Three lessons about diffusion gradients:   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, Turing's mechanism depends on diffusion gradients; and 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     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. Analogy to caloric: Until the mid 1800s, physicists firmly believed that heat must be a chemical substance, which they called "caloric". The evidence was that heat diffuses. What else diffuses besides chemicals? (What else floats besides wood? A duck!)     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. Let's not make the same mistakes as physicists did with "caloric" and "the ether". Triple-branching of 180-degree-rotated limb grafts is an example of diffusion-like filling-in of intermediate behaviors of cells.   original limb ABCDEFGHIJKL rotated graft: ABCD/HGFE/IJKL "regeneration" ABCDefgHGFEfghIJKL D and H didn't want to be adjacent to each other; Neither did E and I. But H is happy being between two Gs, one of them newly made. (Even if H apparently doesn't care not having any nearby "i".) This must be telling us something profound about how regeneration works. Being next to a "wrong" neighbor is what gets fixed. (by replicating extra mirror-image duplicates of "correct" neighbor.) But tissues are NOT disturbed by absence of a normal neighbor. They hate discontinuity! But they don't mind duplication!! This must be telling us something about underlying control mechanisms. (But it sure isn't easy to put into words whatever it's telling us.) One question is how cells detect being next to "wrong" neighbors.. Maybe "wrongness" consists of which hox genes you and they transcribe? Suppose each cell "knows" which hox genes it is itself transcribing, and also detects which hox genes are being transcribed by nearby cells. You are happy when your neighbors transcribe hox genes that are adjacent on your chromosomes to the hox genes that you, yourself are transcribing. But it's intolerable for nearby cells not to transcribe hox genes whose positions on your chromosomes close to whatever hox genes you are transcribing. (Discontinuity!) I hope you will think about these issues, but not worry if you can't devise answers. One final note: Genetic linkage was discovered years before Morgan figured out that its explanation was the relative positions of genes on the chromosomes.

 

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