What has always attracted me to developmental biology is the ability to see the unfolding of pattern—simplicity becomes complexity in a process made up of small steps, comprehensible physical and chemical interactions that build a series of states leading to a mostly robust conclusion. It's a bit like Conway's Game of Life in reverse, where we see the patterns and can manipulate them to some degree, but we don't know the underlying rules, and that's our job—to puzzle out how it all works.
Another fascinating aspect of development is that all the intricate, precise steps are carried out without agency: everything is explained and explainable in terms of local, autonomous interactions. Genes are switched on in response to activation by proteins not conscious action, domains of expression are refined without an interfering hand nudging them along towards a defined goal. It's teleonomy, not teleology. We see gorgeously regular structures like the insect compound eye to the right arise out of a smear of cells, and there is no magic involved—it's wonderfully empowering. We don't throw up our hands and declare a miracle, but instead science gives us the tools to look deeper and work out (with much effort, admittedly) how seeming miracles occur.
One more compelling aspect of development: it's reliable, but not rigid. Rather than being simply deterministic, development is built up on stochastic processes—ultimately, it's all chemistry, and cells changing their states are simply ping-ponging through a field of potential interactions to arrive at an equilibrium state probabilistically. When I'd peel open a grasshopper embryo and look at its ganglia, I'd have an excellent idea of what cells I'd find there, and what they'd be doing…but the fine details would vary every time. I can watch a string of neural crest cells in a zebrafish crawl out of the dorsal midline and stream over generally predictable paths to their destinations, but the actions of an individual melanocyte, for instance, are variable and beautiful to see. We developmental biologists get the best of all situations, a generally predictable pattern coupled to and generated by diversity and variation.
One of the best known examples of chance and regularity in development is the compound eye of insects, shown above, which is as lovely and crystalline as a snowflake, yet is visibly assembled from an apparently homogenous field of cells in the embryo. And looking closer, we discover a combination of very tight precision sprinkled with random variation.
That compound eye is even more precisely organized when you look below the surface. Each facet is a structure called an ommatidium, or little eye, and each has its own collection of cells. It's ringed with a set of supporting cells, pigment cells, and mechanosensory bristle cells, and capped with four cells that make a lens. The lens focuses light on photoreceptor cells. There are exactly 8 of them, R1-R8, and each has a rod-like organelle called the rhabdomere, in red in the diagram below, which is the actual light-sensing part of the cell.
When you look at a section through the eye the rhabdomeres are visible as dark spots with a characteristic orientation—look at the repeating "
" pattern of 7 dots in the electron micrograph to the left (you see 7 instead of 8 because the central pair, R7 and R8, are stacked one on top of the other, so you only see one in a single plane of section). Notice how uniform those rhabdomeric spots are—every one has the same arrangement, and the same orientation, with one consistent difference. All the ommatidia in the top half look like , while every one in the bottom half is flipped upside down (
), and if you look carefully, you can probably figure out where the equatorial dividing line falls.
The whole assembly is going to form a visual processing device, so this specific organization is going to contribute to visual acuity. Each ommatidium has a lens that focuses an image of the world on those 8 photoreceptors, and each photoreceptor sees a specific small spot of the visual field. Different, adjacent ommatidia will see the same spot, but it will fall on a different rhabdomere in each one, in a predictable pattern—the diagram below shows in red which rhabdomeres would see the same point in the visual field.
The specificity goes remarkably deep: each of those red rhabdomeres projects an axon into the fly's brain that find each other and synapse with the same cell in the lamina. The whole thing has an intricacy that makes a human-made watch look like clumsy hackwork. You might even say, if you found a fly eye upon a heath, that you could not imagine how something so beautiful and perfectly arranged and organized could possibly have come into existence without some superhuman engineering.
Except us developmental biologists, of course: the fly eye is an extremely well studied developmental system, and we know that it is assembled by unthinking cellular processes with no design or engineering required.
That splendid organization emerges from an initially uniform sheet of cells, the eye imaginal disk. It arises progressively, too, in tidy order from the posterior edge to the front, so when we look at a slice of the eye, like that below, we actually see all the developmental steps at once, from the earliest, youngest parts at the front of the eye (to the left in this picture), to the progressively more mature pieces as we look towards the right.
The process begins with a wave of synchronized cell divisions sweeping from posterior to anterior. As cells enter the mitotic cycle, they tend to hunker down deep in the epithelial layers, and when all the cells in a region divide at the same time, that region dimples downward. When a whole line of cells divide at the same moment, you get a furrow forming—the morphogenetic furrow. After the cells finish, they pop back up, and the next row of cells to the anterior begin their divisions.
This is easy to understand: the cells in the fly eye are doing The Wave. After the wave has passed, cells form small clusters and signal each other; one cell sets itself apart and begins to differentiate into the R8 cell, and recruits two neighbors to form the R2 and R5 cells. Subsequently, R3 and R4 are drawn in, then R1 and R6, and finally, R7. The cells all have the same orientation to one another (later, the clusters rotate 90° one way in the upper half of the eye and 90° the other way in the lower half, to generate the mirror symmetry). It's all quite mechanical and reliable, mediated by a small set of genes; one common sort of experiment is to knock out a gene involved in these pathways, and see that some of the later cells fail to form in the absence of a signal, and so we know that genes like Notch and boss and rough are involved in particular steps in the process.
So, a series of specific molecular interactions establish the regularity of many features of the fly eye. It's not all rigid and deterministic, however, and some features are set up randomly.
In particular, flies have rhabdomeres specialized for color vision, analogous to our system of cones and rods. We have three kinds of cone cells which express different kinds of opsin proteins (the visual pigment) that make them specific to different wavelengths of light, and we also have rods, which are sensitive to a broader range of wavelengths and detect intensity rather than color. In the fly ommatidium, most of the rhabdomeres, R1-R6, the ones arranged around the outside of the structure, are like our rods—they don't detect color, but just shape and brightness. The central pair, R7 and R8, express specialized opsins that are tuned for different wavelengths. Some (about 30%) of the R6-R8 pairs express an opsion called Rh3 in the R7 cells, and Rh5 in R8; these are called 'pale' ommatidia, and are specialized to detect short wavelengths. Most of the remaining ommatidia Rh4 in R7 and Rh6 in R8, the 'yellow' ommatidia, and are sensitive to longer wavelengths. Which set of opsins will be expressed in a particular pair of central rhabdomeres is determined randomly, so what you see is a variable salt-and-pepper arrangement of 'pale' blue receptors sprinkled among a sea of 'yellow' photoreceptors, as shown in the wild type diagram below. (There are also some special pink photoreceptors in the dorsal rim; these are ommatidia where both R7 and R8 express Rh3, in a set of cells used for detecting the plane of polarized light.)
a, Three subtypes can be identified on the basis of molecular markers: 'pale' (blue), 'yellow' (yellow) and DRA (pink) ommatidia together form the wild-type retinal mosaic (schematic representation;dorsal is to the top). b, Schematic representation of the ss phenotype in R7 cells. c, Transverse section through a wild-type (WT) adult eye (left panel; dorsal is to the left). The arrow denotes the DRA. Ratio of R7 opsins in a wild-type whole-mount adult retina (right panel; dorsal is to the top) stained for Rh3 (red) and Rh4 (cyan). d, Transverse section through a ssD115.7 whole-mutant adult eye (left panel). Rh3 (red) is expanded and Rh4 (cyan) is completely lost. Opsin expression in a mutant whole-mount adult retina is also shown (right panel).
The random distribution of the color receptors is regulated by a particular protein, spineless. The default fate for an R7 receptor is to express the Rh3 (blue) opsin, but the presence of the spineless protein above a certain level is sufficient to induce it to express Rh4 instead. In a mutant in which no spineless is present, the R7 cells all make the blue protein—this would be a kind of color blind fly.
When such a mutant eye is stained for the Rh5 and Rh6 gene products, which are expressed in the R8 receptor, there is a similar result—the eye has gone almost entirely blue.
Whole-mount retina from a ss mutant fly. The pR8 subtype (Rh5, blue) is expanded to almost all R8 cells (Rh6, green).
Complementary experiments with a gain-of-function mutant that turns on excessive spineless expression also has an expected result: the whole eye turns yellow as Rh3 is suppressed and Rh4 is activated, and we get a fly with a different kind of color blindness.
What is happening is that during pupation, the fly turns on a brief pulse of spineless before the expression of the opsin genes; different cells acquire different levels of spineless expression, in red below, and any spineless activity above a threshold leads to that ommatidium forming the Rh4/Rh6 opsin combination and becoming a 'yellow' type of receptor. Spineless is acting as a binary switch controlled stochastically to produce a random distribution of cell types.
Top: transient expression of sseye-Gal4 (red) during pupation before the onset of opsin expression (blue). Bottom: variable expression of ss (different tones of red) in R7 cells.
Although the overall effect is random, there are some specific interactions. The R8 opsin type is correlated with the R7 opsin type, so the first step is a choice made by R7 under the influence of spineless; R8 cells default to expressing Rh7, except that the Rh3-expressing R7 cells can instruct R8 to express Rh5.
Left: the ss data suggest that ˜70% of the R7 cells get promoted into the yR7 fate (Rh4, yellow) by expressing ss. The pR7 subtype (Rh3, red) therefore represents the R7 'default state'. Right: in ss-positive yR7 cells, the ability to communicate with the underlying R8 is abolished, resulting in y ommatidia as the R8 default state is expression of Rh6 (green). Only pR7 retain the competence to instruct the pR8 fate (Rh5, blue).
I know, it's all a little bewildering and complicated—intensely complicated with all kinds of interactions between cells. However, when you dig into it and explore the literature, what you find is the successful application of a reductionist program of study, with each piece of the story a fully comprehensible and actually rather simple product of a molecular/cellular interaction. Complexity is the result of simple, repetitive, iterated processes which can yield regularity and chance variation…but at no point are there any events beyond local chemistry and cell biology.
Lawrence PA (1992) The Making of a Fly: The Genetics of Animal Design(amzn/b&n/abe/pwll). Blackwell Publishers, Cambridge.
Wernet MF, Mazzoni EO, Çelik A, Duncan DM, Duncan I, Desplan I (2006) Stochastic spineless expression creates the retinal mosaic for colour vision. Nature 440:174-180.
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Nice post. This reminded me of the Gerhart & Kirschner's Cells, Embryos & Evolution book where they have a small but interesting section on ants -- to quote "..although the swarm of ants seem organized and directed, its morphology depends not on leadership but on the individual behaviors of the ants, often with little communication among them". It gets more interesting when the authors then compare the morphology of ant foraging patterns to that of a Purkinje cell -- and the similarities are striking. Evidence that complex behavior generated using simple rules occurs across scales? Computer simulations seem to confirm that -- there are a ton of them beyond Conway's Life. Generating complex patterns in Cellular Automata (like the Life game) is a matter of finding the right "rules" that govern interactions between individuals. Not sure if such simulations have found much acceptance among the biologists though....
Emergence is a fascinating topic, the relatively simple behavior of individual cells/ants leads to a complexity which is not evident from looking at the parts.
This is exactly what ID activists claim cannot happen under chance and regularity without some external (wink wink) input. That the external input need not be intelligent seems lost on many ID activists.
AJ
In AI area it's called Swarm Intelligence. And I'm really interesting...But as far as I know we still haven't got a theoretical model how to generate truly complex behavior with limited number of simple rules. It's a core issue.
PZ Myers
You're great at this post. Though when you say "simple product of a molecular/cellular interaction" it's kind of strong hypothesis. To make it strong evidence you have to build a reductionist model - based on physics (am I right?). But for now it's just a goal. And these rules - where are they from? - Embryogenesis was included in 125 Big Questions by Sciense (2005). And you say everything is fully comprehensible here....
There are bits and pieces where the molecules are still being tracked down, but I don't think it's a particularly dazzling hypothesis to say that we're going to find genes and proteins interacting all the way down.
What else would you propose is involved?
Wow, that's lovely. You're giving this mathematician biology envy.
Hi nature-wonder,
I am familiar with swarm intelligence -- however that whole track seems to be very application oriented, and the technique is treated as just a better way of finding solutions for problems (say, business operations). The inspiration comes from the the effectiveness of decentralized behavior of social insects, but beyond that it is just applied problem solving. I dont know how many researchers try to design computer models of biological systems to try and find these "rules". Stephen Wolfram ("A New Kind of Science") does his bit in his book (specifically the chapter "Mechanisms in Programs and Nature") to find CA rules for various biological features, but I am not sure how his ideas hold up...
PZ Myers
I don't know, I'm just wondering...As I see it, biological systems are considerably those with memory and rather non-markov processes. And a communication among cells should partly regulate such collective dynamics. It can be ultrasonic for example...If so and history & information flows matters - then emergence is hardly reducable only to molecule interactions. Or more precisely: we won't be able to describe it in molecular terms only. - But I may be wrong in this view.
It's a bit like Conway�s Game of Life in reverse, where we see the patterns and can manipulate them to some degree
Interesting. Stephen Wolfram in A New Kind of Science writes: (page 1001):
Observing nature
In her unclothed pulchritude
Brings light to the eye...
Compound Eye Candy
NatureSelectedMe, quoting Wolfram:
"My own work on cellular automata in the ealy 1980s showed that great complexity could be generated just from simple programs, without any process like natural selection."
I suspect there is an implicit selection process in cellular automata studies. Rule sets that don't produce interesting patterns or complex results are boring and receive very little attention. Rule sets that display emergent properties survive because they are interesting enough to cover the cost of the researcher's attention.
AJ
Agree with you. Few people try to dig deep...bit it seems there are common principles. Social insects have them - cells have them - communities have them. It's the way how simplicity turns to complexity. I hope the problem will be resolved at the theoretical level someday.
Virge: Wolfram exhaustively examined the possible one-dimensional two-color cellular automata.
Most of them he was able to fully examine and address very briefly.
Some displayed simple nesting patterns - which look complicated, but can be described mathematically in a simple fashion.
Some displayed fully emergent behaviour (one was proven to be turing-complete, in fact).
And some displayed RANDOM behaviour - as in it was essentially impossible to predict anything about the result short of running the successor function.
So. Yes, the simple ones get little attention. But Wolfram's point was that the complex ones can be a very simple ruleset - and a lot of speckled patterns seen in nature, for instance, look a lot like a pretty simple ruleset in action (with uncertainty etc, but hey.)
So... eh.
I suspect there is an implicit selection process in cellular automata studies.
That could very well be true. If you've ever played the game of life there are a lot of boring patterns.
speaking of grasshopper ganglia (that phrase may be a first, ahh the infinite possibilities of language), I was just citing "myers and bastiani, 1993" in a paper and did a double take...it was pz myers. all this time i've been reading pharyngula i didn't know i had read your research too...
Dang! I must stop coming here: I get envious of you developmental biologists taking all the really cool photos....
Would you mind not posting such interesting articles, so that I don't get lured here? :-)
Bob
Thanks Michael. That gives me a better perspective on Wolfram's statements.
Wolfram:
Wolfram is both overstating the claims of biologists and underestimating the importance of natural selection.
It's certainly true that many of the forms seen in nature are a consequence of CA-like emergence and not natural selection. Some, like cracks in dried mud, clearly aren't selected for. Others, like the shape of bacteria colonies, might (I'm not sure) confer some advantage on individual bacteria, but are also constrained to the kinds of forms that can be produced by such a distributed process.
On the other hand, when a CA-like emergence process produces, say, a kidney and that kidney just happens to play a vital role in a multicellular organism, this is not just something that happens because CA produce complex results. In this case, the CA produce a particular set of complex results that is functionally correlated to other parts of the organism in a way that cannot be explained by the development process alone. The best available explanation for this correlation is natural selection.
I'm pretty sure that there is a germ of truth in Wolfram's statement. Namely, nature is an opportunistic co-opter of the kinds of forms most readily produced by natural emergent systems. The set of organisms that can develop from a single eukaryote cell given some particular DNA is amazingly robust, but it's probably not the set of every physically realizable thing (*). So when looking at the forms that show up in the development process: (a) Wolfram's right that some are there because they are the direct result of the development process (b) Wolfram's wrong in thinking that this is a complete explanation, because it does not address why these forms are functionally related to other parts of the system that are not developmentally related; that requires natural selection to explain.
Virge:
Someone else addressed this already with respect to Wolfram's early work, but the point to consider is that so many CA rules produce "interesting" behavior that it does not require a lot of selection. For instance, David Eppstein has catalogued semi-totalistic 2D rules that produce "gliders" like Conway's Game of Life http://www.ics.uci.edu/~eppstein/ca/. The probablity of picking a rule with gliders out of all 2^18 semi-totalistic rules is reasonably high. If you restrict things to those with birth on 3 neighbors like Life, for instance, you can see from this map that having gliders is more likely than not: http://www.ics.uci.edu/~eppstein/ca/map.html
(*) The only exception I can think of is that the DNA defines an intelligent organism and some kind of instructions to start building extracellular components like bicycles and electron microscopes. I think that this could be separated from the development process, which seems to be a robust but limited kind of "universal constructor." Anyway, personally, I have trouble picturing something like an electron microscope developing from an embryo. I would never argue from incredulity, so who knows, but it doesn't fit with the other kinds of things that we've observed developing from embryos.
Paul: You're misunderstanding Wolfram's statement. Or at least, how I understood it based on the examples he was providing.
His examples in New Kind of Science were things like pigmentation patterns - and his claim was that mixed patterns tend to be selectively advantageous over solid patterns, and that the specific NATURE of the pattern (speckles vs lines, horizontal vs vertical, etc) is far more likely to be comparatively irrelevant.
Basically, what it seemed to me that he was saying was that a lot of complex phenomenon in biology are adaptive as a whole, but that we should be wary of ascribing adaptivity to the DETAILS of these phenomena, because (he continues to claim), a lot of them stem from simple rules, and evolution can't operate on the details - because it's impossible to make a "small change".
(If your pigments are showing up as the result of a CA-like process... how do you change them from a speckled pattern to a linelike pattern, say?)
Michael "Sotek" Ralston:
I admit I am looking at the quote without any context. It still strikes me that he is constructing a strawman with respect to what biologists think. I'm pretty sure any biologist will agree that some things are a certain way because they confer an advantage, and other things are a certain way because that's just what happens during the development process (PZ has made this point on several occasions). Based on your comment, it seems Wolfram also agrees, and would not claim that the functional correlation between distinct parts of an organism could happen just through CA-like complexity without natural selection.
Turing, by the way, was the first person I can think of to propose CA-like models for stripes and spots. This was in his paper "The Chemical Basis of Morphogenesis" (1953) He actually used differential equations in keeping with more standard math of the time, but 2-dimensional differential equation integration at any given precision is much like carrying out CA rules.
Wolfram's case would be more compelling if he gave a specific example of a biologist claiming that the precise nature of some variegated pattern was always selected for. E.g., does any biologist claim that those shells with the Sierpinski-gasket like patterns are the result of selecting for exactly that pattern? I agree that there is no a priori reason to expect patterns to be solid, periodic, or what have you. In fact, there are some good reasons to expect them to look like CA output or fractals.
I would also add that in the case of mimicry (e.g. Viceroy and Monarch butterflies) there is an advantage to producing a pattern down to its details and natural selection is the only plausible mechanism explaining how the patterns could be so similar, although it is true that neither butterfly could easily produce such a pattern if it were not possible to realize it through the kinds of distributed cell interactions we associate with CA.