RNA folding and evolutionary dynamics:
Evolution and development at the level of a single molecule

With my colleagues from Vienna, I used the computational folding of RNA sequences into minimum free energy secondary structures (henceforth shapes) as a simple biophysical toy-model of the mapping from genotype to phenotype¹. The goal is to characterize the statistical features of this mapping and to understand their consequences for evolutionary dynamics (Schuster et al., 1994; Fontana and Schuster, 1998; Stadler et al., 2001).

The most important features are:

Typical shapes. There are many more sequences than shapes and shapes do not occur with the same frequency. In fact, a small fraction of shapes is realized significantly more often than others. These shapes are termed ``typical'' and they dominate the evolutionary process. Typicality is best appreciated by considering sequences of increasing length. In the limit of long sequences, the fraction of typical shapes tends to zero, while the fraction of sequences folding into them tends to one. (Consider, for example, binary GC-sequences of length 30: A total of 1.07 billion sequences fold into a total of 218,820 shapes. 22,718 of these shapes (10.4%) are typical in the sense of being formed more frequently than the average number of sequences per shape. 93.4% of all sequences fold into these 10.4% shapes. As we increase the length of sequences, we observe that an increasing percentage of sequences folds into a decreasing percentage of shapes.)

Neutral networks. A sequence folding into a typical shape is characterized by a high degree of neutrality expressed as the fraction of 1-error mutants (genetic neighbors) that retain that shape. Neutrality here means equivalence with regard to shape. The same holds for these neighbors. In this way, jumping from neighbor to neighbor, we can map an extensive mutationally connected network of sequences that fold into the same shape. We termed such networks ``neutral networks''. A neutral network expresses the stability of a phenotype against genetic mutations. Yet, it also enables phenotypic change to occur. Consider an evolving population whose currently best phenotype is shape A. Suppose further that shape B is the better phenotype, but that it can't be accessed by a small (and hence probable) mutation from the population's current location in genetic space. The population, however, is not stuck. Because of connected neutrality, the population can drift in genetic space while preserving the currently best phenotype until it eventually comes close to sequences that fold into the better shape B. The significance of neutrality consists, therefore, in enabling the preparation of a genetic context in which a subsequent mutation becomes phenotypically consequential. Phenotypic change appears suddenly, but the underlying genetic make-up changes all the time. When a population drifts over a neutral network, the phenotype does not change, but the potential for change changes.

Shape space covering. Neutral networks should be imagined as high-dimensional sponges that are heavily entangled with one another. In fact, they are so much intertwined that all typical shapes are realized within a small neighborhood (compared to sequence length) of any random sequence. For example, for sequences of length 100, at least one instance of every typical shape is, on average, no more than 15 mutations away from any random sequence.

The Topology of the Possible: 'A is near B' does not imply 'B is near A'

Neutral networks have a straightforward, yet subtle, consequence. The adjacency of one neutral network to another in sequence space, expressed as the relative size of shared boundary, defines a relationship of accessibility among phenotypes. This can be used to construct a space that reflects how likely one phenotype appears as an innovation of the other by genetic mutation. The formal structure of that space is a pre-topology, a rather unfamiliar animal. The main point is that for RNA this space lacks a notion of distance, because nearness understood as accessibility is not symmetric. The reason is that neutral networks can differ vastly in size. Shape B may be easily accessible by genetic mutation from shape A without the reverse being true. Think of the United States in terms of such a boundary topology: Pennsylvania is near New Jersey, but New Jersey is not near Pennsylvania, since a random step out of NJ is likely to end up in PA, but not vice versa.

The genotype-phenotype map (that is, development) induces the topological structure of phenotype space by determining the evolutionary routes along which phenotype B can be obtained from phenotype A. This is quite different from the traditional image of phenotype space as a highly regular metric space constructed around a notion of similarity (morphological or other) between phenotypes. Punctuated equilibria, constraints to variation and irreversibility in evolution become intelligible in this new space, its unfamiliar structure notwithstanding.

The conceptual position developed here is, historically, not a new one. It has been expressed informally by many biologists since the beginning of the 20th century. The RNA model simply provides a concrete mechanistic illustration that places the discussion within a framework of formal theory (in which, for example, notions like continuity and discontinuity of evolutionary trajectories and the genotype-phenotype map can be made precise) rather than leaving it to confusion generated by incommensurate interpretations and people arguing at cross purposes.

Our theory motivated Eric Schultes and David Bartel from the Whitehead Institute to a beautiful RNA experiment reported in the journal Science (Schultes and Bartel, 2000). The experiment provides strong evidence for the existence of neutral networks and shape space covering.

Plasticity mirrors Variability ... and the Origin of Modularity

Lauren Ancel and I have recently extended the notion of RNA phenotype to include phenotypic plasticity (Ancel and Fontana, 2000). Plasticity means that a given genotype provides several alternative phenotypes to an individual². In the simple case of RNA, plasticity means that the phenotype is no longer just the minimum free energy shape (ground state), but consists in a set of alternative shapes in the energetic vicinity of the ground state. Thermal fluctuations cause the molecule to wiggle among these alternative shapes.

Analysis of the plastic genotype-phenotype map led to the discovery of a further statistical feature with evolutionary consequences. First, there is a positive correlation between plasticity (alternative shapes available to a single sequence) and variability (the degree to which new shapes can be generated by mutating that sequence). Second, the set of ground states realized in the genetic vicinity of a sequence is typically a subset of the plastic repertoire of that sequence. We termed this correspondence between plastic accessibility of alternative shapes and genetic accessibility of ground states ``plasto-genetic congruence''. In more traditional biological terms, plasto-genetic congruence states that environmental and genetic canalization are flip sides of the same coin.

Quite generally, such congruences are a consequence of one and the same mechanism underlying different phenotypic features. Because of this coupling, selection acting on one feature also affects the other. For example, in computer simulations we found that selection for highly stable ground states (low plasticity) dramatically reduces genetic variability - even to the point of grinding evolution to a halt, because of insufficient variation. However, we also found that low-plasticity shapes are modular, consisting of kinetically, thermodynamically and genetically autonomous pieces of shape. A selection regime for low plasticity therefore drives the population into an evolutionary trap with respect to point mutations as the source of variation. Yet, curiously, this trap has precisely the necessary structural organization to eliminate itself by enabling a new source of variation through the shuffling of modules.

Walter Fontana, Santa Fe Institute