White-noise analysis of nonlinear behavior in an insect sensory neuron: Kernel and cascade approaches

A functional expansion was used to model the relationship between a Gaussian white noise stimulus current and the resulting action potential output in the single sensory neuron of the cockroach femoral tactile spine. A new precise procedure was used to measure the kernels of the functional expansion. Very similar kernel estimates were obtained from separate sections of the data produced by the same neuron with the same input noise power level, although some small time-varying effects were detectable in moving through the data. Similar kernel estimates were measured using different input noise power levels for a given cell, or when comparing different cells under similar stimulus conditions. The kernels were used to identify a model for sensory encoding in the neuron, comprising a cascade of dynamic linear, static nonlinear, and dynamic linear elements. Only a single slice of the estimated experimental second-order kernel was used in identifying the cascade model. However, the complete second-order kernel of the cascade model closely resembled the estimated experimental kernel. Moreover, the model could closely predict the experimental action potential train obtained with novel white noise inputs.     

A nonlinear cascade model for action potential encoding in an insect sensory neuron.

Action potential encoding in the cockroach tactile spine neuron can be represented as a single-input single-output nonlinear dynamic process. We have used a new functional expansion method to characterize the nonlinear behavior of the neural encoder. This method, which yields similar kernels to the Wiener method, is more accurate than the latter and is efficient enough to obtain reasonable kernels in less than 15 min using a personal computer. The input stimulus was band-limited white Gaussian noise and the output consisted of the resulting train of action potentials, which were unitized to give binary values. The kernels and the system input-output signals were used to identify a model for encoding comprising a cascade of dynamic linear, static nonlinear, and dynamic linear components. The two dynamic linear components had repeatable and distinctive forms with the first being low-pass and the second being high-pass. The static nonlinearity was fitted with a fifth-order polynomial function over several input amplitude ranges and had the form of a half-wave rectifier. The complete model gave a good approximation to the output of the neuron when both were subjected to the same novel white noise input signal.     

From spiking neuron models to linear-nonlinear models

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.     

Membrane potential changes of skeletomotor neurons in response to random stretches of the triceps surae muscles in decerebrate cats

 The properties of membrane potential changes of skeletomotor neurons (S, FR, and FF) innervating triceps surae muscles during pseudorandom stretching of these muscles were studied in decerebrate cats. Peak amplitudes of pseudorandom muscle stretches ranged from 119 μm to 4.15 mm peak-to-peak. Sequences of ten identical stretching periods were applied for averaging. Shapes of membrane potential changes and probability density distribution of amplitudes of the input and output signals and power spectra suggest that the skeletomotor neuron membrane has nonlinear properties. First- and second-order Wiener kernels were determined by applying the cross-correlation (Lee-Schetzen) method. The results suggest that the transfer function between muscle stretches and subthreshold membrane potentials is a Wiener-type cascade. This cascade is consistent with a linear, second-order, underdamped transfer function followed by a simple quadratic nonlinearity [linear (L) system followed by nonlinear (N) system, or LN cascade]. Including the nonlinear component calculated from the second-order Wiener kernel improved the model significantly over its linear counterpart, especially in S-type motoneurons. Qualitatively similar results were obtained with all types of motoneurons studied. Received: 1 April 1993/Accepted in revised form: 24 March 1994     

Neural mechanism of dynamic responses of neurons in inferior temporal cortex in face perception

Understanding the neural mechanisms of object and face recognition is one of the fundamental challenges of visual neuroscience. The neurons in inferior temporal (IT) cortex have been reported to exhibit dynamic responses to face stimuli. However, little is known about how the dynamic properties of IT neurons emerge in the face information processing. To address this issue, we made a model of IT cortex, which performs face perception via an interaction between different IT networks. The model was based on the face information processed by three resolution maps in early visual areas. The network model of IT cortex consists of four kinds of networks, in which the information about a whole face is combined with the information about its face parts and their arrangements. We show here that the learning of face stimuli makes the functional connections between these IT networks, causing a high spike correlation of IT neuron pairs. A dynamic property of subthreshold membrane potential of IT neuron, produced by Hodgkin–Huxley model, enables the coordination of temporal information without changing the firing rate, providing the basis of the mechanism underlying face perception. We show also that the hierarchical processing of face information allows IT cortex to perform a “coarse-to-fine” processing of face information. The results presented here seem to be compatible with experimental data about dynamic properties of IT neurons.     

Synaptic inputs to the omega neuron of the cricket Teleogryllus oceanicus: differences in EPSP waveforms evoke by low and high sound frequencies

EPSP waveforms were recorded from the omega neuron of Teleogryllus oceanicus for 5 kHz and ultrasonic sound stimuli. EPSPs in response to 5 kHz stimuli were smooth in shape and increased in amplitude with increasing stimulus intensity, while responses to ultrasound consisted of series' of large, discrete, unitary EPSPs, which increased in frequency with stimulus intensity.The hypothesis that a few, synaptically potent receptors might account for ultrasound sensitivity was tested by examining temporal coupling between ultrasound responses of the omega neuron and of another ultrasound-sensitive neuron, INT-1. INT-1 spikes were temporally correlated both to omega neuron spikes and to the large EPSPs recorded in the omega neuron. Coupling was not apparent for 5 kHz stimuli.The omega neuron encodes the intensity of 5 kHz and ultrasonic stimuli with similar resolution. Response latencies are markedly shorter for ultrasonic stimuli.These findings suggest that 5 kHz information is carried by a relatively large number of receptors, each of which has only a small effect on central neurons, while ultrasound information is carried by a few, synaptically potent, receptors.     

Nonlinear effects of intrinsic dynamics on temporal encoding in a model of avian auditory cortex

Neurons exhibit diverse intrinsic dynamics, which govern how they integrate synaptic inputs to produce spikes. Intrinsic dynamics are often plastic during development and learning, but the effects of these changes on stimulus encoding properties are not well known. To examine this relationship, we simulated auditory responses to zebra finch song using a linear-dynamical cascade model, which combines a linear spectrotemporal receptive field with a dynamical, conductance-based neuron model, then used generalized linear models to estimate encoding properties from the resulting spike trains. We focused on the effects of a low-threshold potassium current (K_LT) that is present in a subset of cells in the zebra finch caudal mesopallium and is affected by early auditory experience. We found that K_LT affects both spike adaptation and the temporal filtering properties of the receptive field. The direction of the effects depended on the temporal modulation tuning of the linear (input) stage of the cascade model, indicating a strongly nonlinear relationship. These results suggest that small changes in intrinsic dynamics in tandem with differences in synaptic connectivity can have dramatic effects on the tuning of auditory neurons.     

Intracellular nonlinear frequency response measurements in the cockroach tactile spine neuron

The threshold of the cockroach tactile neuron increases strongly with depolarization by a process involving at least two time constants. This effect is probably responsible for the rapid and complete adaptation of the neuron's response to step inputs. A technique for intracellular recording and stimulation of the neuron has recently been established and this allows direct observation of the dynamic response of the neuronal encoder. A white noise stimulus was used to modulate the membrane potential of the neuron. The first-order frequency response function between membrane potential and action potential discharge could be explained by a variable threshold model with two time constants. Second-order frequency response functions could be accounted for by a Wiener cascade model. The dynamic nonlinear behavior of the encoder can therefore be explained by a unidirectional threshold which increases linearly and dynamically with membrane potential.     

Stimulus and network dynamics collide in a ratiometric model of the antennal lobe macroglomerular complex

Time is considered to be an important encoding dimension in olfaction, as neural populations generate odour-specific spatiotemporal responses to constant stimuli. However, during pheromone mediated anemotactic search insects must discriminate specific ratios of blend components from rapidly time varying input. The dynamics intrinsic to olfactory processing and those of naturalistic stimuli can therefore potentially collide, thereby confounding ratiometric information. In this paper we use a computational model of the macroglomerular complex of the insect antennal lobe to study the impact on ratiometric information of this potential collision between network and stimulus dynamics. We show that the model exhibits two different dynamical regimes depending upon the connectivity pattern between inhibitory interneurons (that we refer to as fixed point attractor and limit cycle attractor), which both generate ratio-specific trajectories in the projection neuron output population that are reminiscent of temporal patterning and periodic hyperpolarisation observed in olfactory antennal lobe neurons. We compare the performance of the two corresponding population codes for reporting ratiometric blend information to higher centres of the insect brain. Our key finding is that whilst the dynamically rich limit cycle attractor spatiotemporal code is faster and more efficient in transmitting blend information under certain conditions it is also more prone to interference between network and stimulus dynamics, thus degrading ratiometric information under naturalistic input conditions. Our results suggest that rich intrinsically generated network dynamics can provide a powerful means of encoding multidimensional stimuli with high accuracy and efficiency, but only when isolated from stimulus dynamics. This interference between temporal dynamics of the stimulus and temporal patterns of neural activity constitutes a real challenge that must be successfully solved by the nervous system when faced with naturalistic input.     

Conditioned reflex: detector and command neuron

Conditioned reflex is characterized by plasticity resulting in a bilateral selective input-output linking. In simple nervous systems, input stimuli are represented by selective detectors connected with command neurons through plastic synapses strengthened during associative learning and weakened during extinction. The process of associative learning is due to temporal coincidence of excitation in both detector and command neurons. Short-term memory within a plastic synapses is mediated by phosphorilation of postsynaptic receptor molecules not requiring protein synthesis. Long-term synaptic memory parallels expression of immediate early genes that mediates structural gene expression and protein synthesis. A simple detector-command neuron association becomes more complex in the course of evolution. Input mechanism is supplemented with predetector interneurons preceding detectors. Detector selectively tuned to specific input stimulus is converging on a command neuron constitute selectivity mechanism for conditioned reflexes to complex stimuli. The complication also concerns the output mechanisms. Command neurons become more specialized, and an additional link of premotor interneurons is incorporated between command neurons and motor neurons. Via synapses, the command neurons can produce excitation in a particular set of premotor neurons controlling a specific set of motor neurons responsible for behavioral act configuration. Specialization of command neurons in combination with premotor neuron structures increases the variability of outputs. Conditioned reflexes with more complex inputs and more flexible outputs determine the diversity of acquired behaviors.     

Interaction of NMDA Receptor and Pacemaking Mechanisms in the Midbrain Dopaminergic Neuron

Dopamine neurotransmission has been found to play a role in addictive behavior and is altered in psychiatric disorders. Dopaminergic (DA) neurons display two functionally distinct modes of electrophysiological activity: low- and high-frequency firing. A puzzling feature of the DA neuron is the following combination of its responses: N-methyl-D-aspartate receptor (NMDAR) activation evokes high-frequency firing, whereas other tonic excitatory stimuli (-amino-3-hydroxyl-5-methyl-4-isoxazolepropionate receptor (AMPAR) activation or applied depolarization) block firing instead. We suggest a new computational model that reproduces this combination of responses and explains recent experimental data. Namely, somatic NMDAR stimulation evokes high-frequency firing and is more effective than distal dendritic stimulation. We further reduce the model to a single compartment and analyze the mechanism of the distinct high-frequency response to NMDAR activation vs. other stimuli. Standard nullcline analysis shows that the mechanism is based on a decrease in the amplitude of calcium oscillations. The analysis confirms that the nonlinear voltage dependence provided by the magnesium block of the NMDAR determine its capacity to elevate the firing frequency. We further predict that the moderate slope of the voltage dependence plays the central role in the frequency elevation. Additionally, we suggest a repolarizing current that sustains calcium-independent firing or firing in the absence of calcium-dependent repolarizing currents. We predict that the ether–a-go-go current (ERG), which has been observed in the DA neuron, is the best fit for this critical role. We show that a calcium-dependent and a calcium-independent oscillatory mechanisms form a structure of interlocked negative feedback loops in the DA neuron. The structure connects research of DA neuron firing with circadian biology and determines common minimal models for investigation of robustness of oscillations, which is critical for normal function of both systems.     

A Neuron Model with Spatially Distributed Synaptic Input

I have assembled a neuron model simulating contiguous patches of nerve cell membrane. With this model I have examined the functional significance of different spatial and temporal distributions of synaptic inputs. The model consists of two terminal electronic analogue circuits with inputs controlled by a LINC computer. One terminal represents the inside of a membrane patch, the other represents the outside. Two circuit designs are used: one simulates spike-generating regions of the neuron, the other simulates subthreshold activity in inexcitable regions. To simulate a neuron, patches are assembled in various spatial arrangements by suitable connection to the “intracellular” nodes. Thus the relation of neuron geometry to aspects of spatiotemporal summation of synaptic inputs can be investigated readily. Performance of the model is assessed by comparison with results from microelectrode studies in the cochlear nucleus of the cat. In particular, the peristimulus time (PST) histogram and averaged membrane potential are used for quantitative comparison. The model suggests that the geometry of the neuron's receptive surface can account for a wide variety of physiologically observed behavior, particularly in response to dynamic stimuli.     

动态神经元网络模型的复杂性问题

在动态神经元网络模型中,当神经元总数仅为３时就观察到了非周期振荡。运用Ｌｅｍｐｅｌ和Ｚｉｖ提出的复杂性度量对这种现象进行了分析,结果表明对于其中一个神经元所发出的脉冲序列来说,至少直到１０００个脉冲为止还不能发现任何的周期性,并且其复杂性可以和由ｌｏｇｉｓｔｉｃ映射所产生的时间序列当其参数落在混沌区中时所具有的复杂性相比拟．这些结果也表明这种方法是所观察的时间范围内区分长周期振荡和非周期活动的好方法。结果还提示神经生理实验记录中所谓的噪声,其中有些可能是来源于生物神经元本身的非线性性质。     

Predicting the synaptic information efficacy in cortical layer 5 pyramidal neurons using a minimal integrate-and-fire model

Synaptic information efficacy (SIE) is a statistical measure to quantify the efficacy of a synapse. It measures how much information is gained, on the average, about the output spike train of a postsynaptic neuron if the input spike train is known. It is a particularly appropriate measure for assessing the input–output relationship of neurons receiving dynamic stimuli. Here, we compare the SIE of simulated synaptic inputs measured experimentally in layer 5 cortical pyramidal neurons in vitro with the SIE computed from a minimal model constructed to fit the recorded data. We show that even with a simple model that is far from perfect in predicting the precise timing of the output spikes of the real neuron, the SIE can still be accurately predicted. This arises from the ability of the model to predict output spikes influenced by the input more accurately than those driven by the background current. This indicates that in this context, some spikes may be more important than others. Lastly we demonstrate another aspect where using mutual information could be beneficial in evaluating the quality of a model, by measuring the mutual information between the model’s output and the neuron’s output. The SIE, thus, could be a useful tool for assessing the quality of models of single neurons in preserving input–output relationship, a property that becomes crucial when we start connecting these reduced models to construct complex realistic neuronal networks.     

Kinetic models of odor transduction implemented as artificial neural networks

We present a formal model of olfactory transduction corresponding to the biochemical reaction cascade found in chemosensory neurons. It assumes that odorants bind to receptor proteins which, in turn, activate transducer mechanisms corresponding to second messenger-mediated processes. The model is reformulated as a mathematically equivalent artificial neural network (ANN). To enable comparison of the computational power of our model, previously suggested models of chemosensory transduction are also presented in ANN versions. In ANNs, certain biological parameters, such as rate constants and affinities, are transformed into weights that can be fitted by training with a given experimental data set. After training, these weights do not necessarily equal the real biological parameters, but represent a set of values that is sufficient to simulate an experimental set of data. We used ANNs to simulate data recorded from bee subplacodes and compare the capacity of our model with ANN versions of other models. Receptor neurons of the nonpheromonal, general odor-processing subsystem of the honeybee are broadly tuned, have overlapping response spectra, and show highly nonlinear concentration dependencies and mixture interactions, i.e., synergistic and inhibitory effects. Our full model alone has the necessary complexity to simulate these complex response characteristics. To account for the complex response characteristics of honeybee receptor neurons, we suggest that several different receptor protein types and at least two second messenger systems are necessary that may interact at various levels of the transduction cascade and may eventually have opposing effects on receptor neuron excitability.     

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.     

A model cortical circuit for the storage of temporal sequences

Despite the fact that temporal information processing is of particular significance in biological memory systems, not much has yet been explored about how these systems manage to store temporal information involved in sequences of stimuli. A neural network model capable of learning and recalling temporal sequences is proposed, based on a neural mechanism in which the sequences are expanded into a series of periodic rectangular oscillations. Thus, the mathematical framework underlying the model, to some extent, is concerned with the Walsh function series. The oscillatory activities generated by the interplay between excitatory and inhibitory neuron pools are transmitted to another neuron pool whose role in learning and retrieval is to modify the rhythms and phases of the rectangular oscillations. Thus, a basic functional neural circuit involves three different neuron pools. The modifiability of rhythms and phases is incorporated into the model with the aim of improving the quality of the retrieval. Numerical simulations were conducted to show the characteristic features of the learning as well as the performance of the model in memory recall.     

Decoding Input Signals in Time Domain—A Model Approach

From an observation of efferent interspike intervals of a neuron, we consider how to decode the input temporal information. It is found that the integrate-and-fire model is blind in the temporal domain due to the fact that its efferent firing rate is independent of the input temporal frequency. The conclusion is then confirmed for the integrate-and-fire model with correlated inputs, with reversal potentials, with a nonlinear leakage and with a subthreshold oscillation. For the Hodgkin-Huxley model, however, in terms of efferent firing rates alone, it is possible to read out the input temporal information.