Introduction to the Symposium: What is Computational Neurobiology?

SYNOPSIS. Current advances in computational biology are derivedfrom two sets of ideas established in the work of Santiago Ramóny Cajal. One is the neuron doctrine, which holds that neuronsare the functional units of the nervous system, and has ledto detailed models of neuronal properties based on increasinginformation on the physical and chemical properties of neurons.The second is the idea of networks of neurons with specificpatterns of interconnections that has led to a variety of mathematicalmethods of analyzing such networks. Future work in computationalneurobiology promises to be a blend of these two modeling approaches.     

Recurring discharge patterns in multiple spike trains

Neural networks are parallel processing structures that provide the capability to perform various pattern recognition tasks. A network is typically trained over a set of exemplars by adjusting the weights of the interconnections using a back propagation algorithm. This gradient search converges to locally optimal solutions which may be far removed from the global optimum. In this paper, evolutionary programming is analyzed as a technique for training a general neural network. This approach can yield faster, more efficient yet robust training procedures that accommodate arbitrary interconnections and neurons possessing additional processing capabilities.     

Bifurcations of lurching waves in a thalamic neuronal network

We consider a two-layer, one-dimensional lattice of neurons; one layer consists of excitatory thalamocortical neurons, while the other is comprised of inhibitory reticular thalamic neurons. Such networks are known to support “lurching” waves, for which propagation does not appear smooth, but rather progresses in a saltatory fashion; these waves can be characterized by different spatial widths (different numbers of neurons active at the same time). We show that these lurching waves are fixed points of appropriately defined Poincaré maps, and follow these fixed points as parameters are varied. In this way, we are able to explain observed transitions in behavior, and, in particular, to show how branches with different spatial widths are linked with each other. Our computer-assisted analysis is quite general and could be applied to other spatially extended systems which exhibit this non-trivial form of wave propagation.     

A two-phase growth strategy in cultured neuronal networks as reflected by the distribution of neurite branching angles

Neurite outgrowth and branching patterns are instrumental in dictating the wiring diagram of developing neuronal networks. We study the self-organization of single cultured neurons into complex networks focusing on factors governing the branching of a neurite into its daughter branches. Neurite branching angles of insect ganglion neurons in vitro were comparatively measured in two neuronal categories: neurons in dense cultures that bifurcated under the presence of extrinsic (cellular environment) cues versus neurons in practical isolation that developed their neurites following predominantly intrinsic cues. Our experimental results were complemented by theoretical modeling and computer simulations. A preferred regime of branching angles was found in isolated neurons. A model based on biophysical constraints predicted a preferred bifurcation angle that was consistent with this range shown by our real neurons. In order to examine the origin of the preferred regime of angles we constructed simulations of neurite outgrowth in a developing network and compared the simulated developing neurons with our experimental results. We tested cost functions for neuronal growth that would be optimized at a specific regime of angles. Our results suggest two phases in the process of neuronal development. In the first, reflected by our isolated neurons, neurons are tuned to make first contact with a target cell as soon as possible, to minimize the time of growth. After contact is made, that is, after neuronal interconnections are formed, a second branching strategy is adopted, favoring higher efficiency in neurite length and volume. The two-phase development theory is discussed in relation to previous results.     

Multiple motor patterns in the stomatogastric ganglion of the shrimp Penaeus japonicus

 Motor patterns of the cardiac sac, the gastric and the pyloric network in the stomatogastric nervous system of the shrimp Penaeus japonicus, the most primitive decapod species, were studied. Single neurons can switch from the gastric or the pyloric pattern to the cardiac sac pattern. Some of the pyloric neurons fire with the gastric pattern. All of the gastric neurons fire with the pyloric pattern, unlike those in reptantians. Proctolin activates and modulates the cardiac sac and the pyloric rhythm, and promotes reconfiguration of the networks. Neurons of the three networks have so many interconnections that they construct a multifunctional neural network like those in Cancer. This network may function in different configurations under the appropriate conditions. Several modes of interactions between the networks found in different reptantian species can apply to the penaeidean shrimp. Such interactions are general features of the stomatogastric nervous system in decapods. Phylogenetic differences among the decapod infraorders are seen in the number and orientation of muscles and the innervation pattern of muscles. The multifunctional networks have existed in the most primitive decapod species, and types of configurations of the networks would have evolved to produce a wide range of motor patterns as the foregut structure has become complex. Accepted: 26 October 1999     

A two‐phase growth strategy in cultured neuronal networks as reflected by the distribution of neurite branching angles

Neurite outgrowth and branching patterns are instrumental in dictating the wiring diagram of developing neuronal networks. We study the self‐organization of single cultured neurons into complex networks focusing on factors governing the branching of a neurite into its daughter branches. Neurite branching angles of insect ganglion neurons in vitro were comparatively measured in two neuronal categories: neurons in dense cultures that bifurcated under the presence of extrinsic (cellular environment) cues versus neurons in practical isolation that developed their neurites following predominantly intrinsic cues. Our experimental results were complemented by theoretical modeling and computer simulations. A preferred regime of branching angles was found in isolated neurons. A model based on biophysical constraints predicted a preferred bifurcation angle that was consistent with this range shown by our real neurons. In order to examine the origin of the preferred regime of angles we constructed simulations of neurite outgrowth in a developing network and compared the simulated developing neurons with our experimental results. We tested cost functions for neuronal growth that would be optimized at a specific regime of angles. Our results suggest two phases in the process of neuronal development. In the first, reflected by our isolated neurons, neurons are tuned to make first contact with a target cell as soon as possible, to minimize the time of growth. After contact is made, that is, after neuronal interconnections are formed, a second branching strategy is adopted, favoring higher efficiency in neurite length and volume. The two‐phase development theory is discussed in relation to previous results. © 2004 Wiley Periodicals, Inc. J Neurobiol, 2005     

Composite cortical networks as systems of multimodal oscillators

This paper uses a theory of coordinated firing patterns in local cortical networks to extend the modular view of cortical organization into a theory of the structure of neuroelectric signaling in composite regions of cortex that are the size of association or primary receiving areas. The theory assumes that individual cortical modules signal informational states according to particular modes of locally sustained recurrent reverberations, and that the resultant equilibrium configurations across entire composite cortical regions are determined by excitatory and inhibitory lateral interactions among large numbers of such modules. Rough computer simulation of the theory indicates the influences of the local, regional, and global interconnections and the general character of the composite network patterns. The work builds a tentative theoretical bridge across the structure of neuroelectric signals in single neurons, in local networks, and in composite networks, and indicates possible relationships to neuropsychological representations in composite networks.     

Divisible Load Scheduling in Systems with Limited Memory

In this work we consider scheduling divisible loads on a distributed computing system with limited available memory. The communication delays and heterogeneity of the system are taken into account. The problem studied consists in finding such a distribution of the load that the communication and computation time is the shortest possible. A new robust method is proposed to solve the problem of finding optimal distribution of computations on star network, and networks in which binomial trees can be embedded (meshes, hypercubes, multistage interconnections). We demonstrate that in many cases memory limitations do not restrict efficiency of parallel processing as much as computation and communication speeds.     

Model of transient oscillatory synchronization in the locust antennal lobe

Transient pairwise synchronization of locust antennal lobe (AL) projection neurons (PNs) occurs during odor responses. In a Hodgkin-Huxley-type model of the AL, interactions between excitatory PNs and inhibitory local neurons (LNs) created coherent network oscillations during odor stimulation. GABAergic interconnections between LNs led to competition among them such that different groups of LNs oscillated with periodic Ca(2+) spikes during different 50-250 ms temporal epochs, similar to those recorded in vivo. During these epochs, LN-evoked IPSPs caused phase-locked, population oscillations in sets of postsynaptic PNs. The model shows how alternations of the inhibitory drive can temporally encode sensory information in networks of neurons without precisely tuned intrinsic oscillatory properties.     

Subcommissural organ-associated neurons in fetal and neonatal rabbit

Neurons which initially lie in the basal region of the subcommissural organ (SCO) were investigated in 20 rabbit fetuses from day 15 to 30 of gestation, and in eight neonatal, 4 and 8 day old rabbits. These SCO-associated neurons, first observed on day 17 of gestation, develop into (1) a rostral mesodiencephalic nerve cell group situated in an area dorsal to the rostral-most part of the SCO and (2) a more caudal layer of single neurons extending throughout the length of the SCO. The present findings are discussed in relation to recent histochemical studies that demonstrated AChE-positive neurons in the pineal complex and subcommissural area of frogs and to recent fluorescence microscopic studies in fetal and adult rats in which a 5-HT system is known to extend from the nucleus raphe dorsalis (B7) along the SCO to the pineal stalk and habenular region. The term "SCO-associated neurons" is a purely morphological way of describing the neurons in question as the neural interconnections of these neurons are still a matter of speculation.     

The Regulative Role of Neurite Mechanical Tension in Network Development

A bewildering series of dynamical processes take part in the development of the nervous system. Neuron branching dynamics, the continuous formation and elimination of neural interconnections, are instrumental in constructing distinct neuronal networks, which are the functional building blocks of the nervous system. In this study, we investigate and validate the important regulative role of mechanical tension in determining the final morphology of neuronal networks. To single out the mechanical effect, we cultured relatively large invertebrate neurons on clean quartz surfaces. Applied to these surfaces were isolated anchoring sites consisting of carbon nanotube islands to which the cells and the neurites could mechanically attach. Inspection of branching dynamics and network wiring upon development revealed an innate selection mechanism in which one axon branch wins over another. The apparent mechanism entails the build-up of mechanical tension in developing axons. The tension is maintained by the attachment of the growth cone to the substrate or, alternatively, to the neurites of a target neuron. The induced tension promotes the stabilization of one set of axon branches while causing retraction or elimination of axon collaterals. We suggest that these findings represent a crucial, early step that precedes the formation of synapses and regulates neuronal interconnections. Mechanical tension serves as a signal for survival of the axonal branch and perhaps for the subsequent formation of synapses.     

Allatostatin A Signalling in Drosophila Regulates Feeding and Sleep and Is Modulated by PDF

Feeding and sleep are fundamental behaviours with significant interconnections and cross-modulations. The circadian system and peptidergic signals are important components of this modulation, but still little is known about the mechanisms and networks by which they interact to regulate feeding and sleep. We show that specific thermogenetic activation of peptidergic Allatostatin A (AstA)-expressing PLP neurons and enteroendocrine cells reduces feeding and promotes sleep in the fruit fly Drosophila. The effects of AstA cell activation are mediated by AstA peptides with receptors homolog to galanin receptors subserving similar and apparently conserved functions in vertebrates. We further identify the PLP neurons as a downstream target of the neuropeptide pigment-dispersing factor (PDF), an output factor of the circadian clock. PLP neurons are contacted by PDF-expressing clock neurons, and express a functional PDF receptor demonstrated by cAMP imaging. Silencing of AstA signalling and continuous input to AstA cells by tethered PDF changes the sleep/activity ratio in opposite directions but does not affect rhythmicity. Taken together, our results suggest that pleiotropic AstA signalling by a distinct neuronal and enteroendocrine AstA cell subset adapts the fly to a digestive energy-saving state which can be modulated by PDF.     

Neural network implementation of a three-phase model of respiratory rhythm generation

A mathematical model of the central neural mechanisms of respiratory rhythm generation is developed. This model assumes that the respiratory cycle consists of three phases: inspiration, post-inspiration, and expiration. Five respiratory neuronal groups are included: inspiratory, late-inspiratory, post-inspiratory, expiratory, and early-inspiratory neurons. Proposed interconnections among these groups are based substantially on previous physiological findings. The model produces a stable limit cycle and generally reproduces the features of the firing patterns of the 5 neuronal groups. When simulated feedback from pulmonary stretch receptors is made to excite late-inspiratory neurons and inhibit early-inspiratory neurons, the model quantitatively reproduces previous observations of the expiratory-prolonging effects of pulses and steps of vagal afferent activity presented in expiration. In addition the model reproduces expected respiratory cycle timing and amplitude responses to change of chemical drive both in the absence and in the presence of simulated stretch receptor feedback. These results demonstrate the feasibility of generating the respiratory rhythm with a simple neural network based on observed respiratory neuronal groups. Other neuronal groups not included in the model may be more important for shaping the waveforms than for generating the basic oscillation.     

Artificial neural networks for decision-making in urologic oncology

Artificial neural networks (ANNs) are computational methodologies that perform multifactorial analyses, inspired by networks of biological neurons. Like neural networks, ANNs contain layers of simple points (nodes) of data that interract through carefully weighted connection lines. ANNs are "trained" and balanced by having been previously fed data, which the ANN uses as the means for adjusting its interconnections. Studies have shown that novel and highly accurate ANNs significantly enhance the ability to detect prostate cancer early (high sensitivity) while avoiding a greater number of unnecessary tissue samplings (high specificity). The use of ANNs in prostate cancer is ideal because of 1) multiple predicting factors that influence outcome; 2) the desire to offer individual consulting based on various tests; 3) the fact that prior logistic regression analysis results have had serious limitations in application; and 4) the need for an up-to-date tool that can apply easily to everyone. An ANN should be seen as an important tool that is complementary to the physician's personal knowledge and judgment in making decisions.     

A model biological neural network: the cephalopod vestibular system

Artificial neural networks (ANNs) have become increasingly sophisticated and are widely used for the extraction of patterns or meaning from complicated or imprecise datasets. At the same time, our knowledge of the biological systems that inspired these ANNs has also progressed and a range of model systems are emerging where there is detailed information not only on the architecture and components of the system but also on their ontogeny, plasticity and the adaptive characteristics of their interconnections. We describe here a biological neural network contained in the cephalopod statocysts; the statocysts are analogous to the vertebrae vestibular system and provide the animal with sensory information on its orientation and movements in space. The statocyst network comprises only a small number of cells, made up of just three classes of neurons but, in combination with the large efferent innervation from the brain, forms an 'active' sense organs that uses feedback and feed-forward mechanisms to alter and dynamically modulate the activity within cells and how the various components are interconnected. The neurons are fully accessible to physiological investigation and the system provides an excellent model for describing the mechanisms underlying the operation of a sophisticated neural network.     

The Mechanism of Saccade Motor Pattern Generation Investigated by a Large-Scale Spiking Neuron Model of the Superior Colliculus

The subcortical saccade-generating system consists of the retina, superior colliculus, cerebellum and brainstem motoneuron areas. The superior colliculus is the site of sensory-motor convergence within this basic visuomotor loop preserved throughout the vertebrates. While the system has been extensively studied, there are still several outstanding questions regarding how and where the saccade eye movement profile is generated and the contribution of respective parts within this system. Here we construct a spiking neuron model of the whole intermediate layer of the superior colliculus based on the latest anatomy and physiology data. The model consists of conductance-based spiking neurons with quasi-visual, burst, buildup, local inhibitory, and deep layer inhibitory neurons. The visual input is given from the superficial superior colliculus and the burst neurons send the output to the brainstem oculomotor nuclei. Gating input from the basal ganglia and an integral feedback from the reticular formation are also included.We implement the model in the NEST simulator and show that the activity profile of bursting neurons can be reproduced by a combination of NMDA-type and cholinergic excitatory synaptic inputs and integrative inhibitory feedback. The model shows that the spreading neural activity observed in vivo can keep track of the collicular output over time and reset the system at the end of a saccade through activation of deep layer inhibitory neurons. We identify the model parameters according to neural recording data and show that the resulting model recreates the saccade size-velocity curves known as the saccadic main sequence in behavioral studies. The present model is consistent with theories that the superior colliculus takes a principal role in generating the temporal profiles of saccadic eye movements, rather than just specifying the end points of eye movements.     

Fine structure of the neural sheath,glia and neurons in the brain of the housefly,Musca domestica

Summary The fine structure of the neural sheath, glial cells and nerve cells in the brain of adult male houseflies is described. The neural sheath is composed of neural lamella and perineurium. The neural lamella consists of an external lamina and collagen-like fibrils which are embedded in an amorphous matrix. The perineurial cells form a continuous layer around the brain. On their inner surface, perineurial cells form junctional complexes with glial cell processes. A cortical cellular layer composed of neurons and glial cells surrounds the centrally located neuropil. Three types of glial cells are identified. Glial cells differ in size and in relative development and distribution of organelles. Thin processes of glioplasm completely surround the cell bodies of the neurons. Five types of neurons are described. Most of the neurons are monopolar, a few are bipolar.Supported by a grant from the National Science Foundation     

The Organization of the lamina ganglionaris of the prawn,Pandalus borealis (Kröyer)

The Lamina ganglionaris (first optic neuropile) of the decapod crustacean Pandalus borealis has its optic cartridges (synaptic compartments) arranged in horizontal rows. Each optic cartridge contains seven receptor axon terminals and the branching axis fibres of five monopolar second order neurons. Four types of monopolar neurons are classified. Their cell bodies are arranged in two layers. The inner layer contains the cell bodies of exclusively one of these types, and each cartridge is invaded by two neurons of this neuron type (type M 1:a and M 1:b). The outer layer contains the cell bodies of the remaining three types (M 2, M3 and M4). One gives rise to a large radially branched axis fibre in the centre of the cartridge. The other two have wide branches which may make inter-cartridge contacts, one proximally and the other distally in the plexiform layer, which is clearly bistratified. The receptor axons terminate in two levels corresponding to these strata. Two sets of tangenital fibres form networks in the proximal and the mid-portion of the lamina. Both networks have fibres with primary branches in the vertical plane and secondary branches in the horizontal plane. The fibres of the networks are derived from axons that pass from the second optic neuropile, the medulla externa.     

The ultrastructure of the non-neurosecretory components in the brain of the midge,Chironomus riparius Mg. (Diptera: Nematocera)

The ultrastruct of the neural sheath, glial cells and neurons in the brain of the neoimaginal male Chironomus riparius is described. The neural sheath comprises a neural lamella and underlying perineurium. The neural lamella consists of an amorphous matrix in which fine fibrils occur. The perineurium is composed of two cell types forming a continuous layer around the brain. The subjacent cortical layer, composed of the cell bodies of neurons and glial cells, varies considerably in thickness and surrounds the centrally located neuropiles. Three types of glial cells are distinguished on the basis of their positions and appearances. Five types of neurons are described which differ in size and relative frequency of organelles. Four types of axons, including those of neurosecretory cells, are distinguished by their size and content.     

Avalanches in a Stochastic Model of Spiking Neurons

Neuronal avalanches are a form of spontaneous activity widely observed in cortical slices and other types of nervous tissue, both in vivo and in vitro. They are characterized by irregular, isolated population bursts when many neurons fire together, where the number of spikes per burst obeys a power law distribution. We simulate, using the Gillespie algorithm, a model of neuronal avalanches based on stochastic single neurons. The network consists of excitatory and inhibitory neurons, first with all-to-all connectivity and later with random sparse connectivity. Analyzing our model using the system size expansion, we show that the model obeys the standard Wilson-Cowan equations for large network sizes ( neurons). When excitation and inhibition are closely balanced, networks of thousands of neurons exhibit irregular synchronous activity, including the characteristic power law distribution of avalanche size. We show that these avalanches are due to the balanced network having weakly stable functionally feedforward dynamics, which amplifies some small fluctuations into the large population bursts. Balanced networks are thought to underlie a variety of observed network behaviours and have useful computational properties, such as responding quickly to changes in input. Thus, the appearance of avalanches in such functionally feedforward networks indicates that avalanches may be a simple consequence of a widely present network structure, when neuron dynamics are noisy. An important implication is that a network need not be “critical” for the production of avalanches, so experimentally observed power laws in burst size may be a signature of noisy functionally feedforward structure rather than of, for example, self-organized criticality.