Arrival of the Fittest: Solving Evolution's Greatest Puzzle (36 page)

37
. See Babu et al. (2004).

38
. Note that pairs (A,B) and (B,A) need to be distinguished, because gene A can regulate B differently from how gene B regulates gene A. In addition, this procedure allows for the possibility that a gene can regulate itself, which is often the case.

39
. The number of Hox genes varies even among chordates and vertebrates. For example, the basal chordate
Amphioxus
has only ten Hox genes, whereas some fish species have many more than forty Hox genes, which is a result of a past duplications of their entire genome. See Amores et al. (1998) and Garcia-Fernandez and Holland (1994).

40
. Much of the work that I summarize in this chapter can be found in Ciliberti, Martin, and Wagner (2007a), as well as in Ciliberti, Martin, and Wagner (2007b) and Martin and Wagner (2008). The message of this chapter holds even when the strengths of regulatory interactions can vary continuously.

41
. In metabolic genotype space, each hypercube vertex corresponds to a binary string that represents a metabolic genotype. A complication for regulatory circuits is that even in the simplest case where regulation can only be activating, repressing, or absent, the relevant strings are no longer binary but trinary—each digit can assume three values. The resulting hypercubes are even less intuitive geometrically, and are sometimes called generalized hypercubes. See, for example, Reidys (1997).

42
. One might argue that there is not one circuit library but many, each one for circuits with different numbers of genes and thus existing in a different dimension. However, one can always view lower-dimensional spaces as being embedded in higher-dimensional spaces. This is why I often use the notion of a library in the singular here.

43
. It may seem far-fetched to speak of meaning outside the context of human language. But as I mentioned in chapter 4, to do so has a long tradition in the field of semiotics. For a concise introduction to semiotics see Eco (1977). For an exploration of different kinds of meaning in living beings see chapter 2 of Wagner (2009b).

44
. It is important to be aware that the evolution of many innovations such as dissected leaves occurred gradually and not in one giant leap. If an increase in leaf dissection is advantageous, then a “weakly” dissected leaf is better to have than a simple leaf, and a strongly dissected leaf is even superior to a weakly dissected leaf. In consequence, the expression codes that mediate leaf dissection may have changed gradually, in small steps, until strongly dissected leaves were fully formed. Such gradual changes may even have occurred in the formation of very complex organs such as eyes—having imperfect eyes is usually better than being blind. See Gerhart and Kirschner (1998), chapter 5, and Land and Fernald (1992). None of this takes away from the observation that new expression codes are much easier to find in circuit libraries that are organized as I describe here. I do not emphasize the gradual notion of evolution, and use the black-and-white distinction between old and new expression codes simply because it illustrates the relevant concepts more clearly.

45
. For pertinent work see Espinosa-Soto, Padilla-Longoria, and Alvarez-Buylla (2004), as well as Albert and Othmer (2003) and Jäger et al. (2004). These researchers model the spatial organization of an embryo in greater detail than the work I describe here, because they focus on only one circuit. That level of detail would be prohibitive for current computational technology if one needed to explore many circuits, except for especially simple circuits like those in Cotterell and Sharpe (2010).

46
. For example, two different types of circuits pattern the dorsoventral axis and the proximodistal axis of our limbs. See chapter 3 of Carroll et al. (2001). I leave out spatial considerations for brevity here, because they do not affect the main principles I discuss.

47
. For evidence that regulatory DNA changes more rapidly than transcriptional regulators themselves see Tirosh et al. (2009), as well as Wittkopp, Haerum, and Clark (2008) and Wittkopp, Haerum, and Clark (2004). Not all detrimental changes in a circuit are immediately lethal to the individual. The vast majority of harmful DNA changes have subtle effects on individuals, and their lethality manifests itself only on evolutionary time scales, when a lineage carrying them gets eliminated.

48
. As shown in Stone and Wray (2001). The changes that occur in such regulatory DNA are not necessarily only changes in individual nucleotide letters of DNA. Deletions or duplications of short stretches of DNA can also occur. I note that some changes in the DNA binding sites of transcriptional regulators may have no effect on regulation, because a regulator may regulate the same gene via multiple different, redundant binding sites.

49
. This possibility is not so far-fetched, even though there are more circuits than equilibrium gene expression patterns: Most circuits in the library do not reach a stable equilibrium gene expression phenotype, but one that varies cyclically. See, for example, Ciliberti, Martin, and Wagner (2007b).

50
. More precisely, I am referring to the Institut des Hautes Études Scientifiques (IHÉS) in Bures-sur-Yvette, near Paris.

51
. On a historical note, mathematical biology, some of which aims to solve similar problems, is a research field with a long tradition in biology. See Murray (1989). Even the notion of systems biology is far from new. See Bertalanffy (1968). However, the mainstream of biology, especially cell and molecular biology, has acknowledged the importance of these ideas only since the late 1990s.

52
. A well-known statistical description of a gas is the ideal gas law, which links pressure, volume, and temperature of a known quantity of gas molecules.

53
. Our explorations of the library were greatly aided by postdoctoral researcher Stefano Ciliberti.

54
. The exact number of neighbors with the same phenotype depends on a circuit’s size and the actual phenotype. Even two circuits in which these properties are the same may have different numbers of neighbors with the same phenotype. See Ciliberti, Martin, and Wagner (2007a) and Ciliberti, Martin, and Wagner (2007b). Here and below, I always discuss
typical
features of circuits. Exceptions may exist, but their overall impact on innovability is small, given that most circuits in the library follow the rules rather than being exceptions.

55
. See Wagner (2011), figure 3.3. Different phenotypes do in fact have different numbers of circuits associated with them, but this number is typically very large regardless of the phenotype, as long as a circuit has a minimum number of genes. The variation in size among different genotype networks has implications for innovability that are too technical to cover here, but see Wagner (2008).

56
. Ciliberti, Martin, and Wagner (2007a).

57
. See Isalan et al. (2008). Gene expression phenotypes may change in these circuits, but what the experiment shows is that the circuits continue to function and sustain life.

58
. See Martchenko et al. (2007).

59
. See Tanay, Regev, and Shamir (2005).

60
. For brevity, the narrative assumes tacitly that a new phenotype will replace the old phenotype. That assumption is not necessary. The same developmental regulation circuit can produce different gene expression patterns in response to different chemical signals, and in different regions of a developing embryo. Suppose that a given expression pattern has a well-established role in structuring one body part, but that a new expression pattern, as yet undiscovered, produced in response to a second chemical signal can help structure a new body part. A population that drifts through the genotype network of the first expression pattern will be able to explore many different phenotypes in response to the second chemical signal, wherever this signal occurs in the body. Thus, even where circuits have multiple signals and multiple expression codes, the circuit space organization I describe facilitates innovation.

CHAPTER SIX: THE HIDDEN ARCHITECTURE

1
. See Waddington (1942) for the quotation, as well as Waddington (1953) and Waddington (1959).

2
. For early reviews, see Tautz (1992). For some later work with useful references, see Wagner (1999) and Wagner (2005a).

3
. The expression of such a gene costs energy, for example in the manufacture of RNA and amino acid building blocks.

4
. See Goffeau et al. (1996).

5
. Biologists had observed the effects of mutations for many years, and they had also been able to introduce random mutations into a genome, but until the late twentieth century they could not engineer mutations in a highly targeted and specific fashion.

6
. See Giaever et al. (2002) and Winzeler et al. (1999) for examples of large-scale knockout studies in the brewer’s yeast
Saccharomyces cerevisiae
. The most important such defect one finds in such mutants is slower reproduction, because it’s the one that nature punishes immediately, but it’s not the only possible defect. Others include a reduced efficiency of mating or spore formation, and a lower chance of survival in stressful chemical environments. I discuss the role of different aspects of fitness and of environmental variation in the interpretation of knockout experiments in Wagner (2011) and Wagner (2005b).

7
. And not just to gene deletions, but to a variety of manipulations that reduce gene expression. One of them takes advantage of a natural process called RNA interference, which is able to block the transcription of specific genes into RNA. For a pertinent study in the worm
Caenorhabditis elegans
see Kamath et al. (2003).

8
. See Lander et al. (2001).

9
. Duplications can affect more than one gene, entire chromosomes, or entire genomes. Also, sometimes the product of a duplication is two genes that are not quite identical. But none of these caveats affect the principles I discuss here.

10
. An intriguing question is whether redundancy in living beings ultimately exists
because
it provides protection against mutations. See Wagner (1999) for a relevant study.

11
. Analyzing how missing chemical reactions affect metabolism is usually more quantitative than I outlined here. One typically either measures the cell division rate in a population of cells or computes the so-called biomass growth flux. In such an analysis, there is no all-or-none distinction between essential and nonessential genes, as some genes slow down “city traffic” more than others when knocked out. In general, the number of reactions that reduce biomass growth flux to zero is small. In the wild, many microbes grow and divide very slowly in their native habitat. Such microbes may have other advantages, such as better survival when starved for nutrients. This means that not only those metabolisms that support rapid cell growth and division are successful in evolution.

12
. For a discussion of the distinction between redundancy and this kind of “distributed robustness” see Wagner (2005a).

13
. These lysozymes in different organisms do not have the same genotype. To the contrary, they are highly diverse, once again reflecting the principle that similar molecular phenotypes can be created by very different genotypes.

14
. See Kun, Santos, and Szathmary. (2005).

15
. Experimental studies often focus on one aspect of a metabolic phenotype, such as viability on the sole carbon source glucose, but computational work demonstrates that other aspects of metabolic phenotypes can be robust to a similar extent.

16
. I note that everything I said thus far about robustness pertains to the robustness of a genotype. One can also define the robustness of a phenotype, a concept that will not play an important role in this book, but that can be important to study the relationship between robustness and innovability. See, for example, Wagner (2008).

17
. The branch of mathematics needed to prove this statement is graph theory, and specifically the theory of generalized hypercube graphs. For a glimpse at some of its arcana see Reidys, Stadler, and Schuster (1997). For a more accessible exposition see Wagner (2011), chapter 6.

18
. See Darwin (1872), chapter 6, page 170. In the same chapter he expresses his faith in selection’s power to preserve small and useful improvements.