Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution
Engineers routinely design systems to be modular and symmetric in order to increase robustness to perturbations and to facilitate alterations at a later date. Biological structures also frequently exhibit modularity and symmetry, but the origin of such trends is much less well understood. It can be tempting to assume – by analogy to engineering design – that symmetry and modularity arise from natural selection. But evolution, unlike engineers, cannot plan ahead, and so these traits must also afford some immediate selective advantage which is hard to reconcile with the breadth of systems where symmetry is observed. Here we introduce an alternative non-adaptive hypothesis based on an algorithmic picture of evolution. It suggests that symmetric structures preferentially arise not just due to natural selection, but also because they require less specific information to encode, and are therefore much more likely to appear as phenotypic variation through random mutations. Arguments from algorithmic information theory can formalise this intuition, leading to the prediction that many genotype-phenotype maps are exponentially biased towards phenotypes with low descriptional complexity. A preference for symmetry is a special case of this bias towards compressible descriptions. We test these predictions with extensive biological data, showing that that protein complexes, RNA secondary structures, and a model gene-regulatory network all exhibit the expected exponential bias towards simpler (and more symmetric) phenotypes. Lower descriptional complexity also correlates with higher mutational robustness, which may aid the evolution of complex modular assemblies of multiple components.
Contingency, convergence and hyper-astronomical numbers in biological evolution.
Abstract:Counterfactual questions such as "what would happen if you re-run the tape of life?" turn on the nature of the landscape of biological possibilities. Since the number of potential sequences that store genetic information grows exponentially with length, genetic possibility spaces can be so unimaginably vast that commentators frequently reach of hyper-astronomical metaphors that compare their size to that of the universe. Re-run the tape of life and the likelihood of encountering the same sequences in such hyper-astronomically large spaces is infinitesimally small, suggesting that evolutionary outcomes are highly contingent. On the other hand, the wide-spread occurrence of evolutionary convergence implies that similar phenotypes can be found again with relative ease. How can this be? Part of the solution to this conundrum must lie in the manner that genotypes map to phenotypes. By studying simple genotype-phenotype maps, where the counterfactual space of all possible phenotypes can be enumerated, it is shown that strong bias in the arrival of variation may explain why certain phenotypes are (repeatedly) observed in nature, while others never appear. This biased variation provides a non-selective cause for certain types of convergence. It illustrates how the role of randomness and contingency may differ significantly between genetic and phenotype spaces.
Maximum mutational robustness in genotype-phenotype maps follows a self-similar blancmange-like curve.
Abstract:Phenotype robustness, defined as the average mutational robustness of all the genotypes that map to a given phenotype, plays a key role in facilitating neutral exploration of novel phenotypic variation by an evolving population. By applying results from coding theory, we prove that the maximum phenotype robustness occurs when genotypes are organized as bricklayer's graphs, so-called because they resemble the way in which a bricklayer would fill in a Hamming graph. The value of the maximal robustness is given by a fractal continuous everywhere but differentiable nowhere sums-of-digits function from number theory. Interestingly, genotype-phenotype maps for RNA secondary structure and the hydrophobic-polar (HP) model for protein folding can exhibit phenotype robustness that exactly attains this upper bound. By exploiting properties of the sums-of-digits function, we prove a lower bound on the deviation of the maximum robustness of phenotypes with multiple neutral components from the bricklayer's graph bound, and show that RNA secondary structure phenotypes obey this bound. Finally, we show how robustness changes when phenotypes are coarse-grained and derive a formula and associated bounds for the transition probabilities between such phenotypes.
Designing the self-assembly of arbitrary shapes using minimal complexity building blocks
Abstract:The design space for self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. We develop a pipeline to explore the design spaces for a set of structures of various sizes and complexities. To understand the implications of the different solutions, we analyze their assembly dynamics using patchy particle simulations and study the influence of the number of distinct building blocks, and the angular and spatial tolerances on their interactions, on the kinetics and yield of the target assembly. We show that the resource-saving solution with a minimum number of distinct blocks can often assemble just as well (or faster) than designs where each building block is unique. We further use our methods to design multifarious structures, where building blocks are shared between different target structures. Finally, we use coarse-grained DNA simulations to investigate the realization of multicomponent shapes using DNA nanostructures as building blocks.
Robustness and stability of spin-glass ground states to perturbed interactions
Across many problems in science and engineering, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we investigate the glassy phase of ± J spin glasses at zero temperature by calculating the robustness of the ground states to flips in the sign of single interactions. For random graphs and the Sherrington-Kirkpatrick model, we find relatively large sets of bond configurations that generate the same ground state. These sets can themselves be analyzed as subgraphs of the interaction domain, and we compute many of their topological properties. In particular, we find that the robustness, equivalent to the average degree, of these subgraphs is much higher than one would expect from a random model. Most notably, it scales in the same logarithmic way with the size of the subgraph as has been found in genotype-phenotype maps for RNA secondary structure folding, protein quaternary structure, gene regulatory networks, as well as for models for genetic programming. The similarity between these disparate systems suggests that this scaling may have a more universal origin.