Traveling electrical waves in cortex: insights from phase dynamics and speculation on a computational role.

The theory of coupled phase oscillators provides a framework to understand the emergent properties of networks of neuronal oscillators. When the architecture of the network is dominated by short-range connections, the pattern of electrical output is predicted to correspond to traveling plane and rotating waves, in addition to synchronized output. We argue that this theory provides the foundation for understanding the traveling electrical waves that are observed across olfactory, visual, and visuomotor areas of cortex in a variety of species. The waves are typically present during periods outside of stimulation, while synchronous activity typically dominates in the presence of a strong stimulus. We suggest that the continuum of phase shifts during epochs with traveling waves provides a means to scan the incoming sensory stream for novel features. Experiments to test our theoretical approach are presented.

Identification of neural circuits by imaging coherent electrical activity with FRET-based dyes.

We show that neurons that underlie rhythmic patterns of electrical output may be identified by optical imaging and frequency-domain analysis. Our contrast agent is a two-component dye system in which changes in membrane potential modulate the relative emission between a pair of fluorophores. We demonstrate our methods with the circuit responsible for fictive swimming in the isolated leech nerve cord. The output of a motor neuron provides a reference signal for the phase-sensitive detection of changes in fluorescence from individual neurons in a ganglion. We identify known and possibly novel neurons that participate in the swim rhythm and determine their phases within a cycle. A variant of this approach is used to identify the postsynaptic followers of intracellularly stimulated neurons.

Dendritic Ca(2+)-activated K(+) conductances regulate electrical signal propagation in an invertebrate neuron.

Activity-dependent changes in the short-term electrical properties of neurites were investigated in the anterior pagoda (AP) cell of leech. Imaging studies revealed that backpropagating Na(+) spikes and synaptically evoked EPSPs caused Ca(2+) entry through low-voltage-activated Ca(2+) channels that are distributed throughout the neurites. Voltage-clamp recordings from the soma revealed a TEA-sensitive outward current that was reduced when Ca(2+) entry was blocked with Co(2+) or when the intracellular concentration of free Ca(2+) was reduced by a high-affinity Ca(2+) buffer. Ca(2+) released in the neurite from a caged Ca(2+) compound caused a hyperpolarization of the membrane potential. These data imply that the AP cell expresses Ca(2+)-activated K(+) conductances, and that these conductances are present in the neurites. When the Ca(2+)-activated K(+) current was reduced through the block of Ca(2+) entry, backpropagating Na(+) spikes and synaptically evoked EPSPs increased in amplitude. Hence, the activity-dependent changes in the intracellular [Ca(2+)] together with the Ca(2+)-activated K(+) conductances participate in the regulation of dendritic signal propagation.

Supralinear summation of synaptic inputs by an invertebrate neuron: dendritic gain is mediated by an "inward rectifier" K(+) current.

Dendritic processing of glutamatergic synaptic inputs was investigated in the anterior pagoda cell of leech. We observed that below spike threshold, the amplitude of individual EPSPs decreased with hyperpolarization and that simultaneous stimulation of pairs of synaptic inputs leads to the supralinear summation of EPSPs. Voltage-clamp measurements revealed a hyperpolarization-activated, Ba(2+)-sensitive, fast, noninactivating K(+) conductance that depends on the external [K(+)]. These features are those of an "inward rectifier," Kir. Microsurgery experiments, in combination with electrophysiological measurements, revealed an inhomogeneous spatial distribution of the Kir conductance. Furthermore, on surgical removal of the neurites that contain the Kir conductance, the amplitude of EPSPs from the remaining synaptic inputs increased with hyperpolarization. A model cell, with the Kir conductance as the sole voltage-dependent conductance, reproduced qualitatively the observed voltage dependence of individual EPSPs as well as the supralinear summation of EPSP pairs.

Distributed and partially separate pools of neurons are correlated with two different components of the gill-withdrawal reflex in Aplysia.

We compared the spike activity of individual neurons in the Aplysia abdominal ganglion with the movement of the gill during the gill-withdrawal reflex. We discriminated four populations that collectively encompass approximately half of the active neurons in the ganglion: (1) second-order sensory neurons that respond to the onset and offset of stimulation of the gill and are active before the movement starts; (2) neurons whose activity is correlated with the position of the gill and typically have a tonic output during gill withdrawal; (3) neurons whose activity is correlated with the velocity of the movement and typically fire in a phasic manner; and (4) neurons whose activity is correlated with both position and velocity. A reliable prediction of the position of the gill is achieved only with the combined output of 15-20 neurons, whereas a reliable prediction of the velocity depends on the combined output of 40 or more cells.

Chattering and differential signal processing in identified motion-sensitive neurons of parallel visual pathways in the chick tectum.

At least three identified cell types in the stratum griseum centrale (SGC) of the chick optic tectum mediate separate pathways from the retina to different subdivisions of the thalamic nucleus rotundus. Two of these, SGC type I and type II, constitute the major direct inputs to rotundal subdivisions that process various aspects of visual information, e.g., motion and luminance changes. Here, we examined the responses of these cell types to somatic current injection and synaptic input. We used a brain slice preparation of the chick tectum and applied whole-cell patch recordings, restricted electrical stimulation of dendritic endings, and subsequent labeling with biocytin. Type I neurons responded with regular sequences of bursts ("chattering") to depolarizing current injection. Electrical stimulation of retinal afferents evoked a sharp-onset EPSP/burst response that was blocked with CNQX. The sharp-onset EPSP/burst response to synaptic stimulation persisted when the soma was hyperpolarized, thus suggesting the presence of dendritic spike generation. In contrast, the type II neurons responded to depolarizing current injection solely with an irregular sequence of individual spikes. Electrical stimulation of retinal afferents led to slow and long-lasting EPSPs that gave rise to one or several action potentials. In conclusion, the morphological distinct SGC type I and II neurons also have different response properties to retinal inputs. This difference is likely to have functional significance for the differential processing of visual information in the separate pathways from the retina to different subdivisions of the thalamic nucleus rotundus.

Electron transfer in reaction centers of Rhodopseudomonas sphaeroides. I. Determination of the charge recombination pathway of D+QAQ(-)B and free energy and kinetic relations between Q(-)AQB and QAQ(-)B.

The electron-transfer reactions and thermodynamic equilibria involving the quinone acceptor complex in bacterial reaction centers from R. sphaeroides were investigated. The reactions are described by the scheme: (Formula: see text). We found that the charge recombination pathway of D+QAQ(-)B proceeds via the intermediate state D+Q(-)AQB, the direct pathway contributing less than approx. 5% to the observed recombination rate. The method used to obtain this result was based on a comparison of the kinetics predicted for the indirect pathway (given by the product kAD-times the fraction of reaction centers in the Q-AQB state) with the observed recombination rate, kobsD+----D. The kinetic measurements were used to obtain the pH dependence (6.1 smaller than or equal to pH smaller than or equal to 11.7) of the free energy difference between the states Q(-)AQB and QAQ(-)B. At low pH (less than 9) QAQ(-)B is stabilized relative to Q(-)AQB by 67 meV, whereas at high pH Q(-)AQB is energetically favored. Both Q(-)A and Q(-)B associate with a proton, with pK values of 9.8 and 11.3, respectively. The stronger interaction of the proton with Q(-)B provides the driving force for the forward electron transfer.

Electron transfer in reaction centers of Rhodopseudomonas sphaeroides. II. Free energy and kinetic relations between the acceptor states Q(-)A Q(-)B and QAQ(2-)B.

Thermodynamic equilibria and electron transfer kinetics involving the quinone acceptor complex in reaction centers from Rhodopseudomonas sphaeroides were investigated. We focussed on reactions involving the two-electron states QA Qn and QAQ~-, described by the scheme DQAQa~-D +X,~~A- , ~~a- ~k~ .~D+ "r~~ AK~'La2- - k~2~ k~lk O~ (2)D+~D The equilibrium partitioning between QA Q n and QAQ 2n- was determined spectroscopically from either the concentration of oxidized cytochrome c or the concentration of semiquinone after successive flashes of light.At pH < 9.5, QAQ2n - is stabilized relative to QAQn, while for pH > 9.5, QAQB is energetically favored.The reduction of QA, to form QAQ~, is not associated with a protonation step (pK< 8). However, the reduction of Q~, to form the final state QAQ~-, is accompanied by an uptake of a proton (pK >/10.7). The preferential interaction of a proton with QAQ2n - provides the driving force for the forward electron transfer.The shift toward the photochemically inactive state QAQa with increasing pH may serve as a feedback mechanism in photosynthetic organisms to limit the rise in intracellular pH. The electron-transfer rate constants were determined from the observed kinetics and the equilibria between the states QAQ2n - and QA Q n. The forward rate constant z-.A~2n~ was approximately proportional to the proton concentration, whereas kta2A~ depended only weakly on pH. The recombination kinetics of D +QAQ2n- was biphasic. The slow rate agreed with the predicted charge recombination via the intermediate state D +QAQff; the fast rate may be due to the recombination from a separate (conformational) state. The results of this work were combined with those of a previous study on reactions involving the one-electron precursor states QAQa and QAQn(Kleinfeld, D., Okamura, M.Y., and Feher, G. (1984) Biochim. Biophys. Acta 766, 126-140). The overall sequence for the protonation of the reaction center in response to successive reductions of the accept or complex involves the uptake of one proton for each electron transferred to QB- This sequential uptake initiates the formation of a proton gradient across the cell membrane.

Damping of oscillations in the semiquinone absorption in reaction centers after successive flashes determination of the equilibrium between Q(-)AQB and QAQ(-)B.

A quantitative model for the damping of oscillations of the semiquinone absorption after successive light flashes is presented. It is based on the equilibrium between the states Q(A)-Q(B) and Q(A) Q(-B). A fit of the model to the experimental results obtained for reaction centers from Rhodopseudomonas sphaeroides gave a value of α = [Q(A)-Q(B)I/(IQ(A)-Q(Bl)+ [Q(A)Q(-B)I) = 0.065 +/- 0.005 (T= 21°C, pH 8).

Distributed representation of vibrissa movement in the upper layers of somatosensory cortex revealed with voltage-sensitive dyes.

We have identified large-scale patterns of electrical activity in circuits that occur in response to stimulation of peripheral receptors. Our focus was on primary (S1) vibrissal cortex of anesthetized rat, and we used optical techniques in conjunction with voltage-sensitive dyes to measure depolarization of the upper layers of cortex. Displacement of one vibrissa produced a field of activity that extends over very many cortical columns in S1. There are multiple, focal maxima within this field. A global maximum is located near the center of the field of activity, and, as determined electrically and histologically, this site maps to the cortical column appropriate for the deflected vibrissa. The amplitude of this component attains a steady-state value under continuous stimulation. Additional temporal characteristics are revealed by the response to a single displacement; the signal was triphasic and began with a prompt depolarization that was followed by a transient phase of inhibition and a final phase of long-lasting depolarization. The somatotopy of the other, satellite maxima in the field of activity were established through the reconstruction of the fields of activity produced by individual stimulation of other vibrissae. Local maxima for one vibrissa were seen to overlie the global maximum found for stimulation of nearest- and next-nearest-neighbor vibrissae. In contrast to the amplitude of the global maxima, the amplitude associated with the local maxima was not maintained with either continuous or infrequent but repetitive stimulation. Finally, the field of activity induced by alternate deflection of two neighboring vibrissae was suppressed in amplitude in comparison to the summed amplitudes of the signals elicited by deflection of each vibrissa alone. We suggest that these patterns of activity are a manifestation of the dynamic interaction among neighboring cortical columns.

Automatic sorting of multiple unit neuronal signals in the presence of anisotropic and non-Gaussian variability.

Neuronal noise sources and systematic variability in the shape of a spike limit the ability to sort multiple unit waveforms recorded from nervous tissue into their single neuron constituents. Here we present a procedure to efficiently sort spikes in the presence of noise that is anisotropic, i.e., dominated by particular frequencies, and whose amplitude distribution may be non-Gaussian, such as occurs when spike waveforms are a function of interspike interval. Our algorithm uses a hierarchical clustering scheme. First, multiple unit records are sorted into an overly large number of clusters by recursive bisection. Second, these clusters are progressively aggregated into a minimal set of putative single units based on both similarities of spike shape as well as the statistics of spike arrival times, such as imposed by the refractory period. We apply the algorithm to waveforms recorded with chronically implanted micro-wire stereotrodes from neocortex of behaving rat. Natural extension of the algorithm may be used to cluster spike waveforms from records with many input channels, such as those obtained with tetrodes and multiple site optical techniques.

Ultra-miniature headstage with 6-channel drive and vacuum-assisted micro-wire implantation for chronic recording from the neocortex.

We describe a head-stage, with precision microtranslators for the chronic placement of micro-wire electrodes in the neocortex, that minimizes compressive damage to the brain. The head-stage has a diameter of 5.8 mm and allows six electrodes, separated by 450 microm on a hexagonal grid, to be individually and continuously positioned throughout a depth of approximately 3 mm. Suction is used to transiently support the dura against a curved array of tubes that guide and stabilize the electrodes as a means to prevent compression of the neocortex as the electrodes breach the dura. With this headstage we recorded extracellular signals in a rat immediately after surgery. Single-unit waveforms at a given electrode position were stable for at least several hours in the freely behaving animal and were obtained throughout the depth of the neocortex for at least 2 months. Electrophysiological records and histological examination showed that the upper layers of the neocortex were intact and minimally damaged after the implantation.

Anatomical and functional imaging of neurons using 2-photon laser scanning microscopy.

Light scattering by brain tissue and phototoxicity are major obstacles to the use of high-resolution optical imaging and photo-activation ('uncaging') of bioactive compounds from inactive ('caged') precursors in intact and semi-intact nervous systems. Optical methods based on 2-photon excitation promise to reduce these obstacles (Denk, 1994; Denk et al., 1990, 1994). Here we show a range of imaging modes based on 2-photon laser scanning microscopy (TPLSM) as applicable to problems in neuroscience. Fluorescence images were taken of neurons labeled with ion-sensitive and voltage-sensitive dyes in invertebrate ganglia, mammalian brain slices, and from the intact mammalian brain. Scanning photochemical images with whole-cell current detection (Denk, 1994) show how the distribution of neurotransmitter receptors on the surface of specific cells can be mapped. All images show strong optical sectioning and usable images can be obtained at depths greater than 100 microns below the surface of the preparation.

Sequential state generation by model neural networks.

Sequential patterns of neural output activity form the basis of many biological processes, such as the cyclic pattern of outputs that control locomotion. I show how such sequences can be generated by a class of model neural networks that make defined sets of transitions between selected memory states. Sequence-generating networks depend upon the interplay between two sets of synaptic connections. One set acts to stabilize the network in its current memory state, while the second set, whose action is delayed in time, causes the network to make specified transitions between the memories. The dynamic properties of these networks are described in terms of motion along an energy surface. The performance of the networks, both with intact connections and with noisy or missing connections, is illustrated by numerical examples. In addition, I present a scheme for the recognition of externally generated sequences by these networks.

Associative neural network model for the generation of temporal patterns. Theory and application to central pattern generators.

Cyclic patterns of motor neuron activity are involved in the production of many rhythmic movements, such as walking, swimming, and scratching. These movements are controlled by neural circuits referred to as central pattern generators (CPGs). Some of these circuits function in the absence of both internal pacemakers and external feedback. We describe an associative neural network model whose dynamic behavior is similar to that of CPGs. The theory predicts the strength of all possible connections between pairs of neurons on the basis of the outputs of the CPG. It also allows the mean operating levels of the neurons to be deduced from the measured synaptic strengths between the pairs of neurons. We apply our theory to the CPG controlling escape swimming in the mollusk Tritonia diomedea. The basic rhythmic behavior is shown to be consistent with a simplified model that approximates neurons as threshold units and slow synaptic responses as elementary time delays. The model we describe may have relevance to other fixed action behaviors, as well as to the learning, recall, and recognition of temporally ordered information.

"Unlearning" increases the storage capacity of content addressable memories.

The storage and retrieval of information in networks of biological neurons can be modeled by certain types of content addressable memories (CAMs). We demonstrate numerically that the amount of information that can be stored in such CAMs is substantially increased by an unlearning algorithm. Mechanisms for the increase in capacity are identified and illustrated in terms of an energy function that describes the convergence properties of the network.

Global processing of visual stimuli in a neural network of coupled oscillators.

An oscillator neural network model is presented that is capable of processing local and global attributes of sensory input. Local features in the input are encoded in the average firing rate of the neurons while the relationships between these features can modulate the temporal structure of the neuronal output. Neurons that share the same receptive field interact via relatively strong feedback connections, while neurons with different fields interact via specific, relatively weak connections. This pattern of connectivity mimics that of primary visual cortex. The model is studied in the context of processing visual stimuli that are coded for orientation. We compare our theoretical results with recent experimental evidence on coherent oscillatory activity in the cat visual cortex. The computational capabilities of the model for performing discrimination and segmentation tasks are demonstrated.

Direct evidence for local oscillatory current sources and intracortical phase gradients in turtle visual cortex.

Visual stimuli induce oscillations in the membrane potential of neurons in cortices of several species. In turtle, these oscillations take the form of linear and circular traveling waves. Such waves may be a consequence of a pacemaker that emits periodic pulses of excitation that propagate across a network of excitable neuronal tissue or may result from continuous and possibly reconfigurable phase shifts along a network with multiple weakly coupled neuronal oscillators. As a means to resolve the origin of wave propagation in turtle visual cortex, we performed simultaneous measurements of the local field potential at a series of depths throughout this cortex. Measurements along a single radial penetration revealed the presence of broadband current sources, with a center frequency near 20 Hz (gamma band), that were activated by visual stimulation. The spectral coherence between sources at two well-separated loci along a rostral-caudal axis revealed the presence of systematic timing differences between localized cortical oscillators. These multiple oscillating current sources and their timing differences in a tangential plane are interpreted as the neuronal activity that underlies the wave motion revealed in previous imaging studies. The present data provide direct evidence for the inference from imaging of bidirectional wave motion that the stimulus-induced electrical waves in turtle visual cortex correspond to phase shifts in a network of coupled neuronal oscillators.