Identifying a developmental transition in honey bees using gene expression data.

In many organisms, interactions among genes lead to multiple functional states, and changes to interactions can lead to transitions into new states. These transitions can be related to bifurcations (or critical points) in dynamical systems theory. Characterizing these collective transitions is a major challenge for systems biology. Here, we develop a statistical method for identifying bistability near a continuous transition directly from high-dimensional gene expression data. We apply the method to data from honey bees, where a known developmental transition occurs between bees performing tasks in the nest and leaving the nest to forage. Our method, which makes use of the expected shape of the distribution of gene expression levels near a transition, successfully identifies the emergence of bistability and links it to genes that are known to be involved in the behavioral transition. This proof of concept demonstrates that going beyond correlative analysis to infer the shape of gene expression distributions might be used more generally to identify collective transitions from gene expression data.

Subcritical escape waves in schooling fish.

Theoretical physics predicts optimal information processing in living systems near transitions (or pseudo-critical points) in their collective dynamics. However, focusing on potential benefits of proximity to a critical point, such as maximal sensitivity to perturbations and fast dissemination of information, commonly disregards possible costs of criticality in the noisy, dynamic environmental contexts of biological systems. Here, we find that startle cascades in fish schools are subcritical (not maximally responsive to environmental cues) and that distance to criticality decreases when perceived risk increases. Considering individuals' costs related to two detection error types, associated to both true and false alarms, we argue that being subcritical, and modulating distance to criticality, can be understood as managing a trade-off between sensitivity and robustness according to the riskiness and noisiness of the environment. Our work emphasizes the need for an individual-based and context-dependent perspective on criticality and collective information processing and motivates future questions about the evolutionary forces that brought about a particular trade-off.

Discovering sparse control strategies in neural activity.

Biological circuits such as neural or gene regulation networks use internal states to map sensory input to an adaptive repertoire of behavior. Characterizing this mapping is a major challenge for systems biology. Though experiments that probe internal states are developing rapidly, organismal complexity presents a fundamental obstacle given the many possible ways internal states could map to behavior. Using C. elegans as an example, we propose a protocol for systematic perturbation of neural states that limits experimental complexity and could eventually help characterize collective aspects of the neural-behavioral map. We consider experimentally motivated small perturbations-ones that are most likely to preserve natural dynamics and are closer to internal control mechanisms-to neural states and their impact on collective neural activity. Then, we connect such perturbations to the local information geometry of collective statistics, which can be fully characterized using pairwise perturbations. Applying the protocol to a minimal model of C. elegans neural activity, we find that collective neural statistics are most sensitive to a few principal perturbative modes. Dominant eigenvalues decay initially as a power law, unveiling a hierarchy that arises from variation in individual neural activity and pairwise interactions. Highest-ranking modes tend to be dominated by a few, "pivotal" neurons that account for most of the system's sensitivity, suggesting a sparse mechanism of collective control.

Innovations are disproportionately likely in the periphery of a scientific network.

The origins of innovation in science are typically understood using historical narratives that tend to be focused on small sets of influential authors, an approach that is rigorous but limited in scope. Here, we develop a framework for rigorously identifying innovation across an entire scientific field through automated analysis of a corpus of over 6000 documents that includes every paper published in the field of evolutionary medicine. This comprehensive approach allows us to explore statistical properties of innovation, asking where innovative ideas tend to originate within a field's pre-existing conceptual framework. First, we develop a measure of innovation based on novelty and persistence, quantifying the collective acceptance of novel language and ideas. Second, we study the field's conceptual landscape through a bibliographic coupling network. We find that innovations are disproportionately more likely in the periphery of the bibliographic coupling network, suggesting that the relative freedom allowed by remaining unconnected with well-established lines of research could be beneficial to creating novel and lasting change. In this way, the emergence of collective computation in scientific disciplines may have robustness-adaptability trade-offs that are similar to those found in other biosocial complex systems.

The basis of easy controllability in Boolean networks.

Effective control of biological systems can often be achieved through the control of a surprisingly small number of distinct variables. We bring clarity to such results using the formalism of Boolean dynamical networks, analyzing the effectiveness of external control in selecting a desired final state when that state is among the original attractors of the dynamics. Analyzing 49 existing biological network models, we find strong numerical evidence that the average number of nodes that must be forced scales logarithmically with the number of original attractors. This suggests that biological networks may be typically easy to control even when the number of interacting components is large. We provide a theoretical explanation of the scaling by separating controlling nodes into three types: those that act as inputs, those that distinguish among attractors, and any remaining nodes. We further identify characteristics of dynamics that can invalidate this scaling, and speculate about how this relates more broadly to non-biological systems.

Quantifying the impact of network structure on speed and accuracy in collective decision-making.

Found in varied contexts from neurons to ants to fish, binary decision-making is one of the simplest forms of collective computation. In this process, information collected by individuals about an uncertain environment is accumulated to guide behavior at the aggregate scale. We study binary decision-making dynamics in networks responding to inputs with small signal-to-noise ratios, looking for quantitative measures of collectivity that control performance in this task. We find that decision accuracy is directly correlated with the speed of collective dynamics, which is in turn controlled by three factors: the leading eigenvalue of the network adjacency matrix, the corresponding eigenvector's participation ratio, and distance from the corresponding symmetry-breaking bifurcation. A novel approximation of the maximal attainable timescale near such a bifurcation allows us to predict how decision-making performance scales in large networks based solely on their spectral properties. Specifically, we explore the effects of localization caused by the hierarchical assortative structure of a "rich club" topology. This gives insight into the trade-offs involved in the higher-order structure found in living networks performing collective computations.

Scaling theory of armed-conflict avalanches.

Armed conflict data display features consistent with scaling and universal dynamics in both social and physical properties like fatalities and geographic extent. We propose a randomly branching armed conflict model to relate the multiple properties to one another. The model incorporates a fractal lattice on which conflict spreads, uniform dynamics driving conflict growth, and regional virulence that modulates local conflict intensity. The quantitative constraints on scaling and universal dynamics we use to develop our minimal model serve more generally as a set of constraints for other models for armed conflict dynamics. We show how this approach akin to thermodynamics imparts mechanistic intuition and unifies multiple conflict properties, giving insight into causation, prediction, and intervention timing.

Tyramine and its receptor TYR1 linked behavior QTL to reproductive physiology in honey bee workers (Apis mellifera).

Honey bees (Apis mellifera) provide an excellent model for studying how complex social behavior evolves and is regulated. Social behavioral traits such as the division of labor have been mapped to specific genomic regions in quantitative trait locus (QTL) studies. However, relating genomic mapping to gene function and regulatory mechanism remains a big challenge for geneticists. In honey bee workers, division of labor is known to be regulated by reproductive physiology, but the genetic basis of this regulation remains unknown. In this case, QTL studies have identified tyramine receptor 1 (TYR1) as a candidate gene in region pln2, which is associated with multiple worker social traits and reproductive anatomy. Tyramine (TA), a neurotransmitter, regulates physiology and behavior in diverse insect species including honey bees. Here, we examine directly the effects of TYR1 and TA on worker reproductive physiology, including ovariole number, ovary function and the production of vitellogenin (VG, an egg yolk precursor). First, we used a pharmacology approach to demonstrate that TA affects ovariole number during worker larval development and increases ovary maturation during the adult stage. Second, we used a gene knockdown approach to show that TYR1 regulates vg transcription in adult workers. Finally, we estimated correlations in gene expression and propose that TYR1 may regulate vg transcription by coordinating hormonal and nutritional signals. Taken together, our results suggest TYR1 and TA play important roles in regulating worker reproductive physiology, which in turn regulates social behavior. Our study exemplifies a successful forward-genetic strategy going from QTL mapping to gene function.

Quantifying Dynamical High-Order Interdependencies From the O-Information: An Application to Neural Spiking Dynamics.

We address the problem of efficiently and informatively quantifying how multiplets of variables carry information about the future of the dynamical system they belong to. In particular we want to identify groups of variables carrying redundant or synergistic information, and track how the size and the composition of these multiplets changes as the collective behavior of the system evolves. In order to afford a parsimonious expansion of shared information, and at the same time control for lagged interactions and common effect, we develop a dynamical, conditioned version of the O-information, a framework recently proposed to quantify high-order interdependencies via multivariate extension of the mutual information. The dynamic O-information, here introduced, allows to separate multiplets of variables which influence synergistically the future of the system from redundant multiplets. We apply this framework to a dataset of spiking neurons from a monkey performing a perceptual discrimination task. The method identifies synergistic multiplets that include neurons previously categorized as containing little relevant information individually.

Individual and collective encoding of risk in animal groups.

The need to make fast decisions under risky and uncertain conditions is a widespread problem in the natural world. While there has been extensive work on how individual organisms dynamically modify their behavior to respond appropriately to changing environmental conditions (and how this is encoded in the brain), we know remarkably little about the corresponding aspects of collective information processing in animal groups. For example, many groups appear to show increased "sensitivity" in the presence of perceived threat, as evidenced by the increased frequency and magnitude of repeated cascading waves of behavioral change often observed in fish schools and bird flocks under such circumstances. How such context-dependent changes in collective sensitivity are mediated, however, is unknown. Here we address this question using schooling fish as a model system, focusing on 2 nonexclusive hypotheses: 1) that changes in collective responsiveness result from changes in how individuals respond to social cues (i.e., changes to the properties of the "nodes" in the social network), and 2) that they result from changes made to the structural connectivity of the network itself (i.e., the computation is encoded in the "edges" of the network). We find that despite the fact that perceived risk increases the probability for individuals to initiate an alarm, the context-dependent change in collective sensitivity predominantly results not from changes in how individuals respond to social cues, but instead from how individuals modify the spatial structure, and correspondingly the topology of the network of interactions, within the group. Risk is thus encoded as a collective property, emphasizing that in group-living species individual fitness can depend strongly on coupling between scales of behavioral organization.

Automated, predictive, and interpretable inference of Caenorhabditis elegans escape dynamics.

The roundworm Caenorhabditis elegans exhibits robust escape behavior in response to rapidly rising temperature. The behavior lasts for a few seconds, shows history dependence, involves both sensory and motor systems, and is too complicated to model mechanistically using currently available knowledge. Instead we model the process phenomenologically, and we use the Sir Isaac dynamical inference platform to infer the model in a fully automated fashion directly from experimental data. The inferred model requires incorporation of an unobserved dynamical variable and is biologically interpretable. The model makes accurate predictions about the dynamics of the worm behavior, and it can be used to characterize the functional logic of the dynamical system underlying the escape response. This work illustrates the power of modern artificial intelligence to aid in discovery of accurate and interpretable models of complex natural systems.

Criticality Distinguishes the Ensemble of Biological Regulatory Networks.

The hypothesis that many living systems should exhibit near-critical behavior is well motivated theoretically, and an increasing number of cases have been demonstrated empirically. However, a systematic analysis across biological networks, which would enable identification of the network properties that drive criticality, has not yet been realized. Here, we provide a first comprehensive survey of criticality across a diverse sample of biological networks, leveraging a publicly available database of 67 Boolean models of regulatory circuits. We find all 67 networks to be near critical. By comparing to ensembles of random networks with similar topological and logical properties, we show that criticality in biological networks is not predictable solely from macroscale properties such as mean degree ⟨K⟩ and mean bias in the logic functions ⟨p⟩, as previously emphasized in theories of random Boolean networks. Instead, the ensemble of real biological circuits is jointly constrained by the local causal structure and logic of each node. In this way, biological regulatory networks are more distinguished from random networks by their criticality than by other macroscale network properties such as degree distribution, edge density, or fraction of activating conditions.

Collective memory in primate conflict implied by temporal scaling collapse.

In biological systems, prolonged conflict is costly, whereas contained conflict permits strategic innovation and refinement. Causes of variation in conflict size and duration are not well understood. We use a well-studied primate society model system to study how conflicts grow. We find conflict duration is a 'first to fight' growth process that scales superlinearly, with the number of possible pairwise interactions. This is in contrast with a 'first to fail' process that characterizes peaceful durations. Rescaling conflict distributions reveals a universal curve, showing that the typical time scale of correlated interactions exceeds nearly all individual fights. This temporal correlation implies collective memory across pairwise interactions beyond those assumed in standard models of contagion growth or iterated evolutionary games. By accounting for memory, we make quantitative predictions for interventions that mitigate or enhance the spread of conflict. Managing conflict involves balancing the efficient use of limited resources with an intervention strategy that allows for conflict while keeping it contained and controlled.

Dual Coding Theory Explains Biphasic Collective Computation in Neural Decision-Making.

A central question in cognitive neuroscience is how unitary, coherent decisions at the whole organism level can arise from the distributed behavior of a large population of neurons with only partially overlapping information. We address this issue by studying neural spiking behavior recorded from a multielectrode array with 169 channels during a visual motion direction discrimination task. It is well known that in this task there are two distinct phases in neural spiking behavior. Here we show Phase I is a distributed or incompressible phase in which uncertainty about the decision is substantially reduced by pooling information from many cells. Phase II is a redundant or compressible phase in which numerous single cells contain all the information present at the population level in Phase I, such that the firing behavior of a single cell is enough to predict the subject's decision. Using an empirically grounded dynamical modeling framework, we show that in Phase I large cell populations with low redundancy produce a slow timescale of information aggregation through critical slowing down near a symmetry-breaking transition. Our model indicates that increasing collective amplification in Phase II leads naturally to a faster timescale of information pooling and consensus formation. Based on our results and others in the literature, we propose that a general feature of collective computation is a "coding duality" in which there are accumulation and consensus formation processes distinguished by different timescales.

Control of finite critical behaviour in a small-scale social system.

Many adaptive systems sit near a tipping or critical point. For systems near a critical point small changes to component behaviour can induce large-scale changes in aggregate structure and function. Criticality can be adaptive when the environment is changing, but entails reduced robustness through sensitivity. This tradeoff can be resolved when criticality can be tuned. We address the control of finite measures of criticality using data on fight sizes from an animal society model system (Macaca nemestrina, n=48). We find that a heterogeneous, socially organized system, like homogeneous, spatial systems (flocks and schools), sits near a critical point; the contributions individuals make to collective phenomena can be quantified; there is heterogeneity in these contributions; and distance from the critical point (DFC) can be controlled through biologically plausible mechanisms exploiting heterogeneity. We propose two alternative hypotheses for why a system decreases the distance from the critical point.

Quantifying collectivity.

In biological function emerges from the interactions of components with only partially aligned interests. An example is the brain-a large aggregation of neurons capable of producing unitary, coherent output. A theory for how such aggregations produce coherent output remains elusive. A first question we might ask is how collective is the behavior of the components? Here we introduce two properties of collectivity and illustrate how these properties can be quantified using approaches from information theory and statistical physics. First, amplification quantifies the sensitivity of the large scale to information at the small scale and is related to the notion of criticality in statistical physics. Second, decomposability reveals the extent to which aggregate behavior is reducible to individual contributions or is the result of synergistic interactions among components forming larger subgroups. These measures facilitate identification of causally important components and subgroups that might be experimentally manipulated to study the evolution and controllability of biological circuits and their outputs.

Automated adaptive inference of phenomenological dynamical models.

Dynamics of complex systems is often driven by large and intricate networks of microscopic interactions, whose sheer size obfuscates understanding. With limited experimental data, many parameters of such dynamics are unknown, and thus detailed, mechanistic models risk overfitting and making faulty predictions. At the other extreme, simple ad hoc models often miss defining features of the underlying systems. Here we develop an approach that instead constructs phenomenological, coarse-grained models of network dynamics that automatically adapt their complexity to the available data. Such adaptive models produce accurate predictions even when microscopic details are unknown. The approach is computationally tractable, even for a relatively large number of dynamical variables. Using simulated data, it correctly infers the phase space structure for planetary motion, avoids overfitting in a biological signalling system and produces accurate predictions for yeast glycolysis with tens of data points and over half of the interacting species unobserved.

Perspective: Sloppiness and emergent theories in physics, biology, and beyond.

Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are "sloppy," i.e., exhibit behavior controlled by a relatively small number of parameter combinations. We review an information theoretic framework for analyzing sloppy models. This formalism is based on the Fisher information matrix, which is interpreted as a Riemannian metric on a parameterized space of models. Distance in this space is a measure of how distinguishable two models are based on their predictions. Sloppy model manifolds are bounded with a hierarchy of widths and extrinsic curvatures. The manifold boundary approximation can extract the simple, hidden theory from complicated sloppy models. We attribute the success of simple effective models in physics as likewise emerging from complicated processes exhibiting a low effective dimensionality. We discuss the ramifications and consequences of sloppy models for biochemistry and science more generally. We suggest that the reason our complex world is understandable is due to the same fundamental reason: simple theories of macroscopic behavior are hidden inside complicated microscopic processes.

Efficient inference of parsimonious phenomenological models of cellular dynamics using S-systems and alternating regression.

The nonlinearity of dynamics in systems biology makes it hard to infer them from experimental data. Simple linear models are computationally efficient, but cannot incorporate these important nonlinearities. An adaptive method based on the S-system formalism, which is a sensible representation of nonlinear mass-action kinetics typically found in cellular dynamics, maintains the efficiency of linear regression. We combine this approach with adaptive model selection to obtain efficient and parsimonious representations of cellular dynamics. The approach is tested by inferring the dynamics of yeast glycolysis from simulated data. With little computing time, it produces dynamical models with high predictive power and with structural complexity adapted to the difficulty of the inference problem.