Why muscle cells multinucleated

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. 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. 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 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.

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. 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 i 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.

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. 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 ].

Zallen, SKI. Whole larvae were mounted in ProLong Gold antifade reagent Invitrogen. 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. 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. 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.

Parameters are shown in Table 1. 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 2 r apart. 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. Simulation details are given below. The curves shown in Fig 4A correspond to the parameters that minimize that error. This yielded a score between 0 and 4 for each model and pair c N , c S , the color in the Fig 4B represents this score. The remaining y -positions in each cell were normalized via 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. 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 size exclusion effects between nuclei and the cell boundary, 2 r was replaced by r. Codes are available upon request.

The simulation software Cytosim Ver. The configuration files are available upon request. This file contains three sections: 1. Effect of internuclear friction.

This section describes the modeling and simulation of nucleus-nucleus friction. Attraction-repulsion internuclear forces. Comparison of numerical and analytical results for MT-mediated forces.

This section compares the shape of a single clamped, confined microtubule, as well as the forces it creates as computed by Cytosim and using an analytical approximation. The video compares the agent-based, stochastic simulations in Cytosim left with an interacting particle simulation right in the thin, VL4 type cell. Microtubuli are shown as white lines, nuclei as red solid circles, the distance dependent force in the interacting particle model is symbolized by shades of red and yellow.

The video compares the agent-based, stochastic simulations in Cytosim left with an interacting particle simulation right in the wide, VL3 type cell. We thank the J. Abstract Many types of large cells have multiple nuclei. Introduction 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.

Download: PPT. Fig 1. Positioning of the myonuclei in Ventral Longitudinal VL muscles 3 and 4. The interacting particle model. Force screen structure.

First filtering step. Fig 3. Sample gallery of the spatial nuclear patterns produced in Filter 1. Table 1. Parameters used for the two filtering steps and the calibration step. Second filtering step. Two model classes result from the screens. The two filtering steps resulted in just two model classes that can predict robust nuclear spreading along the cell long axis and correct behavior of x -positions with respect to cell width: Model Class 1: The internuclear forces are repulsive and decrease with internuclear distance.

Zig-zag patterns in the double file of the nuclei in wide cells. Transition from single to double file in the nuclear pattern. Nuclear shapes. Applying the same argument to deformations caused by forces from above and below, we approximated the nuclear aspect ratio as: 5 We used the equations determining the forces between the nuclei and between the nuclei and cell sides and the nuclear equilibrium positions to calculate the left-right and up-down forces f x and f y.

Denoting by the equilibrium position for DF as given by 4 , the forces f x , y are given by the formula: For each variant of Models M1 and M2 short and long range , we applied Eq 5 to all imaged cells geometric parameters of each cell were substituted into the formula to evaluate f x and f y forces.

Comparison to agent-based, stochastic simulations The screen of the interacting particle models resulted in a single model that fits the data best. Table 2. Parameters in the agent-based, stochastic simulation using Cytosim.

Calculating distance-dependent forces from agent-based simulations. Agent-based and interacting particle simulations match closely. Image processing and quantification Quantification of confocal z -projections was performed using standard ImageJ and Matlab measurement tools. Filter 1 Parameters are shown in Table 1.

Filter 2 Parameters are shown in Table 1. Simulation: Interacting particle model To determine equilibrium positions, Eq 1 was solved on a rectangular domain using Matlabs ode solver ode15 , a variable-step, variable-order solver. Simulation: Stochastic agent-based model The simulation software Cytosim Ver. Supporting information. S1 Text. S1 Video. Agent-based and interacting particle model—Thin cell. S2 Video. Agent-based and interacting particle model—Wide cell. Acknowledgments We thank the J.

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A primer of swarm equilibria. In looking through a microscope how could you distinguish skeletal muscle tissue from smooth muscle? The three types of muscle cells are skeletal, cardiac, and smooth. Their morphologies match their specific functions in the body. Skeletal muscle is voluntary and responds to conscious stimuli. The cells are striated and multinucleated appearing as long, unbranched cylinders.

Cardiac muscle is involuntary and found only in the heart. Each cell is striated with a single nucleus and they attach to one another to form long fibers. Cells are attached to one another at intercalated disks. The cells are interconnected physically and electrochemically to act as a syncytium. Cardiac muscle cells contract autonomously and involuntarily. Smooth muscle is involuntary. Each cell is a spindle-shaped fiber and contains a single nucleus.

No striations are evident because the actin and myosin filaments do not align in the cytoplasm. You are watching cells in a dish spontaneously contract. They are all contracting at different rates, some fast, some slow. After a while, several cells link up and they begin contracting in synchrony. Discuss what is going on and what type of cells you are looking at. The cells in the dish are cardiomyocytes, cardiac muscle cells.

They have an intrinsic ability to contract. When they link up, they form intercalating discs that allow the cells to communicate with each other and begin contracting in synchrony. Under the light microscope, cells appear striated due to the arrangement of the contractile proteins actin and myosin. Provided by the Springer Nature SharedIt content-sharing initiative. Oncogene Molecular Biology Reports By submitting a comment you agree to abide by our Terms and Community Guidelines.

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