Three lessons about diffusion gradients: These notes are from a web page written for Biology 441, but the same ideas were covered in Biology 446 on October 30, and also referred to in later lectures. Embryonic development needs long-range coordination of cells' differentiation and geometric rearrangement. Most theories about spatial coordination are based on hypothetical diffusion gradients. For example, Lewis Wolpert's concept of "positional information" requires three perpendicular gradients. The main theories about regeneration in hydra and flat-worms also assume diffusion gradients. So do theories about limb bud development and regeneration. Researchers tend to assume that chemical patterns need to form first, and that cells can only respond to pre-existing gradients of chemicals. Actual concentration gradients of transcription factor proteins have been discovered in Drosophila embryos. The best example is the "bicoid" protein, which forms an anterior-posterior concentration gradient. Also, the "dorsal" protein redistributes into nuclei in a gradient-like pattern. And don't forget Hox genes, that also get transcribed in gradient-like patterns, that are co-linear with the spatial locations of hox genes on chromosomes. I wrote computer programs to simulate the formation of diffusion gradients. These programs taught me some unexpected lessons. Lesson #1) What is the algorithm for simulating diffusion? * Visualize a square grid of mail-boxes, each box with a number in it. (Although I started by using hexagonal neighbors, it turns out not to matter). ** For each box, add up the numbers in the eight neighboring boxes. *** Divide this sum by 8, to get the average. **** Compare this sum with the number in the central mailbox. ***** Change the central number to make it closer to the sum of the neighbors. ****** Repeat...repeat...repeat Two computer simulations of this: number_diffusion_1 number_diffusion_2 Also remember The Parable of the Nearsighted Conformists and the Bald Professor, which was told in class. Any variable that equilibrates repeatedly will create gradients of amounts.   Lesson #2) Chemical concentrations aren't the only quantities that behave according to this algorithm. The point is that you can get identical, indistinguishable gradients from any variable whose amounts change to become closer to the average amount at their neighboring locations. Population densities of cells could obey the same algorithm, & make gradients. Tensions in extracellular matrix are also capable of "diffusing". Lots and lots of properties are able to behave as if diffusing. Lesson #3) What else can make spatial gradations, as if diffusing? -> Imagine a row of genes, adjacent to each other on a chromosome? Gene_A; Gene_B; Gene_C; Gene_D ;Gene_E; Gene_F; Gene_G; Gene_H; -> Let each cell compare itself with its 8 adjacent cells.    Cells can then obey any diffusion-like algorithm:    Any cell transcribing the same genes as its neighbors, doesn't change.   A cell transcribing genes adjacent to its neighbors, don't change.   Cells transcribing non-adjacent genes, change to express adjacent genes. The Big Lesson: Patterns that look exactly like diffusion gradients can be produced by repeated local interactions. Chemical diffusion is only one of many different methods for generating geometrical patterns.