How Entorhinal Grid Cells May Learn Multiple Spatial Scales from a Dorsoventral Gradient of Cell Response Rates in a Self-organizing Map

Place cells in the hippocampus of higher mammals are critical for spatial navigation. Recent modeling clarifies how this may be achieved by how grid cells in the medial entorhinal cortex (MEC) input to place cells. Grid cells exhibit hexagonal grid firing patterns across space in multiple spatial scales along the MEC dorsoventral axis. Signals from grid cells of multiple scales combine adaptively to activate place cells that represent much larger spaces than grid cells. But how do grid cells learn to fire at multiple positions that form a hexagonal grid, and with spatial scales that increase along the dorsoventral axis? In vitro recordings of medial entorhinal layer II stellate cells have revealed subthreshold membrane potential oscillations (MPOs) whose temporal periods, and time constants of excitatory postsynaptic potentials (EPSPs), both increase along this axis. Slower (faster) subthreshold MPOs and slower (faster) EPSPs correlate with larger (smaller) grid spacings and field widths. A self-organizing map neural model explains how the anatomical gradient of grid spatial scales can be learned by cells that respond more slowly along the gradient to their inputs from stripe cells of multiple scales, which perform linear velocity path integration. The model cells also exhibit MPO frequencies that covary with their response rates. The gradient in intrinsic rhythmicity is thus not compelling evidence for oscillatory interference as a mechanism of grid cell firing. A response rate gradient combined with input stripe cells that have normalized receptive fields can reproduce all known spatial and temporal properties of grid cells along the MEC dorsoventral axis. This spatial gradient mechanism is homologous to a gradient mechanism for temporal learning in the lateral entorhinal cortex and its hippocampal projections. Spatial and temporal representations may hereby arise from homologous mechanisms, thereby embodying a mechanistic “neural relativity” that may clarify how episodic memories are learned.     

System analysis of the goldfish olfactory bulb: Spatio-temporal transfer properties of the mitral cell granule cell complex

In this paper the goldfish olfactory bulb is described from a systems theoretical point of view. A chain of nine interacting circuits, each one mitral cell and one granule cell, is modelled. Glomerular synapses are assumed to have variable strengths. The analysis of the model system leads to the following conclusions:

1. The temporal input pattern of a mitral cell—granule cell circuit is either maintained by the circuit or inverted (lateral inhibition effect). This property together with available receptor data allows the theoretical explanation of experimentally recorded mitral cell patterns.
2. The sensitivity of a mitral cell—granule cell circuit is a function of the input signal's frequency. This provides an explanation for mitral cell cluster activity patterns measured in experiments.
3. Given a spatial input pattern to adjacent mitral cell—granule cell circuits, the output pattern depends largely upon the ratio between the feedback parameter p and the similarity β of the inputs to adjacent circuits. For appropriate p and β a local order between the responses of single neighbouring circuits is established. This local order can lead to a globally ordered mapping of odours onto mitral cell activities, thus providing a coding concept for the bulb. Some consequences of this concept coincide well with the spatial activity patterns found in 2-DOG-studies.
4. Glomerular synapses endowed with plasticity could account for long term effects such as degeneration and sensitivity changes with respect to certain odours.

     

Dynamics of learning in cultured neuronal networks with antagonists of glutamate receptors

Cognitive dysfunction may result from abnormality of ionotropic glutamate receptors. Although various forms of synaptic plasticity in learning that rely on altering of glutamate receptors have been considered, the evidence is insufficient from an informatics view. Dynamics could reflect neuroinformatics encoding, including temporal pattern encoding, spatial pattern encoding, and energy distribution. Discovering informatics encoding is fundamental and crucial to understanding the working principle of the neural system. In this article, we analyzed the dynamic characteristics of response activities during learning training in cultured hippocampal networks under normal and abnormal conditions of ionotropic glutamate receptors, respectively. The rate, which is one of the temporal configurations, was decreased markedly by inhibition of α-amino-3-hydroxy-5-methylisoxazole-4-proprionic acid (AMPA) receptors. Moreover, the energy distribution in different characteristic frequencies was changed markedly by inhibition of AMPA receptors. Spatial configurations, including regularization, correlation, and synchrony, were changed significantly by inhibition of N-methyl-d-aspartate receptors. These results suggest that temporal pattern encoding and energy distribution of response activities in cultured hippocampal neuronal networks during learning training are modulated by AMPA receptors, whereas spatial pattern encoding of response activities is modulated by N-methyl-d-aspartate receptors.     

The spatiotemporal learning rule and its efficiency in separating spatiotemporal patterns

The hippocampus plays an important role in the course of establishing long-term memory, i.e., to make short-term memory of spatially and temporally associated input information. In 1996 (Tsukada et al. 1996), the spatiotemporal learning rule was proposed based on differences observed in hippocampal long-term potentiation (LTP) induced by various spatiotemporal pattern stimuli. One essential point of this learning rule is that the change of synaptic weight depends on both spatial coincidence and the temporal summation of input pulses. We applied this rule to a single-layered neural network and compared its ability to separate spatiotemporal patterns with that of other rules, including the Hebbian learning rule and its extended rules. The simulated results showed that the spatiotemporal learning rule had the highest efficiency in discriminating spatiotemporal pattern sequences, while the Hebbian learning rule (including its extended rules) was sensitive to differences in spatial patterns.     

Synaptic depression increases the selectivity of a neuron to its preferred pattern and binarizes the neural code

The preferred pattern of a neuron is defined here by the set of features detected by its excitatory inputs. It is shown that the Leaky integrate-and-fire (LIF) model of a neuron has a poor selectivity to its preferred pattern. Its response is determined by the total current injected by input spike trains. Thus, a few inputs with a high activity (an incomplete pattern) can elicit the same response as many inputs (a complete pattern) with a weak activity. A theoretical model of depressing synapse with linear recovery is proposed which eliminates this problem. Using this model, the time-averaged current injected in the soma by a spike train becomes independent on its frequency. The neural code thus becomes binary, and the response strength of the target neuron depends only on the number of active inputs. Simulations show that a biological model of strong synaptic depression has effects similar to those of the ideal linear model. The best selectivity is obtained with long somatic decay time constants (>50 ms) and with depression recovery time constants larger or equal to the somatic decay time constant. Thus, by eliminating information carried in the input firing rate, a neuron can improve its pattern recognition performance.     

Adaptive Spike Threshold Enables Robust and Temporally Precise Neuronal Encoding

Neural processing rests on the intracellular transformation of information as synaptic inputs are translated into action potentials. This transformation is governed by the spike threshold, which depends on the history of the membrane potential on many temporal scales. While the adaptation of the threshold after spiking activity has been addressed before both theoretically and experimentally, it has only recently been demonstrated that the subthreshold membrane state also influences the effective spike threshold. The consequences for neural computation are not well understood yet. We address this question here using neural simulations and whole cell intracellular recordings in combination with information theoretic analysis. We show that an adaptive spike threshold leads to better stimulus discrimination for tight input correlations than would be achieved otherwise, independent from whether the stimulus is encoded in the rate or pattern of action potentials. The time scales of input selectivity are jointly governed by membrane and threshold dynamics. Encoding information using adaptive thresholds further ensures robust information transmission across cortical states i.e. decoding from different states is less state dependent in the adaptive threshold case, if the decoding is performed in reference to the timing of the population response. Results from in vitro neural recordings were consistent with simulations from adaptive threshold neurons. In summary, the adaptive spike threshold reduces information loss during intracellular information transfer, improves stimulus discriminability and ensures robust decoding across membrane states in a regime of highly correlated inputs, similar to those seen in sensory nuclei during the encoding of sensory information.     

Adaptation of transient responses of a movement-sensitive neuron in the visual system of the blowfly Calliphora erythrocephala

We studied temporal response properties of the H1 neuron by extracellular recording. This neuron is a wide-field movement-sensitive element in the visual system of the blowfly (Calliphora erythrocephala). If the neuron is stimulated with a stepwise pattern displacement in its preferred direction, it responds with a burst of action potentials. By repeating the stimulus step one obtains the average of the step response: a 20ms latency time followed by a sharp increase in average firing rate and a slower decay to the resting activity. We report that the characteristic decay time of the step response depends on the stimulus history. If the stimulus moved prior to the step, the higher the pattern velocity, the faster was the decay of the step response to the resting level. In quantitative terms, for velocities in the range 0.4–100°/s, the decay time-constant varies from 300–10ms and is smaller for higher velocities. The time-constant is only weakly affected by other stimulus parameters such as modulation depth or spatial wavelength, and is set independently in different areas of the visual field where it is tuned to the local velocity. We discuss a possible advantage of this form of adaptation for the processing of visual signals: The performance of the nolinear operations that extract information from the visual input can be optimized by prefiltering signals in the individual visual columns with a time-constant that decreases with stimulus velocity. It will be shown that both the test step response and the response to continuous movement can be described reasonably well by a correlation model with input filters that adapt their time-constants.     

Spatial and temporal coding in single neurons

Convergence between cells which differ in both spatial and temporal properties create higher order neurons with response properties that are distinctly different from those of the input neurons. The spatial properties of target neurons are not necessarily cosinetuned. In addition, unlike the independence between spatial and temporal properties in cosine-tuned afferent neurons, higher-order target cells generally exhibit a dependence of temporal dynamics on spatial properties. The response properties of target neurons receiving spatio-temporal convergence (STC) from tonic and phasic-tonic or phasic afferents is investigated here by considering a general case where the dynamic input is represented by a fractional, leaky, derivative transfer function. It is shown that, at frequencies below the corner frequency of the dynamic input, the temporal properties of target neurons can be described by leaky differentiators having time constants that are a function of spatial direction. Thus, STC target neurons exhibit tonic temporal response properties during stimulation along some spatial directions (having small time constants) and phasic properties along other directions (having large time constants). Specifically, target neurons encode the complete derivative of the stimulus along certain spatial directions. Thus, STC acts as a directionally specific high-pass filter and produces complete derivatives from fractional, leaky derivative afferent signals. In addition, spatio-temporal transformations can generate novel temporal dynamics in the central nervous system. These observations suggest that spatio-temporal computations might constitute an alternative to parallel, independent spatial and temporal channels.     

Probabilistic secretion of quanta in the central nervous system: granule cell synaptic control of pattern separation and activity regulation.

The implications of probabilistic secretion of quanta for the functioning of neural networks in the central nervous system have been explored. A model of stochastic secretion at synapses in simple networks, consisting of large numbers of granule cells and a relatively small number of inhibitory interneurons, has been analysed. Such networks occur in the input to the cerebellum Purkinje cells as well as to hippocampal CA3 pyramidal cells and to pyramidal cells in the visual cortex. In this model the input axons terminate on granule cells as well as on an inhibitory interneuron that projects to the granule cells. Stochastic secretion at these synapses involves both temporal variability in secretion at single synapses in the network as well as spatial variability in the secretion at different synapses. The role of this stochastic variability in controlling the size of the granule cell output to a level independent of the size of the input and in separating overlapping inputs has been determined analytically as well as by simulation. The regulation of granule-cell output activity to a reasonably constant value for different size inputs does not occur in the absence of an inhibitory interneuron when both spatial and temporal stochastic variability occurs at the remaining synapses; it is still very poor in the presence of such an interneuron but in the absence of stochastic variability. However, quite good regulation is achieved when the inhibitory interneuron is present with spatial and temporal stochastic variability of secretion at synapses in the network. Excellent regulation is achieved if, in addition, allowance is made for the nonlinear behaviour of the input-output characteristics of inhibitory interneurons. The capacity of granule-cell networks to separate overlapping patterns of activity on their inputs is adequate, with spatial variability in the secretion at synapses, but is improved if there is also temporal variability in the stochastic secretion at individual synapses, although this is at the expense of reliability in the network. Other factors which improve pattern separation are control of the output to very low activity levels, and a restriction on the cumulative size of the excitatory input terminals of each granule cell. Application of the theory to the input neural networks of the cerebellum and the hippocampus shows the role of stochastic variability in quantal transmission in determining the capacity of these networks for pattern separation and activity regulation.     

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.     

Spatial information enhanced by non-spatial information in hippocampal granule cells

The hippocampus organizes sequential memory composed of non-spatial information (such as objects and odors) and spatial information (places). The dentate gyrus (DG) in the hippocampus receives two types of information from the lateral and medial entorhinal cortices. Non-spatial and spatial information is delivered respectively to distal and medial dendrites (MDs) of granule cells (GCs) within the molecular layer in the DG. To investigate the role of the association of those two inputs, we measured the response characteristics of distal and MDs of a GC in a rat hippocampal slice and developed a multi-compartment GC model with dynamic synapses; this model reproduces the response characteristics of the dendrites. Upon applying random inputs or input sequences generated by a Markov process to the computational model, it was found that a high-frequency random pulse input to distal dendrites (DDs) and, separately, regular burst inputs to MDs were effective for inducing GC activation. Furthermore, when the random and theta burst inputs were simultaneously applied to the respective dendrites, the pattern discrimination for theta burst input to MDs that caused slight GC activation was enhanced in the presence of random input to DDs. These results suggest that the temporal pattern discrimination of spatial information is originally involved in a synaptic characteristic in GCs and is enhanced by non-spatial information input to DDs. Consequently, the co-activation of two separate inputs may play a crucial role in the information processing on dendrites of GCs by usefully combing each temporal sequence.     

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

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

Mathematical Study of the Role of Delta/Notch Lateral Inhibition during Primary Branching of Drosophila Trachea Development

A wide range of cellular developmental processes employ intercellular signaling via the Delta/Notch lateral inhibitory pathway to achieve stable spatial patterning. Recent genetic experiments have shown the importance of Delta/Notch lateral inhibition for regulating the number of tip cells in the tracheal primary branching of Drosophila. To examine the role of Delta/Notch regulation in the tip-cell selection, we analyzed a mathematical model of a simple lateral inhibitory system having input signals. Mathematical and numerical analyses revealed that the lateral inhibition did not amplify the signal difference between neighboring cells over the parameter ranges in which the spatial pattern of tip selection was realized. We also show that the number of tip cells becomes less affected by a fluctuation of the input gradient signal as the lateral inhibition becomes stronger. In addition, we demonstrate that the lateral inhibitory regulation enhances the robustness of the tip-cell selection compared with a system regulated by self-inhibition, an alternative means of inhibitory regulation. These results suggest that the lateral inhibition promotes the robustness of tip-cell selection in the tracheal development of Drosophila.     

A method of nonlinear analysis in the frequency domain.

A method is developed for the analysis of nonlinear biological systems based on an input temporal signal that consists of a sum of a large number of sinusoids. Nonlinear properties of the system are manifest by responses at harmonics and intermodulation frequencies of the input frequencies. The frequency kernels derived from these nonlinear responses are similar to the Fourier transforms of the Wiener kernels. Guidelines for the choice of useful input frequency sets, and examples satisfying these guidelines, are given. A practical algorithm for varying the relative phases of the input sinusoids to separate high-order interactions is presented. The utility of this technique is demonstrated with data obtained from a cat retinal ganglion cell of the Y type. For a high spatial frequency grafting, the entire response is contained in the even-order nonlinear components. Even at low contrast, fourth-order components are detectable. This suggests the presence of an essential nonlinearity in the functional pathway of the Y cell, with its singularity at zero contrast.     

A template matching model for pattern recognition: Self-organization of templates and template matching by a disinhibitory neural network

A template matching model for pattern recognition is proposed. By following a previouslyproposed algorithm for synaptic modification (Hirai, 1980), the template of a stimulus pattern is selforganized as a spatial distribution pattern of matured synapses on the cells receiving modifiable synapses. Template matching is performed by the disinhibitory neural network cascaded beyond the neural layer composed of the cells receiving the modifiable synapses. The performance of the model has been simulated on a digital computer. After repetitive presentations of a stimulus pattern, a cell receiving the modifiable synapses comes to have the template of that pattern. And the cell in the latter layer of the disinhibitory bitory neural network that receives the disinhibitory input from that cell becomes electively sensitive to that pattern. Learning patterns are not restricted by previously learned ones. They can be subset or superset patterns of the ones previously learned. If an unknown pattern is presented to the model, no cell beyond the disinhibitory neural network will respond. However, if previously learned patterns are embedded in that pattern, the cells which have the templates of those patterns respond and are assumed to transmit the information to higher center. The computer simulation also shows that the model can organize a clean template under a noisy environment.     

Contrast transfer function of the visual system]

Visually evoked potentials were used to determine the spatial contrast response function of the visual system and the visual acuity of the pigeon. The spatial contrast response describes the relationship between the contrast in a pattern of vertical stripes, whose luminance is a function of position, and the amplitude of the visually evoked response at various spatial frequencies for a given temporal frequency (pattern reversal frequency); it indicates how particular spatial frequencies are attenuated in the visual system. The visually evoked responses were recorded using monopolar stainless steel electrodes inserted into the stratum griseum superficiale of the optic tectum; the depth of penetration was determined on the basis of a stereotactic atlas. The stimulus patterns were generated on a video monitor placed 75 cm in front of the animal's eye perpendicular to the optic axis. The spatial contrast response function measured at 10% contrast and 0.5 Hz reversal frequency shows a peak at a spatial frequency of 0.5 c/deg, corresponding to 1 degree of visual angle, and decreases progressively at higher spatial frequencies. The high-frequency limit (cut-off frequency) for resolution of sinusoidal gratings, estimated from the contrast response function, is 15.5 c/deg, corresponding to a visual acuity of 1.9 min of arc.     

Transient Responses to Rapid Changes in Mean and Variance in Spiking Models

The mean input and variance of the total synaptic input to a neuron can vary independently, suggesting two distinct information channels. Here we examine the impact of rapidly varying signals, delivered via these two information conduits, on the temporal dynamics of neuronal firing rate responses. We examine the responses of model neurons to step functions in either the mean or the variance of the input current. Our results show that the temporal dynamics governing response onset depends on the choice of model. Specifically, the existence of a hard threshold introduces an instantaneous component into the response onset of a leaky-integrate-and-fire model that is not present in other models studied here. Other response features, for example a decaying oscillatory approach to a new steady-state firing rate, appear to be more universal among neuronal models. The decay time constant of this approach is a power-law function of noise magnitude over a wide range of input parameters. Understanding how specific model properties underlie these response features is important for understanding how neurons will respond to rapidly varying signals, as the temporal dynamics of the response onset and response decay to new steady-state determine what range of signal frequencies a population of neurons can respond to and faithfully encode.     

综述: 初级视皮层的亮度信息加工

亮度(luminance)是最基本的视觉信息.与其他视觉特征相比,由于视神经元对亮度刺激的反应较弱,并且许多神经元对均匀亮度无反应,对亮度信息编码的神经机制知之甚少.初级视皮层部分神经元对亮度的反应要慢于对比度反应,被认为是由边界对比度诱导的亮度知觉(brightness)的神经基础.我们的研究表明,初级视皮层许多神经元的亮度反应要快于对比度反应,并且这些神经元偏好低的空间频率、高的时间频率和高的运动速度,提示皮层下具有低空间频率和高运动速度通路的信息输入对产生初级视皮层神经元的亮度反应有贡献.已经知道初级视皮层神经元对空间频率反应的时间过程是从低空间频率到高空间频率,我们发现的早期亮度反应是对极低空间频率的反应,与这一时间过程是一致的,是这一从粗到细的视觉信息加工过程的第一步,揭示了处理最早的粗的视觉信息的神经基础.另外,初级视皮层含有偏好亮度下降和高运动速度的神经元,这群神经元的活动有助于在光照差的环境中检测高速运动的低亮度物体.     

Is song special?

Akutagawa and Konishi (2001)([this issue of Neuron]) describe the spatial and temporal pattern of SNAg (song system nuclear antigen) expression within a subset of song-associated forebrain nuclei of grass finches. The timing and estrogen inducibility of SNAg expression suggest that it may function in establishing neural connections key to vocal learning.