Papers in computational evolutionary biology

Archive for April 2010

Does evolutionary plasticity evolve?

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Andreas Wagner Does evolutionary plasticity evolve? Evolution 50(3), 1996. pdf

The focus is on epigenetic buffering of mutations, the phenomenon called here (perhaps unfortunately) evolutionary plasticity. With the help of a simple computational model of regulatory networks, Wagner shows that the plasticity can increase when the network’s stable state is put under stabilising selection. This is an indication that stabilising selection can alone explain the canalisation observed in real regulatory networks.

A regulatory network is modelled as a discrete-time dynamical system, which in turn is encoded as a real matrix. The matrix together with an initial state determines the steady state (if any), which is treated as a phenotype. Matrices “evolve” through recombination (swapping rows between pairs of different matrices), mutation (random alteration of entries) and stabilising selection (deviations from the target steady state are punished). Epigenetic stability of such networks was assessed before and after 400 rounds of evolution, and found to have increased significantly in the process. In addition, the evolved networks converge to their stable states much faster.

Apart from the valuable scientific findings, the paper is notable for the dilligence with which Wagner (now heading a successful lab in Zurich) sets up and carries out his experiments. For example, networks and their stable states are chosen independently; and stability is assessed with respect to the original mutation constructs and an additional one, which was not used during the simulated evolution. While this is perhaps no more than good practice, it is still good to see these measures taken.


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April 28, 2010 at 13:18

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Curvature in Metabolic Scaling

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Tom Kolokotrones, Van M. Savage, Eric J. Deeds and Walter Fontana Curvature in Metabolic Scaling Nature 464:753-756, 2010. Nature page

This paper is not about evolution, but it is short, recent, published in Nature and comes from Fontana Lab, so there is definitely no harm in reviewing it. It deals with metabolic scaling, that is the relationship between an organism’s metabolic rate and its body mass. Experimental measurements seem to indicate that the metabolic rate is proportional to the body mass raised to a fixed power. The actual value of the exponent was first thought to be 2/3, and then 3/4; the latter was also derived by West et. al. from an involved theoretical model of vascular system [1].

Kolokotrones et. al. took a large dataset and showed that instead of a simple power law a more complex expression involving two exponents is a much better fit. When plotted on a log-log scale, the graph of this function is a slightly convex curve, rather than the straight line resulting from a pure power law; hence the title of the paper. Of course by introducing a new degree of freedom you will always get a better fit, but the improvement in this case is considerable, and, crucially, the curve can be approximated in different regions by pure power laws with the well-established exponents. This shows that essentially both the 2/3 and 3/4 hypotheses were correct.

A mechanistic explanation for the 3/4 theory was provided by West’s model, and so the authors set out to modify it to get a two-exponent formula instead. Apparently it is possible by postulating a different moment of transition between the pulsatile and smooth blood flow dynamics. More details can be found in Supplementary Information, if you’re interested (I am not).

Now, it is possible that the curved fit does not represent any underlying biological principle. As mentioned above, the curve can be approximated by two or more power laws acting on different parts of the data. It is conceivable that the relationship is in fact a pure power law, but evolutionary distant families of mammals (the study is on mammals) evolved—for whatever reasons—different exponents. Through phylogenetic analysis, Kolokotrones et.al. show that this is not the case, and that curvature is observed in subsets of data corresponding to closely related species. Other factors, such as habitat and food type were also excluded, suggesting that there is an underlying mechanistic principle at work.

[1] West, G. B., Brown, J. H. & Enquist, B. J. A general model for the origin of allometric scaling laws in biology. Science 276, 122–126 (1997).

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April 7, 2010 at 17:44

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Marc Kirschner and John Gerhart Evolvability. Proc. Natl. Acad. Sci. USA 95(15), 1998.  PNAS page pdf

This hugely influential paper attempts to uncover the high-level features of complex biological architectures that facilitate their phenotypical variation. The authors analyse several examples of  highly conserved mechanisms they call “core processes” and argue that

the conservation of these core processes for the past 530 million years is related less to the processes’ own constraint, embedment and optimization than to the deconstraint they provide for phenotypic variation of other processes, on the basis of which they are continually coselected.

Now, the obvious interpretation of evolutionary conservation is that the conserved process plays an important role in a crucial function of the organism and/or confers a significant fitness advantage. Kirschner’s and Gerhart’s suggestion that this advantage is in fact evolvability itself goes (in general) dangerously close to invoking group selection, and they acknowledge as much. I do not feel (yet) competent to comment on this, so I will review instead the excellent observations that the authors make about the high-level organisational priciples that contribute to evolvability.

Versatile proteins are pretty much what it says on the tin: proteins that are not very specific, but admit a range of targets. The example given in the paper is that of calmodulin, a prominent player in various calcium-based signalling pathways. Calmodulin usually inhibits the function of the protein it binds to, but because the range of targets it recognises is so broad, the inhibited agent can be an inhibitor itself, or maybe an activator, etc. As a result, calmodulin has great value as an universal negation gate in many different regulatory contexts. Dually, because of the low general specificity, a random regulator protein is presumably just a few mutations away from responding to calmodulin and the emergence of a new regulatory connection. Thus the versatility of calmodulin faciliates phenotypic variation of a regulatory network.

Weak linkage means that “the activity of a process depends minimally on other components or processes”. This is a fuzzy concept to me. Judging by the examples given in the paper, this is yet another face of the flexibility and versatility covered in the previous paragraph and it is unclear to me why the two should be treated separately, other than perhaps the fact that weak linkage refers not as much to the individual components of the system as to the way they are put together. The authors discuss weak linkage in eukariotic transcription and this is perhaps what the paper is known for the most: bringing to the fore the evolution of regulation (as opposed to the evolution of structural genes).

Exploratory processes perform their function relying as little as possible on the particulars of their client/target processes. One example given in the paper is the microtubule cytoskeleton helping to separate chromosomes before cell differentiation: the tubules grow in random directions, but stablise only when they find the chromosome. In this way, the skeleton is built correctly regardless of the initial positions of the chromosomes, cell size and shape, etc. These parameters are thus free to change, and this is why the exploratory formation of the cytoskeleton facilitates phenotypic variation. Another example is the immune system, which randomly generates antibodies until the right one is recognised. The authors also refer to this design principle as “epigenetic variation and selection”.

Compartmentation is just an ugly word for modularity, only that the modules/compartments may be genomic (different genes for different things), temporal (i.e. processes happen in stages), spatial, or even target-spatial i.e. the same process is independently deployed and regulated in different regions of cell/tissue (example: drosophila bristle development). This kind of architecture facilitates phenotypic variation because brakedown of one module does not necessarily entail the brakedown of the whole system. A computer scientist would probably advocate the value of interfacing and hiding at this point.

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April 3, 2010 at 19:20

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