Detecting controlling nodes of boolean regulatory networks

Boolean models of regulatory networks are assumed to be tolerant to perturbations. That qualitatively implies that each function can only depend on a few nodes. Biologically motivated constraints further show that functions found in Boolean regulatory networks belong to certain classes of functions, for example, the unate functions. It turns out that these classes have specific properties in the Fourier domain. That motivates us to study the problem of detecting controlling nodes in classes of Boolean networks using spectral techniques. We consider networks with unbalanced functions and functions of an average sensitivity less than ?k, where k is the number of controlling variables for a function. Further, we consider the class of 1-low networks which include unate networks, linear threshold networks, and networks with nested canalyzing functions. We show that the application of spectral learning algorithms leads to both better time and sample complexity for the detection of controlling nodes compared with algorithms based on exhaustive search. For a particular algorithm, we state analytical upper bounds on the number of samples needed to find the controlling nodes of the Boolean functions. Further, improved algorithms for detecting controlling nodes in large-scale unate networks are given and numerically studied.     

Processing of tactile information in neuronal networks controlling leg movements of the Locust

The successful, coordinated, posture and locomotion of any animal requires a precise and continuous adjustment of limb movements by sensory feedback from extero- and proprioceptors associated with the legs. We here review the recent advances in our understanding of how specific local adjustments of the hind legs of the desert locust, Schistocerca gregaria, are made in response to tactile signals from two different classes of exteroceptor on a leg. The aim is to understand particular features of the organization of neuronal networks and how different types of constituent interneurones contribute to the processing of sensory signals. This information can then be used to define the design principles that govern the organization of sensory-motor networks.     

Dynamic memorization characteristics in neural networks with different neuronal dynamics

We introduce a stimulus-response scheme that supports plastic variation of synapse weights in neural networks, and analyze how memory formation evolves under external stimulation. In so doing, chaotic networks and stochastic networks that have very different dynamics are compared. Experimental results suggest that chaotic activity remarkably outperforms stochastic activity in stimulus-response memorization. This seems to be indicative of effectiveness of the chaos in dynamic learning by stimulus-response scheme oriented to natural learning.     

Modelling in molecular biology: describing transcription regulatory networks at different scales

Approaches to describe gene regulation networks can be categorized by increasing detail, as network parts lists, network topology models, network control logic models or dynamic models. We discuss the current state of the art for each of these approaches. We study the relationship between different topology models, and give examples how they can be used to infer functional annotations for genes of unknown function. We introduce a new simple way of describing dynamic models called finite state linear model (FSLM). We discuss the gap between the parts list and topology models on one hand, and network logic and dynamic models, on the other hand. The first two classes of models have reached a genome-wide scale, while for the other model classes high-throughput technologies are yet to make a major impact.     

Self-stabilization of neuronal networks

Between the extreme views concerning ontogenesis (genetic vs. environmental determination), we use a moderate approach: a somehow pre-established neuronal model network reacts to activity deviations (reflecting input to be compensated), and stabilizes itself during a complex feed-back process. Morphogenesis is based on an algorithm formalizing the compensation theory of synaptogenesis (Wolff and Wagner 1983). This algorithm is applied to randomly connected McCulloch-Pitts networks that are able to maintain oscillations of their activity patterns over time. The algorithm can lead to networks which are morphogenetically stable but preserve self-maintained oscillations in activity. This is in contrast to most of the current models of synaptogenesis and synaptic modification based on Hebbian rules of plasticity. Hebbian networks are morphogenetically unstable without additional assumptions. The effects of compensation on structural and functional properties of the networks are described. It is concluded that the compensation theory of synaptogenesis can account for the development of morphogenetically stable neuronal networks out of randomly connected networks via selective stabilization and elimination of synapses.The logic of the compensation algorithm is based on experimental results. The present paper shows that the compensation theory can not only predict the behavior of synaptic populations (Wagner and Wolff, in preparation), but it can also describe the behavior of neurons interconnected in a network, with the resulting additional system properties. The neuronal interactions-leading to equilibrium in certain cases-are a self-organizing process in the sense that all decisions are performed on the individual cell level without knowing the overall network situation or goal.     

Self-stabilization of neuronal networks

This study is concerned with synaptic reorganization in local neuronal networks. Within networks of 30 neurons, an initial disequilibrium in connectivity has to be compensated by reorganization of synapses. Such plasticity is not a genetically determined process, but depends on results of neuronal interaction. Neurobiological experiments have lead to a model of the behavior of individual neurons during neuroplastic reorganization, formalized as a synaptogenetic rule that governs changes in the amount of synaptic elements on each neuron. — When this synaptogenetic rule is applied to a system of neurons, there is some freedom left to the choice of further conditions. In this study it is examined, which assumptions additional to the synaptogenetic rule are essential in order to obtain morphogenetic stability. By explicating these assumptions, their plausibility can be tested. It is analysed, in which respect these conditions are important, in which part of the model they exert their influence, and what kind of instability and degeneration happens if the assumptions are violated. —Our essentials for reaching morphogenetic stability are: (1) A network structure that guarantees the possibility of oscillations, (2) a compensation algorithm that guarantees a smooth morphogenesis, (3) kinetic parameters that guarantee convergence in the synaptic elements' change, and (4) a synaptic modification rule that prohibits Hebb-like as well as anti-Hebb-like synaptic changes. — It is concluded that many structural features of the mammalian cerebral cortex are in accordance with the requirements of the model.     

Self-organized criticality in developing neuronal networks

Recently evidence has accumulated that many neural networks exhibit self-organized criticality. In this state, activity is similar across temporal scales and this is beneficial with respect to information flow. If subcritical, activity can die out, if supercritical epileptiform patterns may occur. Little is known about how developing networks will reach and stabilize criticality. Here we monitor the development between 13 and 95 days in vitro (DIV) of cortical cell cultures (n = 20) and find four different phases, related to their morphological maturation: An initial low-activity state (≈19 DIV) is followed by a supercritical (≈20 DIV) and then a subcritical one (≈36 DIV) until the network finally reaches stable criticality (≈58 DIV). Using network modeling and mathematical analysis we describe the dynamics of the emergent connectivity in such developing systems. Based on physiological observations, the synaptic development in the model is determined by the drive of the neurons to adjust their connectivity for reaching on average firing rate homeostasis. We predict a specific time course for the maturation of inhibition, with strong onset and delayed pruning, and that total synaptic connectivity should be strongly linked to the relative levels of excitation and inhibition. These results demonstrate that the interplay between activity and connectivity guides developing networks into criticality suggesting that this may be a generic and stable state of many networks in vivo and in vitro.     

Imaging neuronal networks in behaving animals

Neuronal activity has recently been imaged with single-cell resolution in behaving vertebrates. This was accomplished by using fluorescent calcium indicators in conjunction with confocal or two-photon microscopy. These optical techniques, along with other new approaches for imaging synaptic activity, second messengers, and neurotransmitters and their receptors offer great promise for the study of neuronal networks at high resolution in vivo.     

Response of de- and hyperpolarizing effects in neuronal networks with different mechanisms for terminating activity

The response of stochastically organized homogeneous neuronal networks and others reacting by pre- and postsynaptic inhibition to external de- and hyperpolarizing effects of different intensity and time course were compared using a simulated mathematical computer model. The area of lasting depolarizing effects extended in those with pre- and postsynaptic inhibition compared with heterogeneous neuronal networks. Effects of brief de- and hyperpolarizing effects in a network depended on fluctuations in the level of the activity it displays; depolarizing effects may shorten and hyperpolarizing influences prolong the activity period of networks. The effects of a shortened network activity stage due to brief depolarizing influences was also more marked in networks with preand postsynaptic inhibition. Findings from this research would lead to the deduction that the presence of additional negative feedback circuits in the form of presynaptic or postsynaptic inhibitory series promotes better control in the mechanisms terminating network activity.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 20, No. 4, pp. 438–447, July–August, 1988.     

Organization of neocortical neuronal networks

Multiple unit activity in deep layers of the frontal and motor cortices was recorded by chronically implanted semimicroelectrodes in waking cats with different levels of food motivation. From four to seven neuronal spike trains were selected from the recorded multiunit activity. Interactions between neighbouring neurons in the motor and frontal areas of the neocortex (within the local neuronal networks) and between the neurons of these areas (distributed neuronal networks) were estimated by means of statistical crosscorrelation analysis of spike trains within the range of delays from 0 to 100 ms. Neurons in the local networks were divided in two subgroups: the neurons with higher spike amplitudes with the dominance of divergent connections and neurons with lower spike amplitudes with the dominance of convergent connections. Strong monosynaptic connections (discharges with a delay of less than 2 ms) between the neurons with high- and low-amplitude spikes formed the background of the local networks. Connections between low-amplitude neurons in the frontal cortex and high-amplitude neurons in the motor cortex dominated in the distributed networks. A 24-hour food deprivation predominantly altered the late interneuronal crosscorrelations with time delays within the range of 2-100 ms in both local and distributed networks.     

Identifying and assessing the efficiency of different networks of a fine-scale hierarchy of biodiversity hotspots

Background: For prioritising practical conservation measures in areas of high endemic plant diversity, a fine-scale hierarchy of sites needs to be established. In this context, conservation sites designed at local and regional levels are considered a network of interconnected areas.

Aims: The main aim was to identify two hierarchical levels of a network of conservation sites, called ‘micro hotspots’ and ‘nano hotspots’, and test their efficiency for achieving conservation objectives across the island of Sardinia, Mediterranean Basin.

Methods: We analysed the spatial distribution of endemic vascular plant species (EVPS) richness. Additionally, the area, perimeter, connectivity and surplus costs for the protection of all endemic plant populations were used as ranking criteria for a hierarchical classification.

Results: We identified eight micro hotspots and 82 nano hotspots. Amongst the three possible solutions compared, the integrated network of micro and nano hotspots resulted in more effective conservation than any of the single-level network solutions with only micro or nano hotspots, and it included 89% of all EVPS in a relatively small areal extent.

Conclusions: The identification of hotspot networks at the regional level allowed determining priority areas to implement conservation efforts for EVPS. The integration of micro hotspots with nano hotspots resulted in the most effective network from both conservation and economic perspectives. We suggest that our model may provide an effective tool for integrated and effective conservation actions in the Mediterranean Basin.     

How structure determines correlations in neuronal networks

Networks are becoming a ubiquitous metaphor for the understanding of complex biological systems, spanning the range between molecular signalling pathways, neural networks in the brain, and interacting species in a food web. In many models, we face an intricate interplay between the topology of the network and the dynamics of the system, which is generally very hard to disentangle. A dynamical feature that has been subject of intense research in various fields are correlations between the noisy activity of nodes in a network. We consider a class of systems, where discrete signals are sent along the links of the network. Such systems are of particular relevance in neuroscience, because they provide models for networks of neurons that use action potentials for communication. We study correlations in dynamic networks with arbitrary topology, assuming linear pulse coupling. With our novel approach, we are able to understand in detail how specific structural motifs affect pairwise correlations. Based on a power series decomposition of the covariance matrix, we describe the conditions under which very indirect interactions will have a pronounced effect on correlations and population dynamics. In random networks, we find that indirect interactions may lead to a broad distribution of activation levels with low average but highly variable correlations. This phenomenon is even more pronounced in networks with distance dependent connectivity. In contrast, networks with highly connected hubs or patchy connections often exhibit strong average correlations. Our results are particularly relevant in view of new experimental techniques that enable the parallel recording of spiking activity from a large number of neurons, an appropriate interpretation of which is hampered by the currently limited understanding of structure-dynamics relations in complex networks.     

Coping with variability in small neuronal networks

Experimental and corresponding modeling studies indicate that there is a 2- to 5-fold variation of intrinsic and synaptic parameters across animals while functional output is maintained. Here, we review experiments, using the heartbeat central pattern generator (CPG) in medicinal leeches, which explore the consequences of animal-to-animal variation in synaptic strength for coordinated motor output. We focus on a set of segmental heart motor neurons that all receive inhibitory synaptic input from the same four premotor interneurons. These four premotor inputs fire in a phase progression and the motor neurons also fire in a phase progression because of differences in synaptic strength profiles of the four inputs among segments. Our work tested the hypothesis that functional output is maintained in the face of animal-to-animal variation in the absolute strength of connections because relative strengths of the four inputs onto particular motor neurons is maintained across animals. Our experiments showed that relative strength is not strictly maintained across animals even as functional output is maintained, and animal-to-animal variations in strength of particular inputs do not correlate strongly with output phase. Further experiments measured the precise temporal pattern of the premotor inputs, the segmental synaptic strength profiles of their connections onto motor neurons, and the temporal pattern (phase progression) of those motor neurons all in the same animal for a series of 12 animals. The analysis of input and output in this sample of 12 individuals suggests that the number (four) of inputs to each motor neuron and the variability of the temporal pattern of input from the CPG across individuals weaken the influence of the strength of individual inputs. Moreover, the temporal pattern of the output varies as much across individuals as that of the input. Essentially, each animal arrives at a unique solution for how the network produces functional output.