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Perioperative Medicine  |   July 2018
γ-Aminobutyric Acid Type A Receptor Potentiation Inhibits Learning in a Computational Network Model
Kingsley P. Storer, M.B.B.S., Ph.D., F.A.N.Z.C.A.; George N. Reeke, Ph.D.
Author Notes
  • From the Department of Anesthesiology, Weill Cornell Medical College, New York, New York (K.P.S); the Laboratory of Biological Modeling, The Rockefeller University, New York, New York (K.P.S, G.N.R.); and the Department of Surgery, Flinders University, Adelaide, Australia (K.P.S).
  • The work presented in this article has been presented at the Anesthesiology 2016 Annual Meeting in Chicago, Illinois, October 23, 2016.
    The work presented in this article has been presented at the Anesthesiology 2016 Annual Meeting in Chicago, Illinois, October 23, 2016.×
  • Submitted for publication September 8, 2017. Accepted for publication March 15, 2018.
    Submitted for publication September 8, 2017. Accepted for publication March 15, 2018.×
  • Address correspondence to Dr. Storer: Department of Anesthesiology, Weill Cornell Medical College, 1300 York Ave., New York, New York 10021. kis9029@med.cornell.edu. Information on purchasing reprints may be found at www.anesthesiology.org or on the masthead page at the beginning of this issue. Anesthesiology’s articles are made freely accessible to all readers, for personal use only, 6 months from the cover date of the issue.
Article Information
Perioperative Medicine / Basic Science / Central and Peripheral Nervous Systems / Pharmacology
Perioperative Medicine   |   July 2018
γ-Aminobutyric Acid Type A Receptor Potentiation Inhibits Learning in a Computational Network Model
Anesthesiology 7 2018, Vol.129, 106-117. doi:10.1097/ALN.0000000000002230
Anesthesiology 7 2018, Vol.129, 106-117. doi:10.1097/ALN.0000000000002230
Abstract

Background: Propofol produces memory impairment at concentrations well below those abolishing consciousness. Episodic memory, mediated by the hippocampus, is most sensitive. Two potentially overlapping scenarios may explain how γ-aminobutyric acid receptor type A (GABAA) potentiation by propofol disrupts episodic memory—the first mediated by shifting the balance from excitation to inhibition while the second involves disruption of rhythmic oscillations. We use a hippocampal network model to explore these scenarios. The basis for these experiments is the proposal that the brain represents memories as groups of anatomically dispersed strongly connected neurons.

Methods: A neuronal network with connections modified by synaptic plasticity was exposed to patterned stimuli, after which spiking output demonstrated evidence of stimulus-related neuronal group development analogous to memory formation. The effect of GABAA potentiation on this memory model was studied in 100 unique networks.

Results: GABAA potentiation consistent with moderate propofol effects reduced neuronal group size formed in response to a patterned stimulus by around 70%. Concurrently, accuracy of a Bayesian classifier in identifying learned patterns in the network output was reduced. Greater potentiation led to near total failure of group formation. Theta rhythm variations had no effect on group size or classifier accuracy.

Conclusions: Memory formation is widely thought to depend on changes in neuronal connection strengths during learning that enable neuronal groups to respond with greater facility to familiar stimuli. This experiment suggests the ability to form such groups is sensitive to alteration in the balance between excitation and inhibition such as that resulting from administration of a γ-aminobutyric acid–mediated anesthetic agent.

What We Already Know about This Topic

  • Episodic memory encoding is dependent upon the hippocampus; repetitive stimuli strengthen synaptic connections and lead to the development of groups of neurons with synchronous activity called polychronous groups.

  • The hippocampal formation has multiple connections, including those with the entorhinal cortex and medial septum. Interactions within these connections lead to synchronized oscillations, primarily theta, that can be detected electroencephalographically.

  • Although propofol and other enhancers of γ-aminobutyric acid receptor type A activity produce amnesia, the precise mechanisms by which they interfere with memory-encoding processes such as synaptic plasticity-induced polychronous neuronal group formation versus theta oscillations are not clear.

What This Article Tells Us That Is New

  • In a computational model of the hippocampus, propofol reduced polychronous group size in a dose-dependent manner. By contrast, modulation of theta oscillations did not affect group size.

  • The results suggest formation of polychronous groups of neurons is more sensitive to the effect of propofol on the balance between excitation and inhibition than on theta oscillations.

THE precise mechanisms by which γ-aminobutyric acid receptor type A (GABAA)–potentiating anesthetics cause memory impairment have yet to be delineated. We know that subpopulations of GABAA receptors composed of specific subunits are responsible for the amnestic effects of propofol and etomidate occurring at plasma concentrations well below that required for loss of consciousness.1,2  While numerous brain structures mediate the various classified memory systems, it is clear that the hippocampus and associated entorhinal cortex are most important in formation of episodic memory. Episodic memories are those that can be consciously recalled; they can include autobiographical events. They are most sensitive to anesthetic agents.
Two scenarios have been proposed for the manner in which GABAA receptor modulation may disrupt hippocampal episodic memory function—classified by Perouansky and Pearce into static and dynamic.3  The static scenario posits that repetitive stimuli are unable to strengthen synaptic connections due to a shift in the balance from excitation to inhibition by GABAA receptor inhibitory postsynaptic currents. The indirect dynamic scenario invokes a GABAA-mediated disruption of the timing of hippocampal theta and/or gamma rhythms that are thought to be essential to induction of synaptic plasticity.4  Currently there is insufficient experimental evidence to indicate the relative importance of these two scenarios.
In this paper we use a computational model of a hippocampal network to explore the validity of each scenario. The basis for these experiments is an essential insight into the mechanism by which the brain represents memories provided by the cell assembly hypothesis. A cell assembly is an anatomically dispersed set of neurons with excitatory connections that have been strengthened by synchronous activity of the pre- and postsynaptic neurons.5  Such cell assemblies can be identified in computational neural networks incorporating synaptic plasticity.6,7  In this context they are termed polychronous groups6  and are defined as strongly connected sets of neurons firing in a reproducible and precisely timed sequential manner.
For our experiments, we use a simple network representing the hippocampus and entorhinal cortex to investigate whether the GABAA facilitatory effects of propofol at clinically relevant plasma concentrations disrupt the process of polychronous group formation (learning) in response to a repeated sensory stimulus.
A distinct but related question concerns the manner in which the brain determines whether the firing of a group of neurons represents activation of a memory trace. A theoretical framework that has been proposed postulates that the brain acts as a Bayesian classifier by maintaining internal probabilistic models that are updated by incoming neural sensory information.8  Of note, Bayesian classifiers have already been used with considerable success in unsupervised machine learning. We investigate the results of our learning experiments in the network model using a Bayesian classifier to determine the extent to which disruption of polychronous group formation by GABAA facilitation may prevent the brain from correctly identifying a previously learned stimulus.
Materials and Methods
Neural Network Model
The neural network model is based on our previously published model.7  Here we summarize the important features of this model and describe in detail departures from the original work.
Anatomy
The model, while not a recreation of a particular hippocampal region, incorporates many quantitative details of the cornu ammonis 3 region of mammalian hippocampus.9  To prevent boundary artifacts, the neurons are randomly distributed on a sphere with a radius of 8 mm (fig. 1). Excitatory cells constitute 80% of the neurons. Each neuron has 896 synapses. Fifty percent of excitatory neurons’ axonal terminals are unmyelinated and synapse on local cells within a radius of 2.5 mm; the remainder synapse on cells within a 2-mm radius of a randomly chosen myelinated axonal terminus at a distance of 10 to 15 mm. Inhibitory neuron synapses occur within a 1-mm radius of the neuronal soma. Spike propagation is much faster in myelinated axons (1 m · s−1) than in unmyelinated axons (0.15 m · s−1).10 
Fig. 1.
Schematic of anatomical properties of the model. Each neuron has 896 synapses. The model is comprised of two distinct modules. The hippocampal module contains 7,680 neurons, of which 80% are excitatory pyramidal cells. Fifty percent of excitatory neuron synapses are via nonmyelinated collaterals, and the remainder connect via a myelinated axon. All inhibitory cells synapse locally. A distinct entorhinal cortical module contains 600 neurons, of which 80% are excitatory stellate cells. All connections within the entorhinal module are via nonmyelinated axon collaterals. The output of the excitatory cells of this module serves as the input for the pyramidal cells of the hippocampal module. r = radius in mm; v = velocity in m · s−1.
Schematic of anatomical properties of the model. Each neuron has 896 synapses. The model is comprised of two distinct modules. The hippocampal module contains 7,680 neurons, of which 80% are excitatory pyramidal cells. Fifty percent of excitatory neuron synapses are via nonmyelinated collaterals, and the remainder connect via a myelinated axon. All inhibitory cells synapse locally. A distinct entorhinal cortical module contains 600 neurons, of which 80% are excitatory stellate cells. All connections within the entorhinal module are via nonmyelinated axon collaterals. The output of the excitatory cells of this module serves as the input for the pyramidal cells of the hippocampal module. r = radius in mm; v = velocity in m · s−1.
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Fig. 1.
Schematic of anatomical properties of the model. Each neuron has 896 synapses. The model is comprised of two distinct modules. The hippocampal module contains 7,680 neurons, of which 80% are excitatory pyramidal cells. Fifty percent of excitatory neuron synapses are via nonmyelinated collaterals, and the remainder connect via a myelinated axon. All inhibitory cells synapse locally. A distinct entorhinal cortical module contains 600 neurons, of which 80% are excitatory stellate cells. All connections within the entorhinal module are via nonmyelinated axon collaterals. The output of the excitatory cells of this module serves as the input for the pyramidal cells of the hippocampal module. r = radius in mm; v = velocity in m · s−1.
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A distinct entorhinal cortical module is comprised of stellate neurons and inhibitory neurons on the surface of a 1-mm sphere. The ratio of excitatory to inhibitory neurons and number of synaptic connections is identical to the hippocampal network. All connections within the entorhinal module are via unmyelinated axons.
In comparison to our original published model, which represented a neocortical region, cells in the hippocampal network have a fourfold greater number of connections with a somewhat greater spread from the soma or axonal termination. These modifications bring neuronal connection probabilities closer to levels found in vivo in rat hippocampus and improve the ability of the network to form memories in response to training stimuli.
Neural Model
The network contains 7,680 neurons in a single hippocampal region and 600 neurons within the entorhinal cortex. The spike timing dynamics of each neuron are simulated using Izhikevich’s quadratic spiking neuron model that reproduces the spiking and bursting characteristics of a vast number of neuronal types. In the Izhikevich formulation, neurons are modeled by a two-dimensional system of ordinary differential equations11 :

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(1)

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(2)

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(3)
where C is the membrane capacitance, v is the membrane potential (mV), vr is the resting potential, vt is the instantaneous threshold potential, u is the recovery variable, c is the postspike membrane potential reset (mV), and I represents the net synaptic and random input currents (pA). The parameters k, a, b, and d are dimensionless and vary according to neuron type (table 1).
Table 1.
Parameters Used for Modeling Neurons
Parameters Used for Modeling Neurons×
Parameters Used for Modeling Neurons
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Table 1.
Parameters Used for Modeling Neurons
Parameters Used for Modeling Neurons×
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By varying the parameters of the differential equations, the model can generate excitatory neuronal spiking patterns ranging from regular spiking to chattering types and inhibitory neurons with a fast spiking response.7,11  The neuronal equations are calculated at 1-ms time steps.
Input
Each neuron receives synaptic input from other neurons. In the absence of external input, the hippocampal network remains quiet. To avoid this silent state of the network, the excitatory neurons are driven by input from the entorhinal stellate cells and spontaneous synaptic release, which is simulated by one (Poissonian) release per synapse per second. The entorhinal module is also driven by the 1-Hz Poisson process simulating spontaneous synaptic release in conjunction with external current of an amplitude chosen to stimulate firing of the stellate cells at around 6 Hz.
Synaptic transmission is modeled by increasing the conductance of the receptor channel in response to a spike event. Conductance for the α-amino-3-hydroxy-5-methylisoxazole-4-proprionic acid, N-methyl-d-aspartate, GABAA, and γ-aminobutyric acid receptor type B receptors12,13  is modeled using equations incorporating parameters for reversal potential and channel decay times consistent with neurophysiologic experimental data.14 
The ratio of α-amino-3-hydroxy-5-methylisoxazole-4-proprionic acid to N-methyl-d-aspartate synapses is set at 1 for the excitatory neurons. Similarly, the ratio of GABAA to γ-aminobutyric acid receptor type B synapses is set at 1 for all inhibitory neurons.
Synaptic Plasticity
At the start of a simulation, excitatory synaptic weights in the hippocampal neurons are set randomly within the range (0 to 1). These are then modified by spike-timing–dependent plasticity, a variant of the classical “Hebbian” plasticity (“when an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficiency, as one of the cells firing B, is increased”15 ) that has been modified to take into account the relative spike timing dependency of these changes.16,17  When a spike from a presynaptic neuron i arrives at a postsynaptic neuron j before it fires, the accumulated synaptic change (cE) is modified in the direction of potentiation according to the difference between the time of arrival of the spike from neuron i (ti) and the time that neuron j spikes (tj), reflecting the notion that the presynaptic spike arrived at a time compatible with having a causal effect on the postsynaptic cell:

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(4)
Similarly, if neuron j spikes before the arrival of the spike from neuron i, accumulated synaptic change is modulated in the direction of depression according to the difference between tj and ti, consistent with the notion that the presynaptic pulse was too late to have any effect on the timing of the postsynaptic spike:

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(5)
Synaptic weights were clipped to remain in the range (0 to 12) simply to prevent “runaway” potentiation. Inhibitory and stellate cell synaptic weights are not modified by spike-timing–dependent plasticity in the model and are fixed.
To model the short-term depression of synaptic weights that occurs with repeated firing of pyramidal cells and some interneurons, a phenomenologic model7,18  was used to scale down synaptic conductance immediately after firing. The synaptic weight was reduced by a per-synapse scalar factor x that recovers with a time constant of 150 ms:

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(6)
Learning Stimuli
During training, four unique spatiotemporal firing patterns are repeatedly presented to the hippocampal network. Each pattern contains the same set of 200 excitatory neurons but with a different (chosen randomly) firing order in which the neurons are fired at consecutive 1-ms time intervals during a 200-ms window. The four patterns, hereinafter referred to as patterns A through D, are presented sequentially to the network with a spacing of 2 s throughout a “learning” epoch (see “Computer Simulation”).
Effects of Propofol
We take propofol as an exemplar of anesthetic agents that act primarily by facilitation of GABAA channels. In clinical use, the effect site concentration of propofol is considerably lower than the total plasma concentration due to sequestration of around 97% by plasma proteins. General anesthesia occurs with a total plasma propofol concentration of around 10 to 30 μM (1.8 to 5.4 μg · ml−1), whereas a widely cited estimate of the EC50 for free blood propofol is 0.4 μM. The free blood propofol EC50 differs considerably from propofol concentrations that facilitate GABAA channels in vitro where the majority of change occurs in a range from 1 to 30 μM. Explanations for this discrepancy may include drug precipitation and nonspecific binding to the experimental reagents and apparatus.19  Currently it is impossible to make a direct correlation between the effects of free propofol in the blood and the calculated or nominal concentration in vitro.
Throughout this paper, propofol concentrations are reported as the in vitro propofol concentration on which GABAA channel effects are based. The action of propofol is simulated by increasing the conductance of the GABAA channels by between 100 and 800% and the decay times to between 12 and 48 ms, consistent with in vitro data in the concentration range 0.05 to 30 μM (0.1 to 5.4 μg · ml−1).7,20–22  For classification purposes, we refer to low-dose propofol as a concentration that potentiates GABAA channel function by up to 200%,22  high-dose propofol as a concentration potentiating GABAA by greater than 500%, and moderate doses as propofol concentrations between these extremes. Based on the range and magnitude of in vitro GABAA channel potentiation change, one could argue that low-dose propofol is linked to minimal clinical effects, moderate dose to sedation, and high-dose to general anesthesia. However, the uncertain linkage between the free plasma propofol and in vitro propofol concentrations makes such comparisons fraught. Given previously demonstrated insensitivity to the potential effects of propofol on long-term potentiation at high plasma concentrations,7  we opted to omit this feature in the current model.
Local Field Potential
A simulated local field potential signal is generated from the mean of the synaptic currents in the excitatory hippocampal network neurons. Power spectral density plots generated by Fourier transform are used to perform frequency analysis of the local field potential.
Theta Rhythm
The hippocampal module alone does not exhibit theta oscillations (see “Results”). To ascertain the importance of an intact theta rhythm,23  a subset of experiments is performed with the entorhinal cortical module removed.
Analysis
Our principal method of assessing memory function in our network is to quantitate the numbers and sizes of intercommunicating collections of neurons, termed polychronous groups,6  formed during exposure to patterned stimuli. We consider such groups to be indicative of the kinds of group responses that may occur in real nervous systems during memory formation. In our previous work,7  we used the original method of template matching described by Izhikevich.6 
Recent work24  has demonstrated that the template-matching technique can underestimate the frequency of polychronous group firing and presents an improved, probabilistic, method termed response fingerprinting. To determine whether a neuron fires as part of a stimulus-related polychronous group, we examine cumulative spike histograms from multiple presentations of the previously learned pattern. During this “recall” epoch (see “Computer Simulation”), synaptic weights are frozen to prevent any further learning. Each pattern A through D or a null pattern is presented to the network on 1,600 occasions to generate a cumulative histogram for every neuron with spike count offset in milliseconds from the start of the pattern presentation (fig. 2). The majority of neurons, not being members of a polychronous group associated with a learned pattern, only fire at random times during the recall epoch. Some neurons consistently fire at fixed intervals following pattern representation, producing one or more peaks in the spike histogram. For these neurons, spiking activity is strongly associated with representation of the original pattern, providing evidence that the neuron is part of a stimulus-related polychronous group. In such cases, we define a temporal window that spans the largest peak of spike counts. The aggregate of temporal windows for all neurons that are associated with the pattern define a response fingerprint, providing a unique spatiotemporal signature of polychronous group neural firing in response to a stimulus.24  The neurons that are directly stimulated as part of the pattern are not included in the response fingerprint. We quantify polychronous group formation by the number of neurons contained in the response fingerprint and polychronous firing activity by the number of neural spikes occurring within the temporal windows throughout the recall epoch. With this method, the delay intervals between spikes and the numbers of spikes in a group are not specified as parameters, but rather emerge as a result of the response fingerprinting analysis.
Fig. 2.
Spike count histograms for two neurons after 1,600 presentations of pattern A during the recall epoch. Offset is time in milliseconds from start of pattern presentation. A neuron that is not part of a polychronous group associated with pattern A (upper panel) fires at random times during replay of the pattern. Some neurons consistently fire at a particular time during pattern replay, producing peaks in the spiking count histogram. These peaks indicate that the neuron fires as part of a stimulus-related polychronous group. The timing of peaks over multiple neurons produces a spatiotemporal signature of group activation in response to the stimulus.
Spike count histograms for two neurons after 1,600 presentations of pattern A during the recall epoch. Offset is time in milliseconds from start of pattern presentation. A neuron that is not part of a polychronous group associated with pattern A (upper panel) fires at random times during replay of the pattern. Some neurons consistently fire at a particular time during pattern replay, producing peaks in the spiking count histogram. These peaks indicate that the neuron fires as part of a stimulus-related polychronous group. The timing of peaks over multiple neurons produces a spatiotemporal signature of group activation in response to the stimulus.
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Fig. 2.
Spike count histograms for two neurons after 1,600 presentations of pattern A during the recall epoch. Offset is time in milliseconds from start of pattern presentation. A neuron that is not part of a polychronous group associated with pattern A (upper panel) fires at random times during replay of the pattern. Some neurons consistently fire at a particular time during pattern replay, producing peaks in the spiking count histogram. These peaks indicate that the neuron fires as part of a stimulus-related polychronous group. The timing of peaks over multiple neurons produces a spatiotemporal signature of group activation in response to the stimulus.
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Bayesian Classifier
To relate the rather abstract results we obtain describing the effects of simulated propofol administration on polychronous group formation during training to possible reduced performance in a recall task, we implement a naive Bayesian classifier.24  Performance of this classifier depends only on the statistics of polychronous groups and not on other possible effects of propofol sedation, such as reduced sensitivity of downstream neuronal areas to spiking from areas included in the model that might further reduce performance; accordingly, results obtained with the Bayesian classifier should not be taken as anything more than a general indicator of network function (see Discussion).
Briefly, we define a spike occurring within a temporal window as a window activation. Applying Bayes’ theorem, for input pattern (ip) and window activation (act), we find

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(7)
Each response fingerprint generally contains more than one temporal window. Here we assume conditional independence of window activations to give

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(8)
A naive Bayesian classifier allows one to decide on the presence or absence of a stimulus given the set of window activations. Our implementation of the classifier simplifies to

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(9)
Equation 9 is applied to the response fingerprints for patterns A through D and the null pattern. The classifier selects the response fingerprint with the highest probability given the observed window activations.
Identification of temporal windows and collection of statistics for the final term of Equation 9 are completed more than 1,600 trials for each pattern. The accuracy of the classifier is then quantified more than 4,800 trials across all patterns. To further investigate the properties of the classifier, receiver operating characteristic curves are calculated by varying the minimum probability threshold required for the classifier to select a particular response fingerprint over the alternate response fingerprints.
Computer Simulation
The code simulating the neural network is purpose-written for parallel processing in the CUDA (Compute Unified Device Architecture, NVIDIA, USA) extension to the C programming language and run on a computational server with eight NVIDIA Tesla K80 graphical processing units (Red Barn High Performance Computing, USA) with the Linux operating system (CentOS, USA). Graphing functions and statistical analysis are performed with Matlab (Mathworks, USA).
Before being used in the memory experiments, each hippocampal network is simulated for 10 h of simulation time, receiving only random input, allowing stabilization of synaptic weights under the spike-timing–dependent plasticity rule. Input from the entorhinal cortical module is incorporated after the initial stabilization period. The remaining simulation time is divided into two distinct epochs (fig. 3). During the learning epoch, each pattern is presented sequentially to the network with a spacing of 2 s. Preliminary experiments determined the optimum duration of the learning epoch to be 120 s (see Results). At the completion of the learning epoch, no further changes in synaptic weight are allowed and the recall epoch commences. The effect of propofol, if present, is simulated during the learning epoch. In experiments investigating the absence of theta, the entorhinal module was not present at any time during the simulation.
Fig. 3.
After sufficient simulation time to allow stabilization of synaptic weights, the network is presented with four stimuli (patterns A through D) comprising the same set of 200 neurons fired in differing orders during a 200-ms interval. During a 120-s learning epoch, the stimuli are presented sequentially with a spacing of 2 s. The γ-aminobutyric acid receptor type A potentiating effects of propofol, if present, are incorporated during this learning epoch. At the completion of learning, propofol effects are withdrawn, synaptic weights are frozen, and patterns A through D and a null pattern are serially presented to the network during a recall epoch to determine whether the spiking output data are consistent with polychronous group formation.
After sufficient simulation time to allow stabilization of synaptic weights, the network is presented with four stimuli (patterns A through D) comprising the same set of 200 neurons fired in differing orders during a 200-ms interval. During a 120-s learning epoch, the stimuli are presented sequentially with a spacing of 2 s. The γ-aminobutyric acid receptor type A potentiating effects of propofol, if present, are incorporated during this learning epoch. At the completion of learning, propofol effects are withdrawn, synaptic weights are frozen, and patterns A through D and a null pattern are serially presented to the network during a recall epoch to determine whether the spiking output data are consistent with polychronous group formation.
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Fig. 3.
After sufficient simulation time to allow stabilization of synaptic weights, the network is presented with four stimuli (patterns A through D) comprising the same set of 200 neurons fired in differing orders during a 200-ms interval. During a 120-s learning epoch, the stimuli are presented sequentially with a spacing of 2 s. The γ-aminobutyric acid receptor type A potentiating effects of propofol, if present, are incorporated during this learning epoch. At the completion of learning, propofol effects are withdrawn, synaptic weights are frozen, and patterns A through D and a null pattern are serially presented to the network during a recall epoch to determine whether the spiking output data are consistent with polychronous group formation.
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Each experiment is performed on 100 unique network instances. Aggregated data from these 100 simulations are described by the mean and SD, unless otherwise specified.
Results
At the start of the network simulation, cell firing activity approaches the frequency of the 1-Hz external excitatory input. During the subsequent 10 h, under the influence of synaptic plasticity responding to random input, synaptic weights distribute more or less uniformly, although around 15% of weights come to lie close to the defined maximum strength. While any given synaptic weight varies continuously during the simulation, by the 10-h time point, the aggregate behavior of the network has reached a steady state as measured by the distribution of synaptic weights and the firing frequency of the neuronal subtypes.
We have previously shown, using methods based on anatomical analysis of connection strengths, that more than 105 polychronous neural groups form in a cortical network of identical size in the presence of synaptic plasticity responding to random input. For the current experiment, our detection method for polychronous groups is restricted to those groups linked to a particular stimulus. Nevertheless, during the recall epoch in the untrained network, we see evidence that some neurons are strongly connected to member neurons of previously unseen patterns. This is to be expected given the proportion of synaptic weights that are close to maximum strength and the random nature of the excitatory input. The randomly formed stimulus-linked groups are not large, generally containing fewer than three neurons. Such findings are not inconsistent with previous experiments given that we only search for groups in a small subset of the range of possible polychronous groups.
Dynamics of Network Learning
In preliminary learning experiments, the duration of the learning epoch ranged from 20 to 200 s. With sequential presentation of the four patterns with a spacing of 2 s, the network was exposed to each pattern between 2 and 25 times. A metric of the extent to which a pattern is learned is the size of the stimulus-related polychronous group determined during the recall epoch. With only two presentations during learning, stimulus-related groups comprise 83 ± 21 neurons, while after a 120-s learning epoch, group sizes are 125 ± 33 neurons (fig. 4). Further lengthening of the learning epoch leads to only modest increases in group sizes, and so a duration of 120 s is used for all subsequent experiments.
Fig. 4.
Stimulus-related polychronous group (PNG) size (in neurons) is dependent on the duration of the learning epoch. The mean size of stimulus-related groups associated with patterns A through D increases with longer duration of the learning epoch. SD for 100 trials is indicated by the shaded region.
Stimulus-related polychronous group (PNG) size (in neurons) is dependent on the duration of the learning epoch. The mean size of stimulus-related groups associated with patterns A through D increases with longer duration of the learning epoch. SD for 100 trials is indicated by the shaded region.
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Fig. 4.
Stimulus-related polychronous group (PNG) size (in neurons) is dependent on the duration of the learning epoch. The mean size of stimulus-related groups associated with patterns A through D increases with longer duration of the learning epoch. SD for 100 trials is indicated by the shaded region.
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To eliminate the possibility that pattern learning increases synaptic strengths in a nonspecific manner for other patterns, we conducted some experiments with single-pattern training. As expected, the polychronous group size associated with the learned pattern is equivalent to that seen during four-pattern training. Reassuringly, when the unseen patterns were presented during recall, the stimulus-related polychronous group contained at most several neurons, much like the results seen with random input alone.
Polychronous Group Size
Potentiation of GABAA receptors during the learning epoch limits the formation of polychronous groups associated with each stimulus. At low propofol concentrations, group size reductions are only modest. At moderate propofol concentrations, group size decreases by 69 ± 11% (fig. 5). The collapse in group formation at this concentration of propofol is also reflected by a 73 ± 10% reduction in spiking associated with representation of the stimulus. At the higher concentrations of propofol, polychronous group size decreases to levels equivalent to those measured when the learning epoch is omitted.
Fig. 5.
γ-Aminobutyric acid receptor type A receptor potentiation reduces stimulus-related polychronous group (PNG) size. The mean size of stimulus-related groups associated with patterns A through D decreases as γ-aminobutyric acid receptor type A channel conductance and decay times increase, consistent with the action of propofol at increasing plasma concentrations. SD for 100 trials is indicated by the correspondingly colored shaded region.
γ-Aminobutyric acid receptor type A receptor potentiation reduces stimulus-related polychronous group (PNG) size. The mean size of stimulus-related groups associated with patterns A through D decreases as γ-aminobutyric acid receptor type A channel conductance and decay times increase, consistent with the action of propofol at increasing plasma concentrations. SD for 100 trials is indicated by the correspondingly colored shaded region.
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Fig. 5.
γ-Aminobutyric acid receptor type A receptor potentiation reduces stimulus-related polychronous group (PNG) size. The mean size of stimulus-related groups associated with patterns A through D decreases as γ-aminobutyric acid receptor type A channel conductance and decay times increase, consistent with the action of propofol at increasing plasma concentrations. SD for 100 trials is indicated by the correspondingly colored shaded region.
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Bayesian Classifier
To link stimulus-related polychronous group size to a quantitative measure of the memory function of our network, we implement a Bayesian classifier using probability scores for stimulus-related spiking calculated during the first part of the recall epoch. Under baseline conditions, the classifier identifies which pattern (A through D or null) is being represented to the network with an accuracy approaching 100%. (Because the length of stimulus presentation was determined as described previously, we did not assess whether shorter learning times would affect results with the Bayesian classifier.) As shown in figure 3, propofol is applied during the learning epoch to model effects on memory formation during propofol treatment. Low doses of propofol have little effect on the accuracy of the classifier.
At 4 μM (0.63 μg · ml−1) propofol concentration, concurrent with substantial reductions in stimulus-related polychronous group sizes, the classifier correctly identifies the represented pattern only 72 ± 13% of the time (fig. 6A). At high concentrations of propofol, the algorithm entirely loses the ability to recognize previously learned patterns. Examination of the association between polychronous group size and classifier accuracy across all propofol concentrations demonstrates a direct relationship (fig. 6B) where the accuracy decreases substantially when group size is lowest and little firing information is present. Receiver operating characteristic analysis (fig. 6C) confirms the reliability of the classifier for propofol concentrations less than 10 μM (1.8 μg · ml−1), at which point significant false-positive contamination indicates a poor discriminating accuracy.
Fig. 6.
(A) Performance of a Bayesian classifier in determining which pattern was presented to the network during the recall epoch based on the spiking output. The mean accuracy of the classifier in the identification of either patterns A through D (cyan) or the null pattern (red) decreases as γ-aminobutyric acid receptor type A channel potentiation increases, consistent with the action of propofol at increasing plasma concentrations. At moderate concentrations of propofol, the classifier accuracy decreases to around 70% and completely loses the ability to reliably recognize previously learned patterns at plasma concentrations consistent with general anesthesia. SD for 100 trials is indicated by the correspondingly colored shaded regions. (B) Scatterplot demonstrating the relationship between polychronous group (PNG) size and classifier accuracy for all plasma propofol concentrations. The classifier fails when the group size decreases to less than 25% of baseline. (C) Receiver operating characteristic analysis demonstrates that at propofol concentrations (conc.) beyond 4 μM, increasing levels of false positives must be accepted to obtain positive identifications with high reliability.
(A) Performance of a Bayesian classifier in determining which pattern was presented to the network during the recall epoch based on the spiking output. The mean accuracy of the classifier in the identification of either patterns A through D (cyan) or the null pattern (red) decreases as γ-aminobutyric acid receptor type A channel potentiation increases, consistent with the action of propofol at increasing plasma concentrations. At moderate concentrations of propofol, the classifier accuracy decreases to around 70% and completely loses the ability to reliably recognize previously learned patterns at plasma concentrations consistent with general anesthesia. SD for 100 trials is indicated by the correspondingly colored shaded regions. (B) Scatterplot demonstrating the relationship between polychronous group (PNG) size and classifier accuracy for all plasma propofol concentrations. The classifier fails when the group size decreases to less than 25% of baseline. (C) Receiver operating characteristic analysis demonstrates that at propofol concentrations (conc.) beyond 4 μM, increasing levels of false positives must be accepted to obtain positive identifications with high reliability.
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Fig. 6.
(A) Performance of a Bayesian classifier in determining which pattern was presented to the network during the recall epoch based on the spiking output. The mean accuracy of the classifier in the identification of either patterns A through D (cyan) or the null pattern (red) decreases as γ-aminobutyric acid receptor type A channel potentiation increases, consistent with the action of propofol at increasing plasma concentrations. At moderate concentrations of propofol, the classifier accuracy decreases to around 70% and completely loses the ability to reliably recognize previously learned patterns at plasma concentrations consistent with general anesthesia. SD for 100 trials is indicated by the correspondingly colored shaded regions. (B) Scatterplot demonstrating the relationship between polychronous group (PNG) size and classifier accuracy for all plasma propofol concentrations. The classifier fails when the group size decreases to less than 25% of baseline. (C) Receiver operating characteristic analysis demonstrates that at propofol concentrations (conc.) beyond 4 μM, increasing levels of false positives must be accepted to obtain positive identifications with high reliability.
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Dynamics of Forgetting
In five network instances, we investigate the dynamics of forgetting by progressively increasing the time between the learning epoch and the recall epoch. During this interval, synaptic plasticity and random excitatory input continue to interact, and GABAA potentiation, if already present, is maintained. Under baseline conditions, the size of the stimulus-related polychronous group decreases in an approximately linear fashion, with a 50% reduction at around 1,600 s after learning (fig. 7, A and B). At propofol concentrations of 4 μM (0.63 μg · ml−1), the group size decreases much more rapidly, with a 62 ± 18% decline at 400 s postlearning, by which time the accuracy of the classifier is only 38 ± 14% (fig. 7C).
Fig. 7.
The dynamics of forgetting are investigated in five network instances by progressively increasing the time between the learning epoch and the recall epoch. During this interval, synaptic plasticity and random excitatory input continue to interact and γ-aminobutyric acid receptor type A potentiation, if already present, is maintained. Mean size of the stimulus-related polychronous group (PNG) associated with patterns A through D decreases with increasing time after the completion of learning, both in absolute terms (A) and as a percentage of the original group size measured immediately after learning (B). (C) The mean Bayesian classifier accuracy decreases in a corresponding manner. Increasing plasma propofol concentrations (conc.) reduce absolute group sizes and classifier accuracy while increasing the rate of decline in these metrics over time.
The dynamics of forgetting are investigated in five network instances by progressively increasing the time between the learning epoch and the recall epoch. During this interval, synaptic plasticity and random excitatory input continue to interact and γ-aminobutyric acid receptor type A potentiation, if already present, is maintained. Mean size of the stimulus-related polychronous group (PNG) associated with patterns A through D decreases with increasing time after the completion of learning, both in absolute terms (A) and as a percentage of the original group size measured immediately after learning (B). (C) The mean Bayesian classifier accuracy decreases in a corresponding manner. Increasing plasma propofol concentrations (conc.) reduce absolute group sizes and classifier accuracy while increasing the rate of decline in these metrics over time.
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Fig. 7.
The dynamics of forgetting are investigated in five network instances by progressively increasing the time between the learning epoch and the recall epoch. During this interval, synaptic plasticity and random excitatory input continue to interact and γ-aminobutyric acid receptor type A potentiation, if already present, is maintained. Mean size of the stimulus-related polychronous group (PNG) associated with patterns A through D decreases with increasing time after the completion of learning, both in absolute terms (A) and as a percentage of the original group size measured immediately after learning (B). (C) The mean Bayesian classifier accuracy decreases in a corresponding manner. Increasing plasma propofol concentrations (conc.) reduce absolute group sizes and classifier accuracy while increasing the rate of decline in these metrics over time.
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Theta Rhythm
Power spectral density plots of the simulated local field potential from combined hippocampal and entorhinal networks demonstrate the presence of a de novo theta rhythm with a frequency of around 6 Hz. Propofol concentrations up to 4 μM (0.63 μg · ml−1) increase theta frequency, while higher concentrations decrease the frequency of the oscillation (fig. 8A). To ascertain the contribution of theta to the memory functions of the network, the experiments were repeated absent the entorhinal cortical module at all propofol concentrations. Power spectral density plots confirmed disappearance of theta. Despite this, there was no measurable effect on the size of stimulus-related groups (fig. 8B) or the accuracy of the Bayesian classifier (data not shown).
Fig. 8.
(A) The influence of γ-aminobutyric acid receptor type A receptor potentiation on theta frequency. Theta frequency increases at low plasma propofol concentrations and decreases at higher concentrations. The inset graph shows representative power spectrogram of local field potential at baseline. (B) The influence of theta rhythm on polychronous group size. Mean size of stimulus-related groups (in neurons) associated with a pattern in the absence (blue) or presence (red) of a theta oscillation originating from the entorhinal cortex. Removal of theta has a minimal effect on polychronous group sizes. SD for 100 trials is indicated by the correspondingly colored shaded regions. f = frequency (Hz).
(A) The influence of γ-aminobutyric acid receptor type A receptor potentiation on theta frequency. Theta frequency increases at low plasma propofol concentrations and decreases at higher concentrations. The inset graph shows representative power spectrogram of local field potential at baseline. (B) The influence of theta rhythm on polychronous group size. Mean size of stimulus-related groups (in neurons) associated with a pattern in the absence (blue) or presence (red) of a theta oscillation originating from the entorhinal cortex. Removal of theta has a minimal effect on polychronous group sizes. SD for 100 trials is indicated by the correspondingly colored shaded regions. f = frequency (Hz).
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Fig. 8.
(A) The influence of γ-aminobutyric acid receptor type A receptor potentiation on theta frequency. Theta frequency increases at low plasma propofol concentrations and decreases at higher concentrations. The inset graph shows representative power spectrogram of local field potential at baseline. (B) The influence of theta rhythm on polychronous group size. Mean size of stimulus-related groups (in neurons) associated with a pattern in the absence (blue) or presence (red) of a theta oscillation originating from the entorhinal cortex. Removal of theta has a minimal effect on polychronous group sizes. SD for 100 trials is indicated by the correspondingly colored shaded regions. f = frequency (Hz).
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Discussion
In this experiment, we studied a computational model of a hippocampal network. Critically, the model demonstrates the ability to learn and recall stimuli—capabilities that follow from the inclusion of important details including synaptic plasticity, realistic neuronal dynamics, and action of excitatory and inhibitory neurotransmitters. By examining spiking output in response to a repeated stimulus, it was shown that the network forms large polychronous neural groups firing consistently at fixed times after stimulus presentation.
The effect of propofol on the network was simulated by increasing conductance and decay times of GABAA channels. At moderate propofol concentrations, GABAA facilitation reduced the size of stimulus-related polychronous groups by around 70% and reduced the number of neuronal spikes associated with a learned stimulus by a similar amount.
A Bayesian classifier was accurate in determining whether neural activity after a stimulus presentation was consistent with pattern A through D or the null pattern. Classifier accuracy is reduced to around 70% at moderate concentrations of propofol and is completely unreliable when GABAA facilitation is consistent with high concentrations. Bayesian classifier performance is sensitive to the complexity of the categorization task. When only two patterns were to be discriminated (data not shown), the classifier was accurate until tested in the presence of high propofol concentrations. Conversely, one might reasonably expect that a greater number of patterns than four will lead to further deterioration in classifier accuracy at low concentrations of propofol.
Bayesian theories of brain function posit that the brain assigns a probability distribution to hypotheses that is then revised according to standard probabilistic rules of inference.8,25,26  Such theories have enjoyed explanatory success in the study of perception and motor control. There is still debate as to how such rules may be represented neurobiologically and whether these theories are merely approximate descriptions of brain behavior.27,28 
If the brain functions in the manner of a Bayesian classifier with comparable accuracy to that implemented here, our results imply that GABAA facilitation at moderate propofol concentrations partially mediates the memory impairment that is observed clinically, at least for four pattern discrimination experiments. Here we consider four possibilities to explain the somewhat better accuracy of the classifier than one would expect at low propofol doses correlated with amnesia: (1) network components or neuronal types necessary for pattern recognition may not have been included in the model and may be subject to propofol effects not considered here, (2) hippocampal GABAA receptors may interact differently than cortical receptors with propofol, (3) alterations of oscillatory patterns within the hippocampus may play an important role, and (4) testing for recall in our experiment occurs earlier than in clinical studies.
First, the Bayesian classifier essentially assumes that all information available in the spiking of representative neuronal areas included in the model is available to other brain areas involved in the production of observable responses to stimuli, and that these areas function at uncompromised levels in the presence of the γ-aminobutyric acid–mediated agonist. This is quite unlikely; some degradation of the function of the classifier itself would need to be considered to obtain better agreement with the behavioral data.
GABAA receptors comprise a family of channels composed of five subunits. Twenty-five percent of hippocampal GABAA receptors incorporate α5 subunits,29  whereas these subunits are sparsely expressed elsewhere in the brain.
The importance of α5-GABAA receptor modulation mediating etomidate-induced memory impairment is well established. The prevailing explanation stressed the importance of extrasynaptic α5-GABAA receptors in enhancement of tonic inhibition of pyramidal cells.30,31  More recent work2  has demonstrated that tonic inhibition of pyramidal cells by etomidate is dissociable from long-term potentiation and that etomidate differentially enhances activity of α5-GABAA receptors on specific inhibitory hippocampal interneuronal subtypes. To explain the counterintuitive notion that inhibition of inhibitory cells prevents memory formation, it has been postulated that the particular interneurons targeted by etomidate are those that predominantly suppress activity of other interneurons.32 
Less is known about the importance of α5-GABAA receptors in propofol-induced memory impairment.33  The measurements upon which we based our propofol parameters were obtained from patch clamp studies of GABAA receptors in hypothalamic neurons20  that would be unlikely to contain α5 given their origin. If the action of propofol on memory is also mediated by facilitation of hippocampal α5-GABAA receptors, our simulated propofol actions do not incorporate extrasynaptic receptor binding and may underestimate the aggregate effects of propofol binding on channel conductance and decay time. This in turn could underestimate the effect of propofol on group formation and artifactually increase classifier accuracy. Clearly, further experiments are required to clarify the nature of the interaction between propofol and α5-GABAA receptors.
The model allowed exploration of the importance of the dynamic scenario proposed by Perouansky and Pearce.3  The combined hippocampal and entorhinal network spontaneously generates theta oscillations, the frequency of which is sensitive to changes in propofol concentration. While in vitro hippocampal preparations can generate theta rhythms,34  the dominant mechanism driving theta in awake behaving animals appears to derive from inputs to hippocampal neurons from pacemaker cells in the entorhinal cortex and medial septum.23,35,36  The structure of our hippocampal network does not reproduce all anatomical and cellular complexities of the hippocampus and associated structures. Thus it was unsurprising that absent the entorhinal module, power spectrograms of the local field potential from the hippocampal network demonstrate no spontaneous theta rhythmicity.
Removal of theta had no measurable effect on memory performance of the network at all propofol concentrations as determined by polychronous group size and classifier accuracy. This lack of difference indicates that changes in GABAA channel conductance and decay times have a substantially greater effect on memory formation than complete disruption of theta.
It is beyond the scope of this paper to explore whether subtler theta changes including alterations in amplitude, frequency, or coherence will influence memory impairment due to propofol. Computer modeling suggests that ketamine may disrupt theta modulation of the gamma rhythm,37  directing another line of inquiry. While the importance of the dynamic scenario in memory impairment is still unclear, preliminary evidence from these experiments suggests at most a nondominant role.
Some of the discrepancy between our experimental classifier results and those reported clinically is accounted for by differences in the timing of the recall epoch.38  Unlike in clinical studies, we are not beholden to propofol’s pharmacokinetics and can test for recall immediately after learning. Polychronous groups in the network at baseline have a half-life in terms of size of around 1,600 s after learning, during which time the accuracy of the classifier drops from near 100% to around 93%. In the presence of a moderate propofol concentration, group size decreases by half within 400 s, at which point the classifier accuracy is less than 40%. In clinical studies, to eliminate the effect of residual propofol on recall, memory is tested at many minutes to hours after the learning tasks.38,39  Testing for immediate recall will underestimate the extent of memory impairment for a given propofol concentration when compared to the results of clinical studies with measurement conducted at later time points.
Here we presented a sequence of four patterns, while in a natural environment it is more likely that a single pattern remains present for some time before being replaced by another. In our simulation protocol, synaptic changes occurring in response to one pattern were constantly subject to partial disruption by the immediate presence of the following pattern, thereby interfering with a more natural course of learning. The suggestion that oscillatory sharp waves and ripples occurring in the hippocampus may allow replay of temporally compressed memories provides a mechanistic bridge for the substantial repetition that may be required to achieve memory consolidation and recall.24,35 
An alternate interpretation of our results may be afforded if we repudiate the concept of the Bayesian brain. The substantial reductions in stimulus-related polychronous group sizes that we see at propofol concentrations of 4 μM (0.63 µg · ml−1) are consistent with clinical memory impairment, even though the Bayesian classifier remains partially accurate because it is able to extract categorical information from the network by its detailed mathematical analysis, which is unlikely to be available to the real nervous system.
Still, we are left with the question of how to correlate reductions in group size with the clinical effects of propofol. Even if the brain does not behave in a Bayesian manner, the use of a classifier for our spiking data provides a useful framework by which we can quantitate impairment in the memory function of our network.
Conclusions
We have studied a computational hippocampal network that is capable of learning, recalling and discriminating patterned stimuli. The substrate for the memory function of the network is the polychronous group. When the balance between excitation and inhibition is shifted toward inhibition by simulating the effects of moderate propofol concentrations on GABAA channels, the size of neural groups associated with a stimulus diminishes substantially. Such a reduction in group size is correlated with a degradation in the ability of a Bayesian classifier to discriminate learned patterns in the network’s spiking output.
Acknowledgments
The authors thank Robert Veselis, M.D., Department of Anesthesiology, Memorial Sloan Kettering Cancer Center, Montvale, New Jersey, for insightful comments on the manuscript.
Research Support
Supported by a Foundation for Anesthesia Education and Research (Schaumburg, Illinois) Mentored Research Training Grant (to Dr. Storer).
Competing Interests
The authors declare no competing interests.
References
Veselis, RA, Pryor, KO, Reinsel, RA, Li, Y, Mehta, M, Johnson, RJr Propofol and midazolam inhibit conscious memory processes very soon after encoding: An event-related potential study of familiarity and recollection in volunteers. Anesthesiology 2009; 110:295–312 [PubMed]
Zarnowska, ED, Rodgers, FC, Oh, I, Rau, V, Lor, C, Laha, KT, Jurd, R, Rudolph, U, Eger, EI, Pearce, RA Etomidate blocks LTP and impairs learning but does not enhance tonic inhibition in mice carrying the N265M point mutation in the beta3 subunit of the GABAA receptor. Neuropharmacology 2015; 93:171–8 [Article] [PubMed]
Perouansky, M, Pearce, RA How we recall (or don’t): The hippocampal memory machine and anesthetic amnesia. Can J Anaesth 2011; 58:157–66 [Article] [PubMed]
Fell, J, Axmacher, N The role of phase synchronization in memory processes. Nat Rev Neurosci 2011; 12:105–18 [Article] [PubMed]
Harris, KD, Csicsvari, J, Hirase, H, Dragoi, G, Buzsáki, G Organization of cell assemblies in the hippocampus. Nature 2003; 424:552–6 [Article] [PubMed]
Izhikevich, EM Polychronization: Computation with spikes. Neural Comput 2006; 282:245–82 [Article]
Storer, KP, Reeke, GN γ-Aminobutyric acid receptor type A receptor potentiation reduces firing of neuronal assemblies in a computational cortical model. Anesthesiology 2012; 117:780–90 [Article] [PubMed]
George, D, Hawkins, J Towards a mathematical theory of cortical micro-circuits. PLoS Comput Biol 2009; 5:e1000532 [Article] [PubMed]
Guzman, SJ, Schlögl, A, Frotscher, M, Jonas, P Synaptic mechanisms of pattern completion in the hippocampal CA3 network. Science 2016; 353:1117–23 [Article] [PubMed]
Izhikevich, EM, Gally, JA, Edelman, GM Spike-timing dynamics of neuronal groups. Cereb Cortex 2004; 14:933–44 [Article] [PubMed]
Izhikevich, EM Simple model of spiking neurons. IEEE Trans Neural Netw 2003; 14:1569–72 [Article] [PubMed]
Otis, TS, Mody, I Differential activation of GABAA and GABAB receptors by spontaneously released transmitter. J Neurophysiol 1992; 67:227–35 [Article] [PubMed]
Stern, P, Edwards, FA, Sakmann, B Fast and slow components of unitary EPSCs on stellate cells elicited by focal stimulation in slices of rat visual cortex. J Physiol 1992; 449:247–78 [Article] [PubMed]
Dayan, P, Abbott, L Theoretical Neuroscience. 2001 Cambridge, Massachusetts, MIT Press,
Hebb, DThe Organization of Behavior. 1949 New York, Wiley, doi:10.2307/1418888
Song, S, Miller, KD, Abbott, LF Competitive Hebbian learning through spike-timing-dependent synaptic plasticity. Nat Neurosci 2000; 3:919–26 [Article] [PubMed]
Mehta, MR, Quirk, MC, Wilson, MA Experience-dependent asymmetric shape of hippocampal receptive fields. Neuron 2000; 25:707–15 [Article] [PubMed]
Izhikevich, EM, Edelman, GM Large-scale model of mammalian thalamocortical systems. Proc Natl Acad Sci USA 2008; 105:3593–8 [Article] [PubMed]
Han, L, Lonart, G, Sugita, S In reply. Anesthesiology 2016; 125:822–3 [Article] [PubMed]
Adodra, S, Hales, TG Potentiation, activation and blockade of GABAA receptors of clonal murine hypothalamic GT1-7 neurones by propofol. Br J Pharmacol 1995; 115:953–60 [Article] [PubMed]
Eghbali, M, Gage, PW, Birnir, B Effects of propofol on GABAA channel conductance in rat-cultured hippocampal neurons. Eur J Pharmacol 2003; 468:75–82 [Article] [PubMed]
McCarthy, MM, Brown, EN, Kopell, N Potential network mechanisms mediating electroencephalographic beta rhythm changes during propofol-induced paradoxical excitation. J Neurosci 2008; 28:13488–504 [Article] [PubMed]
Colgin, LL Rhythms of the hippocampal network. Nat Rev Neurosci 2016; 17:239–49 [Article] [PubMed]
Guise, M, Knott, A, Benuskova, L A bayesian model of polychronicity. Neural Comput 2014; 26:2052–73 [Article] [PubMed]
Fiorillo, CD, Kim, JK, Hong, SZ The meaning of spikes from the neuron’s point of view: Predictive homeostasis generates the appearance of randomness. Front Comput Neurosci 2014; 8:49 [Article] [PubMed]
Fiorillo, CDA neurocentric approach to Bayesian inference. Nat Rev Neurosci 2010; 11:605; author reply 605 [Article] [PubMed]
Bowers, JS, Davis, CJ Bayesian just-so stories in psychology and neuroscience. Psychol Bull 2012; 138:389–414 [Article] [PubMed]
Eberhardt, F, Danks, D Confirmation in the cognitive sciences: The problematic case of Bayesian models. Minds Mach 2011; 21:389–410 [Article]
Pirker, S, Schwarzer, C, Wieselthaler, A, Sieghart, W, Sperk, G GABA(A) receptors: Immunocytochemical distribution of 13 subunits in the adult rat brain. Neuroscience 2000; 101:815–50 [Article] [PubMed]
Caraiscos, VB, Elliott, EM, You-Ten, KE, Cheng, VY, Belelli, D, Newell, JG, Jackson, MF, Lambert, JJ, Rosahl, TW, Wafford, KA, MacDonald, JF, Orser, BA Tonic inhibition in mouse hippocampal CA1 pyramidal neurons is mediated by alpha5 subunit-containing gamma-aminobutyric acid type A receptors. Proc Natl Acad Sci USA 2004; 101:3662–7 [Article] [PubMed]
Martin, LJ, Zurek, AA, MacDonald, JF, Roder, JC, Jackson, MF, Orser, BA Alpha5GABAA receptor activity sets the threshold for long-term potentiation and constrains hippocampus-dependent memory. J Neurosci 2010; 30:5269–82 [Article] [PubMed]
Rodgers, FC, Zarnowska, ED, Laha, KT, Engin, E, Zeller, A, Keist, R, Rudolph, U, Pearce, R Etomidate impairs long-term potentiation in vitro by targeting α5-subunit containing GABA-A receptors on nonpyramidal cells. J Neurosci 2015; 35:9707–16 [Article] [PubMed]
Orser, BA Lifting the fog around anesthesia. Sci Am 2007; 296:54–61 [Article] [PubMed]
Kubota, D, Colgin, LL, Casale, M, Brucher, FA, Lynch, G Endogenous waves in hippocampal slices. J Neurophysiol 2003; 89:81–9 [Article] [PubMed]
Cutsuridis, V, Hasselmo, M GABAergic contributions to gating, timing, and phase precession of hippocampal neuronal activity during theta oscillations. Hippocampus 2012; 22:1597–621 [Article] [PubMed]
Orbán, G, Kiss, T, Erdi, P Intrinsic and synaptic mechanisms determining the timing of neuron population activity during hippocampal theta oscillation. J Neurophysiol 2006; 96:2889–904 [Article] [PubMed]
Neymotin, SA, Lazarewicz, MT, Sherif, M, Contreras, D, Finkel, LH, Lytton, WW Ketamine disrupts θ modulation of γ in a computer model of hippocampus. J Neurosci 2011; 31:11733–43 [Article] [PubMed]
Pryor, KO, Reinsel, RA, Mehta, M, Li, Y, Wixted, JT, Veselis, RA Visual P2-N2 complex and arousal at the time of encoding predict the time domain characteristics of amnesia for multiple intravenous anesthetic drugs in humans. Anesthesiology 2010; 113:313–26 [Article] [PubMed]
Pryor, KO, Root, JC, Mehta, M, Stern, E, Pan, H, Veselis, RA, Silbersweig, DA Effect of propofol on the medial temporal lobe emotional memory system: A functional magnetic resonance imaging study in human subjects. Br J Anaesth 2015; 115 Suppl 1:i104–13 [Article] [PubMed]
Fig. 1.
Schematic of anatomical properties of the model. Each neuron has 896 synapses. The model is comprised of two distinct modules. The hippocampal module contains 7,680 neurons, of which 80% are excitatory pyramidal cells. Fifty percent of excitatory neuron synapses are via nonmyelinated collaterals, and the remainder connect via a myelinated axon. All inhibitory cells synapse locally. A distinct entorhinal cortical module contains 600 neurons, of which 80% are excitatory stellate cells. All connections within the entorhinal module are via nonmyelinated axon collaterals. The output of the excitatory cells of this module serves as the input for the pyramidal cells of the hippocampal module. r = radius in mm; v = velocity in m · s−1.
Schematic of anatomical properties of the model. Each neuron has 896 synapses. The model is comprised of two distinct modules. The hippocampal module contains 7,680 neurons, of which 80% are excitatory pyramidal cells. Fifty percent of excitatory neuron synapses are via nonmyelinated collaterals, and the remainder connect via a myelinated axon. All inhibitory cells synapse locally. A distinct entorhinal cortical module contains 600 neurons, of which 80% are excitatory stellate cells. All connections within the entorhinal module are via nonmyelinated axon collaterals. The output of the excitatory cells of this module serves as the input for the pyramidal cells of the hippocampal module. r = radius in mm; v = velocity in m · s−1.
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Fig. 1.
Schematic of anatomical properties of the model. Each neuron has 896 synapses. The model is comprised of two distinct modules. The hippocampal module contains 7,680 neurons, of which 80% are excitatory pyramidal cells. Fifty percent of excitatory neuron synapses are via nonmyelinated collaterals, and the remainder connect via a myelinated axon. All inhibitory cells synapse locally. A distinct entorhinal cortical module contains 600 neurons, of which 80% are excitatory stellate cells. All connections within the entorhinal module are via nonmyelinated axon collaterals. The output of the excitatory cells of this module serves as the input for the pyramidal cells of the hippocampal module. r = radius in mm; v = velocity in m · s−1.
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Fig. 2.
Spike count histograms for two neurons after 1,600 presentations of pattern A during the recall epoch. Offset is time in milliseconds from start of pattern presentation. A neuron that is not part of a polychronous group associated with pattern A (upper panel) fires at random times during replay of the pattern. Some neurons consistently fire at a particular time during pattern replay, producing peaks in the spiking count histogram. These peaks indicate that the neuron fires as part of a stimulus-related polychronous group. The timing of peaks over multiple neurons produces a spatiotemporal signature of group activation in response to the stimulus.
Spike count histograms for two neurons after 1,600 presentations of pattern A during the recall epoch. Offset is time in milliseconds from start of pattern presentation. A neuron that is not part of a polychronous group associated with pattern A (upper panel) fires at random times during replay of the pattern. Some neurons consistently fire at a particular time during pattern replay, producing peaks in the spiking count histogram. These peaks indicate that the neuron fires as part of a stimulus-related polychronous group. The timing of peaks over multiple neurons produces a spatiotemporal signature of group activation in response to the stimulus.
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Fig. 2.
Spike count histograms for two neurons after 1,600 presentations of pattern A during the recall epoch. Offset is time in milliseconds from start of pattern presentation. A neuron that is not part of a polychronous group associated with pattern A (upper panel) fires at random times during replay of the pattern. Some neurons consistently fire at a particular time during pattern replay, producing peaks in the spiking count histogram. These peaks indicate that the neuron fires as part of a stimulus-related polychronous group. The timing of peaks over multiple neurons produces a spatiotemporal signature of group activation in response to the stimulus.
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Fig. 3.
After sufficient simulation time to allow stabilization of synaptic weights, the network is presented with four stimuli (patterns A through D) comprising the same set of 200 neurons fired in differing orders during a 200-ms interval. During a 120-s learning epoch, the stimuli are presented sequentially with a spacing of 2 s. The γ-aminobutyric acid receptor type A potentiating effects of propofol, if present, are incorporated during this learning epoch. At the completion of learning, propofol effects are withdrawn, synaptic weights are frozen, and patterns A through D and a null pattern are serially presented to the network during a recall epoch to determine whether the spiking output data are consistent with polychronous group formation.
After sufficient simulation time to allow stabilization of synaptic weights, the network is presented with four stimuli (patterns A through D) comprising the same set of 200 neurons fired in differing orders during a 200-ms interval. During a 120-s learning epoch, the stimuli are presented sequentially with a spacing of 2 s. The γ-aminobutyric acid receptor type A potentiating effects of propofol, if present, are incorporated during this learning epoch. At the completion of learning, propofol effects are withdrawn, synaptic weights are frozen, and patterns A through D and a null pattern are serially presented to the network during a recall epoch to determine whether the spiking output data are consistent with polychronous group formation.
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Fig. 3.
After sufficient simulation time to allow stabilization of synaptic weights, the network is presented with four stimuli (patterns A through D) comprising the same set of 200 neurons fired in differing orders during a 200-ms interval. During a 120-s learning epoch, the stimuli are presented sequentially with a spacing of 2 s. The γ-aminobutyric acid receptor type A potentiating effects of propofol, if present, are incorporated during this learning epoch. At the completion of learning, propofol effects are withdrawn, synaptic weights are frozen, and patterns A through D and a null pattern are serially presented to the network during a recall epoch to determine whether the spiking output data are consistent with polychronous group formation.
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Fig. 4.
Stimulus-related polychronous group (PNG) size (in neurons) is dependent on the duration of the learning epoch. The mean size of stimulus-related groups associated with patterns A through D increases with longer duration of the learning epoch. SD for 100 trials is indicated by the shaded region.
Stimulus-related polychronous group (PNG) size (in neurons) is dependent on the duration of the learning epoch. The mean size of stimulus-related groups associated with patterns A through D increases with longer duration of the learning epoch. SD for 100 trials is indicated by the shaded region.
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Fig. 4.
Stimulus-related polychronous group (PNG) size (in neurons) is dependent on the duration of the learning epoch. The mean size of stimulus-related groups associated with patterns A through D increases with longer duration of the learning epoch. SD for 100 trials is indicated by the shaded region.
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Fig. 5.
γ-Aminobutyric acid receptor type A receptor potentiation reduces stimulus-related polychronous group (PNG) size. The mean size of stimulus-related groups associated with patterns A through D decreases as γ-aminobutyric acid receptor type A channel conductance and decay times increase, consistent with the action of propofol at increasing plasma concentrations. SD for 100 trials is indicated by the correspondingly colored shaded region.
γ-Aminobutyric acid receptor type A receptor potentiation reduces stimulus-related polychronous group (PNG) size. The mean size of stimulus-related groups associated with patterns A through D decreases as γ-aminobutyric acid receptor type A channel conductance and decay times increase, consistent with the action of propofol at increasing plasma concentrations. SD for 100 trials is indicated by the correspondingly colored shaded region.
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Fig. 5.
γ-Aminobutyric acid receptor type A receptor potentiation reduces stimulus-related polychronous group (PNG) size. The mean size of stimulus-related groups associated with patterns A through D decreases as γ-aminobutyric acid receptor type A channel conductance and decay times increase, consistent with the action of propofol at increasing plasma concentrations. SD for 100 trials is indicated by the correspondingly colored shaded region.
Full Size  |  Slide (.ppt)
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Fig. 6.
(A) Performance of a Bayesian classifier in determining which pattern was presented to the network during the recall epoch based on the spiking output. The mean accuracy of the classifier in the identification of either patterns A through D (cyan) or the null pattern (red) decreases as γ-aminobutyric acid receptor type A channel potentiation increases, consistent with the action of propofol at increasing plasma concentrations. At moderate concentrations of propofol, the classifier accuracy decreases to around 70% and completely loses the ability to reliably recognize previously learned patterns at plasma concentrations consistent with general anesthesia. SD for 100 trials is indicated by the correspondingly colored shaded regions. (B) Scatterplot demonstrating the relationship between polychronous group (PNG) size and classifier accuracy for all plasma propofol concentrations. The classifier fails when the group size decreases to less than 25% of baseline. (C) Receiver operating characteristic analysis demonstrates that at propofol concentrations (conc.) beyond 4 μM, increasing levels of false positives must be accepted to obtain positive identifications with high reliability.
(A) Performance of a Bayesian classifier in determining which pattern was presented to the network during the recall epoch based on the spiking output. The mean accuracy of the classifier in the identification of either patterns A through D (cyan) or the null pattern (red) decreases as γ-aminobutyric acid receptor type A channel potentiation increases, consistent with the action of propofol at increasing plasma concentrations. At moderate concentrations of propofol, the classifier accuracy decreases to around 70% and completely loses the ability to reliably recognize previously learned patterns at plasma concentrations consistent with general anesthesia. SD for 100 trials is indicated by the correspondingly colored shaded regions. (B) Scatterplot demonstrating the relationship between polychronous group (PNG) size and classifier accuracy for all plasma propofol concentrations. The classifier fails when the group size decreases to less than 25% of baseline. (C) Receiver operating characteristic analysis demonstrates that at propofol concentrations (conc.) beyond 4 μM, increasing levels of false positives must be accepted to obtain positive identifications with high reliability.
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Fig. 6.
(A) Performance of a Bayesian classifier in determining which pattern was presented to the network during the recall epoch based on the spiking output. The mean accuracy of the classifier in the identification of either patterns A through D (cyan) or the null pattern (red) decreases as γ-aminobutyric acid receptor type A channel potentiation increases, consistent with the action of propofol at increasing plasma concentrations. At moderate concentrations of propofol, the classifier accuracy decreases to around 70% and completely loses the ability to reliably recognize previously learned patterns at plasma concentrations consistent with general anesthesia. SD for 100 trials is indicated by the correspondingly colored shaded regions. (B) Scatterplot demonstrating the relationship between polychronous group (PNG) size and classifier accuracy for all plasma propofol concentrations. The classifier fails when the group size decreases to less than 25% of baseline. (C) Receiver operating characteristic analysis demonstrates that at propofol concentrations (conc.) beyond 4 μM, increasing levels of false positives must be accepted to obtain positive identifications with high reliability.
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Fig. 7.
The dynamics of forgetting are investigated in five network instances by progressively increasing the time between the learning epoch and the recall epoch. During this interval, synaptic plasticity and random excitatory input continue to interact and γ-aminobutyric acid receptor type A potentiation, if already present, is maintained. Mean size of the stimulus-related polychronous group (PNG) associated with patterns A through D decreases with increasing time after the completion of learning, both in absolute terms (A) and as a percentage of the original group size measured immediately after learning (B). (C) The mean Bayesian classifier accuracy decreases in a corresponding manner. Increasing plasma propofol concentrations (conc.) reduce absolute group sizes and classifier accuracy while increasing the rate of decline in these metrics over time.
The dynamics of forgetting are investigated in five network instances by progressively increasing the time between the learning epoch and the recall epoch. During this interval, synaptic plasticity and random excitatory input continue to interact and γ-aminobutyric acid receptor type A potentiation, if already present, is maintained. Mean size of the stimulus-related polychronous group (PNG) associated with patterns A through D decreases with increasing time after the completion of learning, both in absolute terms (A) and as a percentage of the original group size measured immediately after learning (B). (C) The mean Bayesian classifier accuracy decreases in a corresponding manner. Increasing plasma propofol concentrations (conc.) reduce absolute group sizes and classifier accuracy while increasing the rate of decline in these metrics over time.
Full Size  |  Slide (.ppt)
Fig. 7.
The dynamics of forgetting are investigated in five network instances by progressively increasing the time between the learning epoch and the recall epoch. During this interval, synaptic plasticity and random excitatory input continue to interact and γ-aminobutyric acid receptor type A potentiation, if already present, is maintained. Mean size of the stimulus-related polychronous group (PNG) associated with patterns A through D decreases with increasing time after the completion of learning, both in absolute terms (A) and as a percentage of the original group size measured immediately after learning (B). (C) The mean Bayesian classifier accuracy decreases in a corresponding manner. Increasing plasma propofol concentrations (conc.) reduce absolute group sizes and classifier accuracy while increasing the rate of decline in these metrics over time.
Full Size  |  Slide (.ppt)
×
Fig. 8.
(A) The influence of γ-aminobutyric acid receptor type A receptor potentiation on theta frequency. Theta frequency increases at low plasma propofol concentrations and decreases at higher concentrations. The inset graph shows representative power spectrogram of local field potential at baseline. (B) The influence of theta rhythm on polychronous group size. Mean size of stimulus-related groups (in neurons) associated with a pattern in the absence (blue) or presence (red) of a theta oscillation originating from the entorhinal cortex. Removal of theta has a minimal effect on polychronous group sizes. SD for 100 trials is indicated by the correspondingly colored shaded regions. f = frequency (Hz).
(A) The influence of γ-aminobutyric acid receptor type A receptor potentiation on theta frequency. Theta frequency increases at low plasma propofol concentrations and decreases at higher concentrations. The inset graph shows representative power spectrogram of local field potential at baseline. (B) The influence of theta rhythm on polychronous group size. Mean size of stimulus-related groups (in neurons) associated with a pattern in the absence (blue) or presence (red) of a theta oscillation originating from the entorhinal cortex. Removal of theta has a minimal effect on polychronous group sizes. SD for 100 trials is indicated by the correspondingly colored shaded regions. f = frequency (Hz).
Full Size  |  Slide (.ppt)
Fig. 8.
(A) The influence of γ-aminobutyric acid receptor type A receptor potentiation on theta frequency. Theta frequency increases at low plasma propofol concentrations and decreases at higher concentrations. The inset graph shows representative power spectrogram of local field potential at baseline. (B) The influence of theta rhythm on polychronous group size. Mean size of stimulus-related groups (in neurons) associated with a pattern in the absence (blue) or presence (red) of a theta oscillation originating from the entorhinal cortex. Removal of theta has a minimal effect on polychronous group sizes. SD for 100 trials is indicated by the correspondingly colored shaded regions. f = frequency (Hz).
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Table 1.
Parameters Used for Modeling Neurons
Parameters Used for Modeling Neurons×
Parameters Used for Modeling Neurons
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Table 1.
Parameters Used for Modeling Neurons
Parameters Used for Modeling Neurons×
Full Size  |  Slide (.ppt)
×