Hebbian plasticity in parallel synaptic pathways: A circuit mechanism for systems memory consolidation

Systems memory consolidation involves the transfer of memories across brain regions and the transformation of memory content. For example, declarative memories that transiently depend on the hippocampal formation are transformed into long-term memory traces in neocortical networks, and procedural memories are transformed within cortico-striatal networks. These consolidation processes are thought to rely on replay and repetition of recently acquired memories, but the cellular and network mechanisms that mediate the changes of memories are poorly understood. Here, we suggest that systems memory consolidation could arise from Hebbian plasticity in networks with parallel synaptic pathways-two ubiquitous features of neural circuits in the brain. We explore this hypothesis in the context of hippocampus-dependent memories. Using computational models and mathematical analyses, we illustrate how memories are transferred across circuits and discuss why their representations could change. The analyses suggest that Hebbian plasticity mediates consolidation by transferring a linear approximation of a previously acquired memory into a parallel pathway. Our modelling results are further in quantitative agreement with lesion studies in rodents. Moreover, a hierarchical iteration of the mechanism yields power-law forgetting-as observed in psychophysical studies in humans. The predicted circuit mechanism thus bridges spatial scales from single cells to cortical areas and time scales from milliseconds to years.

Soma-axon coupling configurations that enhance neuronal coincidence detection

Coincidence detector neurons transmit timing information by responding preferentially to concurrent synaptic inputs. Principal cells of the medial superior olive (MSO) in the mammalian auditory brainstem are superb coincidence detectors. They encode sound source location with high temporal precision, distinguishing submillisecond timing differences among inputs. We investigate computationally how dynamic coupling between the input region (soma and dendrite) and the spike-generating output region (axon and axon initial segment) can enhance coincidence detection in MSO neurons. To do this, we formulate a two-compartment neuron model and characterize extensively coincidence detection sensitivity throughout a parameter space of coupling configurations. We focus on the interaction between coupling configuration and two currents that provide dynamic, voltage-gated, negative feedback in subthreshold voltage range: sodium current with rapid inactivation and low-threshold potassium current, I_KLT. These currents reduce synaptic summation and can prevent spike generation unless inputs arrive with near simultaneity. We show that strong soma-to-axon coupling promotes the negative feedback effects of sodium inactivation and is, therefore, advantageous for coincidence detection. Furthermore, the feedforward combination of strong soma-to-axon coupling and weak axon-to-soma coupling enables spikes to be generated efficiently (few sodium channels needed) and with rapid recovery that enhances high-frequency coincidence detection. These observations detail the functional benefit of the strongly feedforward configuration that has been observed in physiological studies of MSO neurons. We find that I_KLT further enhances coincidence detection sensitivity, but with effects that depend on coupling configuration. For instance, in models with weak soma-to-axon and weak axon-to-soma coupling, I_KLT in the axon enhances coincidence detection more effectively than I_KLT in the soma. By using a minimal model of soma-to-axon coupling, we connect structure, dynamics, and computation. Although we consider the particular case of MSO coincidence detectors, our method for creating and exploring a parameter space of two-compartment models can be applied to other neurons.

Brain cells (neurons) are spatially extended structures. The locations at which neurons receive inputs and generate outputs are often distinct. We formulate and study a minimal mathematical model that describes the dynamical coupling between the input and output regions of a neuron. We construct our model to reflect known properties of neurons in the auditory brainstem that play an important role in our ability to locate sound sources. These neurons are known as coincidence detectors because they are most likely to respond when they receive simultaneous inputs. We use simulations to explore coincidence detection sensitivity throughout the parameter space of input-output coupling and to identify the coupling configurations that are best for neural coincidence detection. We find that strong forward coupling (from input region to output region), enhances coincidence detection sensitivity in our model and that low-threshold potassium current further improves coincidence detection. Our study is significant in that we detail how cell structure affects neuronal dynamics and, consequently, the ability of neurons to perform as temporally-precise coincidence detectors.

Function and energy consumption constrain neuronal biophysics in a canonical computation: Coincidence detection

Neural morphology and membrane properties vary greatly between cell types in the nervous system. The computations and local circuit connectivity that neurons support are thought to be the key factors constraining the cells' biophysical properties. Nevertheless, additional constraints can be expected to further shape neuronal design. Here, we focus on a particularly energy-intense system (as indicated by metabolic markers): principal neurons in the medial superior olive (MSO) nucleus of the auditory brainstem. Based on a modeling approach, we show that a trade-off between the level of performance of a functionally relevant computation and energy consumption predicts optimal ranges for cell morphology and membrane properties. The biophysical parameters appear most strongly constrained by functional needs, while energy use is minimized as long as function can be maintained. The key factors that determine model performance and energy consumption are 1) the saturation of the synaptic conductance input and 2) the temporal resolution of the postsynaptic signals as they reach the soma, which is largely determined by active membrane properties. MSO cells seem to operate close to pareto optimality, i.e., the trade-off boundary between performance and energy consumption that is formed by the set of optimal models. Good performance for drastically lower costs could in theory be achieved by small neurons without dendrites, as seen in the avian auditory system, pointing to additional constraints for mammalian MSO cells, including their circuit connectivity.

Extracellular waveforms reveal an axonal origin of spikelets in pyramidal neurons

Spikelets are small spike-like membrane depolarizations measured at the soma whose origin in pyramidal neurons is still unresolved. We investigated the mechanism of spikelet generation using detailed models of pyramidal neurons. We simulated extracellular waveforms associated with action potentials and spikelets and compared these with experimental data obtained by Chorev and Brecht ( J Neurophysiol 108: 1584-1593, 2012) from hippocampal pyramidal neurons in vivo. We considered spikelets originating in the axon of a single cell as well as spikelets generated in two cells coupled with gap junctions. We found that in both cases the experimental data can be explained by an axonal origin of spikelets: in the single-cell case, action potentials are generated in the axon but fail to activate the soma. Such spikelets can be evoked by dendritic input. Alternatively, spikelets resulting from axoaxonal gap junction coupling with a large (greater than several hundred μm) distance between the somata of the coupled cells are also consistent with the data. Our results demonstrate that a cell firing a somatic spikelet generates a detectable extracellular potential that is different from the action potential-correlated extracellular waveform generated by the same cell and recorded at the same location. This, together with the absence of a refractory period between action potentials and spikelets, implies that spikelets and action potentials generated in one cell may easily get misclassified in extracellular recordings as two different cells, albeit they both constitute the output of a single pyramidal neuron. NEW & NOTEWORTHY We addressed the origin of spikelets, using compartmental models of pyramidal neurons. Comparing our simulation results with published extracellular spikelet recordings revealed an axonal origin of spikelets. Our results imply that action potential- and spikelet-associated extracellular waveforms may easily get misclassified as two different cells, albeit they both constitute the output of a single pyramidal cell.

Differential polarization of cortical pyramidal neuron dendrites through weak extracellular fields

The rise of transcranial current stimulation (tCS) techniques have sparked an increasing interest in the effects of weak extracellular electric fields on neural activity. These fields modulate ongoing neural activity through polarization of the neuronal membrane. While the somatic polarization has been investigated experimentally, the frequency-dependent polarization of the dendritic trees in the presence of alternating (AC) fields has received little attention yet. Using a biophysically detailed model with experimentally constrained active conductances, we analyze the subthreshold response of cortical pyramidal cells to weak AC fields, as induced during tCS. We observe a strong frequency resonance around 10-20 Hz in the apical dendrites sensitivity to polarize in response to electric fields but not in the basal dendrites nor the soma. To disentangle the relative roles of the cell morphology and active and passive membrane properties in this resonance, we perform a thorough analysis using simplified models, e.g. a passive pyramidal neuron model, simple passive cables and reconstructed cell model with simplified ion channels. We attribute the origin of the resonance in the apical dendrites to (i) a locally increased sensitivity due to the morphology and to (ii) the high density of h-type channels. Our systematic study provides an improved understanding of the subthreshold response of cortical cells to weak electric fields and, importantly, allows for an improved design of tCS stimuli.

Spikelets in Pyramidal Neurons: Action Potentials Initiated in the Axon Initial Segment That Do Not Activate the Soma

Spikelets are small spike-like depolarizations that can be measured in somatic intracellular recordings. Their origin in pyramidal neurons remains controversial. To explain spikelet generation, we propose a novel single-cell mechanism: somato-dendritic input generates action potentials at the axon initial segment that may fail to activate the soma and manifest as somatic spikelets. Using mathematical analysis and numerical simulations of compartmental neuron models, we identified four key factors controlling spikelet generation: (1) difference in firing threshold, (2) impedance mismatch, and (3) electrotonic separation between the soma and the axon initial segment, as well as (4) input amplitude. Because spikelets involve forward propagation of action potentials along the axon while they avoid full depolarization of the somato-dendritic compartments, we conjecture that this mode of operation saves energy and regulates dendritic plasticity while still allowing for a read-out of results of neuronal computations.

Action potentials (APs) are digital, all-or-none signals by which neurons communicate with each other. Therefore, APs are the basis of neural function, yet some of their fundamental features are still not well understood. Here we focus on pyramidal cells, which are the principal neurons in neocortex and hippocampus. According to textbook knowledge, an AP in pyramidal neurons is initiated at the axon initial segment and propagates along the axon to the next cell. Concurrently, the AP also propagates back to the soma and into the dendrites where it might trigger synaptic plasticity, which is the basis of learning and memory. However, besides APs, pyramidal cells sometimes also show somatic spikelets—small depolarizations with an AP-like shape—whose origin remains unclear. Here, we propose that spikelets occur when an AP initiated at the axon initial segment only propagates down the axon, but fails to activate sodium currents in the soma and dendrites. As a result, spikelet firing saves energy, and moreover, might be a means to control synaptic plasticity and thereby control learning and memory.

Active subthreshold dendritic conductances shape the local field potential

Key points

The local field potential (LFP), the low‐frequency part of extracellular potentials recorded in neural tissue, is often used for probing neural circuit activity. Interpreting the LFP signal is difficult, however.

While the cortical LFP is thought mainly to reflect synaptic inputs onto pyramidal neurons, little is known about the role of the various subthreshold active conductances in shaping the LFP.

By means of biophysical modelling we obtain a comprehensive qualitative understanding of how the LFP generated by a single pyramidal neuron depends on the type and spatial distribution of active subthreshold currents.

For pyramidal neurons, the h‐type channels probably play a key role and can cause a distinct resonance in the LFP power spectrum.

Our results show that the LFP signal can give information about the active properties of neurons and imply that preferred frequencies in the LFP can result from those cellular properties instead of, for example, network dynamics.

Abstract

The main contribution to the local field potential (LFP) is thought to stem from synaptic input to neurons and the ensuing subthreshold dendritic processing. The role of active dendritic conductances in shaping the LFP has received little attention, even though such ion channels are known to affect the subthreshold neuron dynamics. Here we used a modelling approach to investigate the effects of subthreshold dendritic conductances on the LFP. Using a biophysically detailed, experimentally constrained model of a cortical pyramidal neuron, we identified conditions under which subthreshold active conductances are a major factor in shaping the LFP. We found that, in particular, the hyperpolarization‐activated inward current, I_h, can have a sizable effect and cause a resonance in the LFP power spectral density. To get a general, qualitative understanding of how any subthreshold active dendritic conductance and its cellular distribution can affect the LFP, we next performed a systematic study with a simplified model. We found that the effect on the LFP is most pronounced when (1) the synaptic drive to the cell is asymmetrically distributed (i.e. either basal or apical), (2) the active conductances are distributed non‐uniformly with the highest channel densities near the synaptic input and (3) when the LFP is measured at the opposite pole of the cell relative to the synaptic input. In summary, we show that subthreshold active conductances can be strongly reflected in LFP signals, opening up the possibility that the LFP can be used to characterize the properties and cellular distributions of active conductances.

The local field potential (LFP), the low‐frequency part of extracellular potentials recorded in neural tissue, is often used for probing neural circuit activity. Interpreting the LFP signal is difficult, however.

While the cortical LFP is thought mainly to reflect synaptic inputs onto pyramidal neurons, little is known about the role of the various subthreshold active conductances in shaping the LFP.

By means of biophysical modelling we obtain a comprehensive qualitative understanding of how the LFP generated by a single pyramidal neuron depends on the type and spatial distribution of active subthreshold currents.

For pyramidal neurons, the h‐type channels probably play a key role and can cause a distinct resonance in the LFP power spectrum.

Our results show that the LFP signal can give information about the active properties of neurons and imply that preferred frequencies in the LFP can result from those cellular properties instead of, for example, network dynamics.

Somatic versus dendritic resonance: differential filtering of inputs through non-uniform distributions of active conductances

Synaptic inputs to neurons are processed in a frequency-dependent manner, with either low-pass or resonant response characteristics. These types of filtering play a key role in the frequency-specific information flow in neuronal networks. While the generation of resonance by specific ionic conductances is well investigated, less attention has been paid to the spatial distribution of the resonance-generating conductances across a neuron. In pyramidal neurons – one of the major excitatory cell-types in the mammalian brain – a steep gradient of resonance-generating h-conductances with a 60-fold increase towards distal dendrites has been demonstrated experimentally. Because the dendritic trees of these cells are large, spatial compartmentalization of resonant properties can be expected. Here, we use mathematical descriptions of spatially extended neurons to investigate the consequences of such a distal, dendritic localization of h-conductances for signal processing. While neurons with short dendrites do not exhibit a pronounced compartmentalization of resonance, i.e. the filter properties of dendrites and soma are similar, we find that neurons with longer dendrites ( space constant) can show distinct filtering of dendritic and somatic inputs due to electrotonic segregation. Moreover, we show that for such neurons, experimental classification as resonant versus nonresonant can be misleading when based on somatic recordings, because for these morphologies a dendritic resonance could easily be undetectable when using somatic input. Nevertheless, noise-driven membrane-potential oscillations caused by dendritic resonance can propagate to the soma where they can be recorded, hence contrasting with the low-pass filtering at the soma. We conclude that non-uniform distributions of active conductances can underlie differential filtering of synaptic input in neurons with spatially extended dendrites, like pyramidal neurons, bearing relevance for the localization-dependent targeting of synaptic input pathways to these cells.

Democracy-independence trade-off in oscillating dendrites and its implications for grid cells

Dendritic democracy and independence have been characterized for near-instantaneous processing of synaptic inputs. However, a wide class of neuronal computations requires input integration on long timescales. As a paradigmatic example, entorhinal grid fields have been thought to be generated by the democratic summation of independent dendritic oscillations performing direction-selective path integration. We analyzed how multiple dendritic oscillators embedded in the same neuron integrate inputs separately and determine somatic membrane voltage jointly. We found that the interaction of dendritic oscillations leads to phase locking, which sets an upper limit on the timescale for independent input integration. Factors that increase this timescale also decrease the influence that the dendritic oscillations exert on somatic voltage. In entorhinal stellate cells, interdendritic coupling dominates and causes these cells to act as single oscillators. Our results suggest a fundamental trade-off between local and global processing in dendritic trees integrating ongoing signals.

The role of ongoing dendritic oscillations in single-neuron dynamics

The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as both temporally and spatially localized. Under this localist account, neurons compute near-instantaneous mappings from their current input to their current output, brought about by somatic summation of dendritic contributions that are generated in functionally segregated compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought; notably that local dendritic activity may be a mechanism for generating on-going whole-cell voltage oscillations.

A central issue in biology is how local processes yield global consequences. This is especially relevant for neurons since these spatially extended cells process local synaptic inputs to generate global action potential output. The dendritic tree of a neuron, which receives most of the inputs, expresses ion channels that can generate nonlinear dynamics. A prominent phenomenon resulting from such ion channels are voltage oscillations. The distribution of the active membrane channels throughout the cell is often highly non-uniform. This can turn the dendritic tree into a network of sparsely spaced local oscillators. Here we analyze whether local dendritic oscillators can produce cell-wide voltage oscillations. Our mathematical theory shows that indeed even when the dendritic oscillators are weakly coupled, they lock their phases and give global oscillations. We show how the biophysical properties of the dendrites determine the global locking and how it can be controlled by synaptic inputs. As a consequence of global locking, even individual synaptic inputs can affect the timing of action potentials. In fact, dendrites locking in synchrony can lead to sustained firing of the cell. We show that dendritic trees can be bistable, with dendrites locking in either synchrony or asynchrony, which may provide a novel mechanism for single cell-based memory.

Different levels of Ih determine distinct temporal integration in bursting and regular-spiking neurons in rat subiculum

Pyramidal neurons in the subiculum typically display either bursting or regular-spiking behaviour. Although this classification into two neuronal classes is well described, it is unknown how these two classes of neurons contribute to the integration of input to the subiculum. Here, we report that bursting neurons possess a hyperpolarization-activated cation current (I(h)) that is two-fold larger (conductance, 5.3 +/- 0.5 nS) than in regular-spiking neurons (2.2 +/- 0.6 nS), whereas I(h) exhibits similar voltage-dependent and kinetic properties in both classes of neurons. Bursting and regular-spiking neurons display similar morphology. The difference in I(h) between the two classes of neurons is not responsible for the distinct firing patterns, as neither pharmacological blockade of I(h) nor enhancement of I(h) using a dynamic clamp affects the qualitative firing patterns. Instead, the difference in I(h) between bursting and regular-spiking neurons determines the temporal integration of evoked synaptic input from the CA1 area. In response to stimulation at 50 Hz, bursting neurons, with a large I(h), show approximately 50% less temporal summation than regular-spiking neurons. The amount of temporal summation in both neuronal classes is equal after pharmacological blockade of I(h). A computer simulation model of a subicular neuron with the properties of either a bursting or a regular-spiking neuron confirmed the pivotal role of I(h) in temporal integration of synaptic input. These data suggest that in the subicular network, bursting neurons are better suited to discriminate the content of high-frequency input, such as that occurring during gamma oscillations, than regular-spiking neurons.

The effect of dendritic topology on firing patterns in model neurons

Neuronal firing patterns are influenced by both membrane properties and dendritic morphology. Distinguishing two sources of morphological variability-metrics and topology-we investigate the extent to which model neurons that have the same metrical and membrane properties can still produce different firing patterns as a result of differences in dendritic topology. Within a set of dendritic trees that have the same number of terminal segments and the same total dendritic length, we show that firing frequency strongly correlates with topology as expressed by the mean dendritic path length. The effect of dendritic topology on firing frequency is bigger for trees with equal segment diameters than for trees whose segment diameters obey Rall's 3/2 power law. If active dendritic channels are present, dendritic topology influences not only firing frequency but also type of firing (regular, bursting).