Protein complexes are under evolutionary selection to assemble via ordered pathways.

Is the order in which proteins assemble into complexes important for biological function? Here, we seek to address this by searching for evidence of evolutionary selection for ordered protein complex assembly. First, we experimentally characterize the assembly pathways of several heteromeric complexes and show that they can be simply predicted from their three-dimensional structures. Then, by mapping gene fusion events identified from fully sequenced genomes onto protein complex assembly pathways, we demonstrate evolutionary selection for conservation of assembly order. Furthermore, using structural and high-throughput interaction data, we show that fusion tends to optimize assembly by simplifying protein complex topologies. Finally, we observe protein structural constraints on the gene order of fusion that impact the potential for fusion to affect assembly. Together, these results reveal the intimate relationships among protein assembly, quaternary structure, and evolution and demonstrate on a genome-wide scale the biological importance of ordered assembly pathways.

Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution.

SignificanceWhy does evolution favor symmetric structures when they only represent a minute subset of all possible forms? Just as monkeys randomly typing into a computer language will preferentially produce outputs that can be generated by shorter algorithms, so the coding theorem from algorithmic information theory predicts that random mutations, when decoded by the process of development, preferentially produce phenotypes with shorter algorithmic descriptions. Since symmetric structures need less information to encode, they are much more likely to appear as potential variation. Combined with an arrival-of-the-frequent mechanism, this algorithmic bias predicts a much higher prevalence of low-complexity (high-symmetry) phenotypes than follows from natural selection alone and also explains patterns observed in protein complexes, RNA secondary structures, and a gene regulatory network.

The Boltzmann distributions of molecular structures predict likely changes through random mutations.

New folded molecular structures can only evolve after arising through mutations. This aspect is modeled using genotype-phenotype maps, which connect sequence changes through mutations to changes in molecular structures. Previous work has shown that the likelihood of appearing through mutations can differ by orders of magnitude from structure to structure and that this can affect the outcomes of evolutionary processes. Thus, we focus on the phenotypic mutation probabilities φqp, i.e., the likelihood that a random mutation changes structure p into structure q. For both RNA secondary structures and the HP protein model, we show that a simple biophysical principle can explain and predict how this likelihood depends on the new structure q: φqp is high if sequences that fold into p as the minimum-free-energy structure are likely to have q as an alternative structure with high Boltzmann frequency. This generalizes the existing concept of plastogenetic congruence from individual sequences to the entire neutral spaces of structures. Our result helps us understand why some structural changes are more likely than others, may be useful for estimating these likelihoods via sampling and makes a connection to alternative structures with high Boltzmann frequency, which could be relevant in evolutionary processes.

The chaperone effect in scientific publishing.

Experience plays a critical role in crafting high-impact scientific work. This is particularly evident in top multidisciplinary journals, where a scientist is unlikely to appear as senior author if he or she has not previously published within the same journal. Here, we develop a quantitative understanding of author order by quantifying this "chaperone effect," capturing how scientists transition into senior status within a particular publication venue. We illustrate that the chaperone effect has a different magnitude for journals in different branches of science, being more pronounced in medical and biological sciences and weaker in natural sciences. Finally, we show that in the case of high-impact venues, the chaperone effect has significant implications, specifically resulting in a higher average impact relative to papers authored by new principal investigators (PIs). Our findings shed light on the role played by experience in publishing within specific scientific journals, on the paths toward acquiring the necessary experience and expertise, and on the skills required to publish in prestigious venues.

Evolution of interface binding strengths in simplified model of protein quaternary structure.

The self-assembly of proteins into protein quaternary structures is of fundamental importance to many biological processes, and protein misassembly is responsible for a wide range of proteopathic diseases. In recent years, abstract lattice models of protein self-assembly have been used to simulate the evolution and assembly of protein quaternary structure, and to provide a tractable way to study the genotype-phenotype map of such systems. Here we generalize these models by representing the interfaces as mutable binary strings. This simple change enables us to model the evolution of interface strengths, interface symmetry, and deterministic assembly pathways. Using the generalized model we are able to reproduce two important results established for real protein complexes: The first is that protein assembly pathways are under evolutionary selection to minimize misassembly. The second is that the assembly pathway of a complex mirrors its evolutionary history, and that both can be derived from the relative strengths of interfaces. These results demonstrate that the generalized lattice model offers a powerful new idealized framework to facilitate the study of protein self-assembly processes and their evolution.

Social network fragmentation and community health.

Community health interventions often seek to intentionally destroy paths between individuals to prevent the spread of infectious diseases. Immunizing individuals through direct vaccination or the provision of health education prevents pathogen transmission and the propagation of misinformation concerning medical treatments. However, it remains an open question whether network-based strategies should be used in place of conventional field approaches to target individuals for medical treatment in low-income countries. We collected complete friendship and health advice networks in 17 rural villages of Mayuge District, Uganda. Here we show that acquaintance algorithms, i.e., selecting neighbors of randomly selected nodes, were systematically more efficient in fragmenting all networks than targeting well-established community roles, i.e., health workers, village government members, and schoolteachers. Additionally, community roles were not good proxy indicators of physical proximity to other households or connections to many sick people. We also show that acquaintance algorithms were effective in offsetting potential noncompliance with deworming treatments for 16,357 individuals during mass drug administration (MDA). Health advice networks were destroyed more easily than friendship networks. Only an average of 32% of nodes were removed from health advice networks to reduce the percentage of nodes at risk for refusing treatment in MDA to below 25%. Treatment compliance of at least 75% is needed in MDA to control human morbidity attributable to parasitic worms and progress toward elimination. Our findings point toward the potential use of network-based approaches as an alternative to role-based strategies for targeting individuals in rural health interventions.

A Gene Regulatory Network for Cellular Reprogramming in Plant Regeneration.

Wounding triggers organ regeneration in many plant species, and application of plant hormones, such as auxin and cytokinin, enhances their regenerative capacities in tissue culture. Recent studies have identified several key players mediating wound- and/or plant hormone-induced cellular reprogramming, but the global architecture of gene regulatory relationships underlying plant cellular reprogramming is still far from clear. In this study, we uncovered a gene regulatory network (GRN) associated with plant cellular reprogramming by using an enhanced yeast one-hybrid (eY1H) screen systematically to identify regulatory relationships between 252 transcription factors (TFs) and 48 promoters. Our network analyses suggest that wound- and/or hormone-invoked signals exhibit extensive cross-talk and regulate many common reprogramming-associated genes via multilayered regulatory cascades. Our data suggest that PLETHORA 3 (PLT3), ENHANCER OF SHOOT REGENERATION 1 (ESR1) and HEAT SHOCK FACTOR B 1 (HSFB1) act as critical nodes that have many overlapping targets and potentially connect upstream stimuli to downstream developmental decisions. Interestingly, a set of wound-inducible APETALA 2/ETHYLENE RESPONSE FACTORs (AP2/ERFs) appear to regulate these key genes, which, in turn, form feed-forward cascades that control downstream targets associated with callus formation and organ regeneration. In addition, we found another regulatory pathway, mediated by LATERAL ORGAN BOUNDARY/ASYMMETRIC LEAVES 2 (LOB/AS2) TFs, which probably plays a distinct but partially overlapping role alongside the AP2/ERFs in the putative gene regulatory cascades. Taken together, our findings provide the first global picture of the GRN governing plant cell reprogramming, which will serve as a valuable resource for future studies.

Genetic Correlations Greatly Increase Mutational Robustness and Can Both Reduce and Enhance Evolvability.

Mutational neighbourhoods in genotype-phenotype (GP) maps are widely believed to be more likely to share characteristics than expected from random chance. Such genetic correlations should strongly influence evolutionary dynamics. We explore and quantify these intuitions by comparing three GP maps-a model for RNA secondary structure, the HP model for protein tertiary structure, and the Polyomino model for protein quaternary structure-to a simple random null model that maintains the number of genotypes mapping to each phenotype, but assigns genotypes randomly. The mutational neighbourhood of a genotype in these GP maps is much more likely to contain genotypes mapping to the same phenotype than in the random null model. Such neutral correlations can be quantified by the robustness to mutations, which can be many orders of magnitude larger than that of the null model, and crucially, above the critical threshold for the formation of large neutral networks of mutationally connected genotypes which enhance the capacity for the exploration of phenotypic novelty. Thus neutral correlations increase evolvability. We also study non-neutral correlations: Compared to the null model, i) If a particular (non-neutral) phenotype is found once in the 1-mutation neighbourhood of a genotype, then the chance of finding that phenotype multiple times in this neighbourhood is larger than expected; ii) If two genotypes are connected by a single neutral mutation, then their respective non-neutral 1-mutation neighbourhoods are more likely to be similar; iii) If a genotype maps to a folding or self-assembling phenotype, then its non-neutral neighbours are less likely to be a potentially deleterious non-folding or non-assembling phenotype. Non-neutral correlations of type i) and ii) reduce the rate at which new phenotypes can be found by neutral exploration, and so may diminish evolvability, while non-neutral correlations of type iii) may instead facilitate evolutionary exploration and so increase evolvability.

The rich club of the C. elegans neuronal connectome.

There is increasing interest in topological analysis of brain networks as complex systems, with researchers often using neuroimaging to represent the large-scale organization of nervous systems without precise cellular resolution. Here we used graph theory to investigate the neuronal connectome of the nematode worm Caenorhabditis elegans, which is defined anatomically at a cellular scale as 2287 synaptic connections between 279 neurons. We identified a small number of highly connected neurons as a rich club (N = 11) interconnected with high efficiency and high connection distance. Rich club neurons comprise almost exclusively the interneurons of the locomotor circuits, with known functional importance for coordinated movement. The rich club neurons are connector hubs, with high betweenness centrality, and many intermodular connections to nodes in different modules. On identifying the shortest topological paths (motifs) between pairs of peripheral neurons, the motifs that are found most frequently traverse the rich club. The rich club neurons are born early in development, before visible movement of the animal and before the main phase of developmental elongation of its body. We conclude that the high wiring cost of the globally integrative rich club of neurons in the C. elegans connectome is justified by the adaptive value of coordinated movement of the animal. The economical trade-off between physical cost and behavioral value of rich club organization in a cellular connectome confirms theoretical expectations and recapitulates comparable results from human neuroimaging on much larger scale networks, suggesting that this may be a general and scale-invariant principle of brain network organization.

The non-deterministic genotype-phenotype map of RNA secondary structure.

Selection and variation are both key aspects in the evolutionary process. Previous research on the mapping between molecular sequence (genotype) and molecular fold (phenotype) has shown the presence of several structural properties in different biological contexts, implying that these might be universal in evolutionary spaces. The deterministic genotype-phenotype (GP) map that links short RNA sequences to minimum free energy secondary structures has been studied extensively because of its computational tractability and biologically realistic nature. However, this mapping ignores the phenotypic plasticity of RNA. We define a GP map that incorporates non-deterministic (ND) phenotypes, and take RNA as a case study; we use the Boltzmann probability distribution of folded structures and examine the structural properties of ND GP maps for RNA sequences of length 12 and coarse-grained RNA structures of length 30 (RNAshapes30). A framework is presented to study robustness, evolvability and neutral spaces in the ND map. This framework is validated by demonstrating close correspondence between the ND quantities and sample averages of their deterministic counterparts. When using the ND framework we observe the same structural properties as in the deterministic GP map, such as bias, negative correlation between genotypic robustness and evolvability, and positive correlation between phenotypic robustness and evolvability.

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.

The emergence of protein complexes: quaternary structure, dynamics and allostery. Colworth Medal Lecture.

All proteins require physical interactions with other proteins in order to perform their functions. Most of them oligomerize into homomers, and a vast majority of these homomers interact with other proteins, at least part of the time, forming transient or obligate heteromers. In the present paper, we review the structural, biophysical and evolutionary aspects of these protein interactions. We discuss how protein function and stability benefit from oligomerization, as well as evolutionary pathways by which oligomers emerge, mostly from the perspective of homomers. Finally, we emphasize the specificities of heteromeric complexes and their structure and evolution. We also discuss two analytical approaches increasingly being used to study protein structures as well as their interactions. First, we review the use of the biological networks and graph theory for analysis of protein interactions and structure. Secondly, we discuss recent advances in techniques for detecting correlated mutations, with the emphasis on their role in identifying pathways of allosteric communication.

Fast free-energy-based neutral set size estimates for the RNA genotype-phenotype map.

The genotype-phenotype (GP) map of RNA secondary structure links each RNA sequence to its corresponding secondary structure. Previous research has shown that the large-scale structural properties of GP maps, such as the size of neutral sets in genotype space, can influence evolutionary outcomes. In order to use neutral set sizes, efficient and accurate computational methods are needed to compute them. Here, we propose a new method, which is based on free energy estimates and is much faster than existing sample-based methods. Moreover, this approach can give insight into the reasons behind neutral set size variations, for example, why structures with fewer stacks tend to have larger neutral set sizes. In addition, we generalize neutral set size calculations from the previously studied many-to-one framework, where each sequence folds into a single energetically preferred structure, to a fuller many-to-many framework, where several low-energy structures are included. We find that structures with high neutral sets in one framework also tend to have large neutral sets in the other framework for a range of parameters and thus the choice of GP map does not fundamentally affect which structures have the largest neutral set sizes.

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.

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.

Insertions and deletions in the RNA sequence-structure map.

Genotype-phenotype maps link genetic changes to their fitness effect and are thus an essential component of evolutionary models. The map between RNA sequences and their secondary structures is a key example and has applications in functional RNA evolution. For this map, the structural effect of substitutions is well understood, but models usually assume a constant sequence length and do not consider insertions or deletions. Here, we expand the sequence-structure map to include single nucleotide insertions and deletions by using the RNAshapes concept. To quantify the structural effect of insertions and deletions, we generalize existing definitions for robustness and non-neutral mutation probabilities. We find striking similarities between substitutions, deletions and insertions: robustness to substitutions is correlated with robustness to insertions and, for most structures, to deletions. In addition, frequent structural changes after substitutions also tend to be common for insertions and deletions. This is consistent with the connection between energetically suboptimal folds and possible structural transitions. The similarities observed hold both for genotypic and phenotypic robustness and mutation probabilities, i.e. for individual sequences and for averages over sequences with the same structure. Our results could have implications for the rate of neutral and non-neutral evolution.

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics.

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

Cell-by-cell dissection of phloem development links a maturation gradient to cell specialization.

In the plant meristem, tissue-wide maturation gradients are coordinated with specialized cell networks to establish various developmental phases required for indeterminate growth. Here, we used single-cell transcriptomics to reconstruct the protophloem developmental trajectory from the birth of cell progenitors to terminal differentiation in the Arabidopsis thaliana root. PHLOEM EARLY DNA-BINDING-WITH-ONE-FINGER (PEAR) transcription factors mediate lineage bifurcation by activating guanosine triphosphatase signaling and prime a transcriptional differentiation program. This program is initially repressed by a meristem-wide gradient of PLETHORA transcription factors. Only the dissipation of PLETHORA gradient permits activation of the differentiation program that involves mutual inhibition of early versus late meristem regulators. Thus, for phloem development, broad maturation gradients interface with cell-type-specific transcriptional regulators to stage cellular differentiation.

Detecting separate time scales in genetic expression data.

BACKGROUND: Biological processes occur on a vast range of time scales, and many of them occur concurrently. As a result, system-wide measurements of gene expression have the potential to capture many of these processes simultaneously. The challenge however, is to separate these processes and time scales in the data. In many cases the number of processes and their time scales is unknown. This issue is particularly relevant to developmental biologists, who are interested in processes such as growth, segmentation and differentiation, which can all take place simultaneously, but on different time scales. RESULTS: We introduce a flexible and statistically rigorous method for detecting different time scales in time-series gene expression data, by identifying expression patterns that are temporally shifted between replicate datasets. We apply our approach to a Saccharomyces cerevisiae cell-cycle dataset and an Arabidopsis thaliana root developmental dataset. In both datasets our method successfully detects processes operating on several different time scales. Furthermore we show that many of these time scales can be associated with particular biological functions. CONCLUSIONS: The spatiotemporal modules identified by our method suggest the presence of multiple biological processes, acting at distinct time scales in both the Arabidopsis root and yeast. Using similar large-scale expression datasets, the identification of biological processes acting at multiple time scales in many organisms is now possible.