Associative neurons as correlators

The paper continues the series of studies devoted to the hypothesis that the brain functioning occurs with the participation of correlation methods. The processing of signals by these methods is sufficiently versatile to provide the solution of diversified problems, which has been shown in studies of the mechanisms of animal echo location (a correlation model of echo location) and recognition of objects at any modality of sensor signals. It was shown that the mode of processing performed by neurons correlometers corresponds to the character of signals coming from the habitat of animals. Problems related to both the peculiarities of a reference signal formed by synaptic inputs of an associative neuron and the process of calculating the correlation function by this neuron were resolved. Two mathematically equivalent ways of physical execution of calculating the correlation function, by a correlometer and a passive correlated filter, were compared. The advantages of the brain that performs the correlation processing of signals by using the aggregates of neurons functioning as systems of correlometers rather than passive filters are analyzed.     

Network, cellular and molecular mechanisms of plasticity in simple nervous systems

In the present study we will try to single out several principles of the nervous system functioning essential for describing mechanisms of learning and memory basing on our own experimental investigation of cellular mechanisms of memory in the nervous system of gastropod molluscs and literature data: main changes in functioning due to learning occur in effectivity of synaptic inputs and in the intrinsic properties of postsynaptic neurons; due to learning some synaptic inputs of neurons selectively change its effectivity due to pre- and postsynaptic changes, but the induction of plasticity always starts in postsynapse, maintaining of long-term memory in postsynapse is also shown; reinforcement is not related to activity of the neural chain receptor-sensory neuron-interneuron-motoneuron-effector; reinforcement is mediated via activity of modulatory neurons, and in some cases can be exerted by a single neuron; activity of modulatory neurons is necessary for development of plastic modifications of behavior (including associative), but is not needed for recall of conditioned responses. At the same time, the modulatory neurons (in fact they constitute a neural reinforcement system) are necessary for recall of context associative memory; changes due to learning occur at least in two independent loci in the nervous system. A possibility for erasure of memory with participation of nitroxide is experimentally and theoretically based.     

Analysis of activity of neuron pairs in the cat caudate nucleus

Activity of neuron pairs in the caudate nucleus, derived simultaneously by a single microelectrode, was investigated in experiments on lightly anesthetized, immobilized cats. Strong temporal correlation was shown to be characteristic of the spontaneous activity of a neuron pair if grouped discharges were present in that activity. If, however, spontaneous activity was characterized by impulses randomly distributed in time, temporal correlation was observed in only 50% of cases, it was weaker, and it reflected excitatory and inhibitory interactions equally. In many cases negative correlation was observed in discharges of neurons within the time interval of 0–4 msec. Electrical stimulation of the various afferent inputs of the caudate nucleus not only did not cause correlation to appear in the discharges of the neurons but, on the contrary, it abolished correlation which existed for that same pair of neurons discharging spontaneously. Comparison of the results with data in the literature indicates that, by the character of interaction of its neurons, the caudate nucleus is one of the group of associative nuclei of the brain.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 10, No. 5, pp. 486–493, September–October, 1978.     

Cellular mechanisms of behavioural plasticity in simple nervous systems

In the present study, we will try to single out several principles of the nervous system functioning essential for describing the mechanisms of learning and memory, basing on our own experimental investigation of cellular mechanisms of memory in the nervous system of gastropod molluscs and literature data as follows: (1) Main changes in functioning due to learning occur in the interneurons; (2) Due to learning some synaptic inputs of command neurons selectively change its effectivity; (3) Reinforcement is not related to activity of the neural chain receptor-sensory neuron-interneuron-motoneuron-effector; reinforcement is mediated via activity of modulatory neurons, and in some cases can be exerted by a single neuron; (4) Activity of modulatory neurons is necessary for development of plastic modifications of behaviour (including associative), but is not needed for recall of conditioned responses. At the same time, the modulatory neurons (in fact they constitute a neural reinforcement system) are necessary for recall of context associative memory; (5) Changes due to learning occur at least in two independent loci in the nervous system.     

Spectral analysis of input spike trains by spike-timing-dependent plasticity

Spike-timing-dependent plasticity (STDP) has been observed in many brain areas such as sensory cortices, where it is hypothesized to structure synaptic connections between neurons. Previous studies have demonstrated how STDP can capture spiking information at short timescales using specific input configurations, such as coincident spiking, spike patterns and oscillatory spike trains. However, the corresponding computation in the case of arbitrary input signals is still unclear. This paper provides an overarching picture of the algorithm inherent to STDP, tying together many previous results for commonly used models of pairwise STDP. For a single neuron with plastic excitatory synapses, we show how STDP performs a spectral analysis on the temporal cross-correlograms between its afferent spike trains. The postsynaptic responses and STDP learning window determine kernel functions that specify how the neuron "sees" the input correlations. We thus denote this unsupervised learning scheme as 'kernel spectral component analysis' (kSCA). In particular, the whole input correlation structure must be considered since all plastic synapses compete with each other. We find that kSCA is enhanced when weight-dependent STDP induces gradual synaptic competition. For a spiking neuron with a "linear" response and pairwise STDP alone, we find that kSCA resembles principal component analysis (PCA). However, plain STDP does not isolate correlation sources in general, e.g., when they are mixed among the input spike trains. In other words, it does not perform independent component analysis (ICA). Tuning the neuron to a single correlation source can be achieved when STDP is paired with a homeostatic mechanism that reinforces the competition between synaptic inputs. Our results suggest that neuronal networks equipped with STDP can process signals encoded in the transient spiking activity at the timescales of tens of milliseconds for usual STDP.     

Transitory memory retrieval in a biologically plausible neural network model

A number of memory models have been proposed. These all have the basic structure that excitatory neurons are reciprocally connected by recurrent connections together with the connections with inhibitory neurons, which yields associative memory (i.e., pattern completion) and successive retrieval of memory. In most of the models, a simple mathematical model for a neuron in the form of a discrete map is adopted. It has not, however, been clarified whether behaviors like associative memory and successive retrieval of memory appear when a biologically plausible neuron model is used. In this paper, we propose a network model for associative memory and successive retrieval of memory based on Pinsky-Rinzel neurons. The state of pattern completion in associative memory can be observed with an appropriate balance of excitatory and inhibitory connection strengths. Increasing of the connection strength of inhibitory interneurons changes the state of memory retrieval from associative memory to successive retrieval of memory. We investigate this transition.     

Beyond Two-Cell Networks: Experimental Measurement of Neuronal Responses to Multiple Synaptic Inputs

Oscillations of large populations of neurons are thought to be important in the normal functioning of the brain. We have used phase response curve (PRC) methods to characterize the dynamics of single neurons and predict population dynamics. Our past experimental work was limited to special circumstances (e.g., 2-cell networks of periodically firing neurons). Here, we explore the feasibility of extending our methods to predict the synchronization properties of stellate cells (SCs) in the rat entorhinal cortex under broader conditions. In particular, we test the hypothesis that PRCs in SCs scale linearly with changes in synaptic amplitude, and measure how well responses to Poisson process-driven inputs can be predicted in terms of PRCs. Although we see nonlinear responses to excitatory and inhibitory inputs, we find that models based on weak coupling account for scaling and Poisson process-driven inputs reasonably accurately.     

Whole-Brain Mapping of Inputs to Projection Neurons and Cholinergic Interneurons in the Dorsal Striatum

The dorsal striatum integrates inputs from multiple brain areas to coordinate voluntary movements, associative plasticity, and reinforcement learning. Its projection neurons consist of the GABAergic medium spiny neurons (MSNs) that express dopamine receptor type 1 (D1) or dopamine receptor type 2 (D2). Cholinergic interneurons account for a small portion of striatal neuron populations, but they play important roles in striatal functions by synapsing onto the MSNs and other local interneurons. By combining the modified rabies virus with specific Cre- mouse lines, a recent study mapped the monosynaptic input patterns to MSNs. Because only a small number of extrastriatal neurons were labeled in the prior study, it is important to reexamine the input patterns of MSNs with higher labeling efficiency. Additionally, the whole-brain innervation pattern of cholinergic interneurons remains unknown. Using the rabies virus-based transsynaptic tracing method in this study, we comprehensively charted the brain areas that provide direct inputs to D1-MSNs, D2-MSNs, and cholinergic interneurons in the dorsal striatum. We found that both types of projection neurons and the cholinergic interneurons receive extensive inputs from discrete brain areas in the cortex, thalamus, amygdala, and other subcortical areas, several of which were not reported in the previous study. The MSNs and cholinergic interneurons share largely common inputs from areas outside the striatum. However, innervations within the dorsal striatum represent a significantly larger proportion of total inputs for cholinergic interneurons than for the MSNs. The comprehensive maps of direct inputs to striatal MSNs and cholinergic interneurons shall assist future functional dissection of the striatal circuits.     

Gamma oscillations as a mechanism for selective information transmission

In the past decades, many studies have focussed on the relation between the input and output of neurons with the aim to understand information processing by neurons. A particular aspect of neuronal information, which has not received much attention so far, concerns the problem of information transfer when a neuron or a population of neurons receives input from two or more (populations of) neurons, in particular when these (populations of) neurons carry different types of information. The aim of the present study is to investigate the responses of neurons to multiple inputs modulated in the gamma frequency range. By a combination of theoretical approaches and computer simulations, we test the hypothesis that enhanced modulation of synchronized excitatory neuronal activity in the gamma frequency range provides an advantage over a less synchronized input for various types of neurons. The results of this study show that the spike output of various types of neurons [i.e. the leaky integrate and fire neuron, the quadratic integrate and fire neuron and the Hodgkin–Huxley (HH) neuron] and that of excitatory–inhibitory coupled pairs of neurons, like the Pyramidal Interneuronal Network Gamma (PING) model, is highly phase-locked to the larger of two gamma-modulated input signals. This implies that the neuron selectively responds to the input with the larger gamma modulation if the amplitude of the gamma modulation exceeds that of the other signals by a certain amount. In that case, the output of the neuron is entrained by one of multiple inputs and that other inputs are not represented in the output. This mechanism for selective information transmission is enhanced for short membrane time constants of the neuron.     

On some properties of stochastic information processes in neurons and neuron populations

The information in the nervous spike trains and its processing by neural units are discussed. In these problems, our attention is focused on the stochastic properties of neurons and neuron populations. There are three subjects in this paper, which are the spontaneous type neuron, the forced type neuron and the reciprocal inhibitory pairs.

1. The spontaneous type neuron produces spikes without excitatory inputs. The mathematical model has the following assumptions. The neuron potential (NP) has the fluctuation and obeys the Ornstein-Uhlenbeck process, because the N P is not so perfectly random as that of the Wiener process but has an attraction to the rest value. The threshold varies exponentially and the NP has the constant lower limit. When the NP reaches the threshold, the neuron fires and the NP is reset to a certain position. After a firing, an absolute refractory period exists. In discussing the stochastic properties of neurons, the transition probability density function and the first passage time density function are the important quantities, which are governed by the Kolmogorov's equations. Although they can be set up easily, we can rarely obtain the analytical solutions in time domain. Moreover, they cover only simple properties. Hence the numerical analysis is performed and a good deal of fair results are obtained and discussed.
2. The forced type neuron has input pulse trains which are assumed to be based on the Poisson process. Other assumptions and methods are almost the same as above except the diffusion approximation of the stochastic process. In this case, we encounter the inhomogeneous process due to the pulse-frequency-modulation, whose first passage time density reveals the multimodal distribution. The numerical analysis is also tried, and the output spike interval density is further discussed in the case of the periodic modulation.
3. Two types of reciprocal inhibitory pairs are discussed. The first type has two excitatory driving inputs which are mutually independent. The second type has one common excitatory input but it advances in two ways, one of which has a time lag. The neuron dynamics is the same as that of the forced type neuron and each neuron has an identical structure. The inputs are assumed to be based on the Poisson process and the inhibition occurs when the companion neuron fires. In this case, the equations of the probability density functions are not obtained. Hence the computer simulation is tried and it is observed that the stochastic rhythm emerges in spite of the temporally homogeneous inputs. Furthermore, the case of inhomogeneous inputs is discussed.

     

Characterising neural representation in terms of the dynamics of cell membrane potential activity: a control theoretic approach using differential geometry

Experimental and theoretical results seem to demand that the study of neural representations in the brain considers both the subthreshold and suprathreshold dynamic activity of the neural membrane potential, rather than be solely focussed on stimulus representation in trains of action potentials. In a dynamical systems formulation, the membrane potential can be regarded as the "state" of the neuron, evolving continuously over time and space, within an infinite dimensional space, in response to ever changing inputs. Formally, the state of the neuron, together with future inputs, is sufficient to fully determine the future behaviour of the neuron. In this paper, the characterisation of membrane potential activity is approached from a control theoretic viewpoint as a "reachability" problem, in which the effect of particular stimulus-evoked synaptic inputs is seen as driving the cell from some initial state of the neuron to a particular terminal state on a given manifold. It is shown that a fluctuating subthreshold membrane potential induced by synaptic background activity, and the cooperative interaction of excitatory and inhibitory inputs, may be important factors in allowing the cell to "reach" a maximal subset of all possible membrane potential states, through the action of its synaptic inputs.     

Exclusive-OR function of single arborized neuron

We designed four arborized neurons which are able to evaluate the exclusive-or (XOR) function from two inputs. The input neurons form exclusively excitatory synapses on a dendritic tree which is a patchwork of passive (ohmic) and active cable segments. The active segments are described by the Hodgkin-Huxley model. The dynamics of the neurons and their output are obtained by numerical integration of the cable equation. In neurons 1 and 2 the XOR function is based on the annihilation of colliding action potentials. In neuron No. 3 the design takes advantage of the refractory period of action potentials. In neuron No. 4 voltage inversion is used as it occurs for inactivated sodium conductance in the Hodgkin-Huxley model. In all cases the XOR function depends critically on an appropriate timing of the input signals and on delays of the voltage transients in different branches of the dendrite.     

Correlative coherence analysis: variation from intrinsic and extrinsic sources in competing populations

The concept of the correlation between two signals is generalized to the correlative coherence of a set of n signals by introducing a Shannon-Weaver-type measure of the entropy of the normalized eigenvalues of the n-dimensional correlation matrix associated with the set of signals. Properties of this measure are stated for canonical cases. The measure is then used to evaluate which subsets of a particular set of n signals are more or less coherent. This set of signals comprises extrinsic, stochastic resource inputs and the population trajectories obtained from simulations of a discrete time model of competing biological populations driven by these resource inputs. The analysis reveals that, at low levels of competition, the correlative coherence of the combined system of intrinsic population and extrinsic resource variables is relatively low, but increases with increasing variation in the resources. Further, at intermediate and high competition levels, the correlative coherence depends more strongly on competition than entrainment of stochasticity in the extrinsic resource variables. Density dependence has the effect of amplifying variation in noise only when this variation is relatively large. Also, chaotic systems appear to be entrained by sufficiently noisy environmental inputs.     

The Xenopus retinal ganglion cell as a model neuron to study the establishment of neuronal connectivity

Neurons receive inputs through their multiple branched dendrites and pass this information on to the next neuron via long axons, which branch within the target. The shape the neuron acquires is thus the key to its proper functioning in the neural circuit in which it participates. Both axons and dendrites grow in a directed fashion to their target partner neurons by responding to a large number of molecular cues in the milieu through which they extend. They then go through the process of synaptogenesis, first choosing a neuron on which to synapse, and then the appropriate subcellular location. How a neuron acquires its unique shape, establishes and modifies appropriate synaptic connectivity, and the molecular signals involved, are key questions in developmental neurobiology. Such questions of nervous system wiring are being pursued actively with a variety of different animal models and neuron types, each with its own unique advantages. Among these, the developing retinal ganglion cell (RGC) of the South African clawed frog, Xenopus laevis, has proven particularly fruitful for revealing the secrets of how axons and dendrites acquire their final morphology and connectivity. In this review, we describe how this system can be used to understand the multiple molecular events that instruct the incorporation of RGCs into the neural circuit that controls vision.     

A novel key–lock mechanism for inactivating amino acid neurotransmitters during transit across extracellular space

There are two kinds of neurotransmissions that occur in brain. One is neuron to neuron at synapses, and the other is neuron to glia via extracellular fluid (ECF), both of which are important for maintenance of proper neuronal functioning. For neuron to neuron communications, several potent amino acid neurotransmitters are used within the confines of synaptic space. However, their presence at elevated concentrations in extra-synaptic space could be detrimental to well organized neuronal functioning. The significance of the synthesis and release of N-acetylaspartylglutamate (NAAG) by neurons has long been a puzzle since glutamate (Glu) itself is the “key” that can interact with all Glu receptors on membranes of all cells. Nonetheless, neurons synthesize this acetylated dipeptide, which cannot be catabolized by neurons, and release it to ECF where its specific physiological target is the Glu metabotropic receptor 3 on the surface of astrocytes. Since Glu is excitotoxic at elevated concentrations, it is proposed that formation and release of NAAG by neurons allows large quantities of Glu to be transported in ECF without the risk of injurious excitotoxic effects. The metabolic mechanism used by neurons is a key–lock system to detoxify Glu during its intercellular transit. This is accomplished by first synthesizing N-acetylaspartate (NAA), and then joining this molecule via a peptide bond to Glu. In this paper, a hypothesis is presented that neurons synthesize a variety of relatively nontoxic peptides and peptide derivatives, including NAA, NAAG, homocarnosine (γ-aminobutyrylhistidine) and carnosine (β-alanylhistidine) from potent excitatory and inhibitory amino acids for the purpose of releasing them to ECF to function as cell-specific neuron-to-glia neurotransmitters.     

Structural and resting state functional connectivity of the subthalamic nucleus: identification of motor STN parts and the hyperdirect pathway

Deep brain stimulation (DBS) for Parkinson's disease often alleviates the motor symptoms, but causes cognitive and emotional side effects in a substantial number of cases. Identification of the motor part of the subthalamic nucleus (STN) as part of the presurgical workup could minimize these adverse effects. In this study, we assessed the STN's connectivity to motor, associative, and limbic brain areas, based on structural and functional connectivity analysis of volunteer data. For the structural connectivity, we used streamline counts derived from HARDI fiber tracking. The resulting tracks supported the existence of the so-called "hyperdirect" pathway in humans. Furthermore, we determined the connectivity of each STN voxel with the motor cortical areas. Functional connectivity was calculated based on functional MRI, as the correlation of the signal within a given brain voxel with the signal in the STN. Also, the signal per STN voxel was explained in terms of the correlation with motor or limbic brain seed ROI areas. Both right and left STN ROIs appeared to be structurally and functionally connected to brain areas that are part of the motor, associative, and limbic circuit. Furthermore, this study enabled us to assess the level of segregation of the STN motor part, which is relevant for the planning of STN DBS procedures.     

Descending influences on escape behavior and motor pattern in the cockroach

The escape behavior of the cockroach is a ballistic behavior with well characterized kinematics. The circuitry known to control the behavior lies in the thoracic ganglia, abdominal ganglia, and abdominal nerve cord. Some evidence suggests inputs may occur from the brain or suboesophageal ganglion. We tested this notion by decapitating cockroaches, removing all descending inputs, and evoking escape responses. The decapitated cockroaches exhibited directionally appropriate escape turns. However, there was a front-to-back gradient of change: the front legs moved little if at all, the middle legs moved in the proper direction but with reduced excursion, and the rear legs moved normally. The same pattern was seen when only inputs from the brain were removed, the suboesophageal ganglion remaining intact and connected to the thoracic ganglia. Electromyogram (EMG) analysis showed that the loss of or reduction in excursion was accompanied by a loss of or reduction in fast motor neuron activity. The loss of fast motor neuron activity was also observed in a reduced preparation in which descending neural signals were reversibly blocked via an isotonic sucrose solution superfusing the neck connectives, indicating that the changes seen were not due to trauma. Our data demonstrate that while the thoracic circuitry is sufficient to produce directional escape, lesion or blockage of the connective affects the excitability of components of the escape circuitry. Because of the rapidity of the escape response, such effects are likely due to the elimination of tonic descending inputs.     

Tuning bat LSO neurons to interaural intensity differences through spike-timing dependent plasticity

Bats, like other mammals, are known to use interaural intensity differences (IID) to determine azimuthal position. In the lateral superior olive (LSO) neurons have firing behaviors which vary systematically with IID. Those neurons receive excitatory inputs from the ipsilateral ear and inhibitory inputs from the contralateral one. The IID sensitivity of a LSO neuron is thought to be due to delay differences between the signals coming from both ears, differences due to different synaptic delays and to intensity-dependent delays. In this paper we model the auditory pathway until the LSO. We propose a learning scheme where inputs to LSO neurons start out numerous with different relative delays. Spike timing-dependent plasticity (STDP) is then used to prune those connections. We compare the pruned neuron responses with physiological data and analyse the relationship between IID’s of teacher stimuli and IID sensitivities of trained LSO neurons.     

Modelling noninvasively measured cerebral signals during a hypoxemia challenge: steps towards individualised modelling

Noninvasive approaches to measuring cerebral circulation and metabolism are crucial to furthering our understanding of brain function. These approaches also have considerable potential for clinical use "at the bedside". However, a highly nontrivial task and precondition if such methods are to be used routinely is the robust physiological interpretation of the data. In this paper, we explore the ability of a previously developed model of brain circulation and metabolism to explain and predict quantitatively the responses of physiological signals. The five signals all noninvasively-measured during hypoxemia in healthy volunteers include four signals measured using near-infrared spectroscopy along with middle cerebral artery blood flow measured using transcranial Doppler flowmetry. We show that optimising the model using partial data from an individual can increase its predictive power thus aiding the interpretation of NIRS signals in individuals. At the same time such optimisation can also help refine model parametrisation and provide confidence intervals on model parameters. Discrepancies between model and data which persist despite model optimisation are used to flag up important questions concerning the underlying physiology, and the reliability and physiological meaning of the signals.     

Adaptive synaptogenesis constructs networks that maintain information and reduce statistical dependence

This report demonstrates the effectiveness of two processes in constructing simple feedforward networks which perform good transformations on their inputs. Good transformations are characterized by the minimization of two information measures: the information loss incurred with the transformation and the statistical dependency of the output. The two processes build appropriate synaptic connections in initially unconnected networks. The first process, synaptogenesis, creates new synaptic connections; the second process, associative synaptic modification, adjusts the connection strength of existing synapses. Synaptogenesis produces additional innervation for each output neuron until each output neuron achieves a firing rate of approximately 0.50. Associative modification of existing synaptic connections lends robustness to network construction by adjusting suboptimal choices of initial synaptic weights. Networks constructed using synaptogenesis and synaptic modification successfully preserve the information content of a variety of inputs. By recording a high-dimensional input into an output of much smaller dimension, these networks drastically reduce the statistical dependence of neuronal representations. Networks constructed with synaptogenesis and associative modification perform good transformations over a wide range of neuron firing thresholds.