The way we usually imagine a cell is like a tiny bawl of soup, a small and confined space containing mostly water but with also some solid or semisolid material. Up to this point such an image is not quite bad as a cell descriptor. The key difference lies in the organization. A soup is an unorganized portion of matter where all its components (i.e. carrot cubes) float around in pointless toil. Unlike our favorite soup, the content of a cell is highly organized spatially and, as far as we know, there are no pointless processes present.

So, what organizes the cell? This task is performed by the cytoskeleton. This molecular size skeleton that extends along the cytoplasm of the cell can be categorized into three subsets: actin cytoskeleton, intermediate filaments and the microtubule network. We'll be focusing only on the microtubules here. Also, what follows will be centered on animal cells but many of the underlying principles apply to other types of cells too.

Fig 1: Fluorescence micrograph of an animal cell. [Note that the microtubules have been stained green and the nucleous in red for easier interpretation.]

What are the microtubules? They are tubes made of a protein called tubulin and they extend from roughly the center of the cell towards the plasma membrane.

Microtubule function

Why would anybody care about microtubules? We can start by realizing that all eukariotic cells have a microtubule network. Why would any cell spend any effort on maintaining a microtubule network? Because it is a requirement for viability: cells depend on microtubules for survival, specially in the long term.

What do microtubules do? (Be prepared and hold on to your chair because you may be fascinated by this.) The microtubule network acts as a structure to keep the cell organized. It allows the cell to position its vesicles and organelles in the right spot. The organelles are not scattered along the cytoplasm like peas in a soup. Also, the microtubules are the machinery that segregate the chromosomes during cell division. This carefully orchestrated operation involves biological checkpoints, pushing/pulling forces and it has to be performed quickly and accurately. Microtubules and their associated proteins do that job.

Challenge your knowledge and imagination: What would happened to a dividing cell that is unable to accurately segregate its chromosomes in two?

Why should we care about microtubules?

Cells seams to care very much about microtubules but why should we? Lets talk about tumors for example. We will not go into the details here but lets just say that cancer is a very complex syndrome. One of the hallmarks of cancer (Tanya. ) is uncontrolled cell division. This is an unwanted cell division that makes "sick" cells proliferate. One of the most potent anticancer drugs is called Paclitaxel.

Interestingly, Paclitaxel can stop cell proliferation by directly interfering with normal microtubule function. In people with tumors, Paclitaxel interferes mostly with "sick" cells but unfortunately it may also affect "healthy" cells. This limits the therapeutical value of Paclitaxel. Somehow disappointing, there is a lesson here. The therapeutical limitation does not prevent us from imagining that if we understood the microtubule cytoskeleton better, we could do more to specifically fight cancer. The impact of a more effective cancer treatment on human health needs not to be stressed.

Not only during cell division are microtubules important. During interphase (when the cell is not dividing) the microtubules act as a cell-wide system of highways through which materials are transported from one place to another.

For cells to survive, they have to constantly interact with the membrane to obtain and secrete substances. Some materials are delivered just to become part of the membrane. For example, proteins are a component of plasma membranes. The DNA contains the information (sequence) to build all proteins. Proteins are synthesized in the rough endoplasmic reticulum, an organelle located near the nucleus. So, how do membrane proteins find their way from roughly the center of the cell to the plasma membrane? The microtubules solve that problem. Vesicles containing proteins are shuttled between the center and the periphery of the cell. Click the image to watch the movie.

These vesicles are carried by the motor proteins kinesin and dynein, that walk along the microtubules. Motor proteins are molecules that use chemical energy to produce force and then movement. They are molecular scale machines.

Challenge your common sense: How likely simple diffusion of organelles is to play a relevant role in 1 meter long neurons?

A good example of how relevant this mechanism is can be seen in the nervous system. In humans some neurons span from the base of the brain to the tip of the fingers (about 1 meter long). Proteins are synthesized in the part of the cell that is near the brain but many of those proteins are needed 1 meter away. The microtubules provide the connection.

How they do it?

Cytoskeleton is a rather misleading word because it leads us to think that its components are static. Microtubules are very dynamic indeed. Cells change internally and change in shape. If microtubules are to be useful, they need to know the cell. This is achieved by a mechanism of exploration called dynamic instability. Videomicroscopy shows that individual microtubules are constantly changing between phases of growth and shortening. Paclitaxel binds to microtubules and although it allows growth, it prevents shortening. This kills dynamic instability preventing cell division.

Characterizing microtubule dynamics:

Classically, microtubules have been studied experimentally, observing them under a microscope and recording the speed at which individual microtubules grow/shorten and how often they switch between those phases. That is called quantitative characterization. It is easy to see in their behavior that their exact position or speed is highly unpredictable. Microtubules clearly seem to follow random laws. Any scientific tool used to predict microtubule behavior and its dynamics should take into account that unpredictability.

One such way to study microtubule dynamics is by modeling. Briefly, a model is a tool that allows the scientist to have predictive power. A simple equation could be a model. Take distance = velocity * time. If you know that an object moves at 100 meter/hour for 2 hours then you can predict exactly (deterministically) that the object will move 200 m. Lets take a very simple random process now. If you roll a dice what will be the outcome? It can't be predicted exactly but it can be foretold probabilistically. The probability of the outcome being, 3 for instance, is 1/6. The equation would be P(3)=1/6. We can accurately predict where Jupiter will be 10 years from now. We cannot predict exactly where a microtubule will be 10 minutes from now. Planet orbiting behaves deterministically but microtubules behave stochastically, like the weather or the stock market.

Fig 4: Types of processes. Left: Planet orbiting, a typical deterministic process. Right: Stock exchange prices, a typical stochastic process.)

 Because microtubules behave so randomly, if we want to understand them through modeling, we have to model them stochastically.

Challenge your common sense: Can you name a series of natural processes and classify them as deterministic or stochastic?

Why modeling?

Deterministic or stochastic, the important thing is its foretelling power. We need to be able to predict how much oxygen an astronaut will breath, how much food a baby will eat, how a drug will be metabolized, how much energy we will need for winter. We better be able to predict and we better do it quantitatively. We actually do it most of the time for simple problems.

Modeling allow us to try or test what happens in a fashion that is faster, cheaper and without risks. It is through testing of ideas and careful interpretation of results that we gain understanding of a biological mystery. In this work, we focus in particular in mathematical modeling.

Challenge your knowledge: Can you compare mathematical modeling to another type of modeling and state what would the be the advantages and disadvantages?

A closer look at microtubules

Microtubules are tubular (25 nm in diameter) polymers made up of tubulin units (monomers). Polymerization occurs by incorporation of monomers to the ends. There is no gain or loss of monomers via the body of the microtubule, only the ends. Although both ends of the microtubule are dynamic, here we'll only focus on the most dynamic of them, the so called plus-end. The other, the minus-end is far less dynamic and attached to a microtubule stabilizing organelle called centrosome.

Tubulin monomers in solution are bound to a molecule called guanosine triphosphate, or GTP. When bound to GTP, tubulin monomers tend to polymerize. A certain time after polymerization, these GTP gets hydrolyzed into GDP. This hydrolysis results in a structural change in the tubulin molecule so that the monomers tend to get released back into the solution. The way we currently understand dynamic instability is that this delay of GTP hydrolysis makes the microtubule a polymer of two behaviors: growing and shortening.