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The most important thing we found in our research was that if you take two locusts coming in one direction and one in the other then these two locusts can turn this individual, and if you don't include this' two meets one' interaction then you find that you can't replicate these startling switches of behavior that you see in the locusts, the same sorts of things that you might see in flocks of starlings changing direction quickly or in schools of fish.
Traditionally people thought that cells didn't make it to the front of embryos to pigment the belly because they just weren't migrating fast enough, what we've been able to show through our studies is that actually, if anything, cells in piebald animals migrate faster but they're just not proliferating enough. They're not making enough daughter cells to colonize - or cover - the whole region of the skin that needs to be covered by the time the pigmentation pattern is set down.
What we've been able to tease out from the mathematical model is it's not necessarily that these cells are migrating in a directed way, actually these cells are diffusing, there's no direction to their migration. It's like when you put a drop of milk into a cup of coffee that you haven't stirred. Eventually that milk will be spread evenly throughout your coffee, and these cells are doing the same sort of thing - they're moving in an undirected manner and eventually, slowly, they manage to fully colonize the skin of this animal.
Piebaldism is actually a disease, it's caused by cells in the early embryo failing to migrate correctly.... failing to get to the right place. The cells which we're interested in, that cause piebaldism, are called melanocytes and they're responsible for pigmentation of hair and of the skin. These cells start at the back of the embryo and they try to migrate round through the skin and cover the whole of the( embryo's) skin. When they fail to do that properly you tend to get regions of skin or hair which are lacking in pigment, often regions at the front of an animal. This is common in cats...... tuxedo cats, and it's also common in horses and pigs and even in humans.
By trying to understand piebaldism, which doesn't have a particularly severe manifestation, so it's just a change in pigmentation, we can try to use the same techniques that we've developed to try and model and understand these other more serious diseases, which effectively are caused by similar mechanisms - cells not migrating properly in the early embryo.
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