The Role of Ongoing Dendritic Oscillations in Single-Neuron Dynamics

The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as both temporally and spatially localized. Under this localist account, neurons compute near-instantaneous mappings from their current input to their current output, brought about by somatic summation of dendritic contributions that are generated in functionally segregated compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought; notably that local dendritic activity may be a mechanism for generating on-going whole-cell voltage oscillations.     

Functional differentiation of the theta-rhythm of the hippocampus in the cat

On the model of discriminating alimentary conditioned reflex with spatial separation of the sources of conditioned (CR, light flashes) and unconditioned (feeding trough) stimuli the theta-rhythm of the dorsal hippocampus was evaluated in cats. Two types of the theta-rhythm were observed in the spectrum of the hippocampal electrical activity: low-amplitude, consisting of a slow growing theta-waves (type I) and high-amplitude consisting of rapidly increasing theta-waves (type II). The type I theta-rhythm is sensitive to noradrenaline and correlates with behavioural forms directed immediately to the realization of alimentary motivation, while the type II is sensitive to serotonin and correlates with behavioural forms directed to the source of the conditioned stimulus. Enhancement of the type II theta-rhythm takes place during a delay of the expected conditioned stimulus. It is suggested that type I theta-rhythm reflects a level of activity of the brain structures connected with unconditioned mechanisms, with realization of biological motivations, while type II theta-rhythm is connected with conditioned reinforcing stimuli; it correlates with various forms of conditioned orienting reflexes and reflects the work of the "nervous model of reinforcing stimulus".     

Differential contributions of synaptic and intrinsic inhibitory currents to speech segmentation via flexible phase-locking in neural oscillators

Current hypotheses suggest that speech segmentation—the initial division and grouping of the speech stream into candidate phrases, syllables, and phonemes for further linguistic processing—is executed by a hierarchy of oscillators in auditory cortex. Theta (∼3-12 Hz) rhythms play a key role by phase-locking to recurring acoustic features marking syllable boundaries. Reliable synchronization to quasi-rhythmic inputs, whose variable frequency can dip below cortical theta frequencies (down to ∼1 Hz), requires “flexible” theta oscillators whose underlying neuronal mechanisms remain unknown. Using biophysical computational models, we found that the flexibility of phase-locking in neural oscillators depended on the types of hyperpolarizing currents that paced them. Simulated cortical theta oscillators flexibly phase-locked to slow inputs when these inputs caused both (i) spiking and (ii) the subsequent buildup of outward current sufficient to delay further spiking until the next input. The greatest flexibility in phase-locking arose from a synergistic interaction between intrinsic currents that was not replicated by synaptic currents at similar timescales. Flexibility in phase-locking enabled improved entrainment to speech input, optimal at mid-vocalic channels, which in turn supported syllabic-timescale segmentation through identification of vocalic nuclei. Our results suggest that synaptic and intrinsic inhibition contribute to frequency-restricted and -flexible phase-locking in neural oscillators, respectively. Their differential deployment may enable neural oscillators to play diverse roles, from reliable internal clocking to adaptive segmentation of quasi-regular sensory inputs like speech.     

A feedforward model for the formation of a grid field where spatial information is provided solely from place cells

Grid cells (GCs) in the medial entorhinal cortex (mEC) have the property of having their firing activity spatially tuned to a regular triangular lattice. Several theoretical models for grid field formation have been proposed, but most assume that place cells (PCs) are a product of the grid cell system. There is, however, an alternative possibility that is supported by various strands of experimental data. Here we present a novel model for the emergence of gridlike firing patterns that stands on two key hypotheses: (1) spatial information in GCs is provided from PC activity and (2) grid fields result from a combined synaptic plasticity mechanism involving inhibitory and excitatory neurons mediating the connections between PCs and GCs. Depending on the spatial location, each PC can contribute with excitatory or inhibitory inputs to GC activity. The nature and magnitude of the PC input is a function of the distance to the place field center, which is inferred from rate decoding. A biologically plausible learning rule drives the evolution of the connection strengths from PCs to a GC. In this model, PCs compete for GC activation, and the plasticity rule favors efficient packing of the space representation. This leads to gridlike firing patterns. In a new environment, GCs continuously recruit new PCs to cover the entire space. The model described here makes important predictions and can represent the feedforward connections from hippocampus CA1 to deeper mEC layers.     

A computational model of cellular mechanisms of temporal coding in the medial geniculate body (MGB)

Acoustic stimuli are often represented in the early auditory pathway as patterns of neural activity synchronized to time-varying features. This phase-locking predominates until the level of the medial geniculate body (MGB), where previous studies have identified two main, largely segregated response types: Stimulus-synchronized responses faithfully preserve the temporal coding from its afferent inputs, and Non-synchronized responses, which are not phase locked to the inputs, represent changes in temporal modulation by a rate code. The cellular mechanisms underlying this transformation from phase-locked to rate code are not well understood. We use a computational model of a MGB thalamocortical neuron to test the hypothesis that these response classes arise from inferior colliculus (IC) excitatory afferents with divergent properties similar to those observed in brain slice studies. Large-conductance inputs exhibiting synaptic depression preserved input synchrony as short as 12.5 ms interclick intervals, while maintaining low firing rates and low-pass filtering responses. By contrast, small-conductance inputs with Mixed plasticity (depression of AMPA-receptor component and facilitation of NMDA-receptor component) desynchronized afferent inputs, generated a click-rate dependent increase in firing rate, and high-pass filtered the inputs. Synaptic inputs with facilitation often permitted band-pass synchrony along with band-pass rate tuning. These responses could be tuned by changes in membrane potential, strength of the NMDA component, and characteristics of synaptic plasticity. These results demonstrate how the same synchronized input spike trains from the inferior colliculus can be transformed into different representations of temporal modulation by divergent synaptic properties.     

Spatial eigenmodes and synchronous oscillation: co-incidence detection in simulated cerebral cortex

 Zero-lag synchronisation arises between points on the cerebral cortex receiving concurrent independent inputs; an observation generally ascribed to nonlinear mechanisms. Using simulations of cerebral cortex and Principal Component Analysis (PCA) we show patterns of zero-lag synchronisation (associated with empirically realistic spectral content) can arise from both linear and nonlinear mechanisms. For low levels of activation, we show the synchronous field is described by the eigenmodes of the resultant damped wave activity. The first and second spatial eigenmodes (which capture most of the signal variance) arise from the even and odd components of the independent input signals. The pattern of zero-lag synchronisation can be accounted for by the relative dominance of the first mode over the second, in the near-field of the inputs. The simulated cortical surface can act as a few millisecond response coincidence detector for concurrent, but uncorrelated, inputs. As cortical activation levels are increased, local damped oscillations in the gamma band undergo a transition to highly nonlinear undamped activity with 40 Hz dominant frequency. This is associated with ``locking' between active sites and spatially segregated phase patterns. The damped wave synchronisation and the locked nonlinear oscillations may combine to permit fast representation of multiple patterns of activity within the same field of neurons. Received: 20 January 1999 / Revised version: 22 September 2000 / Second revised version: 20 December 2001 / Published online: 26 June 2002     

Biodiversity and endemism mapping as a tool for regional conservation planning – case study of the Pleurothallidinae (Orchidaceae) of the Andean rain forests in Bolivia

Analyses of species diversity and endemism patterns provide vital inputs for conservation planning. Therefore, it is an important dilemma of biodiversity conservation that in very diverse but poorly studied tropical countries those patterns can hardly be considered. Consequently, there is an urgent need to develop prediction models that make the best use of existing data on species distribution and that can give hints on spatial conservation priorities. This paper presents the results of a pilot study on the diversity of the orchid subtribe Pleurothallidinae (331 mapped species) in the Andean rain forests of Bolivia. Results of a taxon-based mapping methodology, using abiotic (humidity and temperature, the latter indicated by altitude) and historical factors (taken into account as distance from collection localities) that determine species ranges, are compared with outcomes of an inventory-based mapping approach. The patterns of taxon-based diversity and endemism show a strong correlation with the distribution of sample localities. The inventory-based approach is more reliable, but it is interesting to apply both mapping methods in order to make a critical interpretation and comparison that facilitates some valuable conservation recommendations. We end with concrete conclusions for conservation planning and action.     

Analysis of theta-rhythms recorded in an isolated strip of rabbit sensomotor cortex

To test the possibility that the theta-rhythm may spread passively from the hippocampus into the neocortex in rabbits and to analyze the properties of these rhythms recorded from the surface of the neocortex, an investigation was made of activity recorded simultaneously from the hippocampus and various points of the neocortex, including from a strip of the sensomotor cortex isolated completely with respect to its nervous connections. The use of special correlation methods showed that an appreciable contribution to the potentials recorded from the isolated strip can be made by the passive conduction of hippocampal activity (provided that it generates a regular high-amplitude theta-rhythm). At the same time, potentials in a theta-rhythm may be generated in the isolated strip itself. The theta-rhythm recorded in the intact rabbit cortex may thus be of combined genesis: generated in the neocortex itself and spreading passively from the hippocampus through the brain tissues as through a volume conductor.     

Effects of Time-Dependent Stimuli in a Competitive Neural Network Model of Perceptual Rivalry

We analyze a competitive neural network model of perceptual rivalry that receives time-varying inputs. Time-dependence of inputs can be discrete or smooth. Spike frequency adaptation provides negative feedback that generates network oscillations when inputs are constant in time. Oscillations that resemble perceptual rivalry involve only one population being “ON” at a time, which represents the dominance of a single percept at a time. As shown in Laing and Chow (J. Comput. Neurosci. 12(1):39–53, 2002), for sufficiently high contrast, one can derive relationships between dominance times and contrast that agree with Levelt’s propositions (Levelt in On binocular rivalry, 1965). Time-dependent stimuli give rise to novel network oscillations where both, one, or neither populations are “ON” at any given time. When a single population receives an interrupted stimulus, the fundamental mode of behavior we find is phase-locking, where the temporally driven population locks its state to the stimulus. Other behaviors are analyzed as bifurcations from this forced oscillation, using fast/slow analysis that exploits the slow timescale of adaptation. When both populations receive time-varying input, we find mixtures of fusion and sole population dominance, and we partition parameter space into particular oscillation types. Finally, when a single population’s input contrast is smoothly varied in time, 1:n mode-locked states arise through period-adding bifurcations beyond phase-locking. Our results provide several testable predictions for future psychophysical experiments on perceptual rivalry.     

Mechanistic home range models capture spatial patterns and dynamics of coyote territories in Yellowstone

Patterns of space-use by individuals are fundamental to the ecology of animal populations influencing their social organization, mating systems, demography and the spatial distribution of prey and competitors. To date, the principal method used to analyse the underlying determinants of animal home range patterns has been resource selection analysis (RSA), a spatially implicit approach that examines the relative frequencies of animal relocations in relation to landscape attributes. In this analysis, we adopt an alternative approach, using a series of mechanistic home range models to analyse observed patterns of territorial space-use by coyote packs in the heterogeneous landscape of Yellowstone National Park. Unlike RSAs, mechanistic home range models are derived from underlying correlated random walk models of individual movement behaviour, and yield spatially explicit predictions for patterns of space-use by individuals. As we show here, mechanistic home range models can be used to determine the underlying determinants of animal home range patterns, incorporating both movement responses to underlying landscape heterogeneities and the effects of behavioural interactions between individuals. Our analysis indicates that the spatial arrangement of coyote territories in Yellowstone is determined by the spatial distribution of prey resources and an avoidance response to the presence of neighbouring packs. We then show how the fitted mechanistic home range model can be used to correctly predict observed shifts in the patterns of coyote space-use in response to perturbation.     

Analysis and modeling of time-variant amplitude–frequency couplings of and between oscillations of EEG bursts

Low-frequency (0.5-2.5 Hz) and individually defined high-frequency (7-11 or 8-12 Hz; 11-15 or 14-18 Hz) oscillatory components of the electroencephalogram (EEG) burst activity derived from thiopental-induced burst-suppression patterns (BSP) were investigated in seven sedated patients (17-26 years old) with severe head injury. The predominant high-frequency burst oscillations (>7 Hz) were detected for each patient by means of time-variant amplitude spectrum analysis. Thereafter, the instantaneous envelope (IE) and the instantaneous frequency (IF) were computed for these low- and high-frequency bands to quantify amplitude-frequency dependencies (envelope-envelope, envelope-frequency, and frequency-frequency correlations). Time-variant phase-locking, phase synchronization, and quadratic phase couplings are associated with the observed amplitude-frequency characteristics. Additionally, these time-variant analyses were carried out for modeled burst patterns. Coupled Duffing oscillators were adapted to each EEG burst and by means of these models data-based burst simulations were generated. Results are: (1) strong envelope-envelope correlations (IE courses) can be demonstrated; (2) it can be shown that a rise of the IE is associated with an increase of the IF (only for the frequency bands 0.5-2.5 and 7-11 or 8-12 Hz); (3) the rise characteristics of all individually averaged envelope-frequency courses (IE-IF) are strongly correlated; (4) for the 7-11 or 8-12 Hz oscillation these associations are weaker and the variation between the time courses of the patients is higher; (5) for both frequency ranges a quantitative amplitude-frequency dependency can be shown because higher IE peak maxima are accompanied by stronger IF changes; (6) the time range of significant phase-locking within the 7-11 or 8-12 Hz frequency bands and of the strongest quadratic phase couplings (between 0.5-2.5 and 7-11 or 8-12 Hz) is between 0 and 1,000 ms; (7) all phase coupling characteristics of the modeled bursts accord well with the corresponding characteristics of the measured EEG burst data. All amplitude-frequency dependencies and phase locking/coupling properties described here are known from and can be discussed using coupled Duffing oscillators which are characterized by autoresonance properties.     

Coexistence of lateral and co-tuned inhibitory configurations in cortical networks

The responses of neurons in sensory cortex depend on the summation of excitatory and inhibitory synaptic inputs. How the excitatory and inhibitory inputs scale with stimulus depends on the network architecture, which ranges from the lateral inhibitory configuration where excitatory inputs are more narrowly tuned than inhibitory inputs, to the co-tuned configuration where both are tuned equally. The underlying circuitry that gives rise to lateral inhibition and co-tuning is yet unclear. Using large-scale network simulations with experimentally determined connectivity patterns and simulations with rate models, we show that the spatial extent of the input determined the configuration: there was a smooth transition from lateral inhibition with narrow input to co-tuning with broad input. The transition from lateral inhibition to co-tuning was accompanied by shifts in overall gain (reduced), output firing pattern (from tonic to phasic) and rate-level functions (from non-monotonic to monotonically increasing). The results suggest that a single cortical network architecture could account for the extended range of experimentally observed response types between the extremes of lateral inhibitory versus co-tuned configurations.     

Comparative characteristics of septal "burst" neurons after elimination of afferent effects of the reticular formation in the rabbit

Comparative analysis of characteristics of rhythmic theta-activity in the neurones of the medial septal nucleus and nucleus of diagonal band was performed in intact rabbits after. i. v. injection of pentobarbital, and in rabbits with chronic lesion of the ascending brain-stem afferent fibers. In both conditions theta-bursts disappeared in some cells with unstable periodic rhythmic modulation; substantial population of the septal units preserved regular burst activity. Main characteristics of theta-bursts were almost identical in both states, their mean frequency decreased to 3.5 Hz. The theta-rhythm in hippocampal EEG was usually absent; but low-frequency rhythmic activity could be evoked by electrical or sensory stimulation as well as by injection of bemegrid or physostigmine. The data show that the ascending brain-stem afferents control: the frequency of the bursts in a population of septal units regarded as bursting pace-maker cells; the total number of the septal cells secondarily (synaptically) involved into rhythmic activity. The effect of pentobarbital upon theta-rhythm results from elimination of these influences upon the septal cells.     

Oscillations and oscillatory behavior in small neural circuits

In order to determine the dynamical properties of central pattern generators (CPGs), we have examined the lobster stomatogastric ganglion using the tools of nonlinear dynamics. The lobster pyloric and gastric mill central pattern generators can be analyzed at both the cellular and network levels because they are small, i.e., contain only 25 neurons between them and each neuron and synapse are repeatedly identifiable from animal to animal. We discuss how the biophysical properties of each neuron and synapse in the two circuits act cooperatively to generate two different patterns of sequential activity, how these patterns are altered by neuromodulators and perturbed by noise and sensory inputs. Finally, we show how simplified Hindmarsh–Rose models can be made into analog electronic neurons that mimic the lobster neurons and in addition be incorporated into artificial CPGs with robotic applications.     

Unravelling the Turing bifurcation using spatially varying diffusion coefficients

. The Turing bifurcation is the basic bifurcation generating spatial pattern, and lies at the heart of almost all mathematical models for patterning in biology and chemistry. In this paper the authors determine the structure of this bifurcation for two coupled reaction diffusion equations on a two-dimensional square spatial domain when the diffusion coefficients have a small explicit variation in space across the domain. In the case of homogeneous diffusivities, the Turing bifurcation is highly degenerate. Using a two variable perturbation method, the authors show that the small explicit spatial inhomogeneity splits the bifurcation into two separate primary and two separate secondary bifurcations, with all solution branches distinct. This splitting of the bifurcation is more effective than that given by making the domain slightly rectangular, and shows clearly the structure of the Turing bifurcation and the way in which the! var ious solution branches collapse together as the spatial variation is reduced. The authors determine the stability of the solution branches, which indicates that several new phenomena are introduced by the spatial variation, including stable subcritical striped patterns, and the possibility that stable stripes lose stability supercritically to give stable spotted patterns.. Received: 10 January 1996/Revised version: 3 July 1996     

The effect of scopolamine on the spatial organization of rat cortical potentials

The influence of scopolamine (1 mg/kg, i.p.) on the spatial organization of the neocortical electrical activity was studied in rats. A decrease in the spectral power and coherence of brain potentials in the range of the dominant theta-rhythm peak (6.00-7.25 Hz) and their increase in the adjacent low-frequency band were observed. Both indices were decreased in the wide beta band (19.00-30.00 Hz). The described changes took place over the whole areas of the right hemisphere and parieto-temporal region of the left hemisphere. The obtained results are discussed with respect to the role of the cholinergic brain system in the higher nervous activity.     

Hypothalamo — Hyppocampal interrelationships

Changes in hippocampal electrical activity in response to electrical and chemical stimulation of different parts of the hypothalamus were studied in cats with permanently implanted metallic electrodes and a chemical electrode. The results showed that: 1) in response to electrical stimulation of the middle part of the lateral hypothalamus, evoking activation of feeding behavior, the hippocampal theta-rhythm is increased and the delta- and alpha-rhythms are simultaneously depressed; 2) the same picture is observed in response to electrical stimulation of other parts of the lateral hypothalamus, evoking a response of alertness, anxiety, and aggression; 3) after injection of 0.007 ml noradrenalin into the lateral hypothalamus of cats the animals develop a food response, and injection of 0.014 ml acetylcholine causes activation of drinking behavior; these responses take place in association with intensification of the hippocampal theta-rhythm; electrical stimulation of the dorsomedial nucleus evokes desynchronization of hyppocampal electrical activity; 5) in response to threshold stimulation of the ventromedial nucleus, feeding behavior is inhibited and this is accompanied by desynchronization of hyppocampal electrical activity, whereas in response to stronger stimulation, a response of aggression develops and the theta-rhythm is intensified.Institute of Physiology, Academy of Sciences of the Georgian SSR, Tbilisi. Translated from Neirofiziologiya, Vol. 2, No. 5, pp. 497–506, September–October, 1970.