A biologically inspired hierarchical goal directed navigation model

We propose an extended version of our previous goal directed navigation model based on forward planning of trajectories in a network of head direction cells, persistent spiking cells, grid cells, and place cells. In our original work the animat incrementally creates a place cell map by random exploration of a novel environment. After the exploration phase, the animat decides on its next movement direction towards a goal by probing linear look-ahead trajectories in several candidate directions while stationary and picking the one activating place cells representing the goal location. In this work we present several improvements over our previous model. We improve the range of linear look-ahead probes significantly by imposing a hierarchical structure on the place cell map consistent with the experimental findings of differences in the firing field size and spacing of grid cells recorded at different positions along the dorsal to ventral axis of entorhinal cortex. The new model represents the environment at different scales by populations of simulated hippocampal place cells with different firing field sizes. Among other advantages this model allows simultaneous constant duration linear look-ahead probes at different scales while significantly extending each probe range. The extension of the linear look-ahead probe range while keeping its duration constant also limits the degrading effects of noise accumulation in the network. We show the extended model’s performance using an animat in a large open field environment.     

Binaural processing in the synthesis of auditory spatial receptive fields

The owls auditory system computes interaural time (ITD) and interaural level (ILD) differences to create a two-dimensional map of auditory space. Space-specific neurons are selective for combinations of ITD and ILD, which define, respectively, the horizontal and vertical dimensions of their receptive fields. ITD curves for postsynaptic potentials indicate that ICx neurons integrate the results of binaural cross correlation in different frequency bands. However, the difference between the main and side peaks is slight. ICx neurons further enhance this difference in the process of converting membrane potentials to impulse rates. Comparison of subthreshold postsynaptic potentials (PSPs) and spike output for the same neurons showed that receptive fields measured in PSPs were much larger than those measured in spikes in both ITD and ILD dimensions. A multiplication of separate postsynaptic potentials tuned to ITD and ILD can account for the combination sensitivity of these neurons to ITD–ILD pairs.     

Somatosensory-motor neuronal activity in the superior colliculus of the primate

The superior colliculus (SC) in primates plays an important role in orienting gaze and arms toward novel stimuli. Here we ask whether neurons in the intermediate and deep layers of the SC are also involved in the interaction with objects. In two trained monkeys we found a large number of SC units that were specifically activated when the monkeys contacted and pushed a target that had been reached with either hand. These neurons, however, were silent when the monkeys simply looked at or reached for the target but did not touch it. The activity related to interacting with objects was spatially tuned and increased with push strength. Neurons in the SC with this type of activity may be involved in a somatosensory-motor feedback loop that monitors the force of the active muscles together with the spatial position of the limb required for proper interaction with an object.     

A feedforward model for the formation of a grid field where spatial information is provided solely from place cells

Grid cells (GCs) in the medial entorhinal cortex (mEC) have the property of having their firing activity spatially tuned to a regular triangular lattice. Several theoretical models for grid field formation have been proposed, but most assume that place cells (PCs) are a product of the grid cell system. There is, however, an alternative possibility that is supported by various strands of experimental data. Here we present a novel model for the emergence of gridlike firing patterns that stands on two key hypotheses: (1) spatial information in GCs is provided from PC activity and (2) grid fields result from a combined synaptic plasticity mechanism involving inhibitory and excitatory neurons mediating the connections between PCs and GCs. Depending on the spatial location, each PC can contribute with excitatory or inhibitory inputs to GC activity. The nature and magnitude of the PC input is a function of the distance to the place field center, which is inferred from rate decoding. A biologically plausible learning rule drives the evolution of the connection strengths from PCs to a GC. In this model, PCs compete for GC activation, and the plasticity rule favors efficient packing of the space representation. This leads to gridlike firing patterns. In a new environment, GCs continuously recruit new PCs to cover the entire space. The model described here makes important predictions and can represent the feedforward connections from hippocampus CA1 to deeper mEC layers.     

Optimal path-finding through mental exploration based on neural energy field gradients

Rodent animal can accomplish self-locating and path-finding task by forming a cognitive map in the hippocampus representing the environment. In the classical model of the cognitive map, the system (artificial animal) needs large amounts of physical exploration to study spatial environment to solve path-finding problems, which costs too much time and energy. Although Hopfield’s mental exploration model makes up for the deficiency mentioned above, the path is still not efficient enough. Moreover, his model mainly focused on the artificial neural network, and clear physiological meanings has not been addressed. In this work, based on the concept of mental exploration, neural energy coding theory has been applied to the novel calculation model to solve the path-finding problem. Energy field is constructed on the basis of the firing power of place cell clusters, and the energy field gradient can be used in mental exploration to solve path-finding problems. The study shows that the new mental exploration model can efficiently find the optimal path, and present the learning process with biophysical meaning as well. We also analyzed the parameters of the model which affect the path efficiency. This new idea verifies the importance of place cell and synapse in spatial memory and proves that energy coding is effective to study cognitive activities. This may provide the theoretical basis for the neural dynamics mechanism of spatial memory.     

The development of spatial behaviour and the hippocampal neural representation of space

The role of the hippocampal formation in spatial cognition is thought to be supported by distinct classes of neurons whose firing is tuned to an organism''s position and orientation in space. In this article, we review recent research focused on how and when this neural representation of space emerges during development: each class of spatially tuned neurons appears at a different age, and matures at a different rate, but all the main spatial responses tested so far are present by three weeks of age in the rat. We also summarize the development of spatial behaviour in the rat, describing how active exploration of space emerges during the third week of life, the first evidence of learning in formal tests of hippocampus-dependent spatial cognition is observed in the fourth week, whereas fully adult-like spatial cognitive abilities require another few weeks to be achieved. We argue that the development of spatially tuned neurons needs to be considered within the context of the development of spatial behaviour in order to achieve an integrated understanding of the emergence of hippocampal function and spatial cognition.     

Synaptic integration by V1 neurons depends on location within the orientation map

Neurons in the primary visual cortex (V1) are organized into an orientation map consisting of orientation domains arranged radially around "pinwheel centers" at which the representations of all orientations converge. We have combined optical imaging of intrinsic signals with intracellular recordings to estimate the subthreshold inputs and spike outputs of neurons located near pinwheel centers or in orientation domains. We find that neurons near pinwheel centers have subthreshold responses to all stimulus orientations but spike responses to only a narrow range of orientations. Across the map, the selectivity of inputs covaries with the selectivity of orientations in the local cortical network, while the selectivity of spike outputs does not. Thus, the input-output transformation performed by V1 neurons is powerfully influenced by the local structure of the orientation map.     

Six types of multistability in a neuronal model based on slow calcium current

Background

Multistability of oscillatory and silent regimes is a ubiquitous phenomenon exhibited by excitable systems such as neurons and cardiac cells. Multistability can play functional roles in short-term memory and maintaining posture. It seems to pose an evolutionary advantage for neurons which are part of multifunctional Central Pattern Generators to possess multistability. The mechanisms supporting multistability of bursting regimes are not well understood or classified.

Methodology/Principal Findings

Our study is focused on determining the bio-physical mechanisms underlying different types of co-existence of the oscillatory and silent regimes observed in a neuronal model. We develop a low-dimensional model typifying the dynamics of a single leech heart interneuron. We carry out a bifurcation analysis of the model and show that it possesses six different types of multistability of dynamical regimes. These types are the co-existence of 1) bursting and silence, 2) tonic spiking and silence, 3) tonic spiking and subthreshold oscillations, 4) bursting and subthreshold oscillations, 5) bursting, subthreshold oscillations and silence, and 6) bursting and tonic spiking. These first five types of multistability occur due to the presence of a separating regime that is either a saddle periodic orbit or a saddle equilibrium. We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate.

Conclusions

We developed a neuronal model which exhibits a rich variety of different types of multistability. We described a novel mechanism supporting the bistability of bursting and silence. This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability.     

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.     

Spatial cognition and neuro-mimetic navigation: a model of hippocampal place cell activity

 A computational model of hippocampal activity during spatial cognition and navigation tasks is presented. The spatial representation in our model of the rat hippocampus is built on-line during exploration via two processing streams. An allothetic vision-based representation is built by unsupervised Hebbian learning extracting spatio-temporal properties of the environment from visual input. An idiothetic representation is learned based on internal movement-related information provided by path integration. On the level of the hippocampus, allothetic and idiothetic representations are integrated to yield a stable representation of the environment by a population of localized overlapping CA3-CA1 place fields. The hippocampal spatial representation is used as a basis for goal-oriented spatial behavior. We focus on the neural pathway connecting the hippocampus to the nucleus accumbens. Place cells drive a population of locomotor action neurons in the nucleus accumbens. Reward-based learning is applied to map place cell activity into action cell activity. The ensemble action cell activity provides navigational maps to support spatial behavior. We present experimental results obtained with a mobile Khepera robot. Received: 02 July 1999 / Accepted in revised form: 20 March 2000     

How could a chirp be more effective than a louder clock--resonant transfer of energy between subthreshold excitation pulses and excitable tissues

By definition, electrical resonance of excitable biomembranes reflects their remarkable ability to select input signals with preferential frequencies as ones that will pass through the chain of information exchange within a coordinated organism. This feature is known to be caused and regulated by the voltage-dependent kinetics of transmembrane ion channels. Knowledge about the resonant behavior of excitable cells may prove crucial toward better underpinning those essential properties of neurons which make them to function as a highly coordinated network. In this work we present novel experimental evidence which strongly supports the paradigm of selective communication between excitable cells, by no more than efficient transfer of energy which takes place when the frequency of subthreshold presynaptic pulses matches the natural, resonant frequency of a target excitable tissue. As a possible direct application, our novel experimental results prove the functional importance of bursting activity of pre-synaptic neurons as an effective physiological mechanism for discriminatory communication between neurons.     

Membrane Resonance and Stochastic Resonance Modulate Firing Patterns of Thalamocortical Neurons

We examined the interactions of subthreshold membrane resonance and stochastic resonance using whole-cell patch clamp recordings in thalamocortical neurons of rat brain slices, as well as with a Hodgkin-Huxley-type mathematical model of thalamocortical neurons. The neurons exhibited the subthreshold resonance when stimulated with small amplitude sine wave currents of varying frequency, and stochastic resonance when noise was added to sine wave inputs. Stochastic resonance was manifest as a maximum in signal-to-noise ratio of output response to subthreshold periodic input combined with noise. Stochastic resonance in conjunction with subthreshold resonance resulted in action potential patterns that showed frequency selectivity for periodic inputs. Stochastic resonance was maximal near subthreshold resonance frequency and a high noise level was required for detection of high frequency signals. We speculate that combined membrane and stochastic resonances have physiological utility in coupling synaptic activity to preferred firing frequency and in network synchronization under noise.     

The effect of dendritic voltage-gated conductances on the neuronal impedance: a quantitative model

Neuronal impedance characterizes the magnitude and timing of the subthreshold response of a neuron to oscillatory input at a given frequency. It is known to be influenced by both the morphology of the neuron and the presence of voltage-gated conductances in the cell membrane. Most existing theoretical accounts of neuronal impedance considered the effects of voltage-gated conductances but neglected the spatial extent of the cell, while others examined spatially extended dendrites with a passive or spatially uniform quasi-active membrane. We derived an explicit mathematical expression for the somatic input impedance of a model neuron consisting of a somatic compartment coupled to an infinite dendritic cable which contained voltage-gated conductances, in the more general case of non-uniform dendritic membrane potential. The validity and generality of this model was verified through computer simulations of various model neurons. The analytical model was then applied to the analysis of experimental data from real CA1 pyramidal neurons. The model confirmed that the biophysical properties and predominantly dendritic localization of the hyperpolarization-activated cation current I (h) were important determinants of the impedance profile, but also predicted a significant contribution from a depolarization-activated fast inward current. Our calculations also implicated the interaction of I (h) with amplifying currents as the main factor governing the shape of the impedance-frequency profile in two types of hippocampal interneuron. Our results provide not only a theoretical advance in our understanding of the frequency-dependent behavior of nerve cells, but also a practical tool for the identification of candidate mechanisms that determine neuronal response properties.     

Neural Computation via Neural Geometry: A Place Code for Inter-whisker Timing in the Barrel Cortex?

The place theory proposed by Jeffress (1948) is still the dominant model of how the brain represents the movement of sensory stimuli between sensory receptors. According to the place theory, delays in signalling between neurons, dependent on the distances between them, compensate for time differences in the stimulation of sensory receptors. Hence the location of neurons, activated by the coincident arrival of multiple signals, reports the stimulus movement velocity. Despite its generality, most evidence for the place theory has been provided by studies of the auditory system of auditory specialists like the barn owl, but in the study of mammalian auditory systems the evidence is inconclusive. We ask to what extent the somatosensory systems of tactile specialists like rats and mice use distance dependent delays between neurons to compute the motion of tactile stimuli between the facial whiskers (or 'vibrissae'). We present a model in which synaptic inputs evoked by whisker deflections arrive at neurons in layer 2/3 (L2/3) somatosensory 'barrel' cortex at different times. The timing of synaptic inputs to each neuron depends on its location relative to sources of input in layer 4 (L4) that represent stimulation of each whisker. Constrained by the geometry and timing of projections from L4 to L2/3, the model can account for a range of experimentally measured responses to two-whisker stimuli. Consistent with that data, responses of model neurons located between the barrels to paired stimulation of two whiskers are greater than the sum of the responses to either whisker input alone. The model predicts that for neurons located closer to either barrel these supralinear responses are tuned for longer inter-whisker stimulation intervals, yielding a topographic map for the inter-whisker deflection interval across the surface of L2/3. This map constitutes a neural place code for the relative timing of sensory stimuli.     

Spiking Neurons in a Hierarchical Self-Organizing Map Model Can Learn to Develop Spatial and Temporal Properties of Entorhinal Grid Cells and Hippocampal Place Cells

Medial entorhinal grid cells and hippocampal place cells provide neural correlates of spatial representation in the brain. A place cell typically fires whenever an animal is present in one or more spatial regions, or places, of an environment. A grid cell typically fires in multiple spatial regions that form a regular hexagonal grid structure extending throughout the environment. Different grid and place cells prefer spatially offset regions, with their firing fields increasing in size along the dorsoventral axes of the medial entorhinal cortex and hippocampus. The spacing between neighboring fields for a grid cell also increases along the dorsoventral axis. This article presents a neural model whose spiking neurons operate in a hierarchy of self-organizing maps, each obeying the same laws. This spiking GridPlaceMap model simulates how grid cells and place cells may develop. It responds to realistic rat navigational trajectories by learning grid cells with hexagonal grid firing fields of multiple spatial scales and place cells with one or more firing fields that match neurophysiological data about these cells and their development in juvenile rats. The place cells represent much larger spaces than the grid cells, which enable them to support navigational behaviors. Both self-organizing maps amplify and learn to categorize the most frequent and energetic co-occurrences of their inputs. The current results build upon a previous rate-based model of grid and place cell learning, and thus illustrate a general method for converting rate-based adaptive neural models, without the loss of any of their analog properties, into models whose cells obey spiking dynamics. New properties of the spiking GridPlaceMap model include the appearance of theta band modulation. The spiking model also opens a path for implementation in brain-emulating nanochips comprised of networks of noisy spiking neurons with multiple-level adaptive weights for controlling autonomous adaptive robots capable of spatial navigation.     

Epileptogenesis: A model for the involvement of slow membrane events and extracellular potassium

A computer model was developed, based in part on voltage-clamp data from Aplysia bursting pacemaker cells. This model was used to explore the interaction of slow subthreshold membrane properties with the synaptic events and the accumulation of extracellular potassium which are thought to occur in experimental epileptic foci. Results of the model suggest a new role for potassium ions and subthreshold membrane events in epileptogenesis—namely, that an increase in extracellular potassium may transform a group of stable cells into unstable, oscillatory cells, independent of synaptic activity. The model also suggests that a population of cells may be more susceptible than single cells to this transformation.     

A topological paradigm for hippocampal spatial map formation using persistent homology

An animal's ability to navigate through space rests on its ability to create a mental map of its environment. The hippocampus is the brain region centrally responsible for such maps, and it has been assumed to encode geometric information (distances, angles). Given, however, that hippocampal output consists of patterns of spiking across many neurons, and downstream regions must be able to translate those patterns into accurate information about an animal's spatial environment, we hypothesized that 1) the temporal pattern of neuronal firing, particularly co-firing, is key to decoding spatial information, and 2) since co-firing implies spatial overlap of place fields, a map encoded by co-firing will be based on connectivity and adjacency, i.e., it will be a topological map. Here we test this topological hypothesis with a simple model of hippocampal activity, varying three parameters (firing rate, place field size, and number of neurons) in computer simulations of rat trajectories in three topologically and geometrically distinct test environments. Using a computational algorithm based on recently developed tools from Persistent Homology theory in the field of algebraic topology, we find that the patterns of neuronal co-firing can, in fact, convey topological information about the environment in a biologically realistic length of time. Furthermore, our simulations reveal a "learning region" that highlights the interplay between the parameters in combining to produce hippocampal states that are more or less adept at map formation. For example, within the learning region a lower number of neurons firing can be compensated by adjustments in firing rate or place field size, but beyond a certain point map formation begins to fail. We propose that this learning region provides a coherent theoretical lens through which to view conditions that impair spatial learning by altering place cell firing rates or spatial specificity.     

Calcium-binding proteins inAplysia neurons

1. Calcium (Ca)-binding proteins of neuronal ganglia and of single, identified neurons of the marine mollusk, Aplysia californica, were investigated. Using transblot/45Ca overlays two proteins, at Mr 45,000 and Mr 23,000, with a high Ca-binding ability were found. 2. Western blot analysis revealed that the protein at Mr 45,000 could be separated by 2D-PAGE into proteins with Mr 40,000 and Mr 43,000. The protein at Mr 40,000 immunocross-reacted with antisera directed against parvalbumin and rat calbindin D-28K, indicating a novel Ca-binding protein sharing common antigenic determinants for both proteins. 3. The protein at Mr 23,000 could be separated into a group of proteins with Mr 13,000-20,000 which showed a high degree of similarity to sarcoplasmatic calcium-binding proteins (SCP). 4. We further investigated the protein pattern of single, identified neurons of different electrical activity (bursting, beating, and silent) by 2D-PAGE. Major differences were found in the range of low Mr and low pI, where Ca-binding proteins are generally located. A protein at high concentrations characteristic for silent cells migrated at a position similar to crayfish SCP. 5. The results show that various Ca-binding proteins are characteristic for neurons in the Aplysia nervous system and support the idea that they may effect the electrical behavior of nerve cells.     

The synthesis and use of the owl’s auditory space map

The barn owl (Tyto alba) is capable of capturing prey by passive hearing alone, guided by a topographic map of auditory space in the external nucleus of its inferior colliculus. The neurons of this auditory space map have discrete spatial receptive fields that result from the computation of interaural differences in the level (ILD) and time-of-arrival (ITD) of sounds. Below we review the synthesis of the spatial receptive fields from the frequency-specific ITDs and ILDs to which the neurons are tuned, concentrating on recent studies exploiting virtual auditory space techniques to analyze the contribution of ILD. We then compared the owls spatial discrimination, assessed behaviorally, with that of its space map neurons. Spatial discrimination was assessed using a novel paradigm involving the pupillary dilation response (PDR), and neuronal acuity was assessed by measuring the changes in firing rate resulting from changes in source location, scaled to the variance. This signal-detection-based approach revealed that the change in the position of the neural image on this map best explains the spatial discrimination measured using the PDR. We compare this result to recent studies in mammalian systems.     

Activity dynamics and behavioral correlates of CA3 and CA1 hippocampal pyramidal neurons

The CA3 and CA1 pyramidal neurons are the major principal cell types of the hippocampus proper. The strongly recurrent collateral system of CA3 cells and the largely parallel-organized CA1 neurons suggest that these regions perform distinct computations. However, a comprehensive comparison between CA1 and CA3 pyramidal cells in terms of firing properties, network dynamics, and behavioral correlations is sparse in the intact animal. We performed large-scale recordings in the dorsal hippocampus of rats to quantify the similarities and differences between CA1 (n > 3,600) and CA3 (n > 2,200) pyramidal cells during sleep and exploration in multiple environments. CA1 and CA3 neurons differed significantly in firing rates, spike burst propensity, spike entrainment by the theta rhythm, and other aspects of spiking dynamics in a brain state-dependent manner. A smaller proportion of CA3 than CA1 cells displayed prominent place fields, but place fields of CA3 neurons were more compact, more stable, and carried more spatial information per spike than those of CA1 pyramidal cells. Several other features of the two cell types were specific to the testing environment. CA3 neurons showed less pronounced phase precession and a weaker position versus spike-phase relationship than CA1 cells. Our findings suggest that these distinct activity dynamics of CA1 and CA3 pyramidal cells support their distinct computational roles.