The locust olfactory system as a case study for modeling dynamics of neurobiological networks: from discrete time neurons to continuous time neurons

Both chaotic and periodic activities are observed in networks of the central nervous systems. We choose the locust olfactory system as a good case study to analyze the relationships between networks' structure and the types of dynamics involved in coding mechanisms. In our modeling approach, we first build a fully connected recurrent network of synchronously updated McCulloch and Pitts neurons (MC-P type). In order to measure the use of the temporal dimension in the complex spatio-temporal patterns produced by the networks, we have defined an index the Normalized Euclidian Distance NED. We find that for appropriate parameters of input and connectivity, when adding some strong connections to the initial random synaptic matrices, it was easy to get the emergence of both robust oscillations and distributed synchrony in the spatiotemporal patterns. Then, in order to validate the MC-P model as a tool for analysis for network properties, we examine the dynamic behavior of networks of continuous time model neuron (Izhikevitch Integrate and Fire model -IFI-), implementing the same network characteristics. In both models, similarly to biological PN, the activity of excitatory neurons are phase-locked to different cycles of oscillations which remind the ones of the local field potential (LFP), and nevertheless exhibit dynamic behavior complex enough to be the basis of spatio-temporal codes.     

Cracking the code of oscillatory activity

Neural oscillations are ubiquitous measurements of cognitive processes and dynamic routing and gating of information. The fundamental and so far unresolved problem for neuroscience remains to understand how oscillatory activity in the brain codes information for human cognition. In a biologically relevant cognitive task, we instructed six human observers to categorize facial expressions of emotion while we measured the observers' EEG. We combined state-of-the-art stimulus control with statistical information theory analysis to quantify how the three parameters of oscillations (i.e., power, phase, and frequency) code the visual information relevant for behavior in a cognitive task. We make three points: First, we demonstrate that phase codes considerably more information (2.4 times) relating to the cognitive task than power. Second, we show that the conjunction of power and phase coding reflects detailed visual features relevant for behavioral response--that is, features of facial expressions predicted by behavior. Third, we demonstrate, in analogy to communication technology, that oscillatory frequencies in the brain multiplex the coding of visual features, increasing coding capacity. Together, our findings about the fundamental coding properties of neural oscillations will redirect the research agenda in neuroscience by establishing the differential role of frequency, phase, and amplitude in coding behaviorally relevant information in the brain.     

Event-driven simulation of cerebellar granule cells

Around half of the neurons of a human brain are granule cells (approximately 10(11)granule neurons) [Kandel, E.R., Schwartz, J.H., Jessell, T.M., 2000. Principles of Neural Science. McGraw-Hill Professional Publishing, New York]. In order to study in detail the functional role of the intrinsic features of this cell we have developed a pre-compiled behavioural model based on the simplified granule-cell model of Bezzi et al. [Bezzi, M., Nieus, T., Arleo, A., D'Angelo, E., Coenen, O.J.-M.D., 2004. Information transfer at the mossy fiber-granule cell synapse of the cerebellum. 34th Annual Meeting. Society for Neuroscience, San Diego, CA, USA]. We can use an efficient event-driven simulation scheme based on lookup tables (EDLUT) [Ros, E., Carrillo, R.R., Ortigosa, E.M., Barbour, B., Ags, R., 2006. Event-driven simulation scheme for spiking neural networks using lookup tables to characterize neuronal dynamics. Neural Computation 18 (12), 2959-2993]. For this purpose it is necessary to compile into tables the data obtained through a massive numerical calculation of the simplified cell model. This allows network simulations requiring minimal numerical calculation. There are three major features that are considered functionally relevant in the simplified granule cell model: bursting, subthreshold oscillations and resonance. In this work we describe how the cell model is compiled into tables keeping these key properties of the neuron model.     

Oscillations and slow patterning in the antennal lobe

Odor presentation generates both fast oscillations and slow patterning in the spiking activity of the projection neurons (PNs) in the antennal lobe (AL) of locusts, moths and bees. Experimental results indicate that the oscillations are the result of the interaction between the PNs and the inhibitory local neurons (LNs) in the AL; e.g., blocking inhibition by application of GABA-receptor antagonists abolishes these oscillations. The slow patterning, on the other hand, was shown to be somewhat resistant to such blockage. In a H-H model, we reproduce both the oscillations and the slow patterning. As previously suggested, the oscillations are the result of the interaction between the PNs and LNs. We suggest that calcium and calcium-dependent potassium channels (found in PNs of bees and moths) are sufficient to account for the slow patterning resistant to the application of GABA-receptor antagonists. The intrinsic bursting property of the PNs, resulting from these additional modeled currents, give rise to another network feature that was seen experimentally in locusts: A relatively small increase in the number of additional generated PN action potentials when LN input is blocked. Consequently, the major effect of network inhibition is to redistribute the action potentials of the PNs from bursting to one action potential per cycle of the oscillations. Action Editor: Christiane Linster     

Predictive Feedback Can Account for Biphasic Responses in the Lateral Geniculate Nucleus

Biphasic neural response properties, where the optimal stimulus for driving a neural response changes from one stimulus pattern to the opposite stimulus pattern over short periods of time, have been described in several visual areas, including lateral geniculate nucleus (LGN), primary visual cortex (V1), and middle temporal area (MT). We describe a hierarchical model of predictive coding and simulations that capture these temporal variations in neuronal response properties. We focus on the LGN-V1 circuit and find that after training on natural images the model exhibits the brain's LGN-V1 connectivity structure, in which the structure of V1 receptive fields is linked to the spatial alignment and properties of center-surround cells in the LGN. In addition, the spatio-temporal response profile of LGN model neurons is biphasic in structure, resembling the biphasic response structure of neurons in cat LGN. Moreover, the model displays a specific pattern of influence of feedback, where LGN receptive fields that are aligned over a simple cell receptive field zone of the same polarity decrease their responses while neurons of opposite polarity increase their responses with feedback. This phase-reversed pattern of influence was recently observed in neurophysiology. These results corroborate the idea that predictive feedback is a general coding strategy in the brain.     

Reading spike timing without a clock: intrinsic decoding of spike trains

The precise timing of action potentials of sensory neurons relative to the time of stimulus presentation carries substantial sensory information that is lost or degraded when these responses are summed over longer time windows. However, it is unclear whether and how downstream networks can access information in precise time-varying neural responses. Here, we review approaches to test the hypothesis that the activity of neural populations provides the temporal reference frames needed to decode temporal spike patterns. These approaches are based on comparing the single-trial stimulus discriminability obtained from neural codes defined with respect to network-intrinsic reference frames to the discriminability obtained from codes defined relative to the experimenter''s computer clock. Application of this formalism to auditory, visual and somatosensory data shows that information carried by millisecond-scale spike times can be decoded robustly even with little or no independent external knowledge of stimulus time. In cortex, key components of such intrinsic temporal reference frames include dedicated neural populations that signal stimulus onset with reliable and precise latencies, and low-frequency oscillations that can serve as reference for partitioning extended neuronal responses into informative spike patterns.     

Identifying temporal codes in spontaneously active sensory neurons

The manner in which information is encoded in neural signals is a major issue in Neuroscience. A common distinction is between rate codes, where information in neural responses is encoded as the number of spikes within a specified time frame (encoding window), and temporal codes, where the position of spikes within the encoding window carries some or all of the information about the stimulus. One test for the existence of a temporal code in neural responses is to add artificial time jitter to each spike in the response, and then assess whether or not information in the response has been degraded. If so, temporal encoding might be inferred, on the assumption that the jitter is small enough to alter the position, but not the number, of spikes within the encoding window. Here, the effects of artificial jitter on various spike train and information metrics were derived analytically, and this theory was validated using data from afferent neurons of the turtle vestibular and paddlefish electrosensory systems, and from model neurons. We demonstrate that the jitter procedure will degrade information content even when coding is known to be entirely by rate. For this and additional reasons, we conclude that the jitter procedure by itself is not sufficient to establish the presence of a temporal code.     

Distributed processing and temporal codes in neuronal networks

The cerebral cortex presents itself as a distributed dynamical system with the characteristics of a small world network. The neuronal correlates of cognitive and executive processes often appear to consist of the coordinated activity of large assemblies of widely distributed neurons. These features require mechanisms for the selective routing of signals across densely interconnected networks, the flexible and context dependent binding of neuronal groups into functionally coherent assemblies and the task and attention dependent integration of subsystems. In order to implement these mechanisms, it is proposed that neuronal responses should convey two orthogonal messages in parallel. They should indicate (1) the presence of the feature to which they are tuned and (2) with which other neurons (specific target cells or members of a coherent assembly) they are communicating. The first message is encoded in the discharge frequency of the neurons (rate code) and it is proposed that the second message is contained in the precise timing relationships between individual spikes of distributed neurons (temporal code). It is further proposed that these precise timing relations are established either by the timing of external events (stimulus locking) or by internal timing mechanisms. The latter are assumed to consist of an oscillatory modulation of neuronal responses in different frequency bands that cover a broad frequency range from <2 Hz (delta) to >40 Hz (gamma) and ripples. These oscillations limit the communication of cells to short temporal windows whereby the duration of these windows decreases with oscillation frequency. Thus, by varying the phase relationship between oscillating groups, networks of functionally cooperating neurons can be flexibly configurated within hard wired networks. Moreover, by synchronizing the spikes emitted by neuronal populations, the saliency of their responses can be enhanced due to the coincidence sensitivity of receiving neurons in very much the same way as can be achieved by increasing the discharge rate. Experimental evidence will be reviewed in support of the coexistence of rate and temporal codes. Evidence will also be provided that disturbances of temporal coding mechanisms are likely to be one of the pathophysiological mechanisms in schizophrenia. This article was part of LNCS 5286 (2008), Maria Marinaro, Silvia Scarpetta, Yoko Yamaguchi (eds.), “Dynamic Brain—from Neural Spikes to Behaviors, 12th International Summer School on Neural Networks Erice, Italy, December 2007 Revised Lectures” and summarized some of the putative functions of temporal codes resulting either from the timing of external events (feed forward/bottom up) or from internal timing mechanisms (top down). For comprehensive reviews of the theoretical prerequisites of synchronization in these processes see Yamaguchi and Shimizu (1994) and Shimizu et al. (1985).     

The Role of Inhibition in a Computational Model of an Auditory Cortical Neuron during the Encoding of Temporal Information

In auditory cortex, temporal information within a sound is represented by two complementary neural codes: a temporal representation based on stimulus-locked firing and a rate representation, where discharge rate co-varies with the timing between acoustic events but lacks a stimulus-synchronized response. Using a computational neuronal model, we find that stimulus-locked responses are generated when sound-evoked excitation is combined with strong, delayed inhibition. In contrast to this, a non-synchronized rate representation is generated when the net excitation evoked by the sound is weak, which occurs when excitation is coincident and balanced with inhibition. Using single-unit recordings from awake marmosets (Callithrix jacchus), we validate several model predictions, including differences in the temporal fidelity, discharge rates and temporal dynamics of stimulus-evoked responses between neurons with rate and temporal representations. Together these data suggest that feedforward inhibition provides a parsimonious explanation of the neural coding dichotomy observed in auditory cortex.     

Central Processing of Communication Sounds in the Anuran Auditory System

SYNOPSIS. The social behavior of anurans (frogs and toads) ismediated by a number of acoustic signals, or calls, that showboth inter- and intraspecific differences in temporal patternand spectral content. These differences provide cues usefulfor call recognition. Neural mechanisms responsible for detectingand analyzing the temporal and spectral cues of the speciesvocalizations have been the subject of investigation for almostthree decades. Here, I summarize the results of studies conductedin the northern leopard frog, Rana pipiens. These results demonstratethat (1) sound analysis is performed in the central auditorysystem of anurans by an array of neural niters operating inthe time and frequency domain, (2) behaviorally relevant soundsare represented by stimulus-dependent spatio-temporal patternsof excitation among differentially tuned filter neurons, and(3) the time and frequency selectivity of these neurons is determined,in part, by GABA-mediated inhibitory interactions that shapetheir excitatory input     

Rates and rhythms: a synergistic view of frequency and temporal coding in neuronal networks

In the CNS, activity of individual neurons has a small but quantifiable relationship to sensory representations and motor outputs. Coactivation of a few 10s to 100s of neurons can code sensory inputs and behavioral task performance within psychophysical limits. However, in a sea of sensory inputs and demand for complex motor outputs how is the activity of such small subpopulations of neurons organized? Two theories dominate in this respect: increases in spike rate (rate coding) and sharpening of the coincidence of spiking in active neurons (temporal coding). Both have computational advantages and are far from mutually exclusive. Here, we review evidence for a bias in neuronal circuits toward temporal coding and the coexistence of rate and temporal coding during population rhythm generation. The coincident expression of multiple types of gamma rhythm in sensory cortex suggests a mechanistic substrate for combining rate and temporal codes?on the basis of stimulus strength.     

Dual coding hypotheses for neural information representation

Information is represented and processed in neural systems in various ways. The rate coding, population coding, and temporal coding are typical examples of representation. It is a hot issue in neuroscience what kinds of coding is used in real neural systems. Different regions of the brain may resort to different coding strategies. Moreover, recent studies suggest the possibility of dual or multiple codes, in which different modes of information are embedded in one neural system. The present paper reviews various possibilities of neural codes focusing on dual codes.     

Temporal population code of concurrent vocal signals in the auditory midbrain

Unique patterns of spike activity across neuron populations have been implicated in the coding of complex sensory stimuli. Delineating the patterns of neural activity in response to varying stimulus parameters and their relationships to the tuning characteristics of individual neurons is essential to ascertaining the nature of population coding within the brain. Here, we address these points in the midbrain coding of concurrent vocal signals of a sound-producing fish, the plainfin midshipman. Midshipman produce multiharmonic vocalizations which frequently overlap to produce beats. We used multivariate statistical analysis from single-unit recordings across multiple animals to assess the presence of a temporal population code. Our results show that distinct patterns of temporal activity emerge among midbrain neurons in response to concurrent signals that vary in their difference frequency. These patterns can serve to code beat difference frequencies. The patterns directly result from the differential temporal coding of difference frequency by individual neurons. Difference frequency encoding, based on temporal patterns of activity, could permit the segregation of concurrent vocal signals on time scales shorter than codes requiring averaging. Given the ubiquity across vertebrates of auditory midbrain tuning to the temporal structure of acoustic signals, a similar temporal population code is likely present in other species.     

Information coding by ensembles of resonant neurons

In the present paper, we propose a novel neural procedure for signal processing and coding based on the subthreshold oscillations and resonance of the neural membrane potential that could be used by real neurons to perform frequency spectra analysis and information coding of incoming signals. Taking into account the biophysical properties of the neural membranes, we note that the subthreshold resonant behaviour they exhibit can be used to analyse incoming signals and represent them in the frequency domain. We study the reliability of the representation of signals depending on the biophysical parameters of the neurons, the fault-tolerance of this coding scheme and its robustness against noise and in the presence of spikes. The principal characteristics of our system are the use of the physical phenomenon of neural resonance (rarely considered in the literature for signal coding); it fits well with the biophysical parameters of most neurons that exhibit subthreshold oscillations; it is compatible with experimental data; and it can be easily integrated in a more general model of information processing and coding that includes communication between neurons based on spikes.     

BDNF boosts spike fidelity in chaotic neural oscillations

Oscillatory activity and its nonlinear dynamics are of fundamental importance for information processing in the central nervous system. Here we show that in aperiodic oscillations, brain-derived neurotrophic factor (BDNF), a member of the neurotrophin family, enhances the accuracy of action potentials in terms of spike reliability and temporal precision. Cultured hippocampal neurons displayed irregular oscillations of membrane potential in response to sinusoidal 20-Hz somatic current injection, yielding wobbly orbits in the phase space, i.e., a strange attractor. Brief application of BDNF suppressed this unpredictable dynamics and stabilized membrane potential fluctuations, leading to rhythmical firing. Even in complex oscillations induced by external stimuli of 40 Hz (gamma) on a 5-Hz (theta) carrier, BDNF-treated neurons generated more precisely timed spikes, i.e., phase-locked firing, coupled with theta-phase precession. These phenomena were sensitive to K252a, an inhibitor of tyrosine receptor kinases and appeared attributable to BDNF-evoked Na(+) current. The data are the first indication of pharmacological control of endogenous chaos. BDNF diminishes the ambiguity of spike time jitter and thereby might assure neural encoding, such as spike timing-dependent synaptic plasticity.     

Ion channel noise can explain firing correlation in auditory nerves

Sensory neurons code information about stimuli in their sequence of action potentials (spikes). Intuitively, the spikes should represent stimuli with high fidelity. However, generating and propagating spikes is a metabolically expensive process. It is therefore likely that neural codes have been selected to balance energy expenditure against encoding error. Our recently proposed optimal, energy-constrained neural coder (Jones et al. Frontiers in Computational Neuroscience, 9, 61 2015) postulates that neurons time spikes to minimize the trade-off between stimulus reconstruction error and expended energy by adjusting the spike threshold using a simple dynamic threshold. Here, we show that this proposed coding scheme is related to existing coding schemes, such as rate and temporal codes. We derive an instantaneous rate coder and show that the spike-rate depends on the signal and its derivative. In the limit of high spike rates the spike train maximizes fidelity given an energy constraint (average spike-rate), and the predicted interspike intervals are identical to those generated by our existing optimal coding neuron. The instantaneous rate coder is shown to closely match the spike-rates recorded from P-type primary afferents in weakly electric fish. In particular, the coder is a predictor of the peristimulus time histogram (PSTH). When tested against in vitro cortical pyramidal neuron recordings, the instantaneous spike-rate approximates DC step inputs, matching both the average spike-rate and the time-to-first-spike (a simple temporal code). Overall, the instantaneous rate coder relates optimal, energy-constrained encoding to the concepts of rate-coding and temporal-coding, suggesting a possible unifying principle of neural encoding of sensory signals.     

Wavelet packet fractal analysis of neuronal morphology

An image analysis method called two-dimensional wavelet packet analysis (2D WPA) is introduced to quantify branching complexity of neurons. Both binary silhouettes and contour profiles of neurons were analyzed to determine accuracy and precision of the fractal dimension in cell classification tasks. Two-dimensional WPA plotted the slope of decay for a sorted list of discrete wavelet packet coefficients belonging to the adapted wavelet best basis to obtain the fractal dimension for test images and binary representations of neurons. Two-dimensional WPA was compared with box counting and mass-radius algorithms. The results for 2D WPA showed that it could differentiate between neural branching complexity in cells of different type in agreement with accepted methods. The importance of the 2D WPA method is that it performs multiresolution decomposition in the horizontal, vertical, and diagonal orientations.     

Diminished behavioral and neural sensitivity to sound modulation is associated with moderate developmental hearing loss

The acoustic rearing environment can alter central auditory coding properties, yet altered neural coding is seldom linked with specific deficits to adult perceptual skills. To test whether developmental hearing loss resulted in comparable changes to perception and sensory coding, we examined behavioral and neural detection thresholds for sinusoidally amplitude modulated (sAM) stimuli. Behavioral sAM detection thresholds for slow (5 Hz) modulations were significantly worse for animals reared with bilateral conductive hearing loss (CHL), as compared to controls. This difference could not be attributed to hearing thresholds, proficiency at the task, or proxies for attention. Detection thresholds across the groups did not differ for fast (100 Hz) modulations, a result paralleling that seen in humans. Neural responses to sAM stimuli were recorded in single auditory cortex neurons from separate groups of awake animals. Neurometric analyses indicated equivalent thresholds for the most sensitive neurons, but a significantly poorer detection threshold for slow modulations across the population of CHL neurons as compared to controls. The magnitude of the neural deficit matched that of the behavioral differences, suggesting that a reduction of sensory information can account for limitations to perceptual skills.