Michiel W. H. Remme

Democracy-Independence Trade-Off in Oscillating Dendrites and Its Implications for Grid Cells

Summary 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.

Active subthreshold dendritic conductances shape the local field potential.

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.

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.

Subthreshold Resonance and Membrane Potential Oscillations in a Neuron with Nonuniform Active Dendritic Properties

Synaptic input to neurons is subject to cell-intrinsic filtering. In the subthreshold membrane potential range this filtering can have either low-pass or resonant characteristics and thereby have a key role in the frequency-dependent information flow in neuronal networks. Experimental classification of neurons as resonant versus nonresonant is usually based on somatic measurements, which, as we demonstrate here, may not accurately reflect neuronal filter properties because of nonuniform distributions of active membrane processes. Using cable theory, we identify conditions under which dendritic currents, in particular I h, can generate somatic resonances. We find that even a strong dendritic resonance may not be detectable somatically in pyramidal cells with a high density of HCN channels in the distal parts of the dendrites. In addition, we show that noise-driven membrane potential oscillations caused by dendritic resonance can propagate to the soma where they can be recorded in the absence of somatic resonance.

A Theoretical Framework for the Dynamics of Multiple Intrinsic Oscillators in Single Neurons

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 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.

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.

Dendritic distribution of synaptic input creates a trade-off between input selectivity and flexibility

Information processing by cortical pyramidal neurons is shaped by the spatial distribution of synapses across the dendrites. A prominent hypothesis is that synapses with similar selectivities cluster on dendritic branches. This enables cooperative interactions between neighboring synapses through activation of voltage-dependent membrane currents, and helps establish independent integrative subunits, thereby expanding the computational power of a single neuron [1]. Some recent in vivo recordings argue against this hypothesis, suggesting that inputs that share the same stimulus selectivity are randomly distributed throughout the dendritic tree (e.g., [2]). Other studies seem to support clustered configurations of input selectivities, showing for example that the activity of a synaptic input is more strongly correlated with its neighbors than with more distant inputs [3]. One fundamental feature of the nervous system that has received little attention in this ongoing discussion is learning; specifically, how is the ability to change a neurons selectivity (i.e., its flexibility) affected by the spatial distribution of synapses? This is highly relevant because the selectivity of many cortical pyramidal neurons is subject to ongoing modification, not only during development, but throughout adulthood (e.g., [4]). Here, we show that the distribution of synapses across active dendrites shapes both the stimulus selectivity of the neuron, as well as the flexibility of the neurons selectivity. Using cable theoretic analysis and numerical simulations of detailed neuron models we show that synapses that are randomly distributed across the dendrites allow for a modest stimulus selectivity that can be flexibly modified through synaptic plasticity. In contrast, a clustered distribution of synapses that encode the same stimulus allows for very strong stimulus selectivity, however, it hinders adjustment of this selectivity through synaptic plasticity, which requires slow and metabolically costly rearrangement of synaptic projections. Hence, the distribution of synapses across active dendrites creates a trade-off between selectivity and plasticity. We suggest that pyramidal neurons with different functions in the cortical information processing hierarchy exploit different ends of this spectrum.

A Trade-Off Between Dendritic Democracy and Independence in Neurons with Intrinsic Subthreshold Membrane Potential Oscillations

Membrane potential oscillations are ubiquitous in neurons and have been proposed to underly important neuronal computations. As a paradigmatic example, the periodic spatial tuning of stellate cells from medial entorhinal cortex neurons is thought to be generated by the interference patterns arising from multiple, independent dendritic oscillators, each controlled by direction-selective input. 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 time scale for independent input integration. Factors that increase this time scale also decrease the influence that the oscillations exert on somatic voltage. In stellate cells, inter-dendritic 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.