Modelling Feedback Excitation,Pacemaker Properties and Sensory Switching of Electrically Coupled Brainstem Neurons Controlling Rhythmic Activity

What cellular and network properties allow reliable neuronal rhythm generation or firing that can be started and stopped by brief synaptic inputs? We investigate rhythmic activity in an electrically-coupled population of brainstem neurons driving swimming locomotion in young frog tadpoles, and how activity is switched on and off by brief sensory stimulation. We build a computational model of 30 electrically-coupled conditional pacemaker neurons on one side of the tadpole hindbrain and spinal cord. Based on experimental estimates for neuron properties, population sizes, synapse strengths and connections, we show that: long-lasting, mutual, glutamatergic excitation between the neurons allows the network to sustain rhythmic pacemaker firing at swimming frequencies following brief synaptic excitation; activity persists but rhythm breaks down without electrical coupling; NMDA voltage-dependency doubles the range of synaptic feedback strengths generating sustained rhythm. The network can be switched on and off at short latency by brief synaptic excitation and inhibition. We demonstrate that a population of generic Hodgkin-Huxley type neurons coupled by glutamatergic excitatory feedback can generate sustained asynchronous firing switched on and off synaptically. We conclude that networks of neurons with NMDAR mediated feedback excitation can generate self-sustained activity following brief synaptic excitation. The frequency of activity is limited by the kinetics of the neuron membrane channels and can be stopped by brief inhibitory input. Network activity can be rhythmic at lower frequencies if the neurons are electrically coupled. Our key finding is that excitatory synaptic feedback within a population of neurons can produce switchable, stable, sustained firing without synaptic inhibition.     

A synaptic modification algorithm in consideration of the generation of rhythmic oscillation in a ring neural network

In consideration of the generation of bursts of nerve impulses (that is, rhythmic oscillation in impulse density) in the ring neural network, a synaptic modification algorithm is newly proposed. Rhythmic oscillation generally occurs in the regular ring network with feedback inhibition and in fact such signals can be observed in the real nervous system. Since, however, various additional connections can cause a disturbance which easily extinguishes the rhythmic oscillation in the network, some function for maintaining the rhythmic oscillation is to be expected to exist in the synapses if such signals play an important part in the nervous system. Our preliminary investigation into the rhythmic oscillation in the regular ring network has led to the selection of the parameters, that is, the average membrane potential (AMP) and the average impulse density (AID) in the synaptic modification algorithm, where the decrease of synaptic strength is supposed to be essential. This synaptic modification algorithm using AMP and AID enables both the rhythmic oscillation and the non-oscillatory state to be dealt with in the algorithm without distinction. Simulation demonstrates cases in which the algorithm catches and holds the rhythmic oscillation in the disturbed ring network where the rhythmic oscillation was previously extinguished.     

Opioid-induced quantal slowing reveals dual networks for respiratory rhythm generation

Current consensus holds that a single medullary network generates respiratory rhythm in mammals. Pre-B?tzinger Complex inspiratory (I) neurons, isolated in transverse slices, and preinspiratory (pre-I) neurons, found only in more intact en bloc preparations and in vivo, are each proposed as necessary for rhythm generation. Opioids slow I, but not pre-I, neuronal burst periods. In slices, opioids gradually lengthened respiratory periods, whereas in more intact preparations, periods jumped nondeterministically to integer multiples of the control period (quantal slowing). These findings suggest that opioid-induced quantal slowing results from transmission failure of rhythmic drive from pre-I neurons to preB?tC I networks, depressed below threshold for spontaneous rhythmic activity. Thus, both I (in the slice), and pre-I neurons are sufficient for respiratory rhythmogenesis.     

An Adaptive Complex Network Model for Brain Functional Networks

Brain functional networks are graph representations of activity in the brain, where the vertices represent anatomical regions and the edges their functional connectivity. These networks present a robust small world topological structure, characterized by highly integrated modules connected sparsely by long range links. Recent studies showed that other topological properties such as the degree distribution and the presence (or absence) of a hierarchical structure are not robust, and show different intriguing behaviors. In order to understand the basic ingredients necessary for the emergence of these complex network structures we present an adaptive complex network model for human brain functional networks. The microscopic units of the model are dynamical nodes that represent active regions of the brain, whose interaction gives rise to complex network structures. The links between the nodes are chosen following an adaptive algorithm that establishes connections between dynamical elements with similar internal states. We show that the model is able to describe topological characteristics of human brain networks obtained from functional magnetic resonance imaging studies. In particular, when the dynamical rules of the model allow for integrated processing over the entire network scale-free non-hierarchical networks with well defined communities emerge. On the other hand, when the dynamical rules restrict the information to a local neighborhood, communities cluster together into larger ones, giving rise to a hierarchical structure, with a truncated power law degree distribution.     

Edge vulnerability in neural and metabolic networks

Biological networks, such as cellular metabolic pathways or networks of corticocortical connections in the brain, are intricately organized, yet remarkably robust toward structural damage. Whereas many studies have investigated specific aspects of robustness, such as molecular mechanisms of repair, this article focuses more generally on how local structural features in networks may give rise to their global stability. In many networks the failure of single connections may be more likely than the extinction of entire nodes, yet no analysis of edge importance (edge vulnerability) has been provided so far for biological networks. We tested several measures for identifying vulnerable edges and compared their prediction performance in biological and artificial networks. Among the tested measures, edge frequency in all shortest paths of a network yielded a particularly high correlation with vulnerability and identified intercluster connections in biological but not in random and scale-free benchmark networks. We discuss different local and global network patterns and the edge vulnerability resulting from them.     

A densely interconnected genome-wide network of microRNAs and oncogenic pathways revealed using gene expression signatures

MicroRNAs (miRNAs) are important components of cellular signaling pathways, acting either as pathway regulators or pathway targets. Currently, only a limited number of miRNAs have been functionally linked to specific signaling pathways. Here, we explored if gene expression signatures could be used to represent miRNA activities and integrated with genomic signatures of oncogenic pathway activity to identify connections between miRNAs and oncogenic pathways on a high-throughput, genome-wide scale. Mapping >300 gene expression signatures to >700 primary tumor profiles, we constructed a genome-wide miRNA-pathway network predicting the associations of 276 human miRNAs to 26 oncogenic pathways. The miRNA-pathway network confirmed a host of previously reported miRNA/pathway associations and uncovered several novel associations that were subsequently experimentally validated. Globally, the miRNA-pathway network demonstrates a small-world, but not scale-free, organization characterized by multiple distinct, tightly knit modules each exhibiting a high density of connections. However, unlike genetic or metabolic networks typified by only a few highly connected nodes ("hubs"), most nodes in the miRNA-pathway network are highly connected. Sequence-based computational analysis confirmed that highly-interconnected miRNAs are likely to be regulated by common pathways to target similar sets of downstream genes, suggesting a pervasive and high level of functional redundancy among coexpressed miRNAs. We conclude that gene expression signatures can be used as surrogates of miRNA activity. Our strategy facilitates the task of discovering novel miRNA-pathway connections, since gene expression data for multiple normal and disease conditions are abundantly available.     

A Family of Algorithms for Computing Consensus about Node State from Network Data

Biological and social networks are composed of heterogeneous nodes that contribute differentially to network structure and function. A number of algorithms have been developed to measure this variation. These algorithms have proven useful for applications that require assigning scores to individual nodes–from ranking websites to determining critical species in ecosystems–yet the mechanistic basis for why they produce good rankings remains poorly understood. We show that a unifying property of these algorithms is that they quantify consensus in the network about a node''s state or capacity to perform a function. The algorithms capture consensus by either taking into account the number of a target node''s direct connections, and, when the edges are weighted, the uniformity of its weighted in-degree distribution (breadth), or by measuring net flow into a target node (depth). Using data from communication, social, and biological networks we find that that how an algorithm measures consensus–through breadth or depth– impacts its ability to correctly score nodes. We also observe variation in sensitivity to source biases in interaction/adjacency matrices: errors arising from systematic error at the node level or direct manipulation of network connectivity by nodes. Our results indicate that the breadth algorithms, which are derived from information theory, correctly score nodes (assessed using independent data) and are robust to errors. However, in cases where nodes “form opinions” about other nodes using indirect information, like reputation, depth algorithms, like Eigenvector Centrality, are required. One caveat is that Eigenvector Centrality is not robust to error unless the network is transitive or assortative. In these cases the network structure allows the depth algorithms to effectively capture breadth as well as depth. Finally, we discuss the algorithms'' cognitive and computational demands. This is an important consideration in systems in which individuals use the collective opinions of others to make decisions.     

Structural Analysis to Determine the Core of Hypoxia Response Network

The advent of sophisticated molecular biology techniques allows to deduce the structure of complex biological networks. However, networks tend to be huge and impose computational challenges on traditional mathematical analysis due to their high dimension and lack of reliable kinetic data. To overcome this problem, complex biological networks are decomposed into modules that are assumed to capture essential aspects of the full network''s dynamics. The question that begs for an answer is how to identify the core that is representative of a network''s dynamics, its function and robustness. One of the powerful methods to probe into the structure of a network is Petri net analysis. Petri nets support network visualization and execution. They are also equipped with sound mathematical and formal reasoning based on which a network can be decomposed into modules. The structural analysis provides insight into the robustness and facilitates the identification of fragile nodes. The application of these techniques to a previously proposed hypoxia control network reveals three functional modules responsible for degrading the hypoxia-inducible factor (HIF). Interestingly, the structural analysis identifies superfluous network parts and suggests that the reversibility of the reactions are not important for the essential functionality. The core network is determined to be the union of the three reduced individual modules. The structural analysis results are confirmed by numerical integration of the differential equations induced by the individual modules as well as their composition. The structural analysis leads also to a coarse network structure highlighting the structural principles inherent in the three functional modules. Importantly, our analysis identifies the fragile node in this robust network without which the switch-like behavior is shown to be completely absent.     

Rhythmic and non-rhythmic attractors in asynchronous random Boolean networks

In multi-component, discrete systems, such as Boolean networks and cellular automata, the scheme of updating of the individual elements plays a crucial role in determining their dynamic properties and their suitability as models of complex phenomena. Many interesting properties of these systems rely heavily on the use of synchronous updating of the individual elements. Considerations of parsimony have motivated the claim that, if the natural systems being modelled lack any clear evidence of synchronously driven elements, then random asynchronous updating should be used by default. The introduction of a random element precludes the possibility of strictly cyclic behaviour. In principle, this poses the question of whether asynchronously driven Boolean networks, cellular automata, etc., are inherently bad choices at the time of modelling rhythmic phenomena. This paper focuses on this subsidiary issue for the case of Asynchronous Random Boolean Networks (ARBNs). It defines measures of pseudo-periodicity between states and sufficiently relaxed statistical constraints. These measures are used to guide a genetic algorithm to find appropriate examples. Success in this search for a number of cases, and the subsequent statistical analysis lead to the conclusion that ARBNs can indeed be used as models of co-ordinated rhythmic phenomena, which may be stronger precisely because of their in-built asynchrony. The same technique is used to find non-stationary attractors that show no rhythm. Evidence suggests that the latter are more abundant than rhythmic attractor. The methodology is flexible, and allows for more demanding statistical conditions for defining pseudo-periodicity, and constraining the evolutionary search.     

Disease contact tracing in random and clustered networks

The efficacy of contact tracing, be it between individuals (e.g. sexually transmitted diseases or severe acute respiratory syndrome) or between groups of individuals (e.g. foot-and-mouth disease; FMD), is difficult to evaluate without precise knowledge of the underlying contact structure; i.e. who is connected to whom? Motivated by the 2001 FMD epidemic in the UK, we determine, using stochastic simulations and deterministic 'moment closure' models of disease transmission on networks of premises (nodes), network and disease properties that are important for contact tracing efficiency. For random networks with a high average number of connections per node, little clustering of connections and short latency periods, contact tracing is typically ineffective. In this case, isolation of infected nodes is the dominant factor in determining disease epidemic size and duration. If the latency period is longer and the average number of connections per node small, or if the network is spatially clustered, then the contact tracing performs better and an overall reduction in the proportion of nodes that are removed during an epidemic is observed.     

Pacemaker and network mechanisms of rhythm generation: cooperation and competition

The origin of rhythmic activity in brain circuits and CPG-like motor networks is still not fully understood. The main unsolved questions are (i) What are the respective roles of intrinsic bursting and network based dynamics in systems of coupled heterogeneous, intrinsically complex, even chaotic, neurons? (ii) What are the mechanisms underlying the coexistence of robustness and flexibility in the observed rhythmic spatio-temporal patterns? One common view is that particular bursting neurons provide the rhythmogenic component while the connections between different neurons are responsible for the regularisation and synchronisation of groups of neurons and for specific phase relationships in multi-phasic patterns. We have examined the spatio-temporal rhythmic patterns in computer-simulated motif networks of H-H neurons connected by slow inhibitory synapses with a non-symmetric pattern of coupling strengths. We demonstrate that the interplay between intrinsic and network dynamics features either cooperation or competition, depending on three basic control parameters identified in our model: the shape of intrinsic bursts, the strength of the coupling and its degree of asymmetry. The cooperation of intrinsic dynamics and network mechanisms is shown to correlate with bistability, i.e., the coexistence of two different attractors in the phase space of the system corresponding to different rhythmic spatio-temporal patterns. Conversely, if the network mechanism of rhythmogenesis dominates, monostability is observed with a typical pattern of winnerless competition between neurons. We analyse bifurcations between the two regimes and demonstrate how they provide robustness and flexibility to the network performance.     

An Efficient Immunization Strategy for Community Networks

An efficient algorithm that can properly identify the targets to immunize or quarantine for preventing an epidemic in a population without knowing the global structural information is of obvious importance. Typically, a population is characterized by its community structure and the heterogeneity in the weak ties among nodes bridging over communities. We propose and study an effective algorithm that searches for bridge hubs, which are bridge nodes with a larger number of weak ties, as immunizing targets based on the idea of referencing to an expanding friendship circle as a self-avoiding walk proceeds. Applying the algorithm to simulated networks and empirical networks constructed from social network data of five US universities, we show that the algorithm is more effective than other existing local algorithms for a given immunization coverage, with a reduced final epidemic ratio, lower peak prevalence and fewer nodes that need to be visited before identifying the target nodes. The effectiveness stems from the breaking up of community networks by successful searches on target nodes with more weak ties. The effectiveness remains robust even when errors exist in the structure of the networks.     

Heartbeat control in the medicinal leech: A model system for understanding the origin,coordination, and modulation of rhythmic motor patterns

We have analyzed in detail the neuronal network that generates heartbeat in the leech. Reciprocally inhibitory pairs of heart interneurons form oscillators that pace the heartbeat rhythm. Other heart interneurons coordinate these oscillators. These coordinating interneurons, along with the oscillator interneurons, form an eight-cell timing oscillator network for heartbeat. Still other interneurons, along with the oscillator interneurons, inhibit heart motor neurons, sculpting their activity into rhythmic bursts. Critical switch interneurons interface between the oscillator interneurons and the other premotor interneurons to produce two alternating coordination states of the motor neurons. The periods of the oscillator interneurons are modulated by endogenous RFamide neuropeptides. We have explored the ionic currents and graded and spike-mediated synaptic transmission that promote oscillation in the oscillator interneurons and have incorporated these data into a conductance-based computer model. This model has been of considerable predictive value and has led to new insights into how reciprocally inhibitory neurons produce oscillation. We are now in a strong position to expand this model upward, to encompass the entire heartbeat network, horizontally, to elucidate the mechanisms of FMRFamide modulation, and downward, to incorporate cellular morphology. By studying the mechanisms of motor pattern formation in the leech, using modeling studies in conjunction with parallel physiological experiments, we can contribute to a deeper understanding of how rhythmic motor acts are generated, coordinated, modulated, and reconfigured at the level of networks, cells, ionic currents, and synapses. © 1995 John Wiley & Sons, Inc.     

Making Large-Scale Networks from fMRI Data

Pairwise correlations are currently a popular way to estimate a large-scale network (> 1000 nodes) from functional magnetic resonance imaging data. However, this approach generally results in a poor representation of the true underlying network. The reason is that pairwise correlations cannot distinguish between direct and indirect connectivity. As a result, pairwise correlation networks can lead to fallacious conclusions; for example, one may conclude that a network is a small-world when it is not. In a simulation study and an application to resting-state fMRI data, we compare the performance of pairwise correlations in large-scale networks (2000 nodes) against three other methods that are designed to filter out indirect connections. Recovery methods are evaluated in four simulated network topologies (small world or not, scale-free or not) in scenarios where the number of observations is very small compared to the number of nodes. Simulations clearly show that pairwise correlation networks are fragmented into separate unconnected components with excessive connectedness within components. This often leads to erroneous estimates of network metrics, like small-world structures or low betweenness centrality, and produces too many low-degree nodes. We conclude that using partial correlations, informed by a sparseness penalty, results in more accurate networks and corresponding metrics than pairwise correlation networks. However, even with these methods, the presence of hubs in the generating network can be problematic if the number of observations is too small. Additionally, we show for resting-state fMRI that partial correlations are more robust than correlations to different parcellation sets and to different lengths of time-series.     

Cineradiography of monkey lip-smacking reveals putative precursors of speech dynamics

A key feature of speech is its stereotypical 5 Hz rhythm. One theory posits that this rhythm evolved through the modification of rhythmic facial movements in ancestral primates. If the hypothesis has any validity, then a comparative approach may shed some light. We tested this idea by using cineradiography (X-ray movies) to characterize and quantify the internal dynamics of the macaque monkey vocal tract during lip-smacking (a rhythmic facial expression) versus chewing. Previous human studies showed that speech movements are faster than chewing movements, and the functional coordination between vocal tract structures is different between the two behaviors. If rhythmic speech evolved through a rhythmic ancestral facial movement, then one hypothesis is that monkey lip-smacking versus chewing should also exhibit these differences. We found that the lips, tongue, and hyoid move with a speech-like 5 Hz rhythm during lip-smacking, but not during chewing. Most importantly, the functional coordination between these structures was distinct for each behavior. These data provide empirical support for the idea that the human speech rhythm evolved from the rhythmic facial expressions of ancestral primates.     

Labeling Nodes Using Three Degrees of Propagation

The properties (or labels) of nodes in networks can often be predicted based on their proximity and their connections to other labeled nodes. So-called “label propagation algorithms” predict the labels of unlabeled nodes by propagating information about local label density iteratively through the network. These algorithms are fast, simple and scale to large networks but nonetheless regularly perform better than slower and much more complex algorithms on benchmark problems. We show here, however, that these algorithms have an intrinsic limitation that prevents them from adapting to some common patterns of network node labeling; we introduce a new algorithm, 3Prop, that retains all their advantages but is much more adaptive. As we show, 3Prop performs very well on node labeling problems ill-suited to label propagation, including predicting gene function in protein and genetic interaction networks and gender in friendship networks, and also performs slightly better on problems already well-suited to label propagation such as labeling blogs and patents based on their citation networks. 3Prop gains its adaptability by assigning separate weights to label information from different steps of the propagation. Surprisingly, we found that for many networks, the third iteration of label propagation receives a negative weight.

Availability

The code is available from the authors by request.     

Application of network theory to potential mycorrhizal networks

The concept of a common mycorrhizal network implies that the arrangement of plants and mycorrhizal fungi in a community shares properties with other networks. A network is a system of nodes connected by links. Here we apply network theory to mycorrhizas to determine whether the architecture of a potential common mycorrhizal network is random or scale-free. We analyzed mycorrhizal data from an oak woodland from two perspectives: the phytocentric view using trees as nodes and fungi as links and the mycocentric view using fungi as nodes and trees as links. From the phytocentric perspective, the distribution of potential mycorrhizal links, as measured by the number of ectomycorrhizal morphotypes on trees of Quercus garryana, was random with a short tail, implying that all the individuals of this species are more or less equal in linking to fungi in a potential network. From the mycocentric perspective, however, the distribution of plant links to fungi was scale-free, suggesting that certain fungus species may act as hubs with frequent connections to the network. Parallels exist between social networks and mycorrhizas that suggest future lines of study on mycorrhizal networks.     

A stimulus-dependent connectivity analysis of neuronal networks

We present an analysis of interactions among neurons in stimulus-driven networks that is designed to control for effects from unmeasured neurons. This work builds on previous connectivity analyses that assumed connectivity strength to be constant with respect to the stimulus. Since unmeasured neuron activity can modulate with the stimulus, the effective strength of common input connections from such hidden neurons can also modulate with the stimulus. By explicitly accounting for the resulting stimulus-dependence of effective interactions among measured neurons, we are able to remove ambiguity in the classification of causal interactions that resulted from classification errors in the previous analyses. In this way, we can more reliably distinguish causal connections among measured neurons from common input connections that arise from hidden network nodes. The approach is derived in a general mathematical framework that can be applied to other types of networks. We illustrate the effects of stimulus-dependent connectivity estimates with simulations of neurons responding to a visual stimulus. This research was supported by the National Science Foundation grants DMS-0415409 and DMS-0748417.     

Analysis of State-Dependent Transitions in Frequency and Long-Distance Coordination in a Model Oscillatory Cortical Circuit

Changes in behavioral state are typically accompanied by changes in the frequency and spatial coordination of rhythmic activity in the neocortex. In this article, we analyze the effects of neuromodulation on ionic conductances in an oscillating cortical circuit model. The model consists of synaptically-coupled excitatory and inhibitory neurons and supports rhythmic activity in the alpha, beta, and gamma ranges. We find that the effects of neuromodulation on ionic conductances are, by themselves, sufficient to induce transitions between synchronous gamma and beta rhythms and asynchronous alpha rhythms. Moreover, these changes are consistent with changes in behavioral state, with the rhythm transitioning from the slower alpha to the faster gamma and beta as arousal increases. We also observe that it is the same set of underlying intrinsic and network mechanisms that appear to be simultaneously responsible for both the observed transitions between the rhythm types and between their synchronization properties. Spike time response curves (STRCs) are used to study the relationship between the transitions in rhythm and the underlying biophysics.