A mammalian cell looks blobby and unstructured when you look at it in a tissue culture dish.  The question of “why is it that shape?” tends not to leap to mind, in much the same way as it doesn’t when you look at a fried egg.  And yet, there are real constraints on the shapes of cells.  A recent paper from Buzz Baum and collaborators (Picone et al. 2010.  A polarized population of dynamic microtubules mediates homeostatic length control in animal cells.  PLoS Biology 8:e1000542) explores both the nature of these constraints and the mechanisms behind them.

The starting point for this work is the observation that many animal cells seem to have limits on how far they can stretch.  Picone et al. set out to probe what determines these limits.  The first and most obvious question they asked was, is it simple geometry?  If you force a cell to be thinner, can it stretch further? Do cells that have a larger volume have a longer reach?

Using micropatterned glass slides carrying fibronectin lines of defined width (sticky), separated by lines of polyethylene glycol (not sticky), Picone et al. forced HeLa cells to grow in skinny or broad shapes.  Surprisingly, the width of the line didn’t make any difference to how far the cell could spread: whether the fibronectin line the cells were growing on was 3 µm wide or 35 µm wide, they always ended up with the same average length.  Cells with different volumes spread to the same length too.  It seems that something other than volume or geometry is determining cell length.  What surprised me most about this observation is that under these circumstances cells decide to be a constant length, not a constant thickness.

Anything to do with controlling cell shape or cell movement probably involves the cytoskeleton.  Cell crawling, for example, is highly dependent on actin-based protrusions such as lamellipodia and filopodia.  Is actin involved in setting the spreading length?  Apparently not.  Knocking down a key actin regulator (WAVE) using RNAi gets rid of the lamellipodia, but doesn’t change the characteristic length the cells attain on the patterned substrate.  Drugs that inhibit Rac, another key actin regulator, or myosin II, the motor protein that coordinates actin-based crawling, also fail to change the spreading length.

Microtubules are the other obvious candidate, and when Picone et al. tried drugs that inhibit the function of microtubules they saw a clear effect; blocking microtubule polymerization prevented cells from elongating.  Watching spreading cells under the microscope, they found that as cells spread out their microtubules become progressively more aligned with the long axis of the cell.  The way this happens is interesting.  In the early stages of cell spreading, the microtubules are growing in all directions; as they grow, they bump into the edge of the cell. The angle of the contact determines what happens next: if the angle is less than about 30°, the microtubule bends but keeps growing, but microtubules that hit the edge at a larger angle mostly collapse.  (Microtubules switch from growing to collapsing in a process called dynamic instability, which can be regulated by other proteins, or by mechanical forces).  This selective culling of microtubules that are going in the wrong direction gradually leads to the observed lining up of microtubules along the cell’s long axis.

Could this arrangement of microtubules somehow be responsible for determining cell length?  Microtubules could in principle affect cell length in at least two ways; they could help push the leading edge outwards, or they could deliver material that’s needed for moving the edge, such as additional membrane.  And microtubules are the only structure we know of in the cell that can be as long as the cell itself.  Leaving aside the question of which of these mechanisms might be operating, can we understand the self-limiting nature of cell extension based on what we know about microtubules?

Picone et al. put together a fairly simple mathematical model to explore this question.  Like many of the most understandable mathematical models, it is not an attempt at a full simulation but an effort to formalize the knowledge we have about the system, and the assumptions that we’re making.  The measurements going into the model include how fast microtubules grow (when they’re growing), how often they collapse when they’re in the cytoplasm, and how often they collapse when they hit the cell cortex.  When microtubules are depolymerized, the cell shortens; they measured the retraction rate, and included that too as the “push-back” the microtubules have to overcome to cause cell lengthening.  The assumptions include the idea that when a microtubule reaches the cell cortex, it helps to push it outwards (it doesn’t matter how), and the idea that the microtubule nucleation sites are located at the center of the cell and fixed in number, so that each microtubule that collapses creates an opportunity for a new microtubule to grow.  Instead of simulating the polarization of the microtubules along the long axis of the cell, they simply assumed it, allowing them to concentrate on the consequences.

This model recapitulates the experimental observations reasonably well.  My intuition for what is going on here is as follows: when the cell is short, it doesn’t take long for a microtubule to grow from the center to the edge.  As the edge is pushed out by the action of the microtubules (whatever it is), the time it takes to get to the edge increases, and so does the chance of collapsing before you get there.  At some point, the pushing due to the microtubules that made it to the edge is only just enough to compensate for the retraction rate, and the cell reaches a steady state.  In the model, the steady state is reached when 2 microtubules, on average, are reaching far enough to touch the cortex.  The critical parameter in the model is the ratio between the collapse rate in the cytoplasm (which determines how many microtubules survive to make it as far as the cortex) and the collapse rate at the cortex (which determines how long they last once they get there).  If the cortex/cytoplasm collapse ratio is high, the length the cells attain is fairly uniform.  If it’s low, fluctuations in the number of microtubules that make it to the cortex become more important, and the lengths of individual cells become more variable.  The factor that’s most important in determining the eventual average length of the cell is the number of microtubule nucleation sites; this makes sense, because for a given cell length a higher number of nucleation sites means that you have more chances to get to the edge and push the edge outwards.

A prediction the model makes is that reducing the rate of microtubule polymerization should cause a reduction in average cell length, but not increase the variability in cell length,  And that prediction seems to be borne out in experiments using low concentrations of a microtubule destabilizer.  I find this whole story inspiring as a demonstration of the power of the self-organizing behavior of microtubules; monomers that are a few nanometers across self-organize into structures that are long enough to set the length of an entire cell, which is 10,000x larger.  And tweaking the behavior of the microtubule — in this case by using drugs to destabilize it, but there are many other ways — leads to a subtle change in its dynamics, causing a different balance to be reached and setting the length of the cell to a new level.  Just the kind of adaptive process you need in development, or for that matter in evolution.

In browsing around this topic, I happened to find another recent paper addressing somewhat related questions in hydra.  In this study, the authors surgically removed part of the hydra’s body column and watched as it recovered its length — which it does by extending the cells that remain, not by growing new ones.  Microtubules line up along the long axis of the cell as it extends, and microtubule-inhibiting drugs block length extension.  Conversely, when the authors grafted extra length onto the body, which you can do in hydra, the cells shorten; during shortening, the microtubules organize themselves perpendicular to the long axis of the cell.  In this case, then, the organism has a way of determining whether its body is too long or too short, and (perhaps) controlling the organization of its microtubules to change the characteristic length of its cells.  It’ll be fascinating to see whether microtubule-driven length control is common or rare.

Picone R, Ren X, Ivanovitch KD, Clarke JD, McKendry RA, & Baum B (2010). A polarised population of dynamic microtubules mediates homeostatic length control in animal cells. PLoS biology, 8 (11) PMID: 21103410

Takaku Y, Shimizu H, & Fujisawa T (2010). Microtubules are involved in regulating body length in hydra. Developmental biology PMID: 21047507

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