Steve Pinker’s hair and the muscles of worms

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I've been guilty of teaching bean-bag genetics this semester. Bean-bag genetics treats individuals as a bag of irrelevant shape containing a collection of alleles (the "beans") that are sorted and disseminated by the rules of Mendel, and at its worst, assigns one trait to one allele; it's highly unrealistic. In my defense, it was necessary — first-year students struggle enough with the basic logic of elementary transmission genetics without adding great complications — and of course, in some contexts, such as population genetics, it is a useful simplification. It's just anathema to anyone more interested in the physiological and developmental side of genetics.

The heart of the problem is that it ignores the issue of translating genotype into phenotype. If you've ever had a basic genetics course, it's quite common to have been taught only one concept about the phenotype problem: that an allele is either dominant, in which case it is expressed as the phenotype, or it's recessive, in which case it is completely ignored unless it's the only allele present. This idea is so 19th century — it's an approximation made in the complete absence of any knowledge of the nature of genes.

And the "one gene, one trait" model violates everything we do know about the phenotype and genotype. Every gene is pleiotropic — it influences multiple traits to varying degrees. Every trait is multigenic — multiple genes contribute to the expression of every phenotypic detail. The bean-bag model is totally inadequate for describing the relationship of genes to physiology and morphology. Instead of a bean-bag, I prefer to think of the genome as comparable to a power spectrum, an expression of the organism in a completely different domain. But I wrote about that previously, and I'll make this explanation a little simpler.

Here's the problem: you can't always reliably predict the phenotype from the genotype. We have a skewed perspective on the problem, because historically, genetics has first searched for strong phenotypes, and then gone looking for the genetic cause. We've been effectively blind to many subtle phenotypic effects, simply because we don't know how to find them. When we go the other way, and start by mutating known genes and then looking for changes in the phenotype, we're often surprised to discover no detectable change. One of the classic examples is the work of Elkins (1990), who found that mutating a neural cell adhesion gene, Fasciclin I, did not generate any gross defects. Mutating another gene, a signal transduction gene called Abelson tyrosine kinase, similarly had no visible effects. Mutating the two together, though — and this is a major clue to how these strange absences of effect could work — did produce gross and obvious effects on nervous system development.

Providing another great example, Steve Pinker examined his own genome, and discovered that his genes said he was predisposed to be red-haired and at high risk for baldness. If you've seen Steve Pinker, you know he's neither.

How can this be? As any geneticist will tell you, the background — the other alleles present in the organism — are important in defining the pattern of expression of a specific gene of interest. One simple possibility is that the genome contains redundancy: that a trait such as adhesion of axons in the nervous system or the amount of hair on the head can be the product of multiple genes, each doing pretty much the same thing, so knocking out one doesn't have a strong effect, because there is a backup present.

pairwise.jpeg
Genetic interactions provide a general model for incomplete penetrance. Representation of a negative (synergistic) genetic interaction between two genes A and B.

So Steve Pinker could have seen that he has a defective Gene A, which is important in regulating hair, but maybe there's another Gene B lurking in the system that we haven't characterized yet, and which can compensate for a missing Gene A, and he has a particularly strong form of it. One explanation for a variable association between an allele and the phenotype, then, is that we simply don't have all the information about the multigenic cause of the phenotype, and there are other genes that can contribute.

This doesn't explain all of the observed phenomena, however. Identical twins who share the same complement of alleles also exhibit variability in the phenotype; we also have isogenic animal lines, where every individual has the same genetic complement, and they also show variability in phenotype. This is the problem of penetrance; penetrance is a genetics term that refers to the likelihood that an individual carrying an allele will actually express the phenotype associated with that allele…and it's not always 100%.

Again, the explanation lies in the other genes present in the organism. No gene functions all by itself; its expression is dependent on a cloud of other proteins — transcription factors, enhancers, chaperones — all of which modulate the gene of interest. We also have to deal with statistical variation in the degree of expression of all those modulatory factors, which vary by chance from cell to cell, and so the actual degree of activation of a gene may follow a kind of bell curve distribution. In the cartoon below, the little diamonds represent these partners; sometimes, just by chance, they'll be present in sufficiently high numbers to boost Gene B's output enough to fully compensate for a defective Gene A; in other cases, just by chance, they're too low in concentration to adequately compensate for the absence.

penetrance.jpeg
Genetic interactions provide a general model for incomplete penetrance. A model for incomplete penetrance based on variation in the activity of genetic interaction partners.

What the above cartoon illustrates is the concept of developmental noise, the idea that the cumulative total of statistical variation in gene expression during development can produce significant phenotypic variation in the absence of any differences in the genotype. Developmental noise is a phrase bruited about quite a bit, and there's good reason to think it's valid: we can see quantitative variation in gene expression with molecular techniques, for instance. But at the same time we have other concepts, like redundancy and canalization, that work to buffer variation and produce reliable outputs from developmental processes, so we don't have many good examples where we can directly correlate subtle variation at the molecular level with clear morphological differences.

To test that, we have to go to simple animal models (it turns out that Steve Pinker is a rather intractable experimental animal). And here we have a very nice example in the nematode worm, C. elegans. In these experiments, the investigators were dealing with an isogenic strain — the genetic background was identical in all of the animals — raised in a uniform environment. They were looking at a mutant in the gene tbf9, which causes defects in muscle formation, but only 50% penetrance; that is, half the time, the mutants appeared completely normal, and the other half of the time they had grossly abnormal muscle development.

devnoise.jpeg
Genetic interactions provide a general model for incomplete penetrance. Inactivation of the gene tbx-9 in C. elegans results in an incompletely penetrant defect, with approximately half of embryos hatching with abnormal morphology (small arrow).

See the big red question mark? That's the big question: can we trace the abnormal phenotype all the way back to random fluctuations in the expression of other genes in the animal? Yes, they can, otherwise it would never have been published in Nature and I wouldn't be writing about it now.

In this case, they have a situation analogous to the Gene A/Gene B cartoons above. Gene B is tbx-9; Gene B is a related gene, a duplicate called tbx-8 which acts as a redundant copy. In the experiments below, they knock out tbx-9 with a mutation, and then measure the quantity of other genes in the system using a very precise technique of quantitative fluorescence. Below, I've reproduced the entirety of their summary figure, because it is awesome — I just love the idea of being able to count the number of molecules expressed in a developing system. In order to avoid overwhelming everyone, though, I'll just describe a couple of the panels to give you the gist of the work.

First, just look at the top left panel, a. It's a plot of the level of expression of the tbx-8 gene over time, where each line in the plot is a different animal. The lines in black are in the wild type animal, with fully functional copies of bothe tbx-8 and tbx-9, and you should be able to see that there's a fair amount of variation in expression, about two-fold, in different individuals. The lines in green are from animals mutant for tbx-9; it's messy, but statistically what happens when tbx-9 is knocked out, more tbx-8 gene product is produced.

Panel e, just below it, shows the complementary experiment: the expression of tbx-9 is shown for both wild type (black) and animals with tbx-8 knocked out. Here, the difference is very clear: tbx-9 levels are greatly elevated in the absence of tbx-8. This shows that tbx-8 and tbx-9 are actually tied together in a regulatory relationship where levels of one rise in response to reduced levels of the other, and vice versa.

quanttbx.jpeg
(Click for larger image)

Early inter-individual variation in the induction of ancestral gene duplicates predicts the outcome of inherited mutations. a, Quantification of total green fluorescent protein (GFP) expression from a tbx-8 reporter during embryonic development in WT (black) and tbx-9(ok2473) (green) individuals. Each individual is a separate line. a.u., Arbitrary units. b, Boxplot of tbx-8 reporter expression (a) showing 1.2-fold upregulation in a tbx-9 mutant at comma stage (~290 min, P=1.6x3 10-3, Wilcoxon rank test). c, Expression of tbx-8 reporter in a tbx-9(ok2473) background for embryos that hatch with (red) or without (blue, WT) a morphological defect. d, Boxplot of c showing tbx-8 expression is higher in tbx-9 embryos that develop a WT phenotype (blue) compared with those that develop an abnormal (red) phenotype at comma stage (P= 6.1x10-3). e, Expression of a ptbx-9::GFP reporter in WT (black) and tbx-8(ok656) mutant (green). f, Boxplot of tbx-9 reporter showing 4.3-fold upregulation at comma stage (~375 min, P=3.6x10-16). g, Expression of tbx-9 reporter in a tbx-8(ok656) mutant background, colour code as in c. h, Boxplot of g showing tbx-9 expression is higher in tbx-8 embryos that develop a WT phenotype (P=0.033). i, Expression of a pflh-2::GFP reporter in WT (black) and flh-1(bc374) mutant (green). j, Boxplot of flh-2 reporter expression (i) showing 1.8-fold upregulation in a flh-1 mutant at comma stage (~180 min, P=2.2x10-16). k, Bright-field and fluorescence image of an approximate 100-cell flh-1; pflh-2::GFP embryo. Red arrow indicates the local expression of flh-2 reporter quantified for flh-1 phenotypic prediction. l, Boxplot showing higher flh-2 reporter expression at approximate 100 cells for WT (blue) compared with abnormal (red) phenotypes (P=0.014). Boxplots show the median, quartiles, maximum and minimum expression in each data set.

Now skip over to the right, to panel c. All of the lines in this plot are of tbx-8 expression in tbx-9 mutants, and again you see a wide variation in levels of gene expression. In addition, the lines are color-coded by whether the worm developed normally (blue), or had the mutant phenotype (red). The answer: worms with low tbx-8 levels were more likely to have the abnormal phenotype than those with high levels.

Panel g, just below it, is the complementary analysis of tbx-9 levels in tbx-8 mutants, and it gives the same answer.

Obviously, though, there is still a lot of variability unaccounted for; having relatively high levels of one or the other of the tbx genes didn't automatically mean the worm developed a wild-type phenotype. There's got to be something more that is varying. Look way back to the second cartoon I showed, with the little diamonds representing the cloud of transcription factors and chaperone proteins that modulate gene expression. Could there also be correlated variation there? And yes, there is. The authors looked at a chaperone protein called daf-21 that is associated with the tbx system, and found, in mutants for tbx-9, that elevated levels of daf-21 were associated with wildtype morphology (in blue), while lowered levels of daf-21 were associated with the mutant phenotype.

daf21.jpeg
(Click for larger image)

Expression of daf-21 reporter in a tbx-9(ok2473) mutant background. Embryos that hatch into phenotypically WT worms (blue) have higher expression than those hatching with a morphological defect (red) at the comma stage (P=1.9x10-3).

I know what you're thinking: there isn't a perfect correlation between high daf-21 levels and wildtype morphology either. But when they do double-label experiments, and take into account both daf-21 and tbx-8 levels in tbx-9 mutants, they found that 92% of the animals with greater than median levels of expression of both daf-21 and tbx-8 had wildtype morphology. It's still not perfect, but it's pretty darned good, and besides, it's no surprise that there are probably other modulatory factors with statistical variation lurking in the system.

What should you learn from this? Developmental noise is real, and is a product of statistical variation in the degree of expression of multiple genetic components that contribute to a phenotype. We can measure that molecular variation in living, developing systems and correlate it phenotypic outcomes. None of this is surprising; we expect that the process of gene expression is going to be a bit noisy, especially in these transcriptional regulators that are present in low concentration in the cell, anyway. But the other cool thing we can observe here is that having multiple noisy systems that interact with each other can produce a more reliable, robust signal and contribute to the fidelity of developmental outcomes.


Burga A, Casanueva MO, Lehner B (2011) Predicting mutation outcome from early stochastic variation in genetic interaction partners. Nature 480(7376):250-3.

Elkins T, Zinn K, McAllister L, Hoffmann FM, Goodman CS (1990) Genetic analysis of a Drosophila neural cell adhesion molecule: interaction of fasciclin I and Abelson tyrosine kinase mutations. Cell 60(4):565-75.

11 Comments

Pinker is misinterpreting the red-hair result. (23andMe’s analysis is confusing about this trait). His “typical odds of having red-hair” result means that he is not a carrier for the most common red-hair allele.

A red-haired person would show up in the analysis as “greatly increased odds of having red hair.”

This terminology is confusing because 23andMe is treating red-hair as a quantitative trait and not a Mendelian trait.

This is a great example of how complex the relationship between genotype and phenotype can be. It doesn’t mean that genetic variation isn’t important in changing phenotypes. It means that we must consider lots of other factors. Fortunately, we now have the technical ability to investigate these factors in a systematic and powerful way. This adds a whole new dimension to the story of how organisms evolve through genetic changes affecting developmental processes. Whereas creationists would just throw up their hands and claim it was too complicated to understand, real scientists love to investigate these types of mechanisms.

DS said:

This is a great example of how complex the relationship between genotype and phenotype can be. It doesn’t mean that genetic variation isn’t important in changing phenotypes. It means that we must consider lots of other factors. Fortunately, we now have the technical ability to investigate these factors in a systematic and powerful way. This adds a whole new dimension to the story of how organisms evolve through genetic changes affecting developmental processes. Whereas creationists would just throw up their hands and claim it was too complicated to understand, real scientists love to investigate these types of mechanisms.

Yes, there’s clearly a huge role for probabilistic trends in biological evolution.

There are probably some (perhaps briefly existing) examples of mutant alleles that behave in a dominant, 100% penetrance, essentially always lead to a phenotype that is strongly selected against, manner.

Most of the time it isn’t that way. All the alleles, broadly defined, of a genotype, interact with the environment and each other, while often also influencing the environment. Phenotypes can have dysfunctional features, but get lucky even though the odds are against them.

PZ’s Fourier transform idea is not without precedent; although, when applied to a soft-matter, living organism it becomes an analysis of many overlaying patterns. These patters developed at different levels of complexity during the growth of the organism, they are based on different underlying patterns, and many of these are influencing each other giving results that are not the linear superposition of both patterns.

Of course, the precedent is that set by the x-ray crystallography done by Roseland Franklin on the DNA molecule. The x-ray spectra are the Fourier transforms of the actual DNA spatial structure; and they represent the power spectrum of the spatial frequencies in that structure.

The difficulty in going from the power spectrum as seen on the photographs is that the photographs are of the square of the absolute values of the frequencies. Phase information is mostly lost except for that which can be inferred by the brightness of some of the peaks.

The reason one can work backwards from the power spectrum for the DNA molecule to its spatial structure – one does this in all forms of x-ray crystallography – is that one is working backward and forward to untangle a “several-to-one” transform from a relatively robust structure to its power spectrum. A number of closely approximate structures could produce almost indistinguishable power spectra. The trick is to find all the clues in the power spectrum that will direct the analysis to the correct structure.

But the problem gets extremely difficult very quickly if one attempts to look at the power spectrum of a structure that was grown from a relatively simple template such as the DNA molecule by importing atoms and molecules that then find their way into constantly emerging spatial arrays of potential wells during the course of the evolution of the structure. Patterns that emerge later in the development are not by any means related in a one-to-one fashion to the basic underlying structure of the DNA.

The fact that living organisms are soft-matter structures makes the problem far more complex. You can’t have a living organism based on structures that are bound as tightly as, say, salt crystals, or polycrystalline structures such as metal. In such structures, the binding energies are sufficiently strong so as to severely restrict the range of possibilities that can emerge later in the development of the structure.

However, as soft-matter structures grow, the myriad of potential wells that emerge and form the templates for subsequent layers of development; these wells become shallower and shallower. As a result, they also are more susceptible to subtle perturbations both from within the developing structure and from the surrounding environment in which the developing structure is immersed.

So, Fourier transform spectroscopy would work on quasi-crystalline creatures bound together by relatively deep mutual potential wells among the atoms and molecules that make up the structure. But such a creature would be too stiff to operate the spectrometer; and it’s “thinking” would be too rigid to discover anything.

Mike Elzinga said:

PZ’s Fourier transform idea is not without precedent; although, when applied to a soft-matter, living organism it becomes an analysis of many overlaying patterns. These patters developed at different levels of complexity during the growth of the organism, they are based on different underlying patterns, and many of these are influencing each other giving results that are not the linear superposition of both patterns.

Of course, the precedent is that set by the x-ray crystallography done by Roseland Franklin on the DNA molecule. The x-ray spectra are the Fourier transforms of the actual DNA spatial structure; and they represent the power spectrum of the spatial frequencies in that structure.

The difficulty in going from the power spectrum as seen on the photographs is that the photographs are of the square of the absolute values of the frequencies. Phase information is mostly lost except for that which can be inferred by the brightness of some of the peaks.

The reason one can work backwards from the power spectrum for the DNA molecule to its spatial structure – one does this in all forms of x-ray crystallography – is that one is working backward and forward to untangle a “several-to-one” transform from a relatively robust structure to its power spectrum. A number of closely approximate structures could produce almost indistinguishable power spectra. The trick is to find all the clues in the power spectrum that will direct the analysis to the correct structure.

But the problem gets extremely difficult very quickly if one attempts to look at the power spectrum of a structure that was grown from a relatively simple template such as the DNA molecule by importing atoms and molecules that then find their way into constantly emerging spatial arrays of potential wells during the course of the evolution of the structure. Patterns that emerge later in the development are not by any means related in a one-to-one fashion to the basic underlying structure of the DNA.

The fact that living organisms are soft-matter structures makes the problem far more complex. You can’t have a living organism based on structures that are bound as tightly as, say, salt crystals, or polycrystalline structures such as metal. In such structures, the binding energies are sufficiently strong so as to severely restrict the range of possibilities that can emerge later in the development of the structure.

However, as soft-matter structures grow, the myriad of potential wells that emerge and form the templates for subsequent layers of development; these wells become shallower and shallower. As a result, they also are more susceptible to subtle perturbations both from within the developing structure and from the surrounding environment in which the developing structure is immersed.

So, Fourier transform spectroscopy would work on quasi-crystalline creatures bound together by relatively deep mutual potential wells among the atoms and molecules that make up the structure. But such a creature would be too stiff to operate the spectrometer; and it’s “thinking” would be too rigid to discover anything.

Another cool drink from a deep spring.

And it is Rosalind Franklin, not Roseland Franklin.

This is also a great example of how developmental pathways can be redundant. This not only helps to buffer development from the deleterious effects of mutations, but also allows more opportunities for variation that can be selected on. Of course, this process is also important in conjunction with gene duplication, providing even more opportunities for developmental plasticity and redundancy.

Being able to determine the spatial and temporal expression patterns of developmental genes, using techniques such as in situ hybridization and microarrays, has been critical to our understanding of how developmental pathways work. Being able to accurately quantify levels of gene expression, using techniques such as quantitative PCR, will provide a whole new dimension to the study of gene regulation and development. This will in turn provide new insights into mechanisms of gene regulation and how these processes can be altered over time, thus ultimately proving a better understanding of the molecular basis of evolution.

So Steve Pinker could have seen that he has a defective Gene A, which is important in regulating hair,

Ummmm…so you’re saying baldness is a defect rather than an advantage because it reduces your external parasite load? ;)

I read that Nature article and had trouble grasping it (outside my field), but now it makes sense and even better, I understand the context into which it falls. Thank you.

Gene interactions are important, as PZ emphasizes, but one can take that too far. The late Ernst Mayr (and sometimes also the late Theodosius Dobzhansky) used to blithely state that nearly all genes interacted strongly with nearly all others. This cannot be true and have evolution work.

In fact William Dembski’s “No Free Lunch” criticism of the effectiveness of natural selection relies precisely on that assumption – that a single change in one gene has (because of infinitely complicated universal gene interactions) just as bad an effect as changing all genes at once. (See a post of mine here for more on why his argument in effect assumes this).

The patterns of gene interaction are fascinating, and lots more needs to be known about them. But let’s not let that casually entice us into thinking like Dobzhansky and Mayr (or Dembski) and believing in infinitely complicated interactions.

Okay. I’m rather out of my depth here, and have forgotten through disuse most of what I had learned. But I’m vaguely remembering some of my early days with Kalman Filters. PZ’s comment about, “having multiple noisy systems that interact with each other can produce a more reliable, robust signal”, reminded me of them. The Space Shuttle navigation system used a Kalman Filter to take multiple noisy sources of navigation data (IMU’s, TACAN, MLS, and (later) GPS) to come up with a relatively reliable navigation solution. Combined with Mike’s suggestion about Fourier Transforms and signal analysis, it sounds like the expression of the phenotype is much like the process of a Kalman Filter (or similar technique) applying dynamic “weighting factors” (developmental noise??) to the varying input gene expressions to generate a consistent phenotype expression. The phenotype expression remains relatively robust until a combination of the the input signals degrades sufficiently, and then the “solution” rapidly falls apart.

The Space Shuttle’s Kalman Filter was obviously digital, but it’s not difficult to imagine a similar process in an analog, chemical form doing effectively the same kind of “signal processing” to “smooth out” the resulting phenotype.

This kind of hand waving obviously isn’t precise, and probably not accurate (it’s not exactly what a Kalman Filter does), but it helps fit the concepts into the pigeon holes that I have available. :-)

Taking that rough analogy (if I’m anywhere near accurate) and the x-ray crystallography analysis one broken step further, I wonder if working backwards from the phenotype to the genotype might not be a similar problem, running the Kalman Filter backwards to try to tease out the input gene signals from the resulting genotype. It’s just(!) a few matrix multiplications, so it should, in principle, be possible to run them backwards. But unlike a digital Kalman Filter, both the input signals (gene expression) and the weighting factors in the matrices aren’t known well, or even known at all.

Sounds like a fun challenge! :-)

Scott F said:

Sounds like a fun challenge! :-)

There is another perspective on this from the perspective of Fourier transforms, and that comes from what most engineers know as the “shift theorem.”

Suppose that F(ω) is the Fourier transform of f(x), where x is a spatial variable. The spatial frequency is ω and it is then measured in reciprocal length units.

Then the Fourier transform of f(x + a) is just

e - i ω aF(ω).

In other words, the Fourier transform is simply multiplied by a phase factor. Notice that the higher spatial frequencies ω produce a greater phase shift for a given shift a.

Now think of a as a random variable that is producing a random variation on x. This produces random shifts in the phases of the Fourier transform, with the higher spatial frequencies shifting the most.

What does this do to the absolute value squared of the Fourier transform? It randomizes the phases more for the higher spatial frequencies than it does for lower spatial frequencies. This means that the higher spatial frequencies are “washed out” in the power spectrum because the larger phase shifts add up randomly while the lower frequency phase shifts are less affected.

This means that the power spectrum of a “dithered” function retains less of the higher spatial frequencies than the non-dithered function. In other words, the higher spatial frequency information is lost. This dithering process is sometimes referred to as a “poor man’s low-pass filter.”

If you attempt to work backward from the Fourier transform of the dithered function, you loose the high spatial resolution. Sometimes you want that.

There is a simple demonstration one can try to actually observe this effect. If you try to look through a bush at some object far beyond the bush, you won’t be able to resolve the distant object very easily because of the high frequency spatial clutter provided by the bush right in front of you. But if you move your head slowly so as to make the high frequency clutter move rapidly on your retina, you can then make out the objects in the distance, whose image is not moving as rapidly on the retina.

I use this technique when looking for oncoming traffic at a corner where vision is blocked by hedges in my neighborhood. I inch slowly past the hedges while peering through them for oncoming cars.

There is also another equivalent mathematical analysis of this using “autocorrelation.” Both analyses rely on “persistence of vision” on the retina.

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This page contains a single entry by PZ Myers published on December 19, 2011 12:32 PM.

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