Using multilayer network analysis to explore the temporal dynamics of collective behavior

Social organisms often show collective behaviors such as group foraging or movement.Collective behaviors can emerge from interactions between group members and may depend on the behavior of key individuals.When social interactions change over time,collective behaviors may change because these behaviors emerge from interactions among individuals.Despite the importance of,and growing interest in,the temporal dynamics of social interactions,it is not clear how to quantify changes in interactions over time or measure their stability.Furthermore,the temporal scale at which we should observe changes in social networks to detect biologically meaningful changes is not always apparent.Here we use multilayer network analysis to quantify temporal dynamics of social networks of the social spider Stegodyphus dumicola and determine how these dynamics relate to individual and group behaviors.We found that social interactions changed over time at a constant rate.Variation in both network structure and the identity of a keystone individual was not related to the mean or variance of the collective prey attack speed.Individuals that maintained a large and stable number of connections,despite changes in network structure,were the boldest individuals in the group.Therefore,social interactions and boldness are linked across time,but group collective behavior is not influenced by the stability of the social network.Our work demonstrates that dynamic social networks can be modeled in a multilayer framework.This approach may reveal biologically important temporal changes to social structure in other systems.     

Network of evolutionary processors with splicing rules and permitting context

In this paper we consider networks of evolutionary processors with splicing rules and permitting context (NEPPS) as language generating and computational devices. Such a network consists of several processors placed on the nodes of a virtual graph and are able to perform splicing (which is a biologically motivated operation) on the words present in that node, according to the splicing rules present there. Before applying the splicing operation on words, we check for the presence of certain symbols (permitting context) in the strings on which the rule is applied. Each node is associated with an input and output filter. When the filters are based on random context conditions, one gets the computational power of Turing machines with networks of size two. We also show how these networks can be used to solve NP-complete problems in linear time.     

Learning the rules of collective cell migration using deep attention networks

Collective, coordinated cellular motions underpin key processes in all multicellular organisms, yet it has been difficult to simultaneously express the ‘rules’ behind these motions in clear, interpretable forms that effectively capture high-dimensional cell-cell interaction dynamics in a manner that is intuitive to the researcher. Here we apply deep attention networks to analyze several canonical living tissues systems and present the underlying collective migration rules for each tissue type using only cell migration trajectory data. We use these networks to learn the behaviors of key tissue types with distinct collective behaviors—epithelial, endothelial, and metastatic breast cancer cells—and show how the results complement traditional biophysical approaches. In particular, we present attention maps indicating the relative influence of neighboring cells to the learned turning decisions of a ‘focal cell’–the primary cell of interest in a collective setting. Colloquially, we refer to this learned relative influence as ‘attention’, as it serves as a proxy for the physical parameters modifying the focal cell’s future motion as a function of each neighbor cell. These attention networks reveal distinct patterns of influence and attention unique to each model tissue. Endothelial cells exhibit tightly focused attention on their immediate forward-most neighbors, while cells in more expansile epithelial tissues are more broadly influenced by neighbors in a relatively large forward sector. Attention maps of ensembles of more mesenchymal, metastatic cells reveal completely symmetric attention patterns, indicating the lack of any particular coordination or direction of interest. Moreover, we show how attention networks are capable of detecting and learning how these rules change based on biophysical context, such as location within the tissue and cellular crowding. That these results require only cellular trajectories and no modeling assumptions highlights the potential of attention networks for providing further biological insights into complex cellular systems.     

On the long-run sensitivity of probabilistic Boolean networks

Boolean networks and, more generally, probabilistic Boolean networks, as one class of gene regulatory networks, model biological processes with the network dynamics determined by the logic-rule regulatory functions in conjunction with probabilistic parameters involved in network transitions. While there has been significant research on applying different control policies to alter network dynamics as future gene therapeutic intervention, we have seen less work on understanding the sensitivity of network dynamics with respect to perturbations to networks, including regulatory rules and the involved parameters, which is particularly critical for the design of intervention strategies. This paper studies this less investigated issue of network sensitivity in the long run. As the underlying model of probabilistic Boolean networks is a finite Markov chain, we define the network sensitivity based on the steady-state distributions of probabilistic Boolean networks and call it long-run sensitivity. The steady-state distribution reflects the long-run behavior of the network and it can give insight into the dynamics or momentum existing in a system. The change of steady-state distribution caused by possible perturbations is the key measure for intervention. This newly defined long-run sensitivity can provide insight on both network inference and intervention. We show the results for probabilistic Boolean networks generated from random Boolean networks and the results from two real biological networks illustrate preliminary applications of sensitivity in intervention for practical problems.     

Collective animal behavior from Bayesian estimation and probability matching

Animals living in groups make movement decisions that depend, among other factors, on social interactions with other group members. Our present understanding of social rules in animal collectives is mainly based on empirical fits to observations, with less emphasis in obtaining first-principles approaches that allow their derivation. Here we show that patterns of collective decisions can be derived from the basic ability of animals to make probabilistic estimations in the presence of uncertainty. We build a decision-making model with two stages: Bayesian estimation and probabilistic matching. In the first stage, each animal makes a Bayesian estimation of which behavior is best to perform taking into account personal information about the environment and social information collected by observing the behaviors of other animals. In the probability matching stage, each animal chooses a behavior with a probability equal to the Bayesian-estimated probability that this behavior is the most appropriate one. This model derives very simple rules of interaction in animal collectives that depend only on two types of reliability parameters, one that each animal assigns to the other animals and another given by the quality of the non-social information. We test our model by obtaining theoretically a rich set of observed collective patterns of decisions in three-spined sticklebacks, Gasterosteus aculeatus, a shoaling fish species. The quantitative link shown between probabilistic estimation and collective rules of behavior allows a better contact with other fields such as foraging, mate selection, neurobiology and psychology, and gives predictions for experiments directly testing the relationship between estimation and collective behavior.     

Parametric construction of episode networks from pseudoperiodic time series based on mutual information

Recently, the construction of networks from time series data has gained widespread interest. In this paper, we develop this area further by introducing a network construction procedure for pseudoperiodic time series. We call such networks episode networks, in which an episode corresponds to a temporal interval of a time series, and which defines a node in the network. Our model includes a number of features which distinguish it from current methods. First, the proposed construction procedure is a parametric model which allows it to adapt to the characteristics of the data; the length of an episode being the parameter. As a direct consequence, networks of minimal size containing the maximal information about the time series can be obtained. In this paper, we provide an algorithm to determine the optimal value of this parameter. Second, we employ estimates of mutual information values to define the connectivity structure among the nodes in the network to exploit efficiently the nonlinearities in the time series. Finally, we apply our method to data from electroencephalogram (EEG) experiments and demonstrate that the constructed episode networks capture discriminative information from the underlying time series that may be useful for diagnostic purposes.     

Modeling collective animal behavior with a cognitive perspective: a methodological framework

The last decades have seen an increasing interest in modeling collective animal behavior. Some studies try to reproduce as accurately as possible the collective dynamics and patterns observed in several animal groups with biologically plausible, individual behavioral rules. The objective is then essentially to demonstrate that the observed collective features may be the result of self-organizing processes involving quite simple individual behaviors. Other studies concentrate on the objective of establishing or enriching links between collective behavior researches and cognitive or physiological ones, which then requires that each individual rule be carefully validated. Here we discuss the methodological consequences of this additional requirement. Using the example of corpse clustering in ants, we first illustrate that it may be impossible to discriminate among alternative individual rules by considering only observational data collected at the group level. Six individual behavioral models are described: They are clearly distinct in terms of individual behaviors, they all reproduce satisfactorily the collective dynamics and distribution patterns observed in experiments, and we show theoretically that it is strictly impossible to discriminate two of these models even in the limit of an infinite amount of data whatever the accuracy level. A set of methodological steps are then listed and discussed as practical ways to partially overcome this problem. They involve complementary experimental protocols specifically designed to address the behavioral rules successively, conserving group-level data for the overall model validation. In this context, we highlight the importance of maintaining a sharp distinction between model enunciation, with explicit references to validated biological concepts, and formal translation of these concepts in terms of quantitative state variables and fittable functional dependences. Illustrative examples are provided of the benefits expected during the often long and difficult process of refining a behavioral model, designing adapted experimental protocols and inversing model parameters.     

Modern termites inherited the potential of collective construction from their common ancestor

Animal collective behaviors give rise to various spatial patterns, such as the nests of social insects. These structures are built by individuals following a simple set of rules, slightly varying within and among species, to produce a large diversity of shapes. However, little is known about the origin and evolution of the behavioral mechanisms regulating nest structures. In this study, we discuss the perspective of inferring the evolution of collective behaviors behind pattern formations using a phylogenetic framework. We review the collective behaviors that can be described by a single set of behavioral rules, and for which variations of the environmental and behavioral parameter values produce diverse patterns. We propose that this mechanism could be at the origin of the pattern diversity observed among related species, and that, when they are placed in the proper conditions, species have the behavioral potential to form patterns observed in related species. The comparative analysis of shelter tube construction by lower termites is consistent with this hypothesis. Although the use of shelter tubes in natural conditions is variable among species, most modern species have the potential to build them, suggesting that the behavioral rules for shelter tube construction evolved once in the common ancestor of modern termites. Our study emphasizes that comparative studies of behavioral rules have the potential to shed light on the evolution of collective behaviors.     

Combinatorial approaches for mass spectra recalibration

Mass spectrometry has become one of the most popular analysis techniques in Proteomics and Systems Biology. With the creation of larger datasets, the automated recalibration of mass spectra becomes important to ensure that every peak in the sample spectrum is correctly assigned to some peptide and protein. Algorithms for recalibrating mass spectra have to be robust with respect to wrongly assigned peaks, as well as efficient due to the amount of mass spectrometry data. The recalibration of mass spectra leads us to the problem of finding an optimal matching between mass spectra under measurement errors. We have developed two deterministic methods that allow robust computation of such a matching: The first approach uses a computational geometry interpretation of the problem, and tries to find two parallel lines with constant distance that stab a maximal number of points in the plane. The second approach is based on finding a maximal common approximate subsequence, and improves existing algorithms by one order of magnitude exploiting the sequential nature of the matching problem. We compare our results to a computational geometry algorithm using a topological line-sweep.     

Connecting the dots in ethology: applying network theory to understand neural and animal collectives

A major goal shared by neuroscience and collective behavior is to understand how dynamic interactions between individual elements give rise to behaviors in populations of neurons and animals, respectively. This goal has recently become within reach, thanks to techniques providing access to the connectivity and activity of neuronal ensembles as well as to behaviors among animal collectives. The next challenge using these datasets is to unravel network mechanisms generating population behaviors. This is aided by network theory, a field that studies structure–function relationships in interconnected systems. Here we review studies that have taken a network view on modern datasets to provide unique insights into individual and collective animal behaviors. Specifically, we focus on how analyzing signal propagation, controllability, symmetry, and geometry of networks can tame the complexity of collective system dynamics. These studies illustrate the potential of network theory to accelerate our understanding of behavior across ethological scales.     

Collective dynamics of active cytoskeletal networks

Self organization mechanisms are essential for the cytoskeleton to adapt to the requirements of living cells. They rely on the intricate interplay of cytoskeletal filaments, crosslinking proteins and molecular motors. Here we present an in vitro minimal model system consisting of actin filaments, fascin and myosin-II filaments exhibiting pulsatile collective dynamics and superdiffusive transport properties. Both phenomena rely on the complex competition of crosslinking molecules and motor filaments in the network. They are only observed if the relative strength of the binding of myosin-II filaments to the actin network allows exerting high enough forces to unbind actin/fascin crosslinks. This is shown by varying the binding strength of the acto-myosin bond and by combining the experiments with phenomenological simulations based on simple interaction rules.     

A mass conserved reaction-diffusion system captures properties of cell polarity

Cell polarity is a general cellular process that can be seen in various cell types such as migrating neutrophils and Dictyostelium cells. The Rho small GTP(guanosine 5'-tri phosphate)ases have been shown to regulate cell polarity; however, its mechanism of emergence has yet to be clarified. We first developed a reaction-diffusion model of the Rho GTPases, which exhibits switch-like reversible response to a gradient of extracellular signals, exclusive accumulation of Cdc42 and Rac, or RhoA at the maximal or minimal intensity of the signal, respectively, and tracking of changes of a signal gradient by the polarized peak. The previous cell polarity models proposed by Subramanian and Narang show similar behaviors to our Rho GTPase model, despite the difference in molecular networks. This led us to compare these models, and we found that these models commonly share instability and a mass conservation of components. Based on these common properties, we developed conceptual models of a mass conserved reaction-diffusion system with diffusion-driven instability. These conceptual models retained similar behaviors of cell polarity in the Rho GTPase model. Using these models, we numerically and analytically found that multiple polarized peaks are unstable, resulting in a single stable peak (uniqueness of axis), and that sensitivity toward changes of a signal gradient is specifically restricted at the polarized peak (localized sensitivity). Although molecular networks may differ from one cell type to another, the behaviors of cell polarity in migrating cells seem similar, suggesting that there should be a fundamental principle. Thus, we propose that a mass conserved reaction-diffusion system with diffusion-driven instability is one of such principles of cell polarity.     

Nutrient complexity triggers transitions between solitary and colonial growth in bacterial populations

Microbial populations often experience fluctuations in nutrient complexity in their natural environment such as between high molecular weight polysaccharides and simple monosaccharides. However, it is unclear if cells can adopt growth behaviors that allow individuals to optimally respond to differences in nutrient complexity. Here, we directly control nutrient complexity and use quantitative single-cell analysis to study the growth dynamics of individuals within populations of the aquatic bacterium Caulobacter crescentus. We show that cells form clonal microcolonies when growing on the polysaccharide xylan, which is abundant in nature and degraded using extracellular cell-linked enzymes; and disperse to solitary growth modes when the corresponding monosaccharide xylose becomes available or nutrients are exhausted. We find that the cellular density required to achieve maximal growth rates is four-fold higher on xylan than on xylose, indicating that aggregating is advantageous on polysaccharides. When collectives on xylan are transitioned to xylose, cells start dispersing, indicating that colony formation is no longer beneficial and solitary behaviors might serve to reduce intercellular competition. Our study demonstrates that cells can dynamically tune their behaviors when nutrient complexity fluctuates, elucidates the quantitative advantages of distinct growth behaviors for individual cells and indicates why collective growth modes are prevalent in microbial populations.Subject terms: Microbial ecology, Water microbiology, Biofilms     

Design of ant-inspired stochastic control policies for collective transport by robotic swarms

In this paper, we present an approach to designing decentralized robot control policies that mimic certain microscopic and macroscopic behaviors of ants performing collective transport tasks. In prior work, we used a stochastic hybrid system model to characterize the observed team dynamics of ant group retrieval of a rigid load. We have also used macroscopic population dynamic models to design enzyme-inspired stochastic control policies that allocate a robotic swarm around multiple boundaries in a way that is robust to environmental variations. Here, we build on this prior work to synthesize stochastic robot attachment–detachment policies for tasks in which a robotic swarm must achieve non-uniform spatial distributions around multiple loads and transport them at a constant velocity. Three methods are presented for designing robot control policies that replicate the steady-state distributions, transient dynamics, and fluxes between states that we have observed in ant populations during group retrieval. The equilibrium population matching method can be used to achieve a desired transport team composition as quickly as possible; the transient matching method can control the transient population dynamics of the team while driving it to the desired composition; and the rate matching method regulates the rates at which robots join and leave a load during transport. We validate our model predictions in an agent-based simulation, verify that each controller design method produces successful transport of a load at a regulated velocity, and compare the advantages and disadvantages of each method.     

A Mass Conserved Reaction–Diffusion System Captures Properties of Cell Polarity

Cell polarity is a general cellular process that can be seen in various cell types such as migrating neutrophils and Dictyostelium cells. The Rho small GTP(guanosine 5′-tri phosphate)ases have been shown to regulate cell polarity; however, its mechanism of emergence has yet to be clarified. We first developed a reaction–diffusion model of the Rho GTPases, which exhibits switch-like reversible response to a gradient of extracellular signals, exclusive accumulation of Cdc42 and Rac, or RhoA at the maximal or minimal intensity of the signal, respectively, and tracking of changes of a signal gradient by the polarized peak. The previous cell polarity models proposed by Subramanian and Narang show similar behaviors to our Rho GTPase model, despite the difference in molecular networks. This led us to compare these models, and we found that these models commonly share instability and a mass conservation of components. Based on these common properties, we developed conceptual models of a mass conserved reaction–diffusion system with diffusion–driven instability. These conceptual models retained similar behaviors of cell polarity in the Rho GTPase model. Using these models, we numerically and analytically found that multiple polarized peaks are unstable, resulting in a single stable peak (uniqueness of axis), and that sensitivity toward changes of a signal gradient is specifically restricted at the polarized peak (localized sensitivity). Although molecular networks may differ from one cell type to another, the behaviors of cell polarity in migrating cells seem similar, suggesting that there should be a fundamental principle. Thus, we propose that a mass conserved reaction–diffusion system with diffusion-driven instability is one of such principles of cell polarity.     

BIO-LGCA: A cellular automaton modelling class for analysing collective cell migration

Collective dynamics in multicellular systems such as biological organs and tissues plays a key role in biological development, regeneration, and pathological conditions. Collective tissue dynamics—understood as population behaviour arising from the interplay of the constituting discrete cells—can be studied with on- and off-lattice agent-based models. However, classical on-lattice agent-based models, also known as cellular automata, fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. To overcome drawbacks of classical on-lattice models, we introduce an on-lattice, agent-based modelling class for collective cell migration, which we call biological lattice-gas cellular automaton (BIO-LGCA). The BIO-LGCA is characterised by synchronous time updates, and the explicit consideration of individual cell velocities. While rules in classical cellular automata are typically chosen ad hoc, rules for cell-cell and cell-environment interactions in the BIO-LGCA can also be derived from experimental cell migration data or biophysical laws for individual cell migration. We introduce elementary BIO-LGCA models of fundamental cell interactions, which may be combined in a modular fashion to model complex multicellular phenomena. We exemplify the mathematical mean-field analysis of specific BIO-LGCA models, which allows to explain collective behaviour. The first example predicts the formation of clusters in adhesively interacting cells. The second example is based on a novel BIO-LGCA combining adhesive interactions and alignment. For this model, our analysis clarifies the nature of the recently discovered invasion plasticity of breast cancer cells in heterogeneous environments.     

Neural networks and logical reasoning systems: a translation table

A correspondence is established between the basic elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the structure and dynamical evolution laws of neural networks. The correspondence is pictured as a translation dictionary which might allow to go back and forth between symbolic and network formulations, a desirable step in learning-oriented systems and multicomputer networks. In the framework of Horn clause logics, it is found that atomic propositions with n arguments correspond to nodes with nth order synapses, rules to synaptic intensity constraints, forward chaining to synaptic dynamics and queries either to simple node activation or to a query tensor dynamics.     

Human matching behavior in social networks: an algorithmic perspective

We argue that algorithmic modeling is a powerful approach to understanding the collective dynamics of human behavior. We consider the task of pairing up individuals connected over a network, according to the following model: each individual is able to propose to match with and accept a proposal from a neighbor in the network; if a matched individual proposes to another neighbor or accepts another proposal, the current match will be broken; individuals can only observe whether their neighbors are currently matched but have no knowledge of the network topology or the status of other individuals; and all individuals have the common goal of maximizing the total number of matches. By examining the experimental data, we identify a behavioral principle called prudence, develop an algorithmic model, analyze its properties mathematically and by simulations, and validate the model with human subject experiments for various network sizes and topologies. Our results include i) a [Formula: see text]-approximate maximum matching is obtained in logarithmic time in the network size for bounded degree networks; ii) for any constant [Formula: see text], a [Formula: see text]-approximate maximum matching is obtained in polynomial time, while obtaining a maximum matching can require an exponential time; and iii) convergence to a maximum matching is slower on preferential attachment networks than on small-world networks. These results allow us to predict that while humans can find a "good quality" matching quickly, they may be unable to find a maximum matching in feasible time. We show that the human subjects largely abide by prudence, and their collective behavior is closely tracked by the above predictions.     

Efficient Network Reconstruction from Dynamical Cascades Identifies Small-World Topology of Neuronal Avalanches

Cascading activity is commonly found in complex systems with directed interactions such as metabolic networks, neuronal networks, or disease spreading in social networks. Substantial insight into a system's organization can be obtained by reconstructing the underlying functional network architecture from the observed activity cascades. Here we focus on Bayesian approaches and reduce their computational demands by introducing the Iterative Bayesian (IB) and Posterior Weighted Averaging (PWA) methods. We introduce a special case of PWA, cast in nonparametric form, which we call the normalized count (NC) algorithm. NC efficiently reconstructs random and small-world functional network topologies and architectures from subcritical, critical, and supercritical cascading dynamics and yields significant improvements over commonly used correlation methods. With experimental data, NC identified a functional and structural small-world topology and its corresponding traffic in cortical networks with neuronal avalanche dynamics.