Encoding of spatio-temporal input characteristics by a CA1 pyramidal neuron model

Lateral entorhinal cortex inputs modulate hippocampal dendritic excitability by recruiting a local disinhibitory microcircuit

The lateral entorhinal cortex (LEC) provides multisensory information to the hippocampus, directly to the distal dendrites of CA1 pyramidal neurons. LEC neurons perform important functions for episodic memory processing, coding for contextually salient elements of an environment or experience. However, we know little about the functional circuit interactions between the LEC and the hippocampus. We combine functional circuit mapping and computational modeling to examine how long-range glutamatergic LEC projections modulate compartment-specific excitation-inhibition dynamics in hippocampal area CA1. We demonstrate that glutamatergic LEC inputs can drive local dendritic spikes in CA1 pyramidal neurons, aided by the recruitment of a disinhibitory VIP interneuron microcircuit. Our circuit mapping and modeling further reveal that LEC inputs also recruit CCK interneurons that may act as strong suppressors of dendritic spikes. These results highlight a cortically driven GABAergic microcircuit mechanism that gates nonlinear dendritic computations, which may support compartment-specific coding of multisensory contextual features within the hippocampus.

Place fields of single spikes in hippocampus involve Kcnq3 channel-dependent entrainment of complex spike bursts

Hippocampal pyramidal cells encode an animal's location by single action potentials and complex spike bursts. These elementary signals are believed to play distinct roles in memory consolidation. The timing of single spikes and bursts is determined by intrinsic excitability and theta oscillations (5-10 Hz). Yet contributions of these dynamics to place fields remain elusive due to the lack of methods for specific modification of burst discharge. In mice lacking Kcnq3-containing M-type K+ channels, we find that pyramidal cell bursts are less coordinated by the theta rhythm than in controls during spatial navigation, but not alert immobility. Less modulated bursts are followed by an intact post-burst pause of single spike firing, resulting in a temporal discoordination of network oscillatory and intrinsic excitability. Place fields of single spikes in one- and two-dimensional environments are smaller in the mutant. Optogenetic manipulations of upstream signals reveal that neither medial septal GABA-ergic nor cholinergic inputs alone, but rather their joint activity, is required for entrainment of bursts. Our results suggest that altered representations by bursts and single spikes may contribute to deficits underlying cognitive disabilities associated with KCNQ3-mutations in humans.

Interaction of nucleus reuniens and entorhinal cortex projections in hippocampal field CA1 of the rat

The nucleus reuniens (RE) and entorhinal cortex (EC) provide monosynaptic excitatory inputs to the apical dendrites of pyramidal cells and to interneurons with dendrites in stratum lacunosum moleculare (LM) of hippocampal field CA1. However, whether the RE and EC inputs interact at the cellular level is unknown. In this electrophysiological in vivo study, low-frequency stimulation was used to selectively activate each projection at its origin; field excitatory postsynaptic potentials (fEPSPs) were recorded in CA1. We applied (1) paired pulses to RE or EC, (2) combined paired pulses to RE and EC, and (3) simultaneously paired pulses to RE/EC. The main findings are that: (a) stimulation of either RE- or EC-evoked subthreshold fEPSPs, displaying paired pulse facilitation (PPF), (b) subthreshold fEPSPs evoked by combined stimulation did not display heterosynaptic PPF, and (c) simultaneous stimulation of RE/EC resulted in enhanced subthreshold fEPSPs in proximal LM displaying a nonlinear interaction. CSD analyses of RE/EC-evoked depth profiles revealed a nonlinear enlargement of the 'LM sink-radiatum source' configuration and the appearance of an additional small sink-source pair close to stratum pyramidale, likely reflecting (peri)somatic inhibition. The nonlinear interaction between both inputs indicates that RE and EC axons form synapses, at least partly, onto the same dendritic compartments of CA1 pyramidal cells. We propose that low-frequency activation of the RE-CA1 input facilitates the entorhinal-hippocampal dialogue, and may synchronize the neocortical-hippocampal slow oscillation which is relevant for hippocampal-dependent memory consolidation.

A computational study on how theta modulated inhibition can account for the long temporal windows in the entorhinal-hippocampal loop

A recent experimental study (Mizuseki, Sirota, Pastalkova, & Buzsaki, 2009) has shown that the temporal delays between population activities in successive entorhinal and hippocampal anatomical stages are longer (about 70-80ms) than expected from axon conduction velocities and passive synaptic integration of feed-forward excitatory inputs. We investigate via computer simulations the mechanisms that give rise to such long temporal delays in the hippocampus structures. A model of the dentate gyrus (DG), CA3 and CA1 microcircuits is presented that uses biophysical representations of the major cell types including granule cells, CA3 and CA1 pyramidal cells (PCs) and six types of interneurons: basket cells (BCs), axo-axonic cells (AACs), bistratified cells (BSCs), oriens lacunosum-moleculare cells (OLMs), mossy cells (MCs) and hilar perforant path associated cells (HC). Inputs to the network came from the entorhinal cortex (EC) (layers 2 and 3) and the medial septum (MS). The model simulates accurately the timing of firing of different hippocampal cells with respect to the theta rhythm. The model shows that the experimentally reported long temporal delays in the DG, CA3 and CA1 hippocampal regions are due to theta modulated somatic and axonic inhibition. The model further predicts that the phase at which the CA1 PCs fire with respect to the theta rhythm is determined primarily by their increased dendritic excitability caused by the decrease of the axial resistance and the A-type K(+) conductance along their dendritic trunk. The model predicted latencies by which the DG, CA3 and CA1 principal cells fire are inline with the experimental evidence. Finally, the model proposes functional roles for the different inhibitory interneurons in the retrieval of the memory pattern by the DG, CA3 and CA1 networks. The model makes a number of predictions, which can be tested experimentally, thus leading to a better understanding of the biophysical computations in the hippocampus.

Spine Head Calcium as a Measure of Summed Postsynaptic Activity for Driving Synaptic Plasticity

We use a computational model of a hippocampal CA1 pyramidal cell to demonstrate that spine head calcium provides an instantaneous readout at each synapse of the postsynaptic weighted sum of all presynaptic activity impinging on the cell. The form of the readout is equivalent to the functions of weighted, summed inputs used in neural network learning rules. Within a dendritic layer, peak spine head calcium levels are either a linear or sigmoidal function of the number of coactive synapses, with nonlinearity depending on the ability of voltage spread in the dendrites to reach calcium spike threshold. This is strongly controlled by the potassium A-type current, with calcium spikes and the consequent sigmoidal increase in peak spine head calcium present only when the A-channel density is low. Other membrane characteristics influence the gain of the relationship between peak calcium and the number of active synapses. In particular, increasing spine neck resistance increases the gain due to increased voltage responses to synaptic input in spine heads. Colocation of stimulated synapses on a single dendritic branch also increases the gain of the response. Input pathways cooperate: CA3 inputs to the proximal apical dendrites can strongly amplify peak calcium levels due to weak EC input to the distal dendrites, but not so strongly vice versa. CA3 inputs to the basal dendrites can boost calcium levels in the proximal apical dendrites, but the relative electrical compactness of the basal dendrites results in the reverse effect being less significant. These results give pointers as to how to better describe the contributions of pre- and postsynaptic activity in the learning “rules” that apply in these cells. The calcium signal is closer in form to the activity measures used in traditional neural network learning rules than to the spike times used in spike-timing-dependent plasticity.

A simulation study on the effects of dendritic morphology on layer V prefrontal pyramidal cell firing behavior

Pyramidal cells, the most abundant neurons in neocortex, exhibit significant structural variability across different brain areas and layers in different species. Moreover, in response to a somatic step current, these cells display a range of firing behaviors, the most common being (1) repetitive action potentials (Regular Spiking-RS), and (2) an initial cluster of 2-5 action potentials with short interspike interval (ISIs) followed by single spikes (Intrinsic Bursting-IB). A correlation between firing behavior and dendritic morphology has recently been reported. In this work we use computational modeling to investigate quantitatively the effects of the basal dendritic tree morphology on the firing behavior of 112 three-dimensional reconstructions of layer V PFC rat pyramidal cells. Particularly, we focus on how different morphological (diameter, total length, volume, and branch number) and passive [Mean Electrotonic Path length (MEP)] features of basal dendritic trees shape somatic firing when the spatial distribution of ionic mechanisms in the basal dendritic trees is uniform or non-uniform. Our results suggest that total length, volume and branch number are the best morphological parameters to discriminate the cells as RS or IB, regardless of the distribution of ionic mechanisms in basal trees. The discriminatory power of total length, volume, and branch number remains high in the presence of different apical dendrites. These results suggest that morphological variations in the basal dendritic trees of layer V pyramidal neurons in the PFC influence their firing patterns in a predictive manner and may in turn influence the information processing capabilities of these neurons.

Sleep and movement differentiates actions of two types of somatostatin-expressing GABAergic interneuron in rat hippocampus

Neuropeptides acting on pre- and postsynaptic receptors are coreleased with GABA by interneurons including bistratified and O-LM cells, both expressing somatostatin but innervating segregated dendritic domains of pyramidal cells. Neuropeptide release requires high-frequency action potentials, but the firing patterns of most peptide/GABA-releasing interneurons during behavior are unknown. We show that behavioral and network states differentiate the activities of bistratified and O-LM cells in freely moving rats. Bistratified cells fire at higher rates during sleep than O-LM cells and, unlike O-LM cells, strongly increase spiking during sharp wave-associated ripples (SWRs). In contrast, O-LM interneurons decrease firing during sleep relative to awake states and are mostly inhibited during SWRs. During movement, both cell types fire cooperatively at the troughs of theta oscillations but with different frequencies. Somatostatin and GABA are differentially released to distinct dendritic zones of CA1 pyramidal cells during sleep and wakefulness to coordinate segregated glutamatergic inputs from entorhinal cortex and CA3.

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Bistratified and O-LM cells release GABA and somatostatin to distinct dendrites

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During movement the two cells cooperate temporally but fire at different frequencies

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During sleep bistratified cells are strongly active, O-LM cells decrease firing

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Behavior differentiates GABA and somatostatin release to distinct dendritic zones

The Green's function formalism as a bridge between single- and multi-compartmental modeling

Neurons are spatially extended structures that receive and process inputs on their dendrites. It is generally accepted that neuronal computations arise from the active integration of synaptic inputs along a dendrite between the input location and the location of spike generation in the axon initial segment. However, many application such as simulations of brain networks use point-neurons-neurons without a morphological component-as computational units to keep the conceptual complexity and computational costs low. Inevitably, these applications thus omit a fundamental property of neuronal computation. In this work, we present an approach to model an artificial synapse that mimics dendritic processing without the need to explicitly simulate dendritic dynamics. The model synapse employs an analytic solution for the cable equation to compute the neuron's membrane potential following dendritic inputs. Green's function formalism is used to derive the closed version of the cable equation. We show that by using this synapse model, point-neurons can achieve results that were previously limited to the realms of multi-compartmental models. Moreover, a computational advantage is achieved when only a small number of simulated synapses impinge on a morphologically elaborate neuron. Opportunities and limitations are discussed.

Perspectives for computational modeling of cell replacement for neurological disorders

Mathematical modeling of anatomically-constrained neural networks has provided significant insights regarding the response of networks to neurological disorders or injury. A logical extension of these models is to incorporate treatment regimens to investigate network responses to intervention. The addition of nascent neurons from stem cell precursors into damaged or diseased tissue has been used as a successful therapeutic tool in recent decades. Interestingly, models have been developed to examine the incorporation of new neurons into intact adult structures, particularly the dentate granule neurons of the hippocampus. These studies suggest that the unique properties of maturing neurons, can impact circuit behavior in unanticipated ways. In this perspective, we review the current status of models used to examine damaged CNS structures with particular focus on cortical damage due to stroke. Secondly, we suggest that computational modeling of cell replacement therapies can be made feasible by implementing approaches taken by current models of adult neurogenesis. The development of these models is critical for generating hypotheses regarding transplant therapies and improving outcomes by tailoring transplants to desired effects.

Induction and modulation of persistent activity in a layer V PFC microcircuit model

Working memory refers to the temporary storage of information and is strongly associated with the prefrontal cortex (PFC). Persistent activity of cortical neurons, namely the activity that persists beyond the stimulus presentation, is considered the cellular correlate of working memory. Although past studies suggested that this type of activity is characteristic of large scale networks, recent experimental evidence imply that small, tightly interconnected clusters of neurons in the cortex may support similar functionalities. However, very little is known about the biophysical mechanisms giving rise to persistent activity in small-sized microcircuits in the PFC. Here, we present a detailed biophysically—yet morphologically simplified—microcircuit model of layer V PFC neurons that incorporates connectivity constraints and is validated against a multitude of experimental data. We show that (a) a small-sized network can exhibit persistent activity under realistic stimulus conditions. (b) Its emergence depends strongly on the interplay of dADP, NMDA, and GABA_B currents. (c) Although increases in stimulus duration increase the probability of persistent activity induction, variability in the stimulus firing frequency does not consistently influence it. (d) Modulation of ionic conductances (I_h, I_D, I_sAHP, I_caL, I_caN, I_caR) differentially controls persistent activity properties in a location dependent manner. These findings suggest that modulation of the microcircuit's firing characteristics is achieved primarily through changes in its intrinsic mechanism makeup, supporting the hypothesis of multiple bi-stable units in the PFC. Overall, the model generates a number of experimentally testable predictions that may lead to a better understanding of the biophysical mechanisms of persistent activity induction and modulation in the PFC.

Active processing of spatio-temporal input patterns in silicon dendrites

Capturing the functionality of active dendritic processing into abstract mathematical models will help us to understand the role of complex biophysical neurons in neuronal computation and to build future useful neuromorphic analog Very Large Scale Integrated (aVLSI) neuronal devices. Previous work based on an aVLSI multi-compartmental neuron model demonstrates that the compartmental response in the presence of either of two widely studied classes of active mechanisms, is a nonlinear sigmoidal function of the degree of either input temporal synchrony OR input clustering level. Using the same silicon model, this work expounds the interaction between both active mechanisms in a compartment receiving input patterns of varying temporal AND spatial clustering structure and demonstrates that this compartmental response can be captured by a combined sigmoid and radial-basis function over both input dimensions. This paper further shows that the response to input spatio-temporal patterns in a one-dimensional multi-compartmental dendrite, can be described by a radial-basis like function of the degree of temporal synchrony between the inter-compartmental inputs.

Coding and decoding with dendrites

Since the discovery of complex, voltage dependent mechanisms in the dendrites of multiple neuron types, great effort has been devoted in search of a direct link between dendritic properties and specific neuronal functions. Over the last few years, new experimental techniques have allowed the visualization and probing of dendritic anatomy, plasticity and integrative schemes with unprecedented detail. This vast amount of information has caused a paradigm shift in the study of memory, one of the most important pursuits in Neuroscience, and calls for the development of novel theories and models that will unify the available data according to some basic principles. Traditional models of memory considered neural cells as the fundamental processing units in the brain. Recent studies however are proposing new theories in which memory is not only formed by modifying the synaptic connections between neurons, but also by modifications of intrinsic and anatomical dendritic properties as well as fine tuning of the wiring diagram. In this review paper we present previous studies along with recent findings from our group that support a key role of dendrites in information processing, including the encoding and decoding of new memories, both at the single cell and the network level.

The energy cost of action potential propagation in dopamine neurons: clues to susceptibility in Parkinson's disease

Dopamine neurons of the substantia nigra pars compacta (SNc) are uniquely sensitive to degeneration in Parkinson's disease (PD) and its models. Although a variety of molecular characteristics have been proposed to underlie this sensitivity, one possible contributory factor is their massive, unmyelinated axonal arbor that is orders of magnitude larger than other neuronal types. We suggest that this puts them under such a high energy demand that any stressor that perturbs energy production leads to energy demand exceeding supply and subsequent cell death. One prediction of this hypothesis is that those dopamine neurons that are selectively vulnerable in PD will have a higher energy cost than those that are less vulnerable. We show here, through the use of a biology-based computational model of the axons of individual dopamine neurons, that the energy cost of axon potential propagation and recovery of the membrane potential increases with the size and complexity of the axonal arbor according to a power law. Thus SNc dopamine neurons, particularly in humans, whose axons we estimate to give rise to more than 1 million synapses and have a total length exceeding 4 m, are at a distinct disadvantage with respect to energy balance which may be a factor in their selective vulnerability in PD.

Recognizing recurrent neural networks (rRNN): Bayesian inference for recurrent neural networks

Recurrent neural networks (RNNs) are widely used in computational neuroscience and machine learning applications. In an RNN, each neuron computes its output as a nonlinear function of its integrated input. While the importance of RNNs, especially as models of brain processing, is undisputed, it is also widely acknowledged that the computations in standard RNN models may be an over-simplification of what real neuronal networks compute. Here, we suggest that the RNN approach may be made computationally more powerful by its fusion with Bayesian inference techniques for nonlinear dynamical systems. In this scheme, we use an RNN as a generative model of dynamic input caused by the environment, e.g. of speech or kinematics. Given this generative RNN model, we derive Bayesian update equations that can decode its output. Critically, these updates define a 'recognizing RNN' (rRNN), in which neurons compute and exchange prediction and prediction error messages. The rRNN has several desirable features that a conventional RNN does not have, e.g. fast decoding of dynamic stimuli and robustness to initial conditions and noise. Furthermore, it implements a predictive coding scheme for dynamic inputs. We suggest that the Bayesian inversion of RNNs may be useful both as a model of brain function and as a machine learning tool. We illustrate the use of the rRNN by an application to the online decoding (i.e. recognition) of human kinematics.

Predictive features of persistent activity emergence in regular spiking and intrinsic bursting model neurons

Proper functioning of working memory involves the expression of stimulus-selective persistent activity in pyramidal neurons of the prefrontal cortex (PFC), which refers to neural activity that persists for seconds beyond the end of the stimulus. The mechanisms which PFC pyramidal neurons use to discriminate between preferred vs. neutral inputs at the cellular level are largely unknown. Moreover, the presence of pyramidal cell subtypes with different firing patterns, such as regular spiking and intrinsic bursting, raises the question as to what their distinct role might be in persistent firing in the PFC. Here, we use a compartmental modeling approach to search for discriminatory features in the properties of incoming stimuli to a PFC pyramidal neuron and/or its response that signal which of these stimuli will result in persistent activity emergence. Furthermore, we use our modeling approach to study cell-type specific differences in persistent activity properties, via implementing a regular spiking (RS) and an intrinsic bursting (IB) model neuron. We identify synaptic location within the basal dendrites as a feature of stimulus selectivity. Specifically, persistent activity-inducing stimuli consist of activated synapses that are located more distally from the soma compared to non-inducing stimuli, in both model cells. In addition, the action potential (AP) latency and the first few inter-spike-intervals of the neuronal response can be used to reliably detect inducing vs. non-inducing inputs, suggesting a potential mechanism by which downstream neurons can rapidly decode the upcoming emergence of persistent activity. While the two model neurons did not differ in the coding features of persistent activity emergence, the properties of persistent activity, such as the firing pattern and the duration of temporally-restricted persistent activity were distinct. Collectively, our results pinpoint to specific features of the neuronal response to a given stimulus that code for its ability to induce persistent activity and predict differential roles of RS and IB neurons in persistent activity expression.

Memory, referred to as the ability to retain, store and recall information, represents one of the most fundamental cognitive functions in daily life. A significant feature of memory processes is selectivity to particular events or items that are important to our survival and relevant to specific situations. For long-term memory, the selectivity to a specific stimulus is seen both at the behavioral as well as the cellular level. For working memory, a type of short-term memory involved in decision making and attention processes, stimulus selectivity has been observed in vivo using spatial working memory tasks. In addition, persistent activity, which is the cellular correlate of working memory, is also selective to specific stimuli for each neuron, suggesting that each neuron has a ‘memory field’. Our study proposes that both the location of incoming inputs onto the neuronal dendritic tree and specific temporal features of the neuronal response can be used to predict the emergence of persistent activity in two neuron models with different firing patterns, revealing possible mechanisms for generating and propagating stimulus-selectivity in working memory processes. The study also reveals that neurons with different firing patterns may have different roles in persistent activity expression.

Distinguishing Linear vs. Non-Linear Integration in CA1 Radial Oblique Dendrites: It's about Time

It was recently shown that multiple excitatory inputs to CA1 pyramidal neuron dendrites must be activated nearly simultaneously to generate local dendritic spikes and supralinear responses at the soma; even slight input desynchronization prevented local spike initiation (Gasparini and Magee, 2006; Losonczy and Magee, 2006). This led to the conjecture that CA1 pyramidal neurons may only express their non-linear integrative capabilities during the highly synchronized sharp waves and ripples that occur during slow wave sleep and resting/consummatory behavior, whereas during active exploration and REM sleep (theta rhythm), inadequate synchronization of excitation would lead CA1 pyramidal cells to function as essentially linear devices. Using a detailed single neuron model, we replicated the experimentally observed synchronization effect for brief inputs mimicking single synaptic release events. When synapses were driven instead by double pulses, more representative of the bursty inputs that occur in vivo, we found that the tolerance for input desynchronization was increased by more than an order of magnitude. The effect depended mainly on paired-pulse facilitation of NMDA receptor-mediated responses at Schaffer collateral synapses. Our results suggest that CA1 pyramidal cells could function as non-linear integrative units in all major hippocampal states.