutes the net force .'], ['In this study , we used a “big” imaging data set generated from 2500 myonuclei from Drosophila larvae to computationally examine potential mechanisms of positioning of multiple nuclei in the cells .', 'Rather than employing a traditional reductionist modeling approach , we used a different modeling philosophy , sometimes called “ensemble modeling” or “reverse engineering” .', 'The idea is to start with multiple possible models and to use the ( predicted ) data to eliminate as many models as possible , dependent on their ability to recapitulate biological systems .', 'This approach was successfully applied to cell signaling dynamics , metabolic networks , cell cycle , and spindle geometry [28 , 39–41] .', 'In some instances , a small number of models can be analyzed one by one , as in a recent study on chemotaxis model inference [42] .', 'In other instances , the number of model variants is so great that an unsupervised or semi-supervised computer screen of the models is necessary [28] .', 'We searched computationally for the types of forces that could occur between pairs of nuclei and between nuclei and the cell boundary and could lead to positioning of the myonuclei .', 'A similar problem , mitotic spindle positioning , has a long history [21] and reductionist modeling proved helpful in that case .', 'However , an approach philosophically similar to ours was recently applied successfully to search for forces positioning the sperm MT aster in sea urchin eggs [43] .', 'We started with a large number of potential forces and formulated a few hundred potential models , each characterized by a few mechanical parameters .', 'We then used 1 . 5 million simulations to solve the differential equations describing movements of the nuclei predicted by each of these models at various parameters .', 'We filtered out the vast majority of the models that were not able to predict the uniform spread of the nuclei along the cell long axis or the tendency of the nuclei to self-organize into the single file in narrow cells and double file in wide cells .', 'The remaining 12 model classes were further tested by their ability to predict correct average nuclear position along the short axis of the cell and on robustness , the relative insensitivity of the models’ behavior to parameter values .', 'These tests left us with two possible models , the parameters of which were fully determined by requiring the models to quantitatively fit the data in 200 imaged cells .', 'The remaining two models made three non-trivial predictions:', '1 ) the double-file pattern in wide cells is a zig-zag;', '2 ) the average nuclear position along the cell short axis has the forked bifurcated dependence on the cell width , and', '3 ) nuclear density is higher near the cell poles .', 'Note that both models closely fit the experimental data very well , even though these data was not used to find the models’ parameters .', 'Remarkably , these two models make opposite predictions about the nuclear shapes .', 'One of the models predicts that the nuclei have ellipsoidal shapes with the long axes oriented perpendicular to the cell long axis , which is contrary to the experimental data .', 'Incidentally , this model is also less robust than the other , ultimate , model , which not only predicts correctly that the ellipsoidal nuclei have long axes oriented along the cell long axis , as observed , but also fits very well the measured dependence of the nuclear aspect ratio as function of the cell width .', 'Ultimately , only one model recapitulates all characteristics of nuclear positioning in VL muscle cells .', 'It suggests that , nuclei repel each other and the cell boundary with forces decreasing with the distance .', 'Our data suggest a simple molecular mechanism , which generates MT pushing forces , either by MT polymerization , or by MT interactions via kinesin motors on the nuclear envelopes and cell cortex .', 'We support the computational screen of the simple models , in which the nuclei interact as particles by isotropic and deterministic forces , with simulations of a detailed agent-based mechanical model , in which we simulate hundreds of MTs undergoing dynamic instability , bending and pushing on the nuclei and boundary with elastic forces .', 'These simulations support the types of forces hypothesized in the simple models , confirming that subtle stochastic , elastic and geometric effects do not invalidate the simple models’ assumptions .', 'More importantly , the agent-based simulations generate the single- and double-file nuclear patterns in narrow and wide cells , respectively , as observed and as predicted by the simple models .', 'Note that each simulation of the microscopic model took hours up to many days on an Linux machine with a Intel Core i7-7700 processor .', 'As such , parameter exploration of the detailed models , or testing whether they reproduce subtle observed data features , is prohibitive .', 'In the future , we plan to use more sophisticated mathematical methods [44] of solving the inverse problems—inferring the models from the data .', 'While the involvement of MTs and molecular motors in the nuclear positioning is firmly established , we do not provide direct proof that a mechanical force balance is the main mechanism of nuclear positioning .', 'Another possibility is that there is a preexistent , perhaps morphogen-governed , pattern in the cell , and that MTs simply tether the nuclei to special locations in this pattern .', 'Relevant to this thought is the fact that small nuclear clusters aggregate at neuromuscular junction in mammalian cells .', 'Our model makes detail predictions about nuclear positions in resting/fixed muscle cells .', 'However , functioning muscle cells contract , and it is likely that the actomyosin contraction forces are orders of magnitude greater than the MT-based forces .', 'Thus , it is hard to imagine that MT asters are sufficient to resist nuclear displacement during muscle contractions , and additional nuclear tethers might be involved in maintainaing an established pattern [15] .', 'Future in vivo experiments , including genetic and biophysical manipulations and live cell imaging , will be required to investigate nuclear positioning in contracting muscle cells .', 'However , we note that our model generates specific , testable predictions about the nuclear pattern in cases where the cells acquire unusual shapes and sizes or contain variable numbers of myonuclei .', 'Another intersting aspect of muscle biology that could benefit from our modeling approch is the initial positioning of nuclei in developing embryonic muscle fibers .', 'In the early embryonic muscle cells in Drosophila , after myoblast fusion , the nuclei initially cluster together , then split into two clusters that segregate to the cell poles , and finally spread along the cell length [16] .', 'It remains to be tested if a force balance model can explain these dynamics .', 'Even more challenging is the problem of coupling of the cell growth , shape change , and protein synthesis with the dynamics of nuclear numbers , positions , sizes and transcriptional activity .', 'Last , but not least , the majority of the muscle cell types are cylindrical , with nuclei positioned at the cell periphery on all the cell’s surfaces .', 'These essentially 3D nuclear patterns require special studies .', 'Active , non-random nuclear positioning has been attracting increasing attention lately [45] .', 'In a number of recent studies , force generated by MTs and motors were shown to be crucial for nuclear positioning and movement [24 , 46 , 47] .', 'We suggest that the approach that we describe here—sequential computational screen of particle interaction models followed by detailed agent based simulation of the force balance model—is the optimal way to incorporate modeling as part of the experiments directed at understanding not only multi-nuclear positioning in mammalian muscle cells , but also in syncytium , giant cells , granulomas and osteosarcomas , as well as mechanisms of other organelles’ positioning .'], ['The following Drosophila stocks were maintained at standard conditions on cornmeal medium: w1118 ( Bloomington 3605 ) , Dmef2-GAL4 [48] , UAS-2xEGFP ( Blomington 6874 ) , UAS-GFP RNAi ( J . Zallen , SKI ) .', 'Crosses ( UASxGAL4 ) were performed at 25°C; embryos hatched within a 2h period were selected and raised to third instar larval stage .', 'Wandering third instar larvae were dissected and fixed in 10% formalin and labeled as previously described [16] .', 'Muscle cells were labeled using Alexa Flour-conjugated phalloidin ( Life Technologies ) ; nuclear DNA was visualized with Hoechst 33342 ( Invitogen ) .', 'Anti-Lamin ( DHSB , ADL 67 . 10 ) and anti-α-Tubulin ( Sigma , T9026 ) primary antibodies , and Alexa Flour-conjugated secondary antibodies ( Life Technologies ) were used to label the nuclei and microtubules , respectively .', 'Whole larvae were mounted in ProLong Gold antifade reagent ( Invitrogen ) .', 'VL3 and VL4 muscles in abdominal hemisegments 2-6 were imaged on a LSM 700 confocal microscope ( Zeiss ) .', 'Quantification of confocal z-projections was performed using standard ImageJ and Matlab measurement tools .', 'VL3 and VL4 cells were traced by hand , based on phalloidin labeling .', 'Automated thresholding of fluorescence intensities of anti-Lamin and/or Hoechst labeling was used to generate binary images of VL nuclei .', 'Nuclear centroids were used to calculate nearest neighbor distances .', 'Cell widths and lengths heights were defined as average widths and lengths of the measured boundary .', 'Nuclear ( x , y ) positions were transformed onto positions in a rectangle using a mapping that preserves relative distances from the boundary .', 'ImageJ’s ellipse fitting tool was used to define nuclear shapes .', 'Nuclear pattern of both experimental and simulated origins were categorized into single file ( SF ) , double file ( DF ) or neither using a histogram of the relative nuclear x-positions with 7 equally spaced bins .', 'If the histogram had only one peak containing at least 60% of all nuclei , the cell was classified as SF .', 'If the histogram had two peaks which together contained at least 60% of all nuclei , and the number of nuclei they contained differed by less than 50% , the cell was classified as DF , in all other cases as neither .', 'Parameters are shown in Table 1 .', 'Simulation details are given below , r = 7μm is the radius of a nucleus .', 'The criteria K1-4 for valid patterns are as follows ( referring to Fig 3 △ = K1 , ◻ = K2 , ▼ = K3 , ○ = K4 , ◼ = K5 ) .', 'K1: All nuclei centroids have to be at least r away from all cell sides and poles .', 'K2: All nuclei centroids have to be at least 2r apart .', 'K3: The nuclear pattern is classified as DF or SF for the wide and thin cell respectively ( see DF/SF classification details ) .', 'K4: max y − min y > 2/3×cell height .', 'K5: The mean nearest neighbor distance is larger than 30μm and 45μm for the wide and thin cell respectively .', 'The last criterion avoids counting random patterns as false-positive ( compare Fig 1E ) .', 'Candidate models have to lead to valid patterns in both cell geometries , but not for the same parameters ( this avoids missing good models ) .', 'Parameters are shown in Table 1 .', 'Simulation details are given below .', 'The criteria for valid patterns are similar to Filter 1 , however since cells of variable width and number of nuclei were used , the SF/DF criteria is dropped and criteria K5 is replaced by K5⋆: We required that the mean NND of all nuclei ( in all 14 cell geometries ) is 40 ± 5μm .', 'For each model , we take only parameter combinations leading to valid patterns ( K1-K4 , K5⋆ ) and minimize the mean error of the predicted average x-position as a function of cell width ( compared to the measured behavior ) .', 'The curves shown in Fig 4A correspond to the parameters that minimize that error .', 'Robustness with respect to the force range ( Fig 4B ) is obtained as follows: For each model and each combination of force ranges cN , cS , for each value of MS the fraction of the 14 cells fulfilling criteria K1-K4 , K5⋆ was determined , then added for all four criteria and finally maximized over the values of MS . This yielded a score between 0 and 4 for each model and pair ( cN , cS ) , the color in the Fig 4B represents this score .', 'Only SF and DF cells ( see above ) were used and nuclei within 10% cell height of the poles were disregarded .', 'The remaining N ^ y-positions in each cell were normalized via y norm = y max y - min y ( N ^ - 1 ) ( if the y-positions were equally spaced , this would yield a y-spacing of exactly 1 ) and all positioned were shifted , such that the middle-most nucleus has y-position zero .', 'Now the normalized y-positions of all cells were collected ( using all SF y-positions for the SF auto-correlation analysis , and separating y-positions of nuclei right , and left of the middle of the cell for the DF correlation analysis ) .', 'For the final histograms a bin spacing of 0 . 25 was used .', 'To determine equilibrium positions , Eq ( 1 ) was solved on a rectangular domain using Matlabs ode solver ode15 , a variable-step , variable-order solver .', 'To model finite size effects of nuclei , a size exclusion term was added in Eq ( 1 ) .', 'For two nuclei whose centroids are a distance d apart , it takes the form', 'f SE = Q SE ( 1 d 2 - 1 ( 2 r ) 2 ) H ( 2 r - d ) ,', 'where r = 7μm is the nuclear radius , H is the Heaviside function and QSE = 2000 describes the strength of the size exclusion .', 'For size exclusion effects between nuclei and the cell boundary , 2r was replaced by r .', 'Simulations were run until all of the right-hand-sides in Eq ( 1 ) had a 2-norm of less than 10−4 .', 'Codes are available upon request .', 'The simulation software Cytosim ( Ver . 3 , 2007 ) [26 , 33] was used .', 'The configuration files are available upon request .', 'To calculate a ( distance dependent ) force from a measured nuclear speed v we used the effective viscosity of the aster ηeff consisting of the sum of the nuclear and MT drag as implemented in Cytosim .', 'The force is then given by f = v ηeff .']]
['Introduction', 'Results', 'Discussion', 'Methods']
['Many types of large cells have multiple nuclei .', 'In skeletal muscle fibers , the nuclei are distributed along the cell to maximize their internuclear distances .', 'This myonuclear positioning is crucial for cell function .', 'Although microtubules , microtubule associated proteins , and motors have been implicated , mechanisms responsible for myonuclear positioning remain unclear .', 'We used a combination of rough interacting particle and detailed agent-based modeling to examine computationally the hypothesis that a force balance generated by microtubules positions the muscle nuclei .', 'Rather than assuming the nature and identity of the forces , we simulated various types of forces between the pairs of nuclei and between the nuclei and cell boundary to position the myonuclei according to the laws of mechanics .', 'We started with a large number of potential interacting particle models and computationally screened these models for their ability to fit biological data on nuclear positions in hundreds of Drosophila larval muscle cells .', 'This reverse engineering approach resulted in a small number of feasible models , the one with the best fit suggests that the nuclei repel each other and the cell boundary with forces that decrease with distance .', 'The model makes nontrivial predictions about the increased nuclear density near the cell poles , the zigzag patterns of the nuclear positions in wider cells , and about correlations between the cell width and elongated nuclear shapes , all of which we confirm by image analysis of the biological data .', 'We support the predictions of the interacting particle model with simulations of an agent-based mechanical model .', 'Taken together , our data suggest that microtubules growing from nuclear envelopes push on the neighboring nuclei and the cell boundaries , which is sufficient to establish the nearly-uniform nuclear spreading observed in muscle fibers .']
['How the cell organizes its interior is one of the fundamental biological questions , but the principles of organelles’ positioning remains largely unclear .', 'In this study we use computational modeling and image analysis to elucidate mechanisms of positioning of multiple nuclei in muscle cells .', 'We start with the general hypothesis , supported by published data , that a force balance generated by microtubule asters growing from the nuclei envelopes are responsible for pushing or pulling neighboring nuclei and cell boundaries , and that these forces position the nuclei .', 'Instead of assuming what these forces are , we computationally screen all possible forces by comparing predictions of hundreds simple mechanical models to experimentally measured nuclear positions and shapes in hundreds of Drosophila muscle cells .', 'This screening results in the model , according to which microtubules from one nucleus push away both neighboring nuclei and cell boundaries .', 'We also perform detailed stochastic simulations of the only surviving model with individual growing , pushing and bending microtubules .', 'This model predicts subtle features of nuclear patterns , all of which we confirm experimentally .', 'Our study sheds light on general principles of organelle positioning .']
['invertebrates', 'medicine and health sciences', 'kinesins', 'microtubules', 'muscle tissue', 'geometry', 'animals', 'aspect ratio', 'simulation and modeling', 'animal models', 'drosophila melanogaster', 'model organisms', 'systems science', 'mathematics', 'molecular motors', 'experimental organism systems', 'cellular structures and organelles', 'drosophila', 'cytoskeleton', 'research and analysis methods', 'computer and information sciences', 'animal cells', 'proteins', 'agent-based modeling', 'biological tissue', 'biophysics', 'insects', 'muscle cells', 'arthropoda', 'physics', 'biochemistry', 'cytoskeletal proteins', 'eukaryota', 'cell biology', 'anatomy', 'biology and life sciences', 'cellular types', 'physical sciences', 'computational biology', 'microtubule motors', 'organisms', 'biophysical simulations']