Understanding Higher-Order Interactions in Information Space.

Methods used in topological data analysis naturally capture higher-order interactions in point cloud data embedded in a metric space. This methodology was recently extended to data living in an information space, by which we mean a space measured with an information theoretical distance. One such setting is a finite collection of discrete probability distributions embedded in the probability simplex measured with the relative entropy (Kullback-Leibler divergence). More generally, one can work with a Bregman divergence parameterized by a different notion of entropy. While theoretical algorithms exist for this setup, there is a paucity of implementations for exploring and comparing geometric-topological properties of various information spaces. The interest of this work is therefore twofold. First, we propose the first robust algorithms and software for geometric and topological data analysis in information space. Perhaps surprisingly, despite working with Bregman divergences, our design reuses robust libraries for the Euclidean case. Second, using the new software, we take the first steps towards understanding the geometric-topological structure of these spaces. In particular, we compare them with the more familiar spaces equipped with the Euclidean and Fisher metrics.

Developing the 'omic toolkit of comparative physiologists.

Typical 'omic analyses reduce complex biological systems to simple lists of supposedly independent variables, failing to account for changes in the wider transcriptional landscape. In this commentary, we discuss the utility of network approaches for incorporating this wider context into the study of physiological phenomena. We highlight opportunities to build on traditional network tools by utilising cutting-edge techniques to account for higher order interactions (i.e. beyond pairwise associations) within datasets, allowing for more accurate models of complex 'omic systems. Finally, we show examples of previous works utilising network approaches to gain additional insight into their organisms of interest. As 'omics grow in both their popularity and breadth of application, so does the requirement for flexible analytical tools capable of interpreting and synthesising complex datasets.

Triadic percolation induces dynamical topological patterns in higher-order networks.

Triadic interactions are higher-order interactions which occur when a set of nodes affects the interaction between two other nodes. Examples of triadic interactions are present in the brain when glia modulate the synaptic signals among neuron pairs or when interneuron axo-axonic synapses enable presynaptic inhibition and facilitation, and in ecosystems when one or more species can affect the interaction among two other species. On random graphs, triadic percolation has been recently shown to turn percolation into a fully fledged dynamical process in which the size of the giant component undergoes a route to chaos. However, in many real cases, triadic interactions are local and occur on spatially embedded networks. Here, we show that triadic interactions in spatial networks induce a very complex spatio-temporal modulation of the giant component which gives rise to triadic percolation patterns with significantly different topology. We classify the observed patterns (stripes, octopus, and small clusters) with topological data analysis and we assess their information content (entropy and complexity). Moreover, we illustrate the multistability of the dynamics of the triadic percolation patterns, and we provide a comprehensive phase diagram of the model. These results open new perspectives in percolation as they demonstrate that in presence of spatial triadic interactions, the giant component can acquire a time-varying topology. Hence, this work provides a theoretical framework that can be applied to model realistic scenarios in which the giant component is time dependent as in neuroscience.

Distinct Network Patterns Emerge from Cartesian and XOR Epistasis Models: A Comparative Network Science Analysis.

Background: Epistasis, the phenomenon where the effect of one gene (or variant) is masked or modified by one or more other genes, can significantly contribute to the observed phenotypic variance of complex traits. To date, it has been generally assumed that genetic interactions can be detected using a Cartesian, or multiplicative, interaction model commonly utilized in standard regression approaches. However, a recent study investigating epistasis in obesity-related traits in rats and mice has identified potential limitations of the Cartesian model, revealing that it only detects some of the genetic interactions occurring in these systems. By applying an alternative approach, the exclusive-or (XOR) model, the researchers detected a greater number of epistatic interactions and identified more biologically relevant ontological terms associated with the interacting loci. This suggests that the XOR model may provide a more comprehensive understanding of epistasis in these species and phenotypes. To further explore these findings and determine if different interaction models also make up distinct epistatic networks, we leverage network science to provide a more comprehensive view into the genetic interactions underlying BMI in this system. Results: Our comparative analysis of networks derived from Cartesian and XOR interaction models in rats (Rattus norvegicus) uncovers distinct topological characteristics for each model-derived network. Notably, we discover that networks based on the XOR model exhibit an enhanced sensitivity to epistatic interactions. This sensitivity enables the identification of network communities, revealing novel trait-related biological functions through enrichment analysis. Furthermore, we identify triangle network motifs in the XOR epistatic network, suggestive of higher-order epistasis, based on the topology of lower-order epistasis. Conclusions: These findings highlight the XOR model's ability to uncover meaningful biological associations as well as higher-order epistasis from lower-order epistatic networks. Additionally, our results demonstrate that network approaches not only enhance epistasis detection capabilities but also provide more nuanced understandings of genetic architectures underlying complex traits. The identification of community structures and motifs within these distinct networks, especially in XOR, points to the potential for network science to aid in the discovery of novel genetic pathways and regulatory networks. Such insights are important for advancing our understanding of phenotype-genotype relationships.

When can higher-order interactions produce stable coexistence?

Most ecological models are based on the assumption that species interact in pairs. Diverse communities, however, can have higher-order interactions, in which two or more species jointly impact the growth of a third species. A pitfall of the common pairwise approach is that it misses the higher-order interactions potentially responsible for maintaining natural diversity. Here, we explore the stability properties of systems where higher-order interactions guarantee that a specified set of abundances is a feasible equilibrium of the dynamics. Even these higher-order interactions which lead to equilibria do not necessarily produce stable coexistence. Instead, these systems are more likely to be stable when the pairwise interactions are weak or facilitative. Correlations between the pairwise and higher-order interactions, however, do permit robust coexistence even in diverse systems. Our work not only reveals the challenges in generating stable coexistence through higher-order interactions but also uncovers interaction patterns that can enable diversity.

Sampling Strategies for Experimentally Mapping Molecular Fitness Landscapes Using High-Throughput Methods.

Empirical studies of genotype-phenotype-fitness maps of proteins are fundamental to understanding the evolutionary process, in elucidating the space of possible genotypes accessible through mutations in a landscape of phenotypes and fitness effects. Yet, comprehensively mapping molecular fitness landscapes remains challenging since all possible combinations of amino acid substitutions for even a few protein sites are encoded by an enormous genotype space. High-throughput mapping of genotype space can be achieved using large-scale screening experiments known as multiplexed assays of variant effect (MAVEs). However, to accommodate such multi-mutational studies, the size of MAVEs has grown to the point where a priori determination of sampling requirements is needed. To address this problem, we propose calculations and simulation methods to approximate minimum sampling requirements for multi-mutational MAVEs, which we combine with a new library construction protocol to experimentally validate our approximation approaches. Analysis of our simulated data reveals how sampling trajectories differ between simulations of nucleotide versus amino acid variants and among mutagenesis schemes. For this, we show quantitatively that marginal gains in sampling efficiency demand increasingly greater sampling effort when sampling for nucleotide sequences over their encoded amino acid equivalents. We present a new library construction protocol that efficiently maximizes sequence variation, and demonstrate using ultradeep sequencing that the library encodes virtually all possible combinations of mutations within the experimental design. Insights learned from our analyses together with the methodological advances reported herein are immediately applicable toward pooled experimental screens of arbitrary design, enabling further assay upscaling and expanded testing of genotype space.

Time-dependent interaction modification generated from plant-soil feedback.

Pairwise interactions between species can be modified by other community members, leading to emergent dynamics contingent on community composition. Despite the prevalence of such higher-order interactions, little is known about how they are linked to the timing and order of species' arrival. We generate population dynamics from a mechanistic plant-soil feedback model, then apply a general theoretical framework to show that the modification of a pairwise interaction by a third plant depends on its germination phenology. These time-dependent interaction modifications emerge from concurrent changes in plant and microbe populations and are strengthened by higher overlap between plants' associated microbiomes. The interaction between this overlap and the specificity of microbiomes further determines plant coexistence. Our framework is widely applicable to mechanisms in other systems from which similar time-dependent interaction modifications can emerge, highlighting the need to integrate temporal shifts of species interactions to predict the emergent dynamics of natural communities.

Higher-order species interactions cause time-dependent niche and fitness differences: Experimental evidence in plant-feeding arthropods.

Species interact in different ways, including competition, facilitation and predation. These interactions can be non-linear or higher order and may depend on time or species densities. Although these higher-order interactions are virtually ubiquitous, they remain poorly understood, as they are challenging both theoretically and empirically. We propose to adapt niche and fitness differences from modern coexistence theory and apply them to species interactions over time. As such, they may not merely inform about coexistence, but provide a deeper understanding of how species interactions change. Here, we investigated how the exploitation of a biotic resource (plant) by phytophagous arthropods affects their interactions. We performed monoculture and competition experiments to fit a generalized additive mixed model to the empirical data, which allowed us to calculate niche and fitness differences. We found that species switch between different types of interactions over time, including intra- and interspecific facilitation, and strong and weak competition.

Learning beyond-pairwise interactions enables the bottom-up prediction of microbial community structure.

Understanding the assembly of multispecies microbial communities represents a significant challenge in ecology and has wide applications in agriculture, wastewater treatment, and human healthcare domains. Traditionally, studies on the microbial community assembly focused on analyzing pairwise relationships among species; however, neglecting higher-order interactions, i.e., the change of pairwise relationships in the community context, may lead to substantial deviation from reality. Herein, we have proposed a simple framework that incorporates higher-order interactions into a bottom-up prediction of the microbial community assembly and examined its accuracy using a seven-member synthetic bacterial community on a host plant, duckweed. Although the synthetic community exhibited emergent properties that cannot be predicted from pairwise coculturing results, our results demonstrated that incorporating information from three-member combinations allows the acceptable prediction of the community structure and actual interaction forces within it. This reflects that the occurrence of higher-order effects follows consistent patterns, which can be predicted even from trio combinations, the smallest unit of higher-order interactions. These results highlight the possibility of predicting, explaining, and understanding the microbial community structure from the bottom-up by learning interspecies interactions from simple beyond-pairwise combinations.

Hyperedge prediction and the statistical mechanisms of higher-order and lower-order interactions in complex networks.

Complex networked systems often exhibit higher-order interactions, beyond dyadic interactions, which can dramatically alter their observed behavior. Consequently, understanding hypergraphs from a structural perspective has become increasingly important. Statistical, group-based inference approaches are well suited for unveiling the underlying community structure and predicting unobserved interactions. However, these approaches often rely on two key assumptions: that the same groups can explain hyperedges of any order and that interactions are assortative, meaning that edges are formed by nodes with the same group memberships. To test these assumptions, we propose a group-based generative model for hypergraphs that does not impose an assortative mechanism to explain observed higher-order interactions, unlike current approaches. Our model allows us to explore the validity of the assumptions. Our results indicate that the first assumption appears to hold true for real networks. However, the second assumption is not necessarily accurate; we find that a combination of general statistical mechanisms can explain observed hyperedges. Finally, with our approach, we are also able to determine the importance of lower and high-order interactions for predicting unobserved interactions. Our research challenges the conventional assumptions of group-based inference methodologies and broadens our understanding of the underlying structure of hypergraphs.

Understanding multimorbidity requires sign-disease networks and higher-order interactions, a perspective.

Background: Count scores, disease clustering, and pairwise associations between diseases remain ubiquitous in multimorbidity research despite two major shortcomings: they yield no insight into plausible mechanisms underlying multimorbidity, and they ignore higher-order interactions such as effect modification. Objectives: We argue that two components are currently missing but vital to develop novel multimorbidity metrics. Firstly, networks should be constructed which consists simultaneously of signs, symptoms, and diseases, since only then could they yield insight into plausible shared biological mechanisms underlying diseases.Secondly, learning pairwise associations is insufficient to fully characterize the correlations in a system. That is, synergistic (e.g., cooperative or antagonistic) effects are widespread in complex systems, where two or more elements combined give a larger or smaller effect than the sum of their individual effects. It can even occur that pairs of symptoms have no pairwise associations whatsoever, but in combination have a significant association. Therefore, higher-order interactions should be included in networks used to study multimorbidity, resulting in so-called hypergraphs. Methods: We illustrate our argument using a synthetic Bayesian Network model of symptoms, signs and diseases, composed of pairwise and higher-order interactions. We simulate network interventions on both individual and population levels and compare the ground-truth outcomes with the predictions from pairwise associations. Conclusion: We find that, when judged purely from the pairwise associations, interventions can have unexpected 'side-effects' or the most opportune intervention could be missed. The hypergraph uncovers links missed in pairwise networks, giving a more complete overview of sign and disease associations.

The existence and strength of higher order interactions is sensitive to environmental context.

One strategy for understanding the dynamics of any complex system, such as a community of competing species, is to study the dynamics of parts of the system in isolation. Ecological communities can be decomposed into single species, and pairs of interacting species. This reductionist strategy assumes that whole-community dynamics are predictable and explainable from knowledge of the dynamics of single species and pairs of species. This assumption will be violated if higher order interactions (HOIs) are strong. Theory predicts that HOIs should be common. But it is difficult to detect HOIs, and to infer their long-term consequences for species coexistence, solely from short-term data. I conducted a protist microcosm experiment to test for HOIs among competing bacterivorous ciliates, and test the sensitivity of HOIs to environmental context. I grew three competing ciliate species in all possible combinations at each of two resource enrichment levels, and used the population dynamic data from the one- and two-species treatments to parameterize a competition model at each enrichment level. I then compared the predictions of the parameterized model to the dynamics of the whole community (three-species treatment). I found that the existence, and thus strength, of HOIs was environment dependent. I found a strong HOI at low enrichment, which enabled the persistence of a species that would otherwise have been competitively excluded. At high enrichment, three-species dynamics could be predicted from a parameterized model of one- and two-species dynamics, provided that the model accounted for nonlinear intraspecific density dependence. The results provide one of the first rigorous demonstrations of the long-term consequences of HOIs for species coexistence, and demonstrate the context dependence of HOIs. HOIs create difficult challenges for predicting and explaining species coexistence in nature.

A three-species synthetic community model whose rapid response to antagonism allows the study of higher-order dynamics and emergent properties in minutes.

Microbial communities can be considered complex adaptive systems. Understanding how these systems arise from different components and how the dynamics of microbial interactions allow for species coexistence are fundamental questions in ecology. To address these questions, we built a three-species synthetic community, called BARS (Bacillota A + S + R). Each species in this community exhibits one of three ecological roles: Antagonistic, Sensitive, or Resistant, assigned in the context of a sediment community. We show that the BARS community reproduces features of complex communities and exhibits higher-order interaction (HOI) dynamics. In paired interactions, the majority of the S species (Sutcliffiella horikoshii 20a) population dies within 5 min when paired with the A species (Bacillus pumilus 145). However, an emergent property appears upon adding the third interactor, as antagonism of species A over S is not observed in the presence of the R species (Bacillus cereus 111). For the paired interaction, within the first 5 min, the surviving population of the S species acquires tolerance to species A, and species A ceases antagonism. This qualitative change reflects endogenous dynamics leading to the expression for tolerance to an antagonistic substance. The stability reached in the triple interaction exhibits a nonlinear response, highly sensitive to the density of the R species. In summary, our HOI model allows the study of the assembly dynamics of a three-species community and evaluating the immediate outcome within a 30 min frame. The BARS has features of a complex system where the paired interactions do not predict the community dynamics. The model is amenable to mechanistic dissection and to modeling how the parts integrate to achieve collective properties.

Wild animals suppress the spread of socially transmitted misinformation.

Understanding the mechanisms by which information and misinformation spread through groups of individual actors is essential to the prediction of phenomena ranging from coordinated group behaviors to misinformation epidemics. Transmission of information through groups depends on the rules that individuals use to transform the perceived actions of others into their own behaviors. Because it is often not possible to directly infer decision-making strategies in situ, most studies of behavioral spread assume that individuals make decisions by pooling or averaging the actions or behavioral states of neighbors. However, whether individuals may instead adopt more sophisticated strategies that exploit socially transmitted information, while remaining robust to misinformation, is unknown. Here, we study the relationship between individual decision-making and misinformation spread in groups of wild coral reef fish, where misinformation occurs in the form of false alarms that can spread contagiously through groups. Using automated visual field reconstruction of wild animals, we infer the precise sequences of socially transmitted visual stimuli perceived by individuals during decision-making. Our analysis reveals a feature of decision-making essential for controlling misinformation spread: dynamic adjustments in sensitivity to socially transmitted cues. This form of dynamic gain control can be achieved by a simple and biologically widespread decision-making circuit, and it renders individual behavior robust to natural fluctuations in misinformation exposure.

A Transcriptomic Analysis of Higher-Order Ecological Interactions in a Eukaryotic Model Microbial Ecosystem.

Nonlinear ecological interactions within microbial ecosystems and their contribution to ecosystem functioning remain largely unexplored. Higher-order interactions, or interactions in systems comprised of more than two members that cannot be explained by cumulative pairwise interactions, are particularly understudied, especially in eukaryotic microorganisms. The wine fermentation ecosystem presents an ideal model to study yeast ecosystem establishment and functioning. Some pairwise ecological interactions between wine yeast species have been characterized, but very little is known about how more complex, multispecies systems function. Here, we evaluated nonlinear ecosystem properties by determining the transcriptomic response of Saccharomyces cerevisiae to pairwise versus tri-species culture. The transcriptome revealed that genes expressed during pairwise coculture were enriched in the tri-species data set but also that just under half of the data set comprised unique genes attributed to a higher-order response. Through interactive protein-association network visualizations, a holistic cell-wide view of the gene expression data was generated, which highlighted known stress response and metabolic adaptation mechanisms which were specifically activated during tri-species growth. Further, extracellular metabolite data corroborated that the observed differences were a result of a biotic stress response. This provides exciting new evidence showing the presence of higher-order interactions within a model microbial ecosystem. IMPORTANCE Higher-order interactions are one of the major blind spots in our understanding of microbial ecosystems. These systems remain largely unpredictable and are characterized by nonlinear dynamics, in particular when the system is comprised of more than two entities. By evaluating the transcriptomic response of S. cerevisiae to an increase in culture complexity from a single species to two- and three-species systems, we were able to confirm the presence of a unique response in the more complex setting that could not be explained by the responses observed at the pairwise level. This is the first data set that provides molecular targets for further analysis to explain unpredictable ecosystem dynamics in yeast.

Revealing the Dynamics of Neural Information Processing with Multivariate Information Decomposition.

The varied cognitive abilities and rich adaptive behaviors enabled by the animal nervous system are often described in terms of information processing. This framing raises the issue of how biological neural circuits actually process information, and some of the most fundamental outstanding questions in neuroscience center on understanding the mechanisms of neural information processing. Classical information theory has long been understood to be a natural framework within which information processing can be understood, and recent advances in the field of multivariate information theory offer new insights into the structure of computation in complex systems. In this review, we provide an introduction to the conceptual and practical issues associated with using multivariate information theory to analyze information processing in neural circuits, as well as discussing recent empirical work in this vein. Specifically, we provide an accessible introduction to the partial information decomposition (PID) framework. PID reveals redundant, unique, and synergistic modes by which neurons integrate information from multiple sources. We focus particularly on the synergistic mode, which quantifies the "higher-order" information carried in the patterns of multiple inputs and is not reducible to input from any single source. Recent work in a variety of model systems has revealed that synergistic dynamics are ubiquitous in neural circuitry and show reliable structure-function relationships, emerging disproportionately in neuronal rich clubs, downstream of recurrent connectivity, and in the convergence of correlated activity. We draw on the existing literature on higher-order information dynamics in neuronal networks to illustrate the insights that have been gained by taking an information decomposition perspective on neural activity. Finally, we briefly discuss future promising directions for information decomposition approaches to neuroscience, such as work on behaving animals, multi-target generalizations of PID, and time-resolved local analyses.

Protein-protein interaction network of E. coli K-12 has significant high-dimensional cavities: new insights from algebraic topological studies.

As a model system, Escherichia coli has been used to study various life processes. A dramatic paradigm shift has occurred in recent years, with the study of single proteins moving toward the study of dynamically interacting proteins, especially protein-protein interaction (PPI) networks. However, despite the importance of PPI networks, little is known about the intrinsic nature of the network structure, especially high-dimensional topological properties. By introducing general hypergeometric distribution, we reconstruct a statistically reliable combined PPI network of E. coli (E. coli-PPI-Network) from several datasets. Unlike traditional graph analysis, algebraic topology was introduced to analyze the topological structures of the E. coli-PPI-Network, including high-dimensional cavities and cycles. Random networks with the same node and edge number (RandomNet) or scale-free networks with the same degree distribution (RandomNet-SameDD) were produced as controls. We discovered that the E. coli-PPI-Network had special algebraic typological structures, exhibiting more high-dimensional cavities and cycles, compared to RandomNets or, importantly, RandomNet-SameDD. Based on these results, we defined degree of involved q-dimensional cycles of proteins (q-DCprotein ) in the network, a novel concept that relies on the integral structure of the network and is different from traditional node degree or hubs. Finally, top proteins ranked by their 1-DCprotein were identified (such as gmhB, rpoA, rplB, rpsF and yfgB). In conclusion, by introducing mathematical and computer technologies, we discovered novel algebraic topological properties of the E. coli-PPI-Network, which has special high-dimensional cavities and cycles, and thereby revealed certain intrinsic rules of information flow underlining bacteria biology.

Challenges for machine learning in RNA-protein interaction prediction.

RNA-protein interactions have long being recognised as crucial regulators of gene expression. Recently, the development of scalable experimental techniques to measure these interactions has revolutionised the field, leading to the production of large-scale datasets which offer both opportunities and challenges for machine learning techniques. In this brief note, we will discuss some of the major stumbling blocks towards the use of machine learning in computational RNA biology, focusing specifically on the problem of predicting RNA-protein interactions from next-generation sequencing data.

Untangling Synergistic Effects of Intersecting Social Identities with Partial Information Decomposition.

The theory of intersectionality proposes that an individual's experience of society has aspects that are irreducible to the sum of one's various identities considered individually, but are "greater than the sum of their parts". In recent years, this framework has become a frequent topic of discussion both in social sciences and among popular movements for social justice. In this work, we show that the effects of intersectional identities can be statistically observed in empirical data using information theory, particularly the partial information decomposition framework. We show that, when considering the predictive relationship between various identity categories such as race and sex, on outcomes such as income, health and wellness, robust statistical synergies appear. These synergies show that there are joint-effects of identities on outcomes that are irreducible to any identity considered individually and only appear when specific categories are considered together (for example, there is a large, synergistic effect of race and sex considered jointly on income irreducible to either race or sex). Furthermore, these synergies are robust over time, remaining largely constant year-to-year. We then show using synthetic data that the most widely used method of assessing intersectionalities in data (linear regression with multiplicative interaction coefficients) fails to disambiguate between truly synergistic, greater-than-the-sum-of-their-parts interactions, and redundant interactions. We explore the significance of these two distinct types of interactions in the context of making inferences about intersectional relationships in data and the importance of being able to reliably differentiate the two. Finally, we conclude that information theory, as a model-free framework sensitive to nonlinearities and synergies in data, is a natural method by which to explore the space of higher-order social dynamics.

Addressing context dependence in ecology.

Context dependence is widely invoked to explain disparate results in ecology. It arises when the magnitude or sign of a relationship varies due to the conditions under which it is observed. Such variation, especially when unexplained, can lead to spurious or seemingly contradictory conclusions, which can limit understanding and our ability to transfer findings across studies, space, and time. Using examples from biological invasions, we identify two types of context dependence resulting from four sources: mechanistic context dependence arises from interaction effects; and apparent context dependence can arise from the presence of confounding factors, problems of statistical inference, and methodological differences among studies. Addressing context dependence is a critical challenge in ecology, essential for increased understanding and prediction.