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The plant cell wall is an important factor for determining cell shape, function and response to the environment. Secondary cell walls, such as those found in xylem, are composed of cellulose, hemicelluloses and lignin and account for the bulk of plant biomass. The coordination between transcriptional regulation of synthesis for each polymer is complex and vital to cell function. A regulatory hierarchy of developmental switches has been proposed, although the full complement of regulators remains unknown. Here we present a protein-DNA network between Arabidopsis thaliana transcription factors and secondary cell wall metabolic genes with gene expression regulated by a series of feed-forward loops. This model allowed us to develop and validate new hypotheses about secondary wall gene regulation under abiotic stress. Distinct stresses are able to perturb targeted genes to potentially promote functional adaptation. These interactions will serve as a foundation for understanding the regulation of a complex, integral plant component.

Abstract 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.

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 φ qp , 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: φ qp 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., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2023 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

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.

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.

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.

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., (© 2022. Crown.)

Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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.

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.

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.

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.

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., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 The Authors. Published by Elsevier B.V. All rights reserved.)

Co-expression networks are a powerful tool to understand gene regulation. They have been used to identify new regulation and function of genes involved in plant development and their response to the environment. Up to now, co-expression networks have been inferred using transcriptomes generated on plants experiencing genetic or environmental perturbation, or from expression time series. We propose a new approach by showing that co-expression networks can be constructed in the absence of genetic and environmental perturbation, for plants at the same developmental stage. For this, we used transcriptomes that were generated from genetically identical individual plants that were grown under the same conditions and for the same amount of time. Twelve time points were used to cover the 24-h light/dark cycle. We used variability in gene expression between individual plants of the same time point to infer a co-expression network. We show that this network is biologically relevant and use it to suggest new gene functions and to identify new targets for the transcriptional regulators GI, PIF4, and PRR5. Moreover, we find different co-regulation in this network based on changes in expression between individual plants, compared to the usual approach requiring environmental perturbation. Our work shows that gene co-expression networks can be identified using variability in gene expression between individual plants, without the need for genetic or environmental perturbations. It will allow further exploration of gene regulation in contexts with subtle differences between plants, which could be closer to what individual plants in a population might face in the wild., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2020 Cortijo, Bhattarai, Locke and Ahnert.)

Genotype-phenotype (GP) maps describe the relationship between biological sequences and structural or functional outcomes. They can be represented as networks in which genotypes are the nodes, and one-point mutations between them are the edges. The genotypes that map to the same phenotype form subnetworks consisting of one or multiple disjoint connected components-so-called neutral components (NCs). For the GP map of RNA secondary structure, the NCs have been found to exhibit distinctive network features that can affect the dynamical processes taking place on them. Here, we focus on the community structure of RNA secondary structure NCs. Building on previous findings, we introduce a method to reveal the hierarchical community structure solely from the sequence constraints and composition of the genotypes that form a given NC. Thereby, we obtain modularity values similar to common community detection algorithms, which are much more complex. From this knowledge, we endorse a sampling method that allows a fast exploration of the different communities of a given NC. Furthermore, we introduce a way to estimate the community structure from genotype samples, which is useful when an exhaustive analysis of the NC is not feasible, as is the case for longer sequence lengths.

In genotype-phenotype (GP) maps, the genotypes that map to the same phenotype are usually not randomly distributed across the space of genotypes, but instead are predominantly connected through one-point mutations, forming network components that are commonly referred to as neutral components (NCs). Because of their impact on evolutionary processes, the characteristics of these NCs, like their size or robustness, have been studied extensively. Here, we introduce a framework that allows the estimation of NC size and robustness in the GP map of RNA secondary structure. The advantage of this framework is that it only requires small samples of genotypes and their local environment, which also allows experimental realizations. We verify our framework by applying it to the exhaustively analysable GP map of RNA sequence length L = 15, and benchmark it against an existing method by applying it to longer, naturally occurring functional non-coding RNA sequences. Although it is specific to the RNA secondary structure GP map in the first place, our framework can probably be transferred and adapted to other sequence-to-structure GP maps.

Vascular cambium, a lateral plant meristem, is a central producer of woody biomass. Although a few transcription factors have been shown to regulate cambial activity 1 , the phenotypes of the corresponding loss-of-function mutants are relatively modest, highlighting our limited understanding of the underlying transcriptional regulation. Here, we use cambium cell-specific transcript profiling followed by a combination of transcription factor network and genetic analyses to identify 62 new transcription factor genotypes displaying an array of cambial phenotypes. This approach culminated in virtual loss of cambial activity when both WUSCHEL-RELATED HOMEOBOX 4 (WOX4) and KNOTTED-like from Arabidopsis thaliana 1 (KNAT1; also known as BREVIPEDICELLUS) were mutated, thereby unlocking the genetic redundancy in the regulation of cambium development. We also identified transcription factors with dual functions in cambial cell proliferation and xylem differentiation, including WOX4, SHORT VEGETATIVE PHASE (SVP) and PETAL LOSS (PTL). Using the transcription factor network information, we combined overexpression of the cambial activator WOX4 and removal of the putative inhibitor PTL to engineer Arabidopsis for enhanced radial growth. This line also showed ectopic cambial activity, thus further highlighting the central roles of WOX4 and PTL in cambium development.

The study of brain networks, including those derived from functional neuroimaging data, attracts a broad interest and represents a rapidly growing interdisciplinary field. Comparing networks of healthy volunteers with those of patients can potentially offer new, quantitative diagnostic methods and a framework for better understanding brain and mind disorders. We explore resting state functional Magnetic Resonance Imaging (fMRI) data through network measures. We construct networks representing 15 healthy individuals and 12 schizophrenia patients (males and females), all of whom are administered three drug treatments: i) a placebo; and two antipsychotic medications ii) aripiprazole and iii) sulpiride. We compare these resting state networks to a performance at an "N-back" working memory task. We demonstrate that not only is there a distinctive network architecture in the healthy brain that is disrupted in schizophrenia but also that both networks respond to antipsychotic medication. We first reproduce the established finding that brain networks of schizophrenia patients exhibit increased efficiency and reduced clustering compared with controls. Our data then reveal that the antipsychotic medications mitigate this effect, shifting the metrics toward those observed in healthy volunteers, with a marked difference in efficacy between the two drugs. Additionally, we find that aripiprazole considerably alters the network statistics of healthy controls. Examining the "N-back" working memory task, we establish that aripiprazole also adversely affects their performance. This suggests that changes to macroscopic brain network architecture result in measurable behavioral differences. This is one of the first studies to directly compare different medications using a whole-brain graph theoretical analysis with accompanying behavioral data. The small sample size is an inherent limitation and means a degree of caution is warranted in interpreting the findings. Our results lay the groundwork for an objective methodology with which to calculate and compare the efficacy of different treatments of mind and brain disorders., (Copyright © 2019 Towlson, Vértes, Müller-Sedgwick and Ahnert.)

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., Competing Interests: The authors have declared that no competing interests exist.

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., Competing Interests: The authors declare no conflict of interest.

Self-assembly processes are widespread in nature and lie at the heart of many biological and physical phenomena. The characteristics of self-assembly building blocks determine the structures that they form. Two crucial properties are the determinism and boundedness of the self-assembly. The former tells us whether the same set of building blocks always generates the same structure, and the latter whether it grows indefinitely. These properties are highly relevant in the context of protein structures, as the difference between deterministic protein self-assembly and nondeterministic protein aggregation is central to a number of diseases. Here we introduce a graph theoretical approach that can determine the determinism and boundedness for several geometries and dimensionalities of self-assembly more accurately and quickly than conventional methods. We apply this methodology to a previously studied lattice self-assembly model and discuss generalizations to a wide range of other self-assembling systems.

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.

The mapping between biological genotypes and phenotypes plays an important role in evolution, and understanding the properties of this mapping is crucial to determine the outcome of evolutionary processes. One of the most striking properties observed in several genotype-phenotype (GP) maps is the positive correlation between the robustness and evolvability of phenotypes. This implies that a phenotype can be strongly robust against mutations and at the same time evolvable to a diverse range of alternative phenotypes. Here, we examine the causes for this positive correlation by introducing two analytically tractable GP map models that follow the principles of real biological GP maps. The first model is based on gene-like GP maps, reflecting the way in which genetic sequences are organized into protein-coding genes, and the second one is based on the GP map of RNA secondary structure. For both models, we find that a positive correlation between phenotype robustness and evolvability only emerges if mutations at one sequence position can have non-local effects on the sequence constraints at another position. This highlights that non-local effects of mutations are closely related to the coexistence of robustness and evolvability in phenotypes, and are likely to be an important feature of many biological GP maps., (© 2018 The Author(s).)

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., Competing Interests: Conflict of interest statement: G.F.C. and S.E.A. declare no competing interests. N.B.K. is employed by the Schistosomiasis Control Initiative (SCI). E.M.T. is the Assistant Commissioner of Health Services for the Vector Control Division of Ministry of Health and the National Coordinator for SCI of the Neglected Tropical Disease Control/Elimination Programme in Uganda.

The map between genotype and phenotype is fundamental to biology. Biological information is stored and passed on in the form of genotypes, and expressed in the form of phenotypes. A growing body of literature has examined a wide range of genotype-phenotype (GP) maps and has established a number of properties that appear to be shared by many GP maps. These properties are 'structural' in the sense that they are properties of the distribution of phenotypes across the point-mutation network of genotypes. They include: a redundancy of genotypes, meaning that many genotypes map to the same phenotypes, a highly non-uniform distribution of the number of genotypes per phenotype, a high robustness of phenotypes and the ability to reach a large number of new phenotypes within a small number of mutational steps. A further important property is that the robustness and evolvability of phenotypes are positively correlated. In this review, I give an overview of the study of GP maps with particular emphasis on these structural properties, and discuss a model that attempts to explain why these properties arise, as well as some of the fundamental ways in which the structure of GP maps can affect evolutionary outcomes., (© 2017 The Author(s).)

Amino acid networks (AANs) abstract the protein structure by recording the amino acid contacts and can provide insight into protein function. Herein, we describe a novel AAN construction technique that employs the rigidity analysis tool, FIRST, to build the AAN, which we refer to as the residue geometry network (RGN). We show that this new construction can be combined with network theory methods to include the effects of allowed conformal motions and local chemical environments. Importantly, this is done without costly molecular dynamics simulations required by other AAN-related methods, which allows us to analyse large proteins and/or data sets. We have calculated the centrality of the residues belonging to 795 proteins. The results display a strong, negative correlation between residue centrality and the evolutionary rate. Furthermore, among residues with high closeness, those with low degree were particularly strongly conserved. Random walk simulations using the RGN were also successful in identifying allosteric residues in proteins involved in GPCR signalling. The dynamic function of these residues largely remain hidden in the traditional distance-cutoff construction technique. Despite being constructed from only the crystal structure, the results in this paper suggests that the RGN can identify residues that fulfil a dynamical function.

We investigate general properties of nondeterministic self-assembly with asymmetric interactions, using a computational model and DNA tile assembly experiments. By contrasting symmetric and asymmetric interactions we show that the latter can lead to self-limiting cluster growth. Furthermore, by adjusting the relative abundance of self-assembly particles in a two-particle mixture, we are able to tune the final sizes of these clusters. We show that this is a fundamental property of asymmetric interactions, which has potential applications in bioengineering, and provides insights into the study of diseases caused by protein aggregation.

Network motifs have been studied extensively over the past decade, and certain motifs, such as the feed-forward loop, play an important role in regulatory networks. Recent studies have used Boolean network motifs to explore the link between form and function in gene regulatory networks and have found that the structure of a motif does not strongly determine its function, if this is defined in terms of the gene expression patterns the motif can produce. Here, we offer a different, higher-level definition of the 'function' of a motif, in terms of two fundamental properties of its dynamical state space as a Boolean network. One is the basin entropy, which is a complexity measure of the dynamics of Boolean networks. The other is the diversity of cyclic attractor lengths that a given motif can produce. Using these two measures, we examine all 104 topologically distinct three-node motifs and show that the structural properties of a motif, such as the presence of feedback loops and feed-forward loops, predict fundamental characteristics of its dynamical state space, which in turn determine aspects of its functional versatility. We also show that these higher-level properties have a direct bearing on real regulatory networks, as both basin entropy and cycle length diversity show a close correspondence with the prevalence, in neural and genetic regulatory networks, of the 13 connected motifs without self-interactions that have been studied extensively in the literature., (© 2016 The Authors.)

Self-assembly is ubiquitous in nature, particularly in biology, where it underlies the formation of protein quaternary structure and protein aggregation. Quaternary structure assembles deterministically and performs a wide range of important functions in the cell, whereas protein aggregation is the hallmark of a number of diseases and represents a nondeterministic self-assembly process. Here we build on previous work on a lattice model of deterministic self-assembly to investigate nondeterministic self-assembly of single lattice tiles and mixtures of two tiles at varying relative concentrations. Despite limiting the simplicity of the model to two interface types, which results in 13 topologically distinct single tiles and 106 topologically distinct sets of two tiles, we observe a wide variety of concentration-dependent behaviors. Several two-tile sets display critical behaviors in the form of a sharp transition from bound to unbound structures as the relative concentration of one tile to another increases. Other sets exhibit gradual monotonic changes in structural density, or nonmonotonic changes, while again others show no concentration dependence at all. We catalog this extensive range of behaviors and present a model that provides a reasonably good estimate of the critical concentrations for a subset of the critical transitions. In addition, we show that the structures resulting from these tile sets are fractal, with one of two different fractal dimensions.

Structural insights into protein complexes have had a broad impact on our understanding of biological function and evolution. In this work, we sought a comprehensive understanding of the general principles underlying quaternary structure organization in protein complexes. We first examined the fundamental steps by which protein complexes can assemble, using experimental and structure-based characterization of assembly pathways. Most assembly transitions can be classified into three basic types, which can then be used to exhaustively enumerate a large set of possible quaternary structure topologies. These topologies, which include the vast majority of observed protein complex structures, enable a natural organization of protein complexes into a periodic table. On the basis of this table, we can accurately predict the expected frequencies of quaternary structure topologies, including those not yet observed. These results have important implications for quaternary structure prediction, modeling, and engineering., (Copyright © 2015, American Association for the Advancement of Science.)

Biological information is stored in DNA, RNA and protein sequences, which can be understood as genotypes that are translated into phenotypes. The properties of genotype-phenotype (GP) maps have been studied in great detail for RNA secondary structure. These include a highly biased distribution of genotypes per phenotype, negative correlation of genotypic robustness and evolvability, positive correlation of phenotypic robustness and evolvability, shape-space covering, and a roughly logarithmic scaling of phenotypic robustness with phenotypic frequency. More recently similar properties have been discovered in other GP maps, suggesting that they may be fundamental to biological GP maps, in general, rather than specific to the RNA secondary structure map. Here we propose that the above properties arise from the fundamental organization of biological information into 'constrained' and 'unconstrained' sequences, in the broadest possible sense. As 'constrained' we describe sequences that affect the phenotype more immediately, and are therefore more sensitive to mutations, such as, e.g. protein-coding DNA or the stems in RNA secondary structure. 'Unconstrained' sequences, on the other hand, can mutate more freely without affecting the phenotype, such as, e.g. intronic or intergenic DNA or the loops in RNA secondary structure. To test our hypothesis we consider a highly simplified GP map that has genotypes with 'coding' and 'non-coding' parts. We term this the Fibonacci GP map, as it is equivalent to the Fibonacci code in information theory. Despite its simplicity the Fibonacci GP map exhibits all the above properties of much more complex and biologically realistic GP maps. These properties are therefore likely to be fundamental to many biological GP maps., (© 2015 The Authors.)

Proteins assemble into complexes with diverse quaternary structures. Although most heteromeric complexes of known structure have even stoichiometry, a significant minority have uneven stoichiometry--that is, differing numbers of each subunit type. To adopt this uneven stoichiometry, sequence-identical subunits must be asymmetric with respect to each other, forming different interactions within the complex. Here we first investigate the occurrence of uneven stoichiometry, demonstrating that it is common in vitro and is likely to be common in vivo. Next, we elucidate the structural determinants of uneven stoichiometry, identifying six different mechanisms by which it can be achieved. Finally, we study the frequency of uneven stoichiometry across evolution, observing a significant enrichment in bacteria compared with eukaryotes. We show that this arises due to a general increased tendency for bacterial proteins to self-assemble and form homomeric interactions, even within the context of a heteromeric complex.

Competition is ubiquitous in many complex biological, social, and technological systems, playing an integral role in the evolutionary dynamics of the systems. It is often useful to determine the dominance hierarchy or the rankings of the components of the system that compete for survival and success based on the outcomes of the competitions between them. Here we propose a ranking method based on the random walk on the network representing the competitors as nodes and competitions as directed edges with asymmetric weights. We use the edge weights and node degrees to define the gradient on each edge that guides the random walker towards the weaker (or the stronger) node, which enables us to interpret the steady-state occupancy as the measure of the node's weakness (or strength) that is free of unwarranted degree-induced bias. We apply our method to two real-world competition networks and explore the issues of ranking stabilization and prediction accuracy, finding that our method outperforms other methods including the baseline win-loss differential method in sparse networks.

The provision of healthcare in rural African communities is a highly complex and largely unsolved problem. Two main difficulties are the identification of individuals that are most likely affected by disease and the prediction of responses to health interventions. Social networks have been shown to capture health outcomes in a variety of contexts. Yet, it is an open question as to what extent social network analysis can identify and distinguish among households that are most likely to report poor health and those most likely to respond to positive behavioural influences. We use data from seven highly remote, post-conflict villages in Liberia and compare two prominent network measures: in-degree and betweenness. We define in-degree as the frequency in which members from one household are named by another household as a friends. Betweenness is defined as the proportion of shortest friendship paths between any two households in a network that traverses a particular household. We find that in-degree explains the number of ill family members, whereas betweenness explains engagement in preventative health. In-degree and betweenness independently explained self-reported health and behaviour, respectively. Further, we find that betweenness predicts susceptibility to, instead of influence over, good health behaviours. The results suggest that targeting households based on network measures rather than health status may be effective for promoting the uptake of health interventions in rural poor villages.

The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here, we introduce a rich, intuitive and biologically realistic genotype-phenotype (GP) map that serves as a model of self-assembling biological structures, such as protein complexes, and remains computationally and analytically tractable. Our GP map arises naturally from the self-assembly of polyomino structures on a two-dimensional lattice and exhibits a number of properties: redundancy (genotypes vastly outnumber phenotypes), phenotype bias (genotypic redundancy varies greatly between phenotypes), genotype component disconnectivity (phenotypes consist of disconnected mutational networks) and shape space covering (most phenotypes can be reached in a small number of mutations). We also show that the mutational robustness of phenotypes scales very roughly logarithmically with phenotype redundancy and is positively correlated with phenotypic evolvability. Although our GP map describes the assembly of disconnected objects, it shares many properties with other popular GP maps for connected units, such as models for RNA secondary structure or the hydrophobic-polar (HP) lattice model for protein tertiary structure. The remarkable fact that these important properties similarly emerge from such different models suggests the possibility that universal features underlie a much wider class of biologically realistic GP maps.

We introduce a framework for the discovery of dominant relationship patterns in complex networks, by compressing the networks into power graphs with overlapping power nodes. When paired with enrichment analysis of node classification terms, the most compressible sets of edges provide a highly informative sketch of the dominant relationship patterns that define the network. In addition, this procedure also gives rise to a novel, link-based definition of overlapping node communities in which nodes are defined by their relationships with sets of other nodes, rather than through connections within the community. We show that this completely general approach can be applied to undirected, directed, and bipartite networks, yielding valuable insights into the large-scale structure of real-world networks, including social networks and food webs. Our approach therefore provides a novel way in which network architecture can be studied, defined and classified.

We introduce a framework for the discovery of dominant relationship patterns in transcription networks, by compressing the network into a power graph with overlapping power nodes. Our application of this approach to the transcription networks of S. cerevisiae and E. coli, paired with GO term enrichment analysis, provides a highly informative overview of the most prominent relationships in the gene regulatory networks of these two organisms.

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., (Copyright © 2013 Elsevier Inc. All rights reserved.)

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.