Simple codes versus efficient codes

Responses of excitatory hippocampal synapses to natural stimulus patterns reveal a decrease in short-term facilitation and increase in short-term depression during postnatal development

Schaffer collateral excitatory synapses onto CA1 pyramidal cells are subject to significant modulation by short-term plasticity. This presynaptic, history-dependent modulation of neurotransmitter release causes synaptic transmission to be sensitive to the frequency of the input. As a result, temporally irregular input patterns, such as those observed in vivo, produce synaptic responses over a very wide dynamic range that reflect a balance of short-term facilitation and short-term depression. The neonatal period is an important developmental period in the hippocampus, when functional representations of an animal's environment are being established through exploratory behavior. The strength of excitatory synapses and their modulation by short-term plasticity are critical to this process. One form of short-term plasticity, paired-pulse facilitation, has been shown to decrease as juvenile rats mature into young adults. However, little is known about the neonatal modulation of other forms of short-term plasticity, including the responses to temporally complex stimuli. We examined developmental modulation of the short-term dynamics of Schaffer collateral excitatory synapses onto CA1 pyramidal cells in acute hippocampal slices, using both constant frequency stimuli and natural stimulus patterns that were taken from in vivo recording of spike patterns of hippocampal cells. In response to constant frequency stimulation, synapses in slices from young adult rats (P28-P35) showed less short-term depression than did those in slices from juveniles (P12-P18). However, when the natural stimulus pattern (containing a wide mix of frequencies) was used, synapses from young adults instead showed more short-term depression and less short-term facilitation than did juveniles. Comparing the natural stimulus pattern responses with constant frequency stimulation of a similar frequency, we found that the average responses were similar in young adults (both showed modest depression). However, in juveniles, the natural pattern produced robust facilitation while constant frequency stimulation caused a large short-term depression. Our results reveal that there are developmental changes both in individual forms of short-term plasticity and in the relative balance between short-term facilitation and short-term depression that will alter the signal transfer characteristics of these synapses.

Organizing principles of real-time memory encoding: neural clique assemblies and universal neural codes

Recent identification of network-level coding units, termed neural cliques, in the hippocampus has enabled real-time patterns of memory traces to be mathematically described, directly visualized, and dynamically deciphered. These memory coding units are functionally organized in a categorical and hierarchical manner, suggesting that internal representations of external events in the brain is achieved not by recording exact details of those events, but rather by recreating its own selective pictures based on cognitive importance. This neural-clique-based hierarchical-extraction and parallel-binding process enables the brain to acquire not only large storage capacity but also abstraction and generalization capability. In addition, activation patterns of the neural clique assemblies can be converted to strings of binary codes that would permit universal categorizations of internal brain representations across individuals and species.

What is signal and what is noise in the brain?

The response of a cortical neuron to a stimulus can show a very large variability when repeatedly stimulated by exactly the same stimulus. This has been quantified in terms of inter-spike-interval (ISI) statistics by several researchers (e.g., [Softky, W., Koch, C., 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13(1), 334-350.]). The common view is that this variability reflects noisy information processing based on redundant representation in large neuron populations. This view has been challenged by the idea that the apparent noise inherent in brain activity that is not strictly related or temporally coupled to the experiment could be functionally significant. In this work we examine the ISI statistics and discuss these views in a recently published model of interacting cortical areas [Knoblauch, A., Palm, G., 2002. Scene segmentation by spike synchronization in reciprocally connected visual areas. I. Local effects of cortical feedback. Biol. Cybernet. 87(3), 151-167.]. From the results of further single neuron simulations we can isolate temporally modulated synaptic input as a main contributor for high ISI variability in our model and possibly in real neurons. In contrast to alternative mechanisms, our model suggests a function of the temporal modulations for short-term binding and segmentation of figures from background. Moreover, we show that temporally modulated inputs lead to ISI statistics which fit better to the neurophysiological data than alternative mechanisms.

Indispensable role of quantum theory in the brain dynamics

Recently, Tegmark pointed out that the superposition of ion states involved in the superposition of firing and resting states of a neuron quickly decohere. It undoubtedly indicates that neural networks cannot work as quantum computers, or computers taking advantage of coherent states. Does it also mean that the brain can be modeled as a neural network obeying classical physics? Here we show that it does not mean that the brain can be modeled as a neural network obeying classical physics. A brand new perspective in research of neural networks from quantum theoretical aspect is presented.

An analysis of globally connected active rotators with excitatory and inhibitory connections having different time constants using the nonlinear Fokker-Planck equations

The globally connected active rotators with excitatory and inhibitory connections having different time constants under noise are analyzed using the nonlinear Fokker-Planck equation, and their oscillatory phenomena are investigated. Based on numerically calculated bifurcation diagrams, both periodic solutions and chaotic solutions are found. The periodic firings are classified based on the firing period, the coefficient of variation, and the correlation coefficient, and weakly synchronized periodic firings which are often observed in physiological experiments are found.

Including Long-Range Dependence in Integrate-and-Fire Models of the High Interspike-Interval Variability of Cortical Neurons

Many different types of integrate-and-fire models have been designed in order to explain how it is possible for a cortical neuron to integrate over many independent inputs while still producing highly variable spike trains. Within this context, the variability of spike trains has been almost exclusively measured using the coefficient of variation of interspike intervals. However, another important statistical property that has been found in cortical spike trains and is closely associated with their high firing variability is long-range dependence. We investigate the conditions, if any, under which such models produce output spike trains with both interspike-interval variability and long-range dependence similar to those that have previously been measured from actual cortical neurons. We first show analytically that a large class of high-variability integrate-and-fire models is incapable of producing such outputs based on the fact that their output spike trains are always mathematically equivalent to renewal processes. This class of models subsumes a majority of previously published models, including those that use excitation-inhibition balance, correlated inputs, partial reset, or nonlinear leakage to produce outputs with high variability. Next, we study integrate-and-fire models that have (non-Poissonian) renewal point process inputs instead of the Poisson point process inputs used in the preceding class of models. The confluence of our analytical and simulation results implies that the renewal-input model is capable of producing high variability and long-range dependence comparable to that seen in spike trains recorded from cortical neurons, but only if the interspike intervals of the inputs have infinite variance, a physiologically unrealistic condition. Finally, we suggest a new integrate-and-fire model that does not suffer any of the previously mentioned shortcomings. By analyzing simulation results for this model, we show that it is capable of producing output spike trains with interspike-interval variability and long-range dependence that match empirical data from cortical spike trains. This model is similar to the other models in this study, except that its inputs are fractional-gaussian-noise-driven Poisson processes rather than renewal point processes. In addition to this model's success in producing realistic output spike trains, its inputs have longrange dependence similar to that found in most subcortical neurons in sensory pathways, including the inputs to cortex. Analysis of output spike trains from simulations of this model also shows that a tight balance between the amounts of excitation and inhibition at the inputs to cortical neurons is not necessary for high interspike-interval variability at their outputs. Furthermore, in our analysis of this model, we show that the superposition of many fractional-gaussian-noise-driven Poisson processes does not approximate a Poisson process, which challenges the common assumption that the total effect of a large number of inputs on a neuron is well represented by a Poisson process.

Genetic methods for illuminating the function of neural circuits

Guided by the notion that biology itself offers some of the most incisive tools for studying biological systems, neurophysiologists rely increasingly on cell biological mechanisms and materials encoded in DNA to visualize and control the activity of neurons in functional circuits. Optical reporter proteins can broadcast the operational states of genetically designated cells and synapses; remote-controlled effectors can suppress or induce electrical activity. Many challenges, however, remain. These include the development of novel gene expression systems that target reporters and effectors to functionally relevant neuronal ensembles, the capacity to monitor and manipulate multiple populations of neurons in parallel, the ability to observe and elicit precisely timed action potentials, and the power to communicate with genetically designated target neurons through electromagnetic signals other than light.

Wavelet-based processing of neuronal spike trains prior to discriminant analysis

Investigations of neural coding in many brain systems have focused on the role of spike rate and timing as two means of encoding information within a spike train. Recently, statistical pattern recognition methods, such as linear discriminant analysis (LDA), have emerged as a standard approach for examining neural codes. These methods work well when data sets are over-determined (i.e., there are more observations than predictor variables). But this is not always the case in many experimental data sets. One way to reduce the number of predictor variables is to preprocess data prior to classification. Here, a wavelet-based method is described for preprocessing spike trains. The method is based on the discriminant pursuit (DP) algorithm of Buckheit and Donoho [Proc. SPIE 2569 (1995) 540-51]. DP extracts a reduced set of features that are well localized in the time and frequency domains and that can be subsequently analyzed with statistical classifiers. DP is illustrated using neuronal spike trains recorded in the motor cortex of an awake, behaving rat [Laubach et al. Nature 405 (2000) 567-71]. In addition, simulated spike trains that differed only in the timing of spikes are used to show that DP outperforms another method for preprocessing spike trains, principal component analysis (PCA) [Richmond and Optican J. Neurophysiol. 57 (1987) 147-61].

Is there chaos in the brain? II. Experimental evidence and related models

The search for chaotic patterns has occupied numerous investigators in neuroscience, as in many other fields of science. Their results and main conclusions are reviewed in the light of the most recent criteria that need to be satisfied since the first descriptions of the surrogate strategy. The methods used in each of these studies have almost invariably combined the analysis of experimental data with simulations using formal models, often based on modified Huxley and Hodgkin equations and/or of the Hindmarsh and Rose models of bursting neurons. Due to technical limitations, the results of these simulations have prevailed over experimental ones in studies on the nonlinear properties of large cortical networks and higher brain functions. Yet, and although a convincing proof of chaos (as defined mathematically) has only been obtained at the level of axons, of single and coupled cells, convergent results can be interpreted as compatible with the notion that signals in the brain are distributed according to chaotic patterns at all levels of its various forms of hierarchy. This chronological account of the main landmarks of nonlinear neurosciences follows an earlier publication [Faure, Korn, C. R. Acad. Sci. Paris, Ser. III 324 (2001) 773-793] that was focused on the basic concepts of nonlinear dynamics and methods of investigations which allow chaotic processes to be distinguished from stochastic ones and on the rationale for envisioning their control using external perturbations. Here we present the data and main arguments that support the existence of chaos at all levels from the simplest to the most complex forms of organization of the nervous system. We first provide a short mathematical description of the models of excitable cells and of the different modes of firing of bursting neurons (Section 1). The deterministic behavior reported in giant axons (principally squid), in pacemaker cells, in isolated or in paired neurons of Invertebrates acting as coupled oscillators is then described (Section 2). We also consider chaotic processes exhibited by coupled Vertebrate neurons and of several components of Central Pattern Generators (Section 3). It is then shown that as indicated by studies of synaptic noise, deterministic patterns of firing in presynaptic interneurons are reliably transmitted, to their postsynaptic targets, via probabilistic synapses (Section 4). This raises the more general issue of chaos as a possible neuronal code and of the emerging concept of stochastic resonance Considerations on cortical dynamics and of EEGs are divided in two parts. The first concerns the early attempts by several pioneer authors to demonstrate chaos in experimental material such as the olfactory system or in human recordings during various forms of epilepsies, and the belief in 'dynamical diseases' (Section 5). The second part explores the more recent period during which surrogate-testing, definition of unstable periodic orbits and period-doubling bifurcations have been used to establish more firmly the nonlinear features of retinal and cortical activities and to define predictors of epileptic seizures (Section 6). Finally studies of multidimensional systems have founded radical hypothesis on the role of neuronal attractors in information processing, perception and memory and two elaborate models of the internal states of the brain (i.e. 'winnerless competition' and 'chaotic itinerancy'). Their modifications during cognitive functions are given special attention due to their functional and adaptive capabilities (Section 7) and despite the difficulties that still exist in the practical use of topological profiles in a state space to identify the physical underlying correlates. The reality of 'neurochaos' and its relations with information theory are discussed in the conclusion (Section 8) where are also emphasized the similarities between the theory of chaos and that of dynamical systems. Both theories strongly challenge computationalism and suggest that new models are needed to describe how the external world is represented in the brain.

On the transmission of rate code in long feedforward networks with excitatory-inhibitory balance

The capability of feedforward networks composed of multiple layers of integrate-and-fire neurons to transmit rate code was examined. Synaptic connections were made only from one layer to the next, and excitation was balanced by inhibition. When time is discrete and the synaptic potentials rise instantaneously, we show that, for random uncorrelated input to layer one, the mean rate of activity in deep layers is essentially independent of input firing rate. This implies that the input rate cannot be transmitted reliably in such feedforward networks because neurons in a given layer tend to synchronize partially with each other because of shared inputs. As a result of this synchronization, the average firing rate in deep layers will either decay to zero or reach a stable fixed point, depending on model parameters. When time is treated continuously and the synaptic potentials rise instantaneously, these effects develop slowly, and rate transmission over a limited number of layers is possible. However, the correlations among neurons at the same layer hamper reliable assessment of firing rate by averaging over 100 msec (or less). When the synaptic potentials develop gradually, as is the realistic case, transmission of rate code fails. In a network in which inhibition only balances the mean excitation but is not timed precisely with it, neurons in each layer fire together, and this volley successively propagates from layer to layer. We conclude that the transmission of rate code in feedforward networks is highly unlikely.

Tuning neocortical pyramidal neurons between integrators and coincidence detectors

Do cortical neurons operate as integrators or as coincidence detectors? Despite the importance of this question, no definite answer has been given yet, because each of these two views can find its own experimental support. Here we investigated this question using models of morphologically-reconstructed neocortical pyramidal neurons under in vivo like conditions. In agreement with experiments we find that the cell is capable of operating in a continuum between coincidence detection and temporal integration, depending on the characteristics of the synaptic inputs. Moreover, the presence of synaptic background activity at a level comparable to intracellular measurements in vivo can modulate the operating mode of the cell, and act as a switch between temporal integration and coincidence detection. These results suggest that background activity can be viewed as an important determinant of the integrative mode of pyramidal neurons. Thus, background activity not only sharpens cortical responses but it can also be used to tune an entire network between integration and coincidence detection modes.

Analysis of globally connected active rotators with excitatory and inhibitory connections using the Fokker-Planck equation

The globally connected active rotators with excitatory and inhibitory connections are analyzed using the nonlinear Fokker-Planck equation. The bifurcation diagram of the system is obtained numerically, and both periodic solutions and chaotic solutions are found. By observing the interspike interval, the coefficient of variance, and the correlation coefficient of the system, the relationship of our model to the biological data is discussed.

Possible neural coding with interevent intervals of synchronous firing

Neural networks composed of excitable neurons with noise generate rich nonlinear dynamics with spatiotemporal structures of neuronal spikes. Among various spatiotemporal patterns of spikes, synchronous firing has been studied most extensively both with physiological experimentation and with theoretical analysis. In this paper, we consider nonlinear neurodynamics in terms of synchronous firing and possibility of neural coding with such synchronous firing, which may be used in the "noisy brain." In particular, reconstruction of a chaotic attractor modeling a dynamical environment is explored with interevent intervals of synchronous firing from the perspective of nonlinear time series analysis and stochastic resonance.

Modeling the process of rate selection in neuronal activity

We present the elements of a mathematical computational model that reflects the experimental finding that the time-scale of a neuron is not fixed; but rather varies with the history of its stimulus. Unlike most physiological models, there are no pre-determined rates associated with transitions between states of the system nor are there pre-determined constants associated with adaptation rates; instead, the model is a kind of "modulating automata" where the rates emerge from the history of the system itself. We focus in this paper on the temporal dynamics of a neuron and show how a simple internal structure will give rise to complex temporal behavior. The internal structure modeled here is an abstraction of a reasonably well-understood physiological structure. We also suggest that this behavior can be used to transform a "rate" code into a "temporal one".

Precision and reliability of periodically and quasiperiodically driven integrate-and-fire neurons

Neurons in the brain communicate via trains of all-or-none electric events known as spikes. How the brain encodes information using spikes-the neural code-remains elusive. Here the robustness against noise of stimulus-induced neural spike trains is studied in terms of attractors and bifurcations. The dynamics of model neurons converges after a transient onto an attractor yielding a reproducible sequence of spike times. At a bifurcation point the spike times on the attractor change discontinuously when a parameter is varied. Reliability, the stability of the attractor against noise, is reduced when the neuron operates close to a bifurcation point. We determined using analytical spike-time maps the attractor and bifurcation structure of an integrate-and-fire model neuron driven by a periodic or a quasiperiodic piecewise constant current and investigated the stability of attractors against noise. The integrate-and-fire model neuron became mode locked to the periodic current with a rational winding number p/q and produced p spikes per q cycles. There were q attractors. p:q mode-locking regions formed Arnold tongues. In the model, reliability was the highest during 1:1 mode locking when there was only one attractor, as was also observed in recent experiments. The quasiperiodically driven neuron mode locked to either one of the two drive periods, or to a linear combination of both of them. Mode-locking regions were organized in Arnold tongues and reliability was again highest when there was only one attractor. These results show that neuronal reliability in response to the rhythmic drive generated by synchronized networks of neurons is profoundly influenced by the location of the Arnold tongues in parameter space.

A novel algorithm to remove electrical cross-talk between surface EMG recordings and its application to the measurement of short-term synchronisation in humans

Pairs of discharges of single motor units recorded in the same or different muscles often show synchronisation above chance levels. If large numbers of units are synchronous within and between muscles then the synchrony will be measurable in population recordings such as surface EMG. Measuring synchrony between surface EMG recordings has a number of practical and scientific advantages compared with single motor units recorded from intramuscular electrodes. However, the measurement of such synchrony in the time domain between surface EMGs is complicated because the recordings are contaminated by electrical cross-talk. In this study we recorded surface EMG simultaneously from five hand and forearm muscles during a precision grip task. Using a novel 'blind signal separation' algorithm, we were able to remove electrical cross-talk. The cross-talk-corrected EMGs could then be used to assess task-dependent modulation in both oscillatory (15-30 Hz) and non-oscillatory synchrony (all other frequencies). In agreement with previous studies, the oscillatory component was maximal during steady holding but abolished during movement. By contrast, the non-oscillatory component of the EMG synchrony appeared remarkably constant throughout all phases of the task. We conclude that surface EMG recordings can be of considerable use in the assessment of population synchrony changes, providing that electrical cross-talk between nearby channels is removed using a statistical signal processing technique. Our results show a striking difference in the task-dependent modulation of oscillatory and non-oscillatory synchrony between muscles during a dynamic precision grip task.

Information transfer in entrained cortical neurons

Cortical interneurons connected by gap junctions can provide a synchronized inhibitory drive that can entrain pyramidal cells. This was studied in a single-compartment Hodgkin-Huxley-type model neuron that was entrained by periodic inhibitory inputs with low jitter in the input spike times (i.e. high precision), and a variable but large number of presynaptic spikes on each cycle. During entrainment the Shannon entropy of the output spike times was reduced sharply compared with its value outside entrainment. Surprisingly, however, the information transfer as measured by the mutual information between the number of inhibitory inputs in a cycle and the phase lag of the subsequent output spike was significantly increased during entrainment. This increase was due to the reduced contribution of the internal correlations to the output variability. These theoretical predictions were supported by experimental recordings from the rat neocortex and hippocampus in vitro.

Dual information representation with stable firing rates and chaotic spatiotemporal spike patterns in a neural network model

Although various means of information representation in the cortex have been considered, the fundamental mechanism for such representation is not well understood. The relation between neural network dynamics and properties of information representation needs to be examined. We examined spatial pattern properties of mean firing rates and spatiotemporal spikes in an interconnected spiking neural network model. We found that whereas the spatiotemporal spike patterns are chaotic and unstable, the spatial patterns of mean firing rates (SPMFR) are steady and stable, reflecting the internal structure of synaptic weights. Interestingly, the chaotic instability contributes to fast stabilization of the SPMFR. Findings suggest that there are two types of network dynamics behind neuronal spiking: internally-driven dynamics and externally driven dynamics. When the internally driven dynamics dominate, spikes are relatively more chaotic and independent of external inputs; the SPMFR are steady and stable. When the externally driven dynamics dominate, the spiking patterns are relatively more dependent on the spatiotemporal structure of external inputs. These emergent properties of information representation imply that the brain may adopt a dual coding system. Recent experimental data suggest that internally driven and externally driven dynamics coexist and work together in the cortex.

Spike timing, synchronization and information processing on the sensory side of the central nervous system

To what extent is the variability of the neuronal responses compatible with the use of spike timing for sensory information processing by the central nervous system? In reviewing the state of the art of this question, I first analyze the characteristics of this variability with its three elements: synaptic noise, impact of ongoing activity and possible fluctuations in evoked responses. I then review the recent literature on the various sensory modalities: somato-sensory, olfactory, gustatory and visual and auditory processing. I emphasize that the conditions in which precise timing, at the millisecond level, is usually obtained, are conditions that usually require dynamic stimulation or sharp changes in the stimuli. By contrast, situations in which stimulation not belonging to the temporal domain is temporally encoded lead to much coarser temporal coding; although in both cases, neural networks transmit the signals with similarly high precision. Synchronization among neurons is an important tool in information processing in both cases but again seems to act either at millisecond or tens of millisecond levels. Information theory applied to both situations confirms that the average rate of information transmission is much higher in dynamic than in static situations. These facts suggest that channels of precise temporal encoding may exist in the brain but imply populations of neurons working in a yet to be discovered way.

Neural representation of alpha-oriented moving light bars in the cortex: a neural network study

A neural computational model is suggested in this paper for investigating the stimulus dependence of spiking patterns and the neural representation of alpha-oriented moving light bars in the cortex. In this model, a stimulus-directed cortical developing algorithm is introduced for training the neural network. Three classes of computer simulations concerned with the orientation of the stimulus are carried out. The simulation results show that the fine temporal structure of spiking patterns of single units depends on the alpha orientation of the two moving light bars, and the fine temporal structure of their combinatorial spiking patterns are also context dependent. They also show that the neural representation of an alpha-oriented moving light bar is determined not only by the stimulus itself but also the architecture of the matured network. In the end, we propose a possible neural coding mechanism underlying the temporal cell subassemblies in the cortex, which could be spontaneously and dynamically organized into a dynamical cell assembly by synchronized activity of these subassemblies.

Variability and coding efficiency of noisy neural spike encoders

Encoding synaptic inputs as a train of action potentials is a fundamental function of nerve cells. Although spike trains recorded in vivo have been shown to be highly variable, it is unclear whether variability in spike timing represents faithful encoding of temporally varying synaptic inputs or noise inherent in the spike encoding mechanism. It has been reported that spike timing variability is more pronounced for constant, unvarying inputs than for inputs with rich temporal structure. This could have significant implications for the nature of neural coding, particularly if precise timing of spikes and temporal synchrony between neurons is used to represent information in the nervous system. To study the potential functional role of spike timing variability, we estimate the fraction of spike timing variability which conveys information about the input for two types of noisy spike encoders--an integrate and fire model with randomly chosen thresholds and a model of a patch of neuronal membrane containing stochastic Na(+) and K(+) channels obeying Hodgkin-Huxley kinetics. The quality of signal encoding is assessed by reconstructing the input stimuli from the output spike trains using optimal linear mean square estimation. A comparison of the estimation performance of noisy neuronal models of spike generation enables us to assess the impact of neuronal noise on the efficacy of neural coding. The results for both models suggest that spike timing variability reduces the ability of spike trains to encode rapid time-varying stimuli. Moreover, contrary to expectations based on earlier studies, we find that the noisy spike encoding models encode slowly varying stimuli more effectively than rapidly varying ones.

Stochastic resonance in a Hodgkin-Huxley neuron in the absence of external noise

We study numerically nonlinear responses of a periodically forced Hodgkin-Huxley neuron. The coherence of the system in the absence of external noise, namely, the "intrinsic stochastic resonance," is evidenced by the multimodal aperiodic firing pattern, a bell-shaped curve in the signal-to-noise ratio, and the statistical features of the mean firing rate. The subthreshold intrinsic oscillations enhance the signal transduction in a manner different from that in models studied previously.

Enhanced spontaneous transmitter release is the earliest consequence of neocortical hypoxia that can explain the disruption of normal circuit function

After the onset of an acute episode of arrested circulation to the brain and consequent cerebral hypoxia, EEG changes and modifications of consciousness ensue within seconds. This in part reflects the rapid effect of hypoxia on the neocortex, where oxygen deprivation leads to impaired neuronal excitability and abnormal synaptic transmission. To identify the cellular mechanisms responsible for the earliest changes in neocortical function and to determine their time course, we have used patch-in-slice recording techniques to investigate the effects of acute hypoxia on the synaptic and intrinsic properties of layer 5 neurons. Coronal slices of mouse somatosensory cortex were maintained at 37 degrees C and challenged with episodes of hypoxia (3-4 min of exposure to 95% N(2), 5% CO(2)). In recordings with cell-attached patch electrodes, activation of ATP-sensitive potassium channels first became detectable 211 +/- 11 sec (range, 185-240 sec; n = 6 patches) after the onset of hypoxia. Similar recording techniques revealed no alterations in the properties of Na(+) currents in the first 4 min after the onset of hypoxia. The earliest hypoxia-induced disturbance was a marked increase in the frequency of spontaneous EPSCs and IPSCs, which began within 15-30 sec of the removal of oxygen. This rapid synaptic effect was not sensitive to TTX and was present in Ca(2+)-free perfusate, indicating that the hypoxia had a direct influence on the vesicular release mechanisms. The incoherent, massive increase in miniature PSCs would be expected to deplete the readily releasable pool of vesicles in cortical terminals, and to thereby markedly distort the neuronal interactions that underlie normal circuit function.

Coding properties of spiking neurons: reverse and cross-correlations

What is the 'meaning' of a single spike? Spike-triggered averaging ('reverse correlations') yields the typical input just before a spike. Similarly, cross-correlations describe the probability of firing an output spike given (one additional) presynaptic input spike. In this paper, we analytically calculate reverse and cross-correlations for a spiking neuron model with escape noise. The influence of neuronal parameters (such as the membrane time constant, the noise level, and the mean firing rate) on the form of the correlation function is illustrated. The calculation is done in the framework of a population theory that is reviewed. The relation of the population activity equations to population density methods is discussed. Finally, we indicate the role of cross-correlations in spike-time dependent Hebbian plasticity.

Rate coding versus temporal order coding: what the retinal ganglion cells tell the visual cortex

It is often supposed that the messages sent to the visual cortex by the retinal ganglion cells are encoded by the mean firing rates observed on spike trains generated with a Poisson process. Using an information transmission approach, we evaluate the performances of two such codes, one based on the spike count and the other on the mean interspike interval, and compare the results with a rank order code, where the first ganglion cells to emit a spike are given a maximal weight. Our results show that the rate codes are far from optimal for fast information transmission and that the temporal structure of the spike train can be efficiently used to maximize the information transfer rate under conditions where each cell needs to fire only one spike.

A laterally interconnected neural architecture in MST accounts for psychophysical discrimination of complex motion patterns

The complex patterns of visual motion formed across the retina during self-motion, often referred to as optic flow, provide a rich source of information describing our dynamic relationship within the environment. Psychophysical studies indicate the existence of specialized detectors for component motion patterns (radial, circular, planar) that are consistent with the visual motion properties of cells in the medial superior temporal area (MST) of nonhuman primates. Here we use computational modeling and psychophysics to investigate the structural and functional role of these specialized detectors in performing a graded motion pattern (GMP) discrimination task. In the psychophysical task perceptual discrimination varied significantly with the type of motion pattern presented, suggesting perceptual correlates to the preferred motion bias reported in MST. Simulated perceptual discrimination in a population of independent MST-like neural responses showed inconsistent psychophysical performance that varied as a function of the visual motion properties within the population code. Robust psychophysical performance was achieved by fully interconnecting neural populations such that they inhibited nonpreferred units. Taken together, these results suggest that robust processing of the complex motion patterns associated with self-motion and optic flow may be mediated by an inhibitory structure of neural interactions in MST.

Solving the binding problem of the brain with bi-directional functional connectivity

We propose a neural network model which gives one solution to the binding problem on the basis of 'functional connectivity' and bidirectional connections. Here, 'functional connectivity' is dynamic neuronal connectivity peculiar to temporal spike coding neural networks with coincidence detector neurons. The model consists of a single primary map and two higher modules which extract two different features shown on the primary map. There exist three layers in each higher module and the layers are connected bi-directionally. An object in the outer world is represented by a 'global dynamical cell assembly' which is organized across the primary map and the two higher modules. Detailed, but spatially localized, information is coded in the primary map, whereas coarse, but spatially extracted information or globally integrated information is coded in the higher modules. Computer simulations of the proposed model show that multiple cell assemblies sharing the same neurons partially can co-exist. Furthermore, we introduce a three-dimensional J-PSTH (Joint-Peri Stimulus Time Histogram) which is capable of tracking such cell assemblies, altering its constituent neurons as in our proposed model.

Frequency dependence of spike timing reliability in cortical pyramidal cells and interneurons

Pyramidal cells and interneurons in rat prefrontal cortical slices exhibit subthreshold oscillations when depolarized by constant current injection. For both types of neurons, the frequencies of these oscillations for current injection just below spike threshold were 2--10 Hz. Above spike threshold, however, the subthreshold oscillations in pyramidal cells remained low, but the frequency of oscillations in interneurons increased up to 50 Hz. To explore the interaction between these intrinsic oscillations and external inputs, the reliability of spiking in these cortical neurons was studied with sinusoidal current injection over a range of frequencies above and below the intrinsic frequency. Cortical neurons produced 1:1 phase locking for a limited range of driving frequencies for fixed amplitude. For low-input amplitude, 1:1 phase locking was obtained in the 5- to 10-Hz range. For higher-input amplitudes, pyramidal cells phase-locked in the 5- to 20-Hz range, whereas interneurons phase-locked in the 5- to 50-Hz range. For the amplitudes studied here, spike time reliability was always highest during 1:1 phase-locking, between 5 and 20 Hz for pyramidal cells and between 5 and 50 Hz for interneurons. The observed differences in the intrinsic frequency preference between pyramidal cells and interneurons have implications for rhythmogenesis and information transmission between populations of cortical neurons.

Frequency tuning of input-output relation in a rat cortical neuron in-vitro

The input-output relation of a single neuron stands at the basis of every biologically oriented description of the brain. This report shows that the input-output relation of cultured cortical neurons is non-linearly tuned by the input frequency. Increasing the rate of stimulation results in the appearance of ordered temporal firing patterns, which are qualitatively different for different input frequencies. The experimental results of this study lead to the conclusion that frequency tuning of neuronal input-output relation arises from activity-dependent rates at the molecular level underlying the mechanism of excitability itself.

Backpropagation of physiological spike trains in neocortical pyramidal neurons: implications for temporal coding in dendrites

In vivo neocortical neurons fire apparently random trains of action potentials in response to sensory stimuli. Does this randomness represent a signal or noise around a mean firing rate? Here we use the timing of action potential trains recorded in vivo to explore the dendritic consequences of physiological patterns of action potential firing in neocortical pyramidal neurons in vitro. We find that action potentials evoked by physiological patterns of firing backpropagate threefold to fourfold more effectively into the distal apical dendrites (>600 microm from the soma) than action potential trains reflecting their mean firing rate. This amplification of backpropagation was maximal during high-frequency components of physiological spike trains (80-300 Hz). The disparity between backpropagation during physiological and mean firing patterns was dramatically reduced by dendritic hyperpolarization. Consistent with this voltage dependence, dendritic depolarization amplified single action potentials by fourfold to sevenfold, with a spatial profile strikingly similar to the amplification of physiological spike trains. Local blockade of distal dendritic sodium channels substantially reduced amplification of physiological spike trains, but did not significantly alter action potential trains reflecting their mean firing rate. Dendritic electrogenesis during physiological spike trains was also reduced by the blockade of calcium channels. We conclude that amplification of backpropagating action potentials during physiological spike trains is mediated by frequency-dependent supralinear temporal summation, generated by the recruitment of distal dendritic sodium and calcium channels. Together these data indicate that the temporal nature of physiological patterns of action potential firing contains a signal that is transmitted effectively throughout the dendritic tree.

Spike-frequency adaptation of a generalized leaky integrate-and-fire model neuron

Although spike-frequency adaptation is a commonly observed property of neurons, its functional implications are still poorly understood. In this work, using a leaky integrate-and-fire neural model that includes a Ca2+-activated K+ current (IAHP), we develop a quantitative theory of adaptation temporal dynamics and compare our results with recent in vivo intracellular recordings from pyramidal cells in the cat visual cortex. Experimentally testable relations between the degree and the time constant of spike-frequency adaptation are predicted. We also contrast the IAHP model with an alternative adaptation model based on a dynamical firing threshold. Possible roles of adaptation in temporal computation are explored, as a a time-delayed neuronal self-inhibition mechanism. Our results include the following: (1) given the same firing rate, the variability of interspike intervals (ISIs) is either reduced or enhanced by adaptation, depending on whether the IAHP dynamics is fast or slow compared with the mean ISI in the output spike train; (2) when the inputs are Poisson-distributed (uncorrelated), adaptation generates temporal anticorrelation between ISIs, we suggest that measurement of this negative correlation provides a probe to assess the strength of IAHP in vivo; (3) the forward masking effect produced by the slow dynamics of IAHP is nonlinear and effective at selecting the strongest input among competing sources of input signals.

Membrane potential fluctuations determine the precision of spike timing and synchronous activity: a model study

It is much debated on what time scale information is encoded by neuronal spike activity. With a phenomenological model that transforms time-dependent membrane potential fluctuations into spike trains, we investigate constraints for the timing of spikes and for synchronous activity of neurons with common input. The model of spike generation has a variable threshold that depends on the time elapsed since the previous action potential and on the preceding membrane potential changes. To ensure that the model operates in a biologically meaningful range, the model was adjusted to fit the responses of a fly visual interneuron to motion stimuli. The dependence of spike timing on the membrane potential dynamics was analyzed. Fast membrane potential fluctuations are needed to trigger spikes with a high temporal precision. Slow fluctuations lead to spike activity with a rate about proportional to the membrane potential. Thus, for a given level of stochastic input, the frequency range of membrane potential fluctuations induced by a stimulus determines whether a neuron can use a rate code or a temporal code. The relationship between the steepness of membrane potential fluctuations and the timing of spikes has also implications for synchronous activity in neurons with common input. Fast membrane potential changes must be shared by the neurons to produce synchronous activity.

Synaptic efficacy and the transmission of complex firing patterns between neurons

In central neurons, the summation of inputs from presynaptic cells combined with the unreliability of synaptic transmission produces incessant variations of the membrane potential termed synaptic noise (SN). These fluctuations, which depend on both the unpredictable timing of afferent activities and quantal variations of postsynaptic potentials, have defied conventional analysis. We show here that, when applied to SN recorded from the Mauthner (M) cell of teleosts, a simple method of nonlinear analysis reveals previously undetected features of this signal including hidden periodic components. The phase relationship between these components is compatible with the notion that the temporal organization of events comprising this noise is deterministic rather than random and that it is generated by presynaptic interneurons behaving as coupled periodic oscillators. Furthermore a model of the presynaptic network shows how SN is shaped both by activities in incoming inputs and by the distribution of their synaptic weights expressed as mean quantal contents of the activated synapses. In confirmation we found experimentally that long-term tetanic potentiation (LTP), which selectively increases some of these synaptic weights, permits oscillating temporal patterns to be transmitted more effectively to the postsynaptic cell. Thus the probabilistic nature of transmitter release, which governs the strength of synapses, may be critical for the transfer of complex timing information within neuronal assemblies.

Comparison of current-driven and conductance-driven neocortical model neurons with Hodgkin-Huxley voltage-gated channels

Intrinsic noise and random synaptic inputs generate a fluctuating current across neuron membranes. We determine the statistics of the output spike train of a biophysical model neuron as a function of the mean and variance of the fluctuating current, when the current is white noise, or when it derives from Poisson trains of excitatory and inhibitory postsynaptic conductances. In the first case, the firing rate increases with increasing variance of the current, whereas in the latter case it decreases. In contrast, the firing rate is independent of variance (for constant mean) in the commonly used random walk, and perfect integrate-and-fire models for spike generation. The model neuron can be in the current-dominated state, representative of neurons in the in vitro slice preparation, or in the fluctuation-dominated state, representative of in vivo neurons. We discuss the functional relevance of these states to cortical information processing.

Neuroscience: breaking down scientific barriers to the study of brain and mind

In this month's essay, Eric R. Kandel and Larry R. Squire chronicle how brain research has migrated from the peripheries of biology and psychology to assume a central position within those disciplines. The multidiscipline of neuroscience that emerged from this process now ranges from genes to cognition, from molecules to minds.

EPSP amplification and the precision of spike timing in hippocampal neurons

The temporal precision with which EPSPs initiate action potentials in postsynaptic cells determines how activity spreads in neuronal networks. We found that small EPSPs evoked from just subthreshold potentials initiated firing with short latencies in most CA1 hippocampal inhibitory cells, while action potential timing in pyramidal cells was more variable due to plateau potentials that amplified and prolonged EPSPs. Action potential timing apparently depends on the balance of subthreshold intrinsic currents. In interneurons, outward currents dominate responses to somatically injected EPSP waveforms, while inward currents are larger than outward currents close to threshold in pyramidal cells. Suppressing outward potassium currents increases the variability in latency of synaptically induced firing in interneurons. These differences in precision of EPSP-spike coupling in inhibitory and pyramidal cells will enhance inhibitory control of the spread of excitation in the hippocampus.

Modeling neuronal dynamic coding in primary visual cortex

The visual system can be considered as a multi-layered and dynamic image processing system. According to experimental evidence, the receptive field (RF) organization is characterized by spatio-temporal properties. The modified extended Gabor (MEG) function model was proposed to describe the main spatio-temporal properties of RF at different levels of visual pathway. Based on the MEG model, a three-layered dynamic coding model was constructed for a complex cell. The responses of the complex cell depend on synaptic events from a simple cell assembly within a time window. The membrane potential evolution equation was applied to the analysis of the length of a time window. The simulation results demonstrated that a complex cell plays as a coincidence detector in encoding synaptic events within the time window.

Rate code input produces temporal code output from cockroach antennal lobes

The experiments presented here were designed to determine the origin of the temporally complex activity of antennal lobe projection neurons in the cockroach olfactory system. We determined this through the use of complex chemical stimuli that evoked neural activity recorded extracellularly from olfactory sensory neurons and intracellularly from antennal lobe projection neurons in the cockroach Periplaneta americana. Olfactory information was represented by a simple, short time-scale rate code in the olfactory sensory neurons. This rate code input from the sensory neurons was processed by the antennal lobe and transformed into a longer time-scale, temporally encoded output expressed across a smaller population of antennal lobe projection neurons. The projection neuron responses comprised temporal patterns of increases and decreases in spike frequency that differed among projection neurons and were consistent among repeated presentations of the same stimulus. Presentation of simple and complex chemical stimuli showed that the complexity of projection neuron activity was a product of the antennal lobes and was not associated with the chemical complexity of the stimulus. To characterize the encoding schemes used by each class of neurons, the responses were decomposed into their principal components. The stimulus was correlated with only the first principal component of the activity of sensory neurons, which is consistent with a rate encoding scheme. The stimulus was correlated with higher order principal components of the activity of projection neurons, which is consistent with a temporal encoding scheme.

Effects of the synaptic transmission's dynamics on possible neural codes

To examine the effects of paired pulse facilitation, long-term synaptic modifications as well as spike frequency adaptation on neural signal transmission, a simple model was applied. This way various input-output properties of the model units were described. Particularly, the transmission of the mean and S.D. of the simulated synaptic currents were studied. The results indicate that the transfer of the mean value of the membrane currents cannot be described in terms of synaptic weights. So firing rate can hardly be an efficient neural code, especially for adaptive channels of the central nervous system (CNS). On the contrary, the transfer of S.D. of synaptic currents behaves in accordance with the synaptic weights. So it is supported that S.D. of the synaptic currents is a biological relevant subclass of the variation codes [see Perkel, H., Bullock, T.H., 1968. Neurol coding. Neurosci. Res. Program Bull. 6, 221-344]. It is discussed how this code can be established and how it works.

Neural representation and the cortical code

The principle function of the central nervous system is to represent and transform information and thereby mediate appropriate decisions and behaviors. The cerebral cortex is one of the primary seats of the internal representations maintained and used in perception, memory, decision making, motor control, and subjective experience, but the basic coding scheme by which this information is carried and transformed by neurons is not yet fully understood. This article defines and reviews how information is represented in the firing rates and temporal patterns of populations of cortical neurons, with a particular emphasis on how this information mediates behavior and experience.

Rate limitations of unitary event analysis

Unitary event analysis is a new method for detecting episodes of synchronized neural activity (Riehle, Grün, Diesmann, & Aertsen, 1997). It detects time intervals that contain coincident firing at higher rates than would be expected if the neurons fired as independent inhomogeneous Poisson processes; all coincidences in such intervals are called unitary events (UEs). Changes in the frequency of UEs that are correlated with behavioral states may indicate synchronization of neural firing that mediates or represents the behavioral state. We show that UE analysis is subject to severe limitations due to the underlying discrete statistics of the number of coincident events. These limitations are particularly stringent for low (0-10 spikes/s) firing rates. Under these conditions, the frequency of UEs is a random variable with a large variation relative to its mean. The relative variation decreases with increasing firing rate, and we compute the lowest firing rate, at which the 95% confidence interval around the mean frequency of UEs excludes zero. This random variation in UE frequency makes interpretation of changes in UEs problematic for neurons with low firing rates. As a typical example, when analyzing 150 trials of an experiment using an averaging window 100 ms wide and a 5 ms coincidence window, firing rates should be greater than 7 spikes per second.