Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution

Selection of a promiscuous minimalist cAMP phosphodiesterase from a library of de novo designed proteins

The ability of unevolved amino acid sequences to become biological catalysts was key to the emergence of life on Earth. However, billions of years of evolution separate complex modern enzymes from their simpler early ancestors. To probe how unevolved sequences can develop new functions, we use ultrahigh-throughput droplet microfluidics to screen for phosphoesterase activity amidst a library of more than one million sequences based on a de novo designed 4-helix bundle. Characterization of hits revealed that acquisition of function involved a large jump in sequence space enriching for truncations that removed >40% of the protein chain. Biophysical characterization of a catalytically active truncated protein revealed that it dimerizes into an α-helical structure, with the gain of function accompanied by increased structural dynamics. The identified phosphodiesterase is a manganese-dependent metalloenzyme that hydrolyses a range of phosphodiesters. It is most active towards cyclic AMP, with a rate acceleration of ~109 and a catalytic proficiency of >1014 M-1, comparable to larger enzymes shaped by billions of years of evolution.

Non-Poissonian Bursts in the Arrival of Phenotypic Variation Can Strongly Affect the Dynamics of Adaptation

Modeling the rate at which adaptive phenotypes appear in a population is a key to predicting evolutionary processes. Given random mutations, should this rate be modeled by a simple Poisson process, or is a more complex dynamics needed? Here we use analytic calculations and simulations of evolving populations on explicit genotype-phenotype maps to show that the introduction of novel phenotypes can be "bursty" or overdispersed. In other words, a novel phenotype either appears multiple times in quick succession or not at all for many generations. These bursts are fundamentally caused by statistical fluctuations and other structure in the map from genotypes to phenotypes. Their strength depends on population parameters, being highest for "monomorphic" populations with low mutation rates. They can also be enhanced by additional inhomogeneities in the mapping from genotypes to phenotypes. We mainly investigate the effect of bursts using the well-studied genotype-phenotype map for RNA secondary structure, but find similar behavior in a lattice protein model and in Richard Dawkins's biomorphs model of morphological development. Bursts can profoundly affect adaptive dynamics. Most notably, they imply that fitness differences play a smaller role in determining which phenotype fixes than would be the case for a Poisson process without bursts.

Theoretical principles explain the structure of the insect head direction circuit

To navigate their environment, insects need to keep track of their orientation. Previous work has shown that insects encode their head direction as a sinusoidal activity pattern around a ring of neurons arranged in an eight-column structure. However, it is unclear whether this sinusoidal encoding of head direction is just an evolutionary coincidence or if it offers a particular functional advantage. To address this question, we establish the basic mathematical requirements for direction encoding and show that it can be performed by many circuits, all with different activity patterns. Among these activity patterns, we prove that the sinusoidal one is the most noise-resilient, but only when coupled with a sinusoidal connectivity pattern between the encoding neurons. We compare this predicted optimal connectivity pattern with anatomical data from the head direction circuits of the locust and the fruit fly, finding that our theory agrees with experimental evidence. Furthermore, we demonstrate that our predicted circuit can emerge using Hebbian plasticity, implying that the neural connectivity does not need to be explicitly encoded in the genetic program of the insect but rather can emerge during development. Finally, we illustrate that in our theory, the consistent presence of the eight-column organisation of head direction circuits across multiple insect species is not a chance artefact but instead can be explained by basic evolutionary principles.

Exploring Simplicity Bias in 1D Dynamical Systems

Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input-output maps. This phenomenon is known as simplicity bias. By viewing the parameters of dynamical systems as inputs, and the resulting (digitised) trajectories as outputs, we study simplicity bias in the logistic map, Gauss map, sine map, Bernoulli map, and tent map. We find that the logistic map, Gauss map, and sine map all exhibit simplicity bias upon sampling of map initial values and parameter values, but the Bernoulli map and tent map do not. The simplicity bias upper bound on the output pattern probability is used to make a priori predictions regarding the probability of output patterns. In some cases, the predictions are surprisingly accurate, given that almost no details of the underlying dynamical systems are assumed. More generally, we argue that studying probability-complexity relationships may be a useful tool when studying patterns in dynamical systems.

Polymorphic Self-Assembly with Procedural Flexibility for Monodisperse Quaternary Protein Structures of DegQ Enzymes

As large molecular tertiary structures, some proteins can act as small robots that find, bind, and chaperone target protein clients, showing the potential to serve as smart building blocks in self-assembly fields. Instead of using such intrinsic functions, most self-assembly methodologies for proteins aim for de novo-designed structures with accurate geometric assemblies, which can limit procedural flexibility. Here, a strategy enabling polymorphic clustering of quaternary proteins, exhibiting simplicity and flexibility of self-assembling paths for proteins in forming monodisperse quaternary cage particles is presented. It is proposed that the enzyme protomer DegQ, previously solved at low resolution, may potentially be usable as a threefold symmetric building block, which can form polyhedral cages incorporated by the chaperone action of DegQ in the presence of protein clients. To obtain highly monodisperse cage particles, soft, and hence, less resistive client proteins, which can program the inherent chaperone activity of DegQ to efficient formations of polymorphic cages, depending on the size of clients are utilized. By reconstructing the atomic resolution cryogenic electron microscopy DegQ structures using obtained 12- and 24-meric clusters, the polymorphic clustering of DegQ enzymes is validated in terms of soft and rigid domains, which will provide effective routes for protein self-assemblies with procedural flexibility.

Impaired face symmetry detection under alcohol, but no 'beer goggles' effect

BACKGROUND

The 'beer goggles' phenomenon describes sexual attraction to individuals when alcohol intoxicated whom we would not desire when sober. One possible explanation of the effect is that alcohol impairs the detection of facial asymmetry, thus lowering the drinker's threshold for physical attraction.

AIMS

We therefore tested the hypotheses that higher breath alcohol drinkers would award more generous ratings of attractiveness to asymmetrical faces, and be poorer at discriminating bilateral facial asymmetry than less intoxicated counterparts.

METHODS

Ninety-nine male and female bar patrons rated 18 individual faces for attractiveness and symmetry. Each type of rating was given twice, once per face with an enhanced asymmetry and once again for each face in its natural form. Participants then judged which of two same-face versions (one normal, the other perfectly symmetrised) was more attractive and, in the final task, more symmetrical.

RESULTS

Alcohol had no influence on attractiveness judgements but higher blood alcohol concentrations were associated with higher symmetry ratings. Furthermore, as predicted, heavily intoxicated individuals were less able to distinguish natural from perfectly symmetrised face versions than more sober drinkers.

CONCLUSIONS

Findings therefore suggest alcohol impairs face asymmetry detection, but it seems that this perceptual distortion does not contribute to the 'beer goggles' phenomenon.

How Turing parasites expand the computational landscape of digital life

Why are living systems complex? Why does the biosphere contain living beings with complexity features beyond those of the simplest replicators? What kind of evolutionary pressures result in more complex life forms? These are key questions that pervade the problem of how complexity arises in evolution. One particular way of tackling this is grounded in an algorithmic description of life: living organisms can be seen as systems that extract and process information from their surroundings to reduce uncertainty. Here we take this computational approach using a simple bit string model of coevolving agents and their parasites. While agents try to predict their worlds, parasites do the same with their hosts. The result of this process is that, to escape their parasites, the host agents expand their computational complexity despite the cost of maintaining it. This, in turn, is followed by increasingly complex parasitic counterparts. Such arms races display several qualitative phases, from monotonous to punctuated evolution or even ecological collapse. Our minimal model illustrates the relevance of parasites in providing an active mechanism for expanding living complexity beyond simple replicators, suggesting that parasitic agents are likely to be a major evolutionary driver for biological complexity.

Maximum mutational robustness in genotype-phenotype maps follows a self-similar blancmange-like curve

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.

Prediction and experimental evidence of different growth phases of the Podospora anserina hyphal network

Under ideal conditions, the growth of the mycelial network of a filamentous fungus is monotonous, showing an ever increasing complexity with time. The components of the network growth are very simple and based on two mechanisms: the elongation of each hypha, and their multiplication by successive branching. These two mechanisms are sufficient to produce a complex network, and could be localized only at the tips of hyphae. However, branching can be of two types, apical or lateral, depending on its location on the hyphae, therefore imposing the redistribution of the necessary material in the whole mycelium. From an evolutionary point of view, maintaining different branching processes, with additional energy needs for structure and metabolism, is intriguing. We propose in this work to discuss the advantages of each branching type using a new observable for the network growth, allowing us to compare growth configurations. For this purpose, we build on experimental observations of the Podospora anserina mycelium growth, enabling us to feed and constrain a lattice-free modeling of this network based on a binary tree. First, we report the set of statistics related to the branches of P. anserina that we have implemented into the model. Then, we build the density observable, allowing us to discuss the succession of growth phases. We predict that density over time is not monotonic, but shows a decay growth phase, clearly separated from an other one by a stationary phase. The time of appearance of this stable region appears to be driven solely by the growth rate. Finally, we show that density is an appropriate observable to differentiate growth stress.

A synaptic molecular dependency network in knockdown of autism- and schizophrenia-associated genes revealed by multiplexed imaging

The complex functions of neuronal synapses depend on their tightly interconnected protein network, and their dysregulation is implicated in the pathogenesis of autism spectrum disorders and schizophrenia. However, it remains unclear how synaptic molecular networks are altered biochemically in these disorders. Here, we apply multiplexed imaging to probe the effects of RNAi knockdown of 16 autism- and schizophrenia-associated genes on the simultaneous joint distribution of 10 synaptic proteins, observing several protein composition phenotypes associated with these risk genes. We apply Bayesian network analysis to infer hierarchical dependencies among eight excitatory synaptic proteins, yielding predictive relationships that can only be accessed with single-synapse, multiprotein measurements performed simultaneously in situ. Finally, we find that central features of the network are affected similarly across several distinct gene knockdowns. These results offer insight into the convergent molecular etiology of these widespread disorders and provide a general framework to probe subcellular molecular networks.

Designing the Self-Assembly of Arbitrary Shapes Using Minimal Complexity Building Blocks

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.

Random and Natural Non-Coding RNA Have Similar Structural Motif Patterns but Differ in Bulge, Loop, and Bond Counts

An important question in evolutionary biology is whether (and in what ways) genotype–phenotype (GP) map biases can influence evolutionary trajectories. Untangling the relative roles of natural selection and biases (and other factors) in shaping phenotypes can be difficult. Because the RNA secondary structure (SS) can be analyzed in detail mathematically and computationally, is biologically relevant, and a wealth of bioinformatic data are available, it offers a good model system for studying the role of bias. For quite short RNA (length L≤126), it has recently been shown that natural and random RNA types are structurally very similar, suggesting that bias strongly constrains evolutionary dynamics. Here, we extend these results with emphasis on much larger RNA with lengths up to 3000 nucleotides. By examining both abstract shapes and structural motif frequencies (i.e., the number of helices, bonds, bulges, junctions, and loops), we find that large natural and random structures are also very similar, especially when contrasted to typical structures sampled from the spaces of all possible RNA structures. Our motif frequency study yields another result, where the frequencies of different motifs can be used in machine learning algorithms to classify random and natural RNA with high accuracy, especially for longer RNA (e.g., ROC AUC 0.86 for L = 1000). The most important motifs for classification are the number of bulges, loops, and bonds. This finding may be useful in using SS to detect candidates for functional RNA within ‘junk’ DNA regions.

Probabilistic Genotype-Phenotype Maps Reveal Mutational Robustness of RNA Folding, Spin Glasses, and Quantum Circuits

Recent studies of genotype-phenotype (GP) maps have reported universally enhanced phenotypic robustness to genotype mutations, a feature essential to evolution. Virtually all of these studies make a simplifying assumption that each genotype maps deterministically to a single phenotype. Here, we introduce probabilistic genotype-phenotype (PrGP) maps, where each genotype maps to a vector of phenotype probabilities, as a more realistic framework for investigating robustness. We study three model systems to show that our generalized framework can handle uncertainty emerging from various physical sources: (1) thermal fluctuation in RNA folding, (2) external field disorder in spin glass ground state finding, and (3) superposition and entanglement in quantum circuits, which are realized experimentally on a 7-qubit IBM quantum computer. In all three cases, we observe a novel biphasic robustness scaling which is enhanced relative to random expectation for more frequent phenotypes and approaches random expectation for less frequent phenotypes.

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.

Genotype-phenotype mapping with polyominos made from DNA origami tiles

The correlation between genetic information and characteristics of a living cell-its genotype and its phenotype-constitutes the basis of genetics. Here, we experimentally realize a primitive form of genotype-phenotype mapping with DNA origami. The DNA origami can polymerize into two-dimensional lattices (phenotype) via blunt-end stacking facilitated by edge staples at the seam of the planar DNA origami. There are 80 binding positions for edge staples, which allow us to translate an 80-bit long binary code (genotype) onto the DNA origami. The presence of an edge staple thus corresponds to a "1" and its absence to a "0." The interactions of our DNA-based system can be reproduced by a polyomino model. Polyomino growth simulations qualitatively reproduce our experimental results. We show that not only the absolute number of base stacks but also their sequence position determine the cluster size and correlation length of the orientation of single DNA origami within the cluster. Importantly, the mutation of a few bits can result in major morphology changes of the DNA origami cluster, while more often, major sequence changes have no impact. Our experimental realization of a correlation between binary information ("genotype") and cluster morphology ("phenotype") thus reproduces key properties of genotype-phenotype maps known from living systems.

Predicting phenotype transition probabilities via conditional algorithmic probability approximations

Unravelling the structure of genotype-phenotype (GP) maps is an important problem in biology. Recently, arguments inspired by algorithmic information theory (AIT) and Kolmogorov complexity have been invoked to uncover simplicity bias in GP maps, an exponentially decaying upper bound in phenotype probability with the increasing phenotype descriptional complexity. This means that phenotypes with many genotypes assigned via the GP map must be simple, while complex phenotypes must have few genotypes assigned. Here, we use similar arguments to bound the probability P(x → y) that phenotype x, upon random genetic mutation, transitions to phenotype y. The bound is [Formula: see text], where [Formula: see text] is the estimated conditional complexity of y given x, quantifying how much extra information is required to make y given access to x. This upper bound is related to the conditional form of algorithmic probability from AIT. We demonstrate the practical applicability of our derived bound by predicting phenotype transition probabilities (and other related quantities) in simulations of RNA and protein secondary structures. Our work contributes to a general mathematical understanding of GP maps and may facilitate the prediction of transition probabilities directly from examining phenotype themselves, without utilizing detailed knowledge of the GP map.

Insights into the biochemical and biophysical mechanisms mediating the longevity of the transparent optics of the eye lens

In the human eye, a transparent cornea and lens combine to form the "refracton" to focus images on the retina. This requires the refracton to have a high refractive index "n," mediated largely by extracellular collagen fibrils in the corneal stroma and the highly concentrated crystallin proteins in the cytoplasm of the lens fiber cells. Transparency is a result of short-range order in the spatial arrangement of corneal collagen fibrils and lens crystallins, generated in part by post-translational modifications (PTMs). However, while corneal collagen is remodeled continuously and replaced, lens crystallins are very long-lived and are not replaced and so accumulate PTMs over a lifetime. Eventually, a tipping point is reached when protein aggregation results in increased light scatter, inevitably leading to the iconic protein condensation-based disease, age-related cataract (ARC). Cataracts account for 50% of vision impairment worldwide, affecting far more people than other well-known protein aggregation-based diseases. However, because accumulation of crystallin PTMs begins before birth and long before ARC presents, we postulate that the lens protein PTMs contribute to a "cataractogenic load" that not only increases with age but also has protective effects on optical function by stabilizing lens crystallins until a tipping point is reached. In this review, we highlight decades of experimental findings that support the potential for PTMs to be protective during normal development. We hypothesize that ARC is preventable by protecting the biochemical and biophysical properties of lens proteins needed to maintain transparency, refraction, and optical function.

Hallucinating symmetric protein assemblies

Deep learning generative approaches provide an opportunity to broadly explore protein structure space beyond the sequences and structures of natural proteins. Here, we use deep network hallucination to generate a wide range of symmetric protein homo-oligomers given only a specification of the number of protomers and the protomer length. Crystal structures of seven designs are very similar to the computational models (median root mean square deviation: 0.6 angstroms), as are three cryo-electron microscopy structures of giant 10-nanometer rings with up to 1550 residues and C33 symmetry; all differ considerably from previously solved structures. Our results highlight the rich diversity of new protein structures that can be generated using deep learning and pave the way for the design of increasingly complex components for nanomachines and biomaterials.

The structure of genotype-phenotype maps makes fitness landscapes navigable

Fitness landscapes are often described in terms of 'peaks' and 'valleys', indicating an intuitive low-dimensional landscape of the kind encountered in everyday experience. The space of genotypes, however, is extremely high dimensional, which results in counter-intuitive structural properties of genotype-phenotype maps. Here we show that these properties, such as the presence of pervasive neutral networks, make fitness landscapes navigable. For three biologically realistic genotype-phenotype map models-RNA secondary structure, protein tertiary structure and protein complexes-we find that, even under random fitness assignment, fitness maxima can be reached from almost any other phenotype without passing through fitness valleys. This in turn indicates that true fitness valleys are very rare. By considering evolutionary simulations between pairs of real examples of functional RNA sequences, we show that accessible paths are also likely to be used under evolutionary dynamics. Our findings have broad implications for the prediction of natural evolutionary outcomes and for directed evolution.

Derivable genetic programming for two-dimensional colloidal materials

We describe a method for deriving surface functionalization patterns for colloidal systems that can induce self-assembly into any chosen periodic symmetry at a planar interface. The result is a sequence of letters, s ∈ {A,T,C,G}, or a gene, that describes the perimeter of the colloidal object and programs its self-assembly. This represents a genome that is finite and can be exhaustively enumerated. These genes derive from symmetry, which may be topologically represented by two-dimensional parabolic orbifolds; since these orbifolds are surfaces that may be derived from first principles, this represents an ab initio route to colloid functionality. The genes are human readable and can be employed to easily design colloidal units. We employ a biological (genetic) analogy to demonstrate this and illustrate their connection to the designs of Maurits Cornelis (M. C.) Escher.

How gene duplication diversifies the landscape of protein oligomeric state and function

Oligomeric proteins are central to cellular life and the duplication and divergence of their genes is a key driver of evolutionary innovations. The duplication of a gene coding for an oligomeric protein has numerous possible outcomes, which motivates questions on the relationship between structural and functional divergence. How do protein oligomeric states diversify after gene duplication? In the simple case of duplication of a homo-oligomeric protein gene, what properties can influence the fate of descendant paralogs toward forming independent homomers or maintaining their interaction as a complex? Furthermore, how are functional innovations associated with the diversification of oligomeric states? Here, we review recent literature and present specific examples in an attempt to illustrate and answer these questions.

Exploring protein symmetry at the RCSB Protein Data Bank

The symmetry of biological molecules has fascinated structural biologists ever since the structure of hemoglobin was determined. The Protein Data Bank (PDB) archive is the central global archive of three-dimensional (3D), atomic-level structures of biomolecules, providing open access to the results of structural biology research with no limitations on usage. Roughly 40% of the structures in the archive exhibit some type of symmetry, including formal global symmetry, local symmetry, or pseudosymmetry. The Research Collaboratory for Structural Bioinformatics (RCSB) Protein Data Bank (founding member of the Worldwide Protein Data Bank partnership that jointly manages, curates, and disseminates the archive) provides a variety of tools to assist users interested in exploring the symmetry of biological macromolecules. These tools include multiple modalities for searching and browsing the archive, turnkey methods for biomolecular visualization, documentation, and outreach materials for exploring functional biomolecular symmetry.

Spatial patterns in ecological systems: from microbial colonies to landscapes

Self-organized spatial patterns are ubiquitous in ecological systems and allow populations to adopt non-trivial spatial distributions starting from disordered configurations. These patterns form due to diverse nonlinear interactions among organisms and between organisms and their environment, and lead to the emergence of new (eco)system-level properties unique to self-organized systems. Such pattern consequences include higher resilience and resistance to environmental changes, abrupt ecosystem collapse, hysteresis loops, and reversal of competitive exclusion. Here, we review ecological systems exhibiting self-organized patterns. We establish two broad pattern categories depending on whether the self-organizing process is primarily driven by nonlinear density-dependent demographic rates or by nonlinear density-dependent movement. Using this organization, we examine a wide range of observational scales, from microbial colonies to whole ecosystems, and discuss the mechanisms hypothesized to underlie observed patterns and their system-level consequences. For each example, we review both the empirical evidence and the existing theoretical frameworks developed to identify the causes and consequences of patterning. Finally, we trace qualitative similarities across systems and propose possible ways of developing a more quantitative understanding of how self-organization operates across systems and observational scales in ecology.

Optimal Mittag–Leffler Summation

A novel method of an optimal summation is developed that allows for calculating from small-variable asymptotic expansions the characteristic amplitudes for variables tending to infinity. The method is developed in two versions, as the self-similar Borel–Leroy or Mittag–Leffler summations. It is based on optimized self-similar iterated roots approximants applied to the Borel–Leroy and Mittag–Leffler- transformed series with the subsequent inverse transformations. As a result, simple and transparent expressions for the critical amplitudes are obtained in explicit form. The control parameters come into play from the Borel–Leroy and Mittag–Leffler transformations. They are determined from the optimization procedure, either from the minimal derivative or minimal difference conditions, imposed on the analytically expressed critical amplitudes. After diff-log transformation, virtually the same procedure can be applied to critical indices at infinity. The results are obtained for a number of various examples. The examples vary from a rapid growth of the coefficients to a fast decay, as well as intermediate cases. The methods give good estimates for the large-variable critical amplitudes and exponents. The Mittag–Leffler summation works uniformly well for a wider variety of examples.