Priming and filtering of antiherbivore defences among Nicotiana attenuata plants connected by mycorrhizal networks

Arbuscular mycorrhizal fungi (AMF) establish symbiotic associations with a majority of terrestrial plants to form underground common mycorrhizal networks (CMNs) that connect neighbouring plants. Because Nicotiana attenuata plants do not respond to herbivory‐elicited volatiles from neighbours, we used this ecological model system to evaluate if CMNs function in interplant transmission of herbivory‐elicited responses. A mesocosm system was designed to establish and remove CMNs linking N. attenuata plants to examine the herbivory‐elicited metabolic and hormone responses in CMNs‐connected “receiver” plants after the elicitation of “donor” plants by wounding (W) treated with Manduca sexta larval oral secretions (OS). AMF colonization increased constitutive jasmonate (JA and JA‐Ile) levels in N. attenuata roots but did not affect well‐characterized JAs‐regulated defensive metabolites in systemic leaves. Interestingly, larger JAs bursts, and higher levels of several amino acids and particular sectors of hydroxygeranyllinalool diterpene glycoside metabolism were elevated in the leaves of W + OS‐elicited “receivers” with CMN connections with “donors” that had been W + OS‐elicited 6 hr previously. Our results demonstrate that AMF colonization alone does not enhance systemic defence responses but that sectors of systemic responses in leaves can be primed by CMNs, suggesting that CMNs can transmit and even filter defence signalling among connected plants.     

Defaunation leads to interaction deficits,not interaction compensation,in an island seed dispersal network

Following defaunation, the loss of interactions with mutualists such as pollinators or seed dispersers may be compensated through increased interactions with remaining mutualists, ameliorating the negative cascading impacts on biodiversity. Alternatively, remaining mutualists may respond to altered competition by reducing the breadth or intensity of their interactions, exacerbating negative impacts on biodiversity. Despite the importance of these responses for our understanding of the dynamics of mutualistic networks and their response to global change, the mechanism and magnitude of interaction compensation within real mutualistic networks remains largely unknown. We examined differences in mutualistic interactions between frugivores and fruiting plants in two island ecosystems possessing an intact or disrupted seed dispersal network. We determined how changes in the abundance and behavior of remaining seed dispersers either increased mutualistic interactions (contributing to “interaction compensation”) or decreased interactions (causing an “interaction deficit”) in the disrupted network. We found a “rich‐get‐richer” response in the disrupted network, where remaining frugivores favored the plant species with highest interaction frequency, a dynamic that worsened the interaction deficit among plant species with low interaction frequency. Only one of five plant species experienced compensation and the other four had significant interaction deficits, with interaction frequencies 56–95% lower in the disrupted network. These results do not provide support for the strong compensating mechanisms assumed in theoretical network models, suggesting that existing network models underestimate the prevalence of cascading mutualism disruption after defaunation. This work supports a mutualist biodiversity‐ecosystem functioning relationship, highlighting the importance of mutualist diversity for sustaining diverse and resilient ecosystems.     

Emergence of symmetric, modular, and reciprocal connections in recurrent networks with Hebbian learning

While learning and development are well characterized in feedforward networks, these features are more difficult to analyze in recurrent networks due to the increased complexity of dual dynamics – the rapid dynamics arising from activation states and the slow dynamics arising from learning or developmental plasticity. We present analytical and numerical results that consider dual dynamics in a recurrent network undergoing Hebbian learning with either constant weight decay or weight normalization. Starting from initially random connections, the recurrent network develops symmetric or near-symmetric connections through Hebbian learning. Reciprocity and modularity arise naturally through correlations in the activation states. Additionally, weight normalization may be better than constant weight decay for the development of multiple attractor states that allow a diverse representation of the inputs. These results suggest a natural mechanism by which synaptic plasticity in recurrent networks such as cortical and brainstem premotor circuits could enhance neural computation and the generation of motor programs. Received: 27 April 1998 / Accepted in revised form: 16 March 1999     

THE EVOLUTION OF PHENOTYPIC CORRELATIONS AND “DEVELOPMENTAL MEMORY”

Development introduces structured correlations among traits that may constrain or bias the distribution of phenotypes produced. Moreover, when suitable heritable variation exists, natural selection may alter such constraints and correlations, affecting the phenotypic variation available to subsequent selection. However, exactly how the distribution of phenotypes produced by complex developmental systems can be shaped by past selective environments is poorly understood. Here we investigate the evolution of a network of recurrent nonlinear ontogenetic interactions, such as a gene regulation network, in various selective scenarios. We find that evolved networks of this type can exhibit several phenomena that are familiar in cognitive learning systems. These include formation of a distributed associative memory that can “store” and “recall” multiple phenotypes that have been selected in the past, recreate complete adult phenotypic patterns accurately from partial or corrupted embryonic phenotypes, and “generalize” (by exploiting evolved developmental modules) to produce new combinations of phenotypic features. We show that these surprising behaviors follow from an equivalence between the action of natural selection on phenotypic correlations and associative learning, well‐understood in the context of neural networks. This helps to explain how development facilitates the evolution of high‐fitness phenotypes and how this ability changes over evolutionary time.     

Neuro-robotics study on integrative learning of proactive visual attention and motor behaviors

The current paper proposes a novel model for integrative learning of proactive visual attention and sensory-motor control as inspired by the premotor theory of visual attention. The model is characterized by coupling a slow dynamics network with a fast dynamics network and by inheriting our prior proposed multiple timescales recurrent neural networks model (MTRNN) that may correspond to the fronto-parietal networks in the cortical brains. The neuro-robotics experiments in a task of manipulating multiple objects utilizing the proposed model demonstrated that some degrees of generalization in terms of position and object size variation can be achieved by organizing seamless integration of the proactive object-related visual attention and the related sensory-motor control into a set of action primitives in the distributed neural activities appearing in the fast dynamics network. It was also shown that such action primitives can be combined in compositional ways in acquiring novel actions in the slow dynamics network. The experimental results presented substantiate the premotor theory of visual attention.     

Memory Capacity of Networks with Stochastic Binary Synapses

In standard attractor neural network models, specific patterns of activity are stored in the synaptic matrix, so that they become fixed point attractors of the network dynamics. The storage capacity of such networks has been quantified in two ways: the maximal number of patterns that can be stored, and the stored information measured in bits per synapse. In this paper, we compute both quantities in fully connected networks of N binary neurons with binary synapses, storing patterns with coding level , in the large and sparse coding limits (). We also derive finite-size corrections that accurately reproduce the results of simulations in networks of tens of thousands of neurons. These methods are applied to three different scenarios: (1) the classic Willshaw model, (2) networks with stochastic learning in which patterns are shown only once (one shot learning), (3) networks with stochastic learning in which patterns are shown multiple times. The storage capacities are optimized over network parameters, which allows us to compare the performance of the different models. We show that finite-size effects strongly reduce the capacity, even for networks of realistic sizes. We discuss the implications of these results for memory storage in the hippocampus and cerebral cortex.     

Accuracy and response-time distributions for decision-making: linear perfect integrators versus nonlinear attractor-based neural circuits

Animals choose actions based on imperfect, ambiguous data. “Noise” inherent in neural processing adds further variability to this already-noisy input signal. Mathematical analysis has suggested that the optimal apparatus (in terms of the speed/accuracy trade-off) for reaching decisions about such noisy inputs is perfect accumulation of the inputs by a temporal integrator. Thus, most highly cited models of neural circuitry underlying decision-making have been instantiations of a perfect integrator. Here, in accordance with a growing mathematical and empirical literature, we describe circumstances in which perfect integration is rendered suboptimal. In particular we highlight the impact of three biological constraints: (1) significant noise arising within the decision-making circuitry itself; (2) bounding of integration by maximal neural firing rates; and (3) time limitations on making a decision. Under conditions (1) and (2), an attractor system with stable attractor states can easily best an integrator when accuracy is more important than speed. Moreover, under conditions in which such stable attractor networks do not best the perfect integrator, a system with unstable initial states can do so if readout of the system’s final state is imperfect. Ubiquitously, an attractor system with a nonselective time-dependent input current is both more accurate and more robust to imprecise tuning of parameters than an integrator with such input. Given that neural responses that switch stochastically between discrete states can “masquerade” as integration in single-neuron and trial-averaged data, our results suggest that such networks should be considered as plausible alternatives to the integrator model.     

Results of a food addition experiment in a north-central Chile small mammal assemblage: evidence for the role of "bottom-up" factors

Since 1989, effects of biotic interactions including predation and herbivory have been examined in a replicated experimental study in a north‐central Chilean semiarid thorn scrub community. Strong responses of small mammals and plants to El Niño Southern Oscillations (ENSO) have also been documented suggesting that “bottom‐up” factors related to high rainfall are important. To simulate increased primary productivity effects on small mammals, ad lib rabbit pellet additions were initiated in mid‐1997 on unfenced grids near the experimental complex. Following the 1997 El Niño event with three times normal precipitation, numbers of small mammals during pre‐addition months and the first treatment year were similar on control and food addition grids. During the second year (1998–1999), a period of severe drought, food additions had significant positive effects on numbers of two predominantly herbivorous “core” (resident) species, Octodon degus and Phyllotis darwini, and an omnivorous “quasi‐core” (resident but highly fluctuating) species, Akodon olivaceus; however, all three species declined towards the end of the second treatment year. Two “opportunistic” (temporarily resident) species, Abrothrix longipilis (an insectivore) and Oligoryzomys longicaudatus (a granivore), showed no responses to food additions. An insectivorous marsupial, Thylamys elegans (also a “core species”), had significantly lower numbers on food addition grids. Changes in body weight distributions and proportions of reproductive individuals particularly in O. degus indicate in situ responses. Whereas no differences in residency, numbers of stations visited, and trappability were observed, energy compensation ratios greater than one suggest significant immigration in the second year. Thus, food additions elicited strong responses by herbivorous/omnivorous “core” and “quasi‐core species” whereas they had no effects on “opportunistic species”. These results reinforce the view that “bottom‐up” factors influencing food availability exert prevailing control on numerically important small mammal species by temporarily increasing carrying capacity, and that “top‐down” factors (i.e., biotic interactions) become important when small mammal numbers are at or near their carrying capacity. Spatial dynamics may be important in explaining declines of species populations exhibiting initially positive responses to food additions.     

Intrinsic properties of Boolean dynamics in complex networks

We study intrinsic properties of attractor in Boolean dynamics of complex networks with scale-free topology, comparing with those of the so-called Kauffman's random Boolean networks. We numerically study both frozen and relevant nodes in each attractor in the dynamics of relatively small networks (20?N?200). We investigate numerically robustness of an attractor to a perturbation. An attractor with cycle length of ?_c in a network of size N consists of ?_c states in the state space of 2^N states; each attractor has the arrangement of N nodes, where the cycle of attractor sweeps ?_c states. We define a perturbation as a flip of the state on a single node in the attractor state at a given time step. We show that the rate between unfrozen and relevant nodes in the dynamics of a complex network with scale-free topology is larger than that in Kauffman's random Boolean network model. Furthermore, we find that in a complex scale-free network with fluctuation of the in-degree number, attractors are more sensitive to a state flip for a highly connected node (i.e. input-hub node) than to that for a less connected node. By some numerical examples, we show that the number of relevant nodes increases, when an input-hub node is coincident with and/or connected with an output-hub node (i.e. a node with large output-degree) one another.     

Reprogramming cell fates: reconciling rarity with robustness

The stunning possibility of “reprogramming” differentiated somatic cells to express a pluripotent stem cell phenotype (iPS, induced pluripotent stem cell) and the “ground state” character of pluripotency reveal fundamental features of cell fate regulation that lie beyond existing paradigms. The rarity of reprogramming events appears to contradict the robustness with which the unfathomably complex phenotype of stem cells can reliably be generated. This apparent paradox, however, is naturally explained by the rugged “epigenetic landscape” with valleys representing “preprogrammed” attractor states that emerge from the dynamical constraints of the gene regulatory network. This article provides a pedagogical primer to the fundamental principles of gene regulatory networks as integrated dynamic systems and reviews recent insights in gene expression noise and fate determination, thereby offering a formal framework that may help us to understand why cell fate reprogramming events are inherently rare and yet so robust.     

Limits and Trade-Offs of Topological Network Robustness

We investigate the trade-off between the robustness against random and targeted removal of nodes from a network. To this end we utilize the stochastic block model to study ensembles of infinitely large networks with arbitrary large-scale structures. We present results from numerical two-objective optimization simulations for networks with various fixed mean degree and number of blocks. The results provide strong evidence that three different blocks are sufficient to realize the best trade-off between the two measures of robustness, i.e. to obtain the complete front of Pareto-optimal networks. For all values of the mean degree, a characteristic three block structure emerges over large parts of the Pareto-optimal front. This structure can be often characterized as a core-periphery structure, composed of a group of core nodes with high degree connected among themselves and to a periphery of low-degree nodes, in addition to a third group of nodes which is disconnected from the periphery, and weakly connected to the core. Only at both extremes of the Pareto-optimal front, corresponding to maximal robustness against random and targeted node removal, a two-block core-periphery structure or a one-block fully random network are found, respectively.     

Using species co‐occurrence networks to assess the impacts of climate change

Viable populations of species occur in a given place if three conditions are met: the environment at the place is suitable; the species is able to colonize it; co‐occurrence is possible despite or because of interactions with other species. Studies investigating the effects of climate change on species have mainly focused on measuring changes in climate suitability. Complex interactions among species have rarely been explored in such studies. We extend network theory to the analysis of complex patterns of co‐occurrence among species. The framework is used to explore the robustness of networks under climate change. With our data, we show that networks describing the geographic pattern of co‐occurrence among species display properties shared by other complex networks, namely that most species are poorly connected to other species in the network and only a few are highly connected. In our example, species more exposed to climate change tended to be poorly connected to other species within the network, while species more connected tended to be less exposed. Such high connectance would make the co‐occurrence networks more robust to climate change. The proposed framework illustrates how network analysis could be used, together with co‐occurrence data, to help addressing the potential consequences of species interactions in studies of climate change and biodiversity. However, more research is needed to test for links between co‐occurrence and network interactions.     

On the existence and the role of chaotic processes in the nervous system

Chaos theory is a rapidly growing field. As a technical term, “chaos” refers to deterministic but unpredictable processes being sensitively dependent upon initial conditions. Neurobiological models and experimental results are very complicated and some research groups have tried to pursue the “neuronal chaos”. Babloyantz's group has studied the fractal dimension (d) of electroencephalograms (EEG) in various physiological and pathological states. From deep sleep (d=4) to full awakening (d>8), a hierarchy of “strange” attractors paralles the hierarchy of states of consciousness. In epilepsy (petit mal), despite the turbulent aspect of a seizure, the attractor dimension was near to 2. In Creutzfeld-Jacob disease, the regular EEG activity corresponded to an attractor dimension less than the one measured in deep sleep. Is it healthy to be chaotic? An “active desynchronisation” could be favourable to a physiological system. Rapp's group reported variations of fractal dimension according to particular tasks. During a mental arithmetic task, this dimension increased. In another task, a P300 fractal index decreased when a target was identified. It is clear that the EEG is not representing noise. Its underlying dynamics depends on only a few degrees of freedom despite yet it is difficult to compute accurately the relevant parameters. What is the cognitive role of such a chaotic dynamics? Freeman has studied the olfactory bulb in rabbits and rats for 15 years. Multi-electrode recordings of a few mm² showed a chaotic hierarchy from deep anaesthesia to alert state. When an animal identified a previously learned odour, the fractal dimension of the dynamics dropped off (near limit cycles). The chaotic activity corresponding to an alert-and-waiting state seems to be a field of all possibilities and a focused activity corresponds to a reduction of the attractor in state space. For a couple of years, Freeman has developed a model of the olfactory bulb-cortex system. The behaviour of the simple model “without learning” was quite similar to the real behaviour and a model “with learning” is developed. Recently, more and more authors insisted on the importance of the dynamic aspect of nervous functioning in cognitive modelling. Most of the models in the neural-network field are designed to converge to a stable state (fixed point) because such behaviour is easy to understand and to control. However, some theoretical studies in physics try to understand how a chaotic behaviour can emerge from neural networks. Sompolinsky's group showed that a sharp transition from a stable state to a chaotic state occurred in totally interconnected networks depending on the value of one control parameter. Learning in such systems is an open field. In conclusion, chaos does exist in neurophysiological processes. It is neither a kind of noise nor a pathological sign. Its main role could be to provide diversity and flexibility to physiological processes. Could “strange” attractors in nervous system embody mental forms? This is a difficult but fascinating question.     

A general-purpose electronic model for arbitrary configurations of neurons

This paper describes a general-purpose electronic model for simulating the electrical activity in small groups of nerve cells arranged in arbitrary configurations. The model consists of 44 realizations of two basic modules (the “cell”, and the “axon with synapses”) which can be connected together in various arrangements by way of snapper-capped wires. The activity of the individual units is displayed via flashing lights atop the constituent cells; also there are taps on each cell from which one can obtain and display more detailed information concerning the electrical activity of each and all cells, including the graded “generator” potential of the triggering section, on for example an oscilloscope. The modules include realistic approximations to basic mechanisms of neuronal activity, but the main advance over previous models is the emphasis on and ability to deal with the network context of neuroelectric signals.Illustrative applications to mutually-inhibiting centers and to our ladder net theory for reticular-like networks are presented. The primary advantages of the electronic model are: actual physical representation of various configurations, asynchronous timing, flexibility with respect to overall configuration and with respect to network parameters, immediate turnaround, and cost.     

A comparative study of electronic and neural networks involved in pattern recognition

The comparative study of electronic and neural networks involved in pattern recognition starts with the analogies of structure and function which exist between the electronic “basic integrative unit” and the neuron. Both elements represent the basic components in each system of networks and may be considered as functionally equivalent.According to the kind of response given to a standard input signal, four types of integrative units, either electronic or neural, may be distinguished: the fixed, the accommodative, the signal prolongating and the adaptive type.The integrative units perform many different functions. Those involved in pattern recognition, however, can all be grouped into three categories according to one of the following functions they perform: contrast detection, pattern detection and pattern discrimination. A “contrast detecting unit” gives responses in two senses, positive or negative, according to the position of the stimulus over its receptive field. A “pattern detecting unit” gives responses in one sense only, with a maximum for a pattern having the spatial distribution corresponding to the positive acting receptors of its receptive field. For performing the function of discrimination, which leads to reliable identification of any pattern, a network arrangement called a “maximum amplitude filter” is necessary. Examples of such units and arrangements existing in the nervous system are provided.It is concluded that a “logical analysis of neural networks” based on engineering principles is possible and that this could provide a new tool to the neurophysiologist in the study of the nervous system.     

Rewiring and indirect effects underpin modularity reshuffling in a marine food web under environmental shifts

Species are characterized by physiological and behavioral plasticity, which is part of their response to environmental shifts. Nonetheless, the collective response of ecological communities to environmental shifts cannot be predicted from the simple sum of individual species responses, since co‐existing species are deeply entangled in interaction networks, such as food webs. For these reasons, the relation between environmental forcing and the structure of food webs is an open problem in ecology. To this respect, one of the main problems in community ecology is defining the role each species plays in shaping community structure, such as by promoting the subdivision of food webs in modules—that is, aggregates composed of species that more frequently interact—which are reported as community stabilizers. In this study, we investigated the relationship between species roles and network modularity under environmental shifts in a highly resolved food web, that is, a “weighted” ecological network reproducing carbon flows among marine planktonic species. Measuring network properties and estimating weighted modularity, we show that species have distinct roles, which differentially affect modularity and mediate structural modifications, such as modules reconfiguration, induced by environmental shifts. Specifically, short‐term environmental changes impact the abundance of planktonic primary producers; this affects their consumers’ behavior and cascades into the overall rearrangement of trophic links. Food web re‐adjustments are both direct, through the rewiring of trophic‐interaction networks, and indirect, with the reconfiguration of trophic cascades. Through such “systemic behavior,” that is, the way the food web acts as a whole, defined by the interactions among its parts, the planktonic food web undergoes a substantial rewiring while keeping almost the same global flow to upper trophic levels, and energetic hierarchy is maintained despite environmental shifts. This behavior suggests the potentially high resilience of plankton networks, such as food webs, to dramatic environmental changes, such as those provoked by global change.     

Loop extrusion driven volume phase transition of entangled chromosomes

Experiments on reconstituted chromosomes have revealed that mitotic chromosomes are assembled even without nucleosomes. When topoisomerase II (topo II) is depleted from such reconstituted chromosomes, these chromosomes are not disentangled and form “sparklers,” where DNA and linker histone are condensed in the core and condensin is localized at the periphery. To understand the mechanism of the assembly of sparklers, we here take into account the loop extrusion by condensin in an extension of the theory of entangled polymer gels. The loop extrusion stiffens an entangled DNA network because DNA segments in the elastically effective chains are translocated to loops, which are elastically ineffective. Our theory predicts that the loop extrusion by condensin drives the volume phase transition that collapses a swollen entangled DNA gel because the stiffening of the network destabilizes the swollen phase. This may be an important piece to understand the mechanism of the assembly of mitotic chromosomes.     

Genome‐wide association mapping of natural variation in odour‐guided behaviour in Drosophila

A defining goal in the field of behavioural genetics is to identify the key genes or genetic networks that shape behaviour. A corollary to this goal is the goal of identifying genetic variants that are responsible for variation in the behaviour. These goals are achieved by measuring behavioural responses to controlled stimuli, in the present case the responses of Drosophila melanogaster to olfactory stimuli. We used a high‐throughput behavioural assay system to test a panel of 157 Drosophila inbred lines derived from a natural population for both temporal and spatial dynamics of odour‐guided behaviour. We observed significant variation in response to the odourant 2,3‐butanedione, a volatile compound present in fermenting fruit. The recent whole genome sequencing of these inbred lines allowed us to then perform genome‐wide association analyses in order to identify genetic polymorphisms underlying variation in responses. These analyses revealed numerous single nucleotide polymorphisms associated with variation in responses. Among the candidate genes identified were both novel and previously identified olfaction‐related genes. Further, gene network analyses suggest that genes influencing variation in odour‐guided behaviour are enriched for functions involving neural processing and that these genes form a pleiotropic interaction network. We examined several of these candidate genes that were highly connected in the protein‐ and genetic interaction networks using RNA interference. Our results showed that subtle changes influencing nervous system function can result in marked differences in behaviour .     

Super folds,networks, and barriers

Exhaustive enumeration of sequences and folds is conducted for a simple lattice model of conformations, sequences, and energies. Examination of all foldable sequences and their nearest connected neighbors (sequences that differ by no more than a point mutation) illustrates the following: (i) There exist unusually large number of sequences that fold into a few structures (super‐folds). The same observation was made experimentally and computationally using stochastic sampling and exhaustive enumeration of related models. (ii) There exist only a few large networks of connected sequences that are not restricted to one fold. These networks cover a significant fraction of fold spaces (super‐networks). (iii) There exist barriers in sequence space that prevent foldable sequences of the same structure to “connect” through a series of single point mutations (super‐barrier), even in the presence of the sequence connection between folds. While there is ample experimental evidence for the existence of super‐folds, evidence for a super‐network is just starting to emerge. The prediction of a sequence barrier is an intriguing characteristic of sequence space, suggesting that the overall sequence space may be disconnected. The implications and limitations of these observations for evolution of protein structures are discussed. Proteins 2012. © 2011 Wiley Periodicals, Inc.     

Accurate Path Integration in Continuous Attractor Network Models of Grid Cells

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal''s position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat''s velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of ∼10–100 meters and ∼1–10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.