Why is it so hard to separate isotopes? I was reading on Wikipedia that heavy water in large amounts is toxic to eukaryotic cells because certain physical properties of deuterium are different enough from those of common protium to disrupt the process of mitosis by which the cells divide.
This brought a question to my mind: if different isotopes of an element behave so differently already at biological temperatures and pressures—as to account for the life or death of a cell like in the case of hydrogen—then why is it so difficult to separate those isotopes in a laboratory? Why is a chemical process similar to what happens during cell division not suitable to separate deuterium from protium, and instead all isotope separation methods normally used are so energy expensive (gas centrifuges, calutrons, etc.)?
 A: Heavy water is easy to separate from regular water because the difference in mass is quite large. The molar mass of heavy water is 11% heavier that regular water.
However if we take uranium separation, then the percentage weight difference between $^{235}$UF$_6$ and $^{238}$UF$_6$ is only 0.9%, so the relative difference is far smaller.
So it's a lot harder to enrich uranium than it is to extract heavy water. That's why a kg of heavy water costs in the range of £100 to £1,000 depending on the purity, while a kg of $^{235}$U requires the resouces of a nation state to produce.
A: The key difference is the complexity scale. In a typical every day reaction involving water, the process is thermodynamically driven; the difference in free energy between the reactants and products is much greater than any effect the extra neutron may have. In short, things happen mostly because there is a loss of energy or gain of entropy; and all the intermediate states are simple enough so they can be equally easily accessed.
As an example, if you have two ions dissolved in water reacting, the differences between normal and heavy water will make them collide at slightly different speeds, and that will yield a tiny difference in the reaction rate. But the process is so simple that it is robust to slight changes in the initial conditions.
On the other hand, in a biological process, we have so much more going on. Let's take a much simpler example: the folding of a protein. Your typical protein is a chain of a few hundred aminoacids (a few thousands atoms). In order to perform its biological function, it has a complex and very determined 3D structure. Anfinsen showed that if you leave an extended protein in water, it will fold itself into a compact structure called the native structure. The interesting bit (and he got a Nobel Prize for this) is that this native state is always the same, this is the structure that allows the protein to function in the cell.
In order to reach this compact shape, among other things, the protein has to expel the water. This process is driven by both kinematics and thermodynamics: close aminoacids create thermodynamically beneficial hydrogen bonds, but first they have to get close enough. This cannot be achieved just by random thermal fluctuations, therefore, there is a kinematic component (how we get there is as important as where we go). Now, moving through the heavy water is different, and we may not reach the same destination. Indeed, water is so important that when doing Molecular Dynamics simulations, the biological complex is placed in a large box full of water, and a large portion of the computer time is spent just simulating the otherwise unexciting movement of these molecules.
The moment one of the myriad of complex molecules in the cell cannot fold correctly, the cell has a problem. The most famous example are prions: proteins that are missfolded, and perturb the natural function of the cell.
Unfortunately, this is useless for the purpose of separating heavy water. Even if you managed to separate "working" proteins with a natural isotope $^{235}U$ and "faulty" ones with the heavy version $^{238}U$ through some complex mechanism, you would still have to extract that particular isotope from the protein. 
A: The problem with using a chemical approach is that isotopes have nearly identical chemical properties.  Anything you can do with water can be done identically with heavy water.  The only real differences are mass and any radioactivity the isotope provides.  Thus the only known effective way to separate isotopes is to rely on mass differences.  Unfortunately, the differences in behavior due to mass is well below thermal noise in most situations, so we have to rely on exotic tools like centrifuges to increase the effect of mass differences,
