The Wisdom of Networks: A General Adaptation and Learning Mechanism of Complex Systems

I hypothesize that re‐occurring prior experience of complex systems mobilizes a fast response, whose attractor is encoded by their strongly connected network core. In contrast, responses to novel stimuli are often slow and require the weakly connected network periphery. Upon repeated stimulus, peripheral network nodes remodel the network core that encodes the attractor of the new response. This “core‐periphery learning” theory reviews and generalizes the heretofore fragmented knowledge on attractor formation by neural networks, periphery‐driven innovation, and a number of recent reports on the adaptation of protein, neuronal, and social networks. The core‐periphery learning theory may increase our understanding of signaling, memory formation, information encoding and decision‐making processes. Moreover, the power of network periphery‐related “wisdom of crowds” inventing creative, novel responses indicates that deliberative democracy is a slow yet efficient learning strategy developed as the success of a billion‐year evolution. Also see the video abstract here: https://youtu.be/IIjP7zWGjVE .     

Behavioral guides for sensory neurophysiology

The study of natural behavior is important for understanding the coding schemes of sensory systems. The jamming avoidance response of the weakly electric fish Eigenmannia is an excellent example of a bottom–up approach, in which behavioral analyses guided neurophysiological studies. These studies started from the electroreceptive sense organs to the motor output consisting of pacemaker neurons. Going in the opposite direction, from the central nervous system to lower centers, is the characteristic of the top–down approach. Although this approach is perhaps more difficult than the bottom–up approach, it was successfully employed in the neuroethological analysis of sound localization in the barn owl. In the latter studies, high-order neurons selective for complex natural stimuli led to the discovery of neural pathways and networks responsible for the genesis of the stimulus selectivity. Comparison of Eigenmannia and barn owls, and their neural systems, has revealed similarities in network designs, such as parallel pathways and their convergence to produce stimulus selectivity necessary for detection of natural stimuli.     

Long-term adaptation of epistatic genetic networks

Gene networks are likely to govern most traits in nature. Mutations at these genes often show functional epistatic interactions that lead to complex genetic architectures and variable fitness effects in different genetic backgrounds. Understanding how epistatic genetic systems evolve in nature remains one of the great challenges in evolutionary biology. Here we combine an analytical framework with individual-based simulations to generate novel predictions about long-term adaptation of epistatic networks. We find that relative to traits governed by independently evolving genes, adaptation with epistatic gene networks is often characterized by longer waiting times to selective sweeps, lower standing genetic variation, and larger fitness effects of adaptive mutations. This may cause epistatic networks to either adapt more slowly or more quickly relative to a nonepistatic system. Interestingly, epistatic networks may adapt faster even when epistatic effects of mutations are on average deleterious. Further, we study the evolution of epistatic properties of adaptive mutations in gene networks. Our results show that adaptive mutations with small fitness effects typically evolve positive synergistic interactions, whereas adaptive mutations with large fitness effects evolve positive synergistic and negative antagonistic interactions at approximately equal frequencies. These results provide testable predictions for adaptation of traits governed by epistatic networks and the evolution of epistasis within networks.     

Trade-off between responsiveness and noise suppression in biomolecular system responses to environmental cues

When living systems detect changes in their external environment their response must be measured to balance the need to react appropriately with the need to remain stable, ignoring insignificant signals. Because this is a fundamental challenge of all biological systems that execute programs in response to stimuli, we developed a generalized time-frequency analysis (TFA) framework to systematically explore the dynamical properties of biomolecular networks. Using TFA, we focused on two well-characterized yeast gene regulatory networks responsive to carbon-source shifts and a mammalian innate immune regulatory network responsive to lipopolysaccharides (LPS). The networks are comprised of two different basic architectures. Dual positive and negative feedback loops make up the yeast galactose network; whereas overlapping positive and negative feed-forward loops are common to the yeast fatty-acid response network and the LPS-induced network of macrophages. TFA revealed remarkably distinct network behaviors in terms of trade-offs in responsiveness and noise suppression that are appropriately tuned to each biological response. The wild type galactose network was found to be highly responsive while the oleate network has greater noise suppression ability. The LPS network appeared more balanced, exhibiting less bias toward noise suppression or responsiveness. Exploration of the network parameter space exposed dramatic differences in system behaviors for each network. These studies highlight fundamental structural and dynamical principles that underlie each network, reveal constrained parameters of positive and negative feedback and feed-forward strengths that tune the networks appropriately for their respective biological roles, and demonstrate the general utility of the TFA approach for systems and synthetic biology.     

Cellular Adaptation Facilitates Sparse and Reliable Coding in Sensory Pathways

Most neurons in peripheral sensory pathways initially respond vigorously when a preferred stimulus is presented, but adapt as stimulation continues. It is unclear how this phenomenon affects stimulus coding in the later stages of sensory processing. Here, we show that a temporally sparse and reliable stimulus representation develops naturally in sequential stages of a sensory network with adapting neurons. As a modeling framework we employ a mean-field approach together with an adaptive population density treatment, accompanied by numerical simulations of spiking neural networks. We find that cellular adaptation plays a critical role in the dynamic reduction of the trial-by-trial variability of cortical spike responses by transiently suppressing self-generated fast fluctuations in the cortical balanced network. This provides an explanation for a widespread cortical phenomenon by a simple mechanism. We further show that in the insect olfactory system cellular adaptation is sufficient to explain the emergence of the temporally sparse and reliable stimulus representation in the mushroom body. Our results reveal a generic, biophysically plausible mechanism that can explain the emergence of a temporally sparse and reliable stimulus representation within a sequential processing architecture.     

Spontaneous Local Gamma Oscillation Selectively Enhances Neural Network Responsiveness

Synchronized oscillation is very commonly observed in many neuronal systems and might play an important role in the response properties of the system. We have studied how the spontaneous oscillatory activity affects the responsiveness of a neuronal network, using a neural network model of the visual cortex built from Hodgkin-Huxley type excitatory (E-) and inhibitory (I-) neurons. When the isotropic local E-I and I-E synaptic connections were sufficiently strong, the network commonly generated gamma frequency oscillatory firing patterns in response to random feed-forward (FF) input spikes. This spontaneous oscillatory network activity injects a periodic local current that could amplify a weak synaptic input and enhance the network's responsiveness. When E-E connections were added, we found that the strength of oscillation can be modulated by varying the FF input strength without any changes in single neuron properties or interneuron connectivity. The response modulation is proportional to the oscillation strength, which leads to self-regulation such that the cortical network selectively amplifies various FF inputs according to its strength, without requiring any adaptation mechanism. We show that this selective cortical amplification is controlled by E-E cell interactions. We also found that this response amplification is spatially localized, which suggests that the responsiveness modulation may also be spatially selective. This suggests a generalized mechanism by which neural oscillatory activity can enhance the selectivity of a neural network to FF inputs.     

Criticality enhances the multilevel reliability of stimulus responses in cortical neural networks

Cortical neural networks exhibit high internal variability in spontaneous dynamic activities and they can robustly and reliably respond to external stimuli with multilevel features–from microscopic irregular spiking of neurons to macroscopic oscillatory local field potential. A comprehensive study integrating these multilevel features in spontaneous and stimulus–evoked dynamics with seemingly distinct mechanisms is still lacking. Here, we study the stimulus–response dynamics of biologically plausible excitation–inhibition (E–I) balanced networks. We confirm that networks around critical synchronous transition states can maintain strong internal variability but are sensitive to external stimuli. In this dynamical region, applying a stimulus to the network can reduce the trial-to-trial variability and shift the network oscillatory frequency while preserving the dynamical criticality. These multilevel features widely observed in different experiments cannot simultaneously occur in non-critical dynamical states. Furthermore, the dynamical mechanisms underlying these multilevel features are revealed using a semi-analytical mean-field theory that derives the macroscopic network field equations from the microscopic neuronal networks, enabling the analysis by nonlinear dynamics theory and linear noise approximation. The generic dynamical principle revealed here contributes to a more integrative understanding of neural systems and brain functions and incorporates multimodal and multilevel experimental observations. The E–I balanced neural network in combination with the effective mean-field theory can serve as a mechanistic modeling framework to study the multilevel neural dynamics underlying neural information and cognitive processes.     

Sensitivity, principal component and flux analysis applied to signal transduction: the case of epidermal growth factor mediated signaling

MOTIVATION: Novel high-throughput genomic and proteomic tools are allowing the integration of information from a range of biological assays into a single conceptual framework. This framework is often described as a network of biochemical reactions. We present strategies for the analysis of such networks. RESULTS: The direct differential method is described for the systematic evaluation of scaled sensitivity coefficients in reaction networks. Principal component analysis, based on an eigenvalue-eigenvector analysis of the scaled sensitivity coefficient matrix, is applied to rank individual reactions in the network based on their effect on system output. When combined with flux analysis, sensitivity analysis allows model reduction or simplification. Using epidermal growth factor (EGF) mediated signaling and trafficking as an example of signal transduction, we demonstrate that sensitivity analysis quantitatively reveals the dependence of dual-phosphorylated extracellular signal-regulated kinase (ERK) concentration on individual reaction rate constants. It predicts that EGF mediated reactions proceed primarily via an Shc-dependent pathway. Further, it suggests that receptor internalization and endosomal signaling are important features regulating signal output only at low EGF dosages and at later times.     

Plant multiscale networks: charting plant connectivity by multi-level analysis and imaging techniques

In multicellular and even single-celled organisms, individual components are interconnected at multiscale levels to produce enormously complex biological networks that help these systems maintain homeostasis for development and environmental adaptation. Systems biology studies initially adopted network analysis to explore how relationships between individual components give rise to complex biological processes. Network analysis has been applied to dissect the complex connectivity of mammalian brains across different scales in time and space in The Human Brain Project. In plant science, network analysis has similarly been applied to study the connectivity of plant components at the molecular, subcellular, cellular, organic, and organism levels. Analysis of these multiscale networks contributes to our understanding of how genotype determines phenotype. In this review, we summarized the theoretical framework of plant multiscale networks and introduced studies investigating plant networks by various experimental and computational modalities. We next discussed the currently available analytic methodologies and multi-level imaging techniques used to map multiscale networks in plants. Finally, we highlighted some of the technical challenges and key questions remaining to be addressed in this emerging field.     

Early Warning Signs in Social-Ecological Networks

A number of social-ecological systems exhibit complex behaviour associated with nonlinearities, bifurcations, and interaction with stochastic drivers. These systems are often prone to abrupt and unexpected instabilities and state shifts that emerge as a discontinuous response to gradual changes in environmental drivers. Predicting such behaviours is crucial to the prevention of or preparation for unwanted regime shifts. Recent research in ecology has investigated early warning signs that anticipate the divergence of univariate ecosystem dynamics from a stable attractor. To date, leading indicators of instability in systems with multiple interacting components have remained poorly investigated. This is a major limitation in the understanding of the dynamics of complex social-ecological networks. Here, we develop a theoretical framework to demonstrate that rising variance—measured, for example, by the maximum element of the covariance matrix of the network—is an effective leading indicator of network instability. We show that its reliability and robustness depend more on the sign of the interactions within the network than the network structure or noise intensity. Mutualistic, scale free and small world networks are less stable than their antagonistic or random counterparts but their instability is more reliably predicted by this leading indicator. These results provide new advances in multidimensional early warning analysis and offer a framework to evaluate the resilience of social-ecological networks.     

Scaling of differentiation in networks: nervous systems,organisms, ant colonies,ecosystems, businesses,universities, cities,electronic circuits,and Legos

Nodes in networks are often of different types, and in this sense networks are differentiated. Here we examine the relationship between network differentiation and network size in networks under economic or natural selective pressure, such as electronic circuits (networks of electronic components), Legos (networks of Lego pieces), businesses (networks of employees), universities (networks of faculty), organisms (networks of cells), ant colonies (networks of ants), and nervous systems (networks of neurons). For each of these we find that (i) differentiation increases with network size, and (ii) the relationship is consistent with a power law. These results are explained by a hypothesis that, because nodes are costly to build and maintain in such "selected networks", network size is optimized, and from this the power-law relationship may be derived. The scaling exponent depends on the particular kind of network, and is determined by the degree to which nodes are used in a combinatorial fashion to carry out network-level functions. We find that networks under natural selection (organisms, ant colonies, and nervous systems) have much higher combinatorial abilities than the networks for which human ingenuity is involved (electronic circuits, Legos, businesses, and universities). A distinct but related optimization hypothesis may be used to explain scaling of differentiation in competitive networks (networks where the nodes themselves, rather than the entire network, are under selective pressure) such as ecosystems (networks of organisms).     

Neural field model of binocular rivalry waves

We present a neural field model of binocular rivalry waves in visual cortex. For each eye we consider a one-dimensional network of neurons that respond maximally to a particular feature of the corresponding image such as the orientation of a grating stimulus. Recurrent connections within each one-dimensional network are assumed to be excitatory, whereas connections between the two networks are inhibitory (cross-inhibition). Slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We derive an analytical expression for the speed of a binocular rivalry wave as a function of various neurophysiological parameters, and show how properties of the wave are consistent with the wave-like propagation of perceptual dominance observed in recent psychophysical experiments. In addition to providing an analytical framework for studying binocular rivalry waves, we show how neural field methods provide insights into the mechanisms underlying the generation of the waves. In particular, we highlight the important role of slow adaptation in providing a “symmetry breaking mechanism” that allows waves to propagate.     

Adaptation and selective information transmission in the cricket auditory neuron AN2

Sensory systems adapt their neural code to changes in the sensory environment, often on multiple time scales. Here, we report a new form of adaptation in a first-order auditory interneuron (AN2) of crickets. We characterize the response of the AN2 neuron to amplitude-modulated sound stimuli and find that adaptation shifts the stimulus-response curves toward higher stimulus intensities, with a time constant of 1.5 s for adaptation and recovery. The spike responses were thus reduced for low-intensity sounds. We then address the question whether adaptation leads to an improvement of the signal's representation and compare the experimental results with the predictions of two competing hypotheses: infomax, which predicts that information conveyed about the entire signal range should be maximized, and selective coding, which predicts that "foreground" signals should be enhanced while "background" signals should be selectively suppressed. We test how adaptation changes the input-response curve when presenting signals with two or three peaks in their amplitude distributions, for which selective coding and infomax predict conflicting changes. By means of Bayesian data analysis, we quantify the shifts of the measured response curves and also find a slight reduction of their slopes. These decreases in slopes are smaller, and the absolute response thresholds are higher than those predicted by infomax. Most remarkably, and in contrast to the infomax principle, adaptation actually reduces the amount of encoded information when considering the whole range of input signals. The response curve changes are also not consistent with the selective coding hypothesis, because the amount of information conveyed about the loudest part of the signal does not increase as predicted but remains nearly constant. Less information is transmitted about signals with lower intensity.     

How robust are neural network models of stimulus generalization?

Artificial feed-forward neural networks are commonly used as a tool for modelling stimulus selection and animal signalling. A key finding of stimulus selection research has been generalization: if a given behaviour has been established to one stimulus, perceptually similar novel stimuli are likely to induce a similar response. Stimulus generalization, in feed-forward neural networks, automatically arises as a property of the network. This network property raises understandable concern regarding the sensitivity of the network to variation in its internal parameter values used in relation to its structure and to its training process. Researchers must have confidence that the predictions of their model follow from the underlying biology that they deliberately incorporated in the model, and not from often arbitrary choices about model implementation. We study how network training and parameter perturbations influence the qualitative and quantitative behaviour of a simple but general network. Specifically, for models of stimulus control we study the effect that parameter variation has on the shape of the generalization curves produced by the network. We show that certain network and training conditions produce undesirable artifacts that need to be avoided (or at least understood) when modelling stimulus selection.     

A system identification analysis of neural adaptation dynamics and nonlinear responses in the local reflex control of locust hind limbs

Nonlinear type system identification models coupled with white noise stimulation provide an experimentally convenient and quick way to investigate the often complex and nonlinear interactions between the mechanical and neural elements of reflex limb control systems. Previous steady state analysis has allowed the neurons in such systems to be categorised by their sensitivity to position, velocity or acceleration (dynamics) and has improved our understanding of network function. These neurons, however, are known to adapt their output amplitude or spike firing rate during repetitive stimulation and this transient response may be more important than the steady state response for reflex control. In the current study previously used system identification methods are developed and applied to investigate both steady state and transient dynamic and nonlinear changes in the neural circuit responsible for controlling reflex movements of the locust hind limbs. Through the use of a parsimonious model structure and Monte Carlo simulations we conclude that key system dynamics remain relatively unchanged during repetitive stimulation while output amplitude adaptation is occurring. Whilst some evidence of a significant change was found in parts of the systems nonlinear response, the effect was small and probably of little physiological relevance. Analysis using biologically more realistic stimulation reinforces this conclusion.     

Persistent activity in neural networks with dynamic synapses

Persistent activity states (attractors), observed in several neocortical areas after the removal of a sensory stimulus, are believed to be the neuronal basis of working memory. One of the possible mechanisms that can underlie persistent activity is recurrent excitation mediated by intracortical synaptic connections. A recent experimental study revealed that connections between pyramidal cells in prefrontal cortex exhibit various degrees of synaptic depression and facilitation. Here we analyze the effect of synaptic dynamics on the emergence and persistence of attractor states in interconnected neural networks. We show that different combinations of synaptic depression and facilitation result in qualitatively different network dynamics with respect to the emergence of the attractor states. This analysis raises the possibility that the framework of attractor neural networks can be extended to represent time-dependent stimuli.     

Discovering adaptation-capable biological network structures using control-theoretic approaches

Constructing biological networks capable of performing specific biological functionalities has been of sustained interest in synthetic biology. Adaptation is one such ubiquitous functional property, which enables every living organism to sense a change in its surroundings and return to its operating condition prior to the disturbance. In this paper, we present a generic systems theory-driven method for designing adaptive protein networks. First, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as ‘design requirements’ for the underlying networks. We go on to prove that a protein network with different input–output nodes (proteins) needs to be at least of third-order in order to provide adaptation. Next, we show that the necessary design principles obtained for a three-node network in adaptation consist of negative feedback or a feed-forward realization. We argue that presence of a particular class of negative feedback or feed-forward realization is necessary for a network of any size to provide adaptation. Further, we claim that the necessary structural conditions derived in this work are the strictest among the ones hitherto existed in the literature. Finally, we prove that the capability of producing adaptation is retained for the admissible motifs even when the output node is connected with a downstream system in a feedback fashion. This result explains how complex biological networks achieve robustness while keeping the core motifs unchanged in the context of a particular functionality. We corroborate our theoretical results with detailed and thorough numerical simulations. Overall, our results present a generic, systematic and robust framework for designing various kinds of biological networks.     

Efficient Transmission of Subthreshold Signals in Complex Networks of Spiking Neurons

We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances—that naturally balances the network with excitatory and inhibitory synapses—and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios, including spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it could also occur in actual neural systems as recent psycho-physical experiments suggest.     

Neural network features distinguish chemosensory stimuli in Caenorhabditis elegans

Nervous systems extract and process information from the environment to alter animal behavior and physiology. Despite progress in understanding how different stimuli are represented by changes in neuronal activity, less is known about how they affect broader neural network properties. We developed a framework for using graph-theoretic features of neural network activity to predict ecologically relevant stimulus properties, in particular stimulus identity. We used the transparent nematode, Caenorhabditis elegans, with its small nervous system to define neural network features associated with various chemosensory stimuli. We first immobilized animals using a microfluidic device and exposed their noses to chemical stimuli while monitoring changes in neural activity of more than 50 neurons in the head region. We found that graph-theoretic features, which capture patterns of interactions between neurons, are modulated by stimulus identity. Further, we show that a simple machine learning classifier trained using graph-theoretic features alone, or in combination with neural activity features, can accurately predict salt stimulus. Moreover, by focusing on putative causal interactions between neurons, the graph-theoretic features were almost twice as predictive as the neural activity features. These results reveal that stimulus identity modulates the broad, network-level organization of the nervous system, and that graph theory can be used to characterize these changes.