Noisy Juxtacellular Stimulation In Vivo Leads to Reliable Spiking and Reveals High-Frequency Coding in Single Neurons

Ultrafast population coding and axo-somatic compartmentalization

Populations of cortical neurons respond to common input within a millisecond. Morphological features and active ion channel properties were suggested to contribute to this astonishing processing speed. Here we report an exhaustive study of ultrafast population coding for varying axon initial segment (AIS) location, soma size, and axonal current properties. In particular, we studied their impact on two experimentally observed features 1) precise action potential timing, manifested in a wide-bandwidth dynamic gain, and 2) high-frequency boost under slowly fluctuating correlated input. While the density of axonal channels and their distance from the soma had a very small impact on bandwidth, it could be moderately improved by increasing soma size. When the voltage sensitivity of axonal currents was increased we observed ultrafast coding and high-frequency boost. We conclude that these computationally relevant features are strongly dependent on axonal ion channels’ voltage sensitivity, but not their number or exact location. We point out that ion channel properties, unlike dendrite size, can undergo rapid physiological modification, suggesting that the temporal accuracy of neuronal population encoding could be dynamically regulated. Our results are in line with recent experimental findings in AIS pathologies and establish a framework to study structure-function relations in AIS molecular design.

In large nervous systems, a signal often diverges to hundreds or thousands of neurons. This population’s spike rate can track changes in this common input for frequencies up to several hundred Hertz. This ultrafast population response is experimentally well established and critically impacts cortical information processing. Its underlying biophysical determinants, however, are not understood. Experiments suggest that the ion channels at the axon initial segment strongly contribute to the ultrafast response, but recent theoretical studies emphasize the importance of neuron morphology and the resulting resistive coupling between axon and somato-dendritic compartments. We provide an exhaustive analysis of the population response of a simplified multi-compartment model. We vary the axo-somatic interaction and also active axonal properties and compare models at equivalent working points, avoiding bias. This approach provides a guideline for future experimental and theoretical studies. In this framework, the population response is closely associated with the AP generation speed at the AP initiation site, which is mostly determined by axonal ion channel voltage sensitivity. The resistive axo-somatic coupling has an additional modulatory influence. These insights are expected to hold for encoding mechanisms of more sophisticated models, suggesting that physiological changes to axonal ion channels could modulate the population response rapidly.

Theta activity paradoxically boosts gamma and ripple frequency sensitivity in prefrontal interneurons

Fast oscillations in cortical circuits critically depend on GABAergic interneurons. Which interneuron types and populations can drive different cortical rhythms, however, remains unresolved and may depend on brain state. Here, we measured the sensitivity of different GABAergic interneurons in prefrontal cortex under conditions mimicking distinct brain states. While fast-spiking neurons always exhibited a wide bandwidth of around 400 Hz, the response properties of spike-frequency adapting interneurons switched with the background input's statistics. Slowly fluctuating background activity, as typical for sleep or quiet wakefulness, dramatically boosted the neurons' sensitivity to gamma and ripple frequencies. We developed a time-resolved dynamic gain analysis and revealed rapid sensitivity modulations that enable neurons to periodically boost gamma oscillations and ripples during specific phases of ongoing low-frequency oscillations. This mechanism predicts these prefrontal interneurons to be exquisitely sensitive to high-frequency ripples, especially during brain states characterized by slow rhythms, and to contribute substantially to theta-gamma cross-frequency coupling.

A network model of the barrel cortex combined with a differentiator detector reproduces features of the behavioral response to single-neuron stimulation

The stimulation of a single neuron in the rat somatosensory cortex can elicit a behavioral response. The probability of a behavioral response does not depend appreciably on the duration or intensity of a constant stimulation, whereas the response probability increases significantly upon injection of an irregular current. Biological mechanisms that can potentially suppress a constant input signal are present in the dynamics of both neurons and synapses and seem ideal candidates to explain these experimental findings. Here, we study a large network of integrate-and-fire neurons with several salient features of neuronal populations in the rat barrel cortex. The model includes cellular spike-frequency adaptation, experimentally constrained numbers and types of chemical synapses endowed with short-term plasticity, and gap junctions. Numerical simulations of this model indicate that cellular and synaptic adaptation mechanisms alone may not suffice to account for the experimental results if the local network activity is read out by an integrator. However, a circuit that approximates a differentiator can detect the single-cell stimulation with a reliability that barely depends on the length or intensity of the stimulus, but that increases when an irregular signal is used. This finding is in accordance with the experimental results obtained for the stimulation of a regularly-spiking excitatory cell.

It is widely assumed that only a large group of neurons can encode a stimulus or control behavior. This tenet of neuroscience has been challenged by experiments in which stimulating a single cortical neuron has had a measurable effect on an animal’s behavior. Recently, theoretical studies have explored how a single-neuron stimulation could be detected in a large recurrent network. However, these studies missed essential biological mechanisms of cortical networks and are unable to explain more recent experiments in the barrel cortex. Here, to describe the stimulated brain area, we propose and study a network model endowed with many important biological features of the barrel cortex. Importantly, we also investigate different readout mechanisms, i.e. ways in which the stimulation effects can propagate to other brain areas. We show that a readout network which tracks rapid variations in the local network activity is in agreement with the experiments. Our model demonstrates a possible mechanism for how the stimulation of a single neuron translates into a signal at the population level, which is taken as a proxy of the animal’s response. Our results illustrate the power of spiking neural networks to properly describe the effects of a single neuron’s activity.

Low-rate firing limit for neurons with axon, soma and dendrites driven by spatially distributed stochastic synapses

Analytical forms for neuronal firing rates are important theoretical tools for the analysis of network states. Since the 1960s, the majority of approaches have treated neurons as being electrically compact and therefore isopotential. These approaches have yielded considerable insight into how single-cell properties affect network activity; however, many neuronal classes, such as cortical pyramidal cells, are electrically extended objects. Calculation of the complex flow of electrical activity driven by stochastic spatio-temporal synaptic input streams in these structures has presented a significant analytical challenge. Here we demonstrate that an extension of the level-crossing method of Rice, previously used for compact cells, provides a general framework for approximating the firing rate of neurons with spatial structure. Even for simple models, the analytical approximations derived demonstrate a surprising richness including: independence of the firing rate to the electrotonic length for certain models, but with a form distinct to the point-like leaky integrate-and-fire model; a non-monotonic dependence of the firing rate on the number of dendrites receiving synaptic drive; a significant effect of the axonal and somatic load on the firing rate; and the role that the trigger position on the axon for spike initiation has on firing properties. The approach necessitates only calculating the mean and variances of the non-thresholded voltage and its rate of change in neuronal structures subject to spatio-temporal synaptic fluctuations. The combination of simplicity and generality promises a framework that can be built upon to incorporate increasing levels of biophysical detail and extend beyond the low-rate firing limit treated in this paper.

Dynamic Gain Analysis Reveals Encoding Deficiencies in Cortical Neurons That Recover from Hypoxia-Induced Spreading Depolarizations

Cortical regions that are damaged by insults, such as ischemia, hypoxia, and trauma, frequently generate spreading depolarization (SD). At the neuronal level, SDs entail complete breakdown of ionic gradients, persisting for seconds to minutes. It is unclear whether these transient events have a more lasting influence on neuronal function. Here, we describe electrophysiological changes in cortical neurons after recovery from hypoxia-induced SD. When examined with standard measures of neuronal excitability several hours after recovery from SD, layer 5 pyramidal neurons in brain slices from mice of either sex appear surprisingly normal. However, we here introduce an additional parameter, dynamic gain, which characterizes the bandwidth of action potential encoding by a neuron, and thereby reflects its potential efficiency in a multineuronal circuit. We find that the ability of neurons that recover from SD to track high-frequency inputs is markedly curtailed; exposure to hypoxia did not have this effect when SD was prevented pharmacologically. Staining for Ankyrin G revealed at least a fourfold decrease in the number of intact axon initial segments in post-SD slices. Since this effect, along with the effect on encoding, was blocked by an inhibitor of the Ca²⁺-dependent enzyme, calpain, we conclude that both effects were mediated by the SD-induced rise in intracellular Ca²⁺ Although effects of calpain activation were detected in the axon initial segment, changes in soma-dendritic compartments may also be involved. Whatever the precise molecular mechanism, our findings indicate that in the context of cortical circuit function, effectiveness of neurons that survive SD may be limited.SIGNIFICANCE STATEMENT Spreading depolarization, which commonly accompanies cortical injury, entails transient massive breakdown of neuronal ionic gradients. The function of cortical neurons that recover from hypoxia-induced spreading depolarization is not obviously abnormal when tested for usual measures of neuronal excitability. However, we now demonstrate that they have a reduced bandwidth, reflecting a significant impairment of their ability to precisely encode high-frequency components of their synaptic input in output spike trains. Thus, neurons that recover from spreading depolarizations are less able to function normally as elements in the multineuronal cortical circuitry. These changes are correlated with activation of the calcium-dependent enzyme, calpain.

How single neuron properties shape chaotic dynamics and signal transmission in random neural networks

While most models of randomly connected neural networks assume single-neuron models with simple dynamics, neurons in the brain exhibit complex intrinsic dynamics over multiple timescales. We analyze how the dynamical properties of single neurons and recurrent connections interact to shape the effective dynamics in large randomly connected networks. A novel dynamical mean-field theory for strongly connected networks of multi-dimensional rate neurons shows that the power spectrum of the network activity in the chaotic phase emerges from a nonlinear sharpening of the frequency response function of single neurons. For the case of two-dimensional rate neurons with strong adaptation, we find that the network exhibits a state of "resonant chaos", characterized by robust, narrow-band stochastic oscillations. The coherence of stochastic oscillations is maximal at the onset of chaos and their correlation time scales with the adaptation timescale of single units. Surprisingly, the resonance frequency can be predicted from the properties of isolated neurons, even in the presence of heterogeneity in the adaptation parameters. In the presence of these internally-generated chaotic fluctuations, the transmission of weak, low-frequency signals is strongly enhanced by adaptation, whereas signal transmission is not influenced by adaptation in the non-chaotic regime. Our theoretical framework can be applied to other mechanisms at the level of single neurons, such as synaptic filtering, refractoriness or spike synchronization. These results advance our understanding of the interaction between the dynamics of single units and recurrent connectivity, which is a fundamental step toward the description of biologically realistic neural networks.

Weak electric fields promote resonance in neuronal spiking activity: Analytical results from two-compartment cell and network models

Transcranial brain stimulation and evidence of ephaptic coupling have sparked strong interests in understanding the effects of weak electric fields on the dynamics of neuronal populations. While their influence on the subthreshold membrane voltage can be biophysically well explained using spatially extended neuron models, mechanistic analyses of neuronal spiking and network activity have remained a methodological challenge. More generally, this challenge applies to phenomena for which single-compartment (point) neuron models are oversimplified. Here we employ a pyramidal neuron model that comprises two compartments, allowing to distinguish basal-somatic from apical dendritic inputs and accounting for an extracellular field in a biophysically minimalistic way. Using an analytical approach we fit its parameters to reproduce the response properties of a canonical, spatial model neuron and dissect the stochastic spiking dynamics of single cells and large networks. We show that oscillatory weak fields effectively mimic anti-correlated inputs at the soma and dendrite and strongly modulate neuronal spiking activity in a rather narrow frequency band. This effect carries over to coupled populations of pyramidal cells and inhibitory interneurons, boosting network-induced resonance in the beta and gamma frequency bands. Our work contributes a useful theoretical framework for mechanistic analyses of population dynamics going beyond point neuron models, and provides insights on modulation effects of extracellular fields due to the morphology of pyramidal cells.

The elongated spatial structure of pyramidal neurons, which possess large apical dendrites, plays an important role for the integration of synaptic inputs and mediates sensitivity to weak extracellular electric fields. Modeling studies at the population level greatly contribute to our mechanistic understanding but face a methodological challenge because morphologically detailed neuron models are too complex for use in noisy, in-vivo like conditions and large networks in particular. Here we present an analytical approach based on a two-compartment spiking neuron model that can distinguish synaptic inputs at the apical dendrite from those at the somatic region and accounts for an extracellular field in a biophysically minimalistic way. We devised efficient methods to approximate the responses of a spatially more detailed pyramidal neuron model, and to study the spiking dynamics of single neurons and sparsely coupled large networks in the presence of fluctuating inputs. Using these methods we focused on how responses are affected by oscillatory weak fields. Our results suggest that ephaptic coupling may play a mechanistic role for oscillations of population activity and indicate the potential to entrain networks by weak electric stimulation.

Information transmission of mean and variance coding in integrate-and-fire neurons

Neurons process information by translating continuous signals into patterns of discrete spike times. An open question is how much information these spike times contain about signals which modulate either the mean or the variance of the somatic currents in neurons, as is observed experimentally. Here we calculate the exact information contained in discrete spike times about a continuous signal in both encoding strategies. We show that the information content about mean modulating signals is generally substantially larger than about variance modulating signals for biological parameters. Our analysis further reveals that higher information transmission is associated with a larger proportion of nonlinear signal encoding. Our study measures the complete information content of mean and variance coding and provides a method to determine what fraction of the total information is linearly decodable.

Improved lower bound for the mutual information between signal and neural spike count

The mutual information between a stimulus signal and the spike count of a stochastic neuron is in many cases difficult to determine. Therefore, it is often approximated by a lower bound formula that involves linear correlations between input and output only. Here, we improve the linear lower bound for the mutual information by incorporating nonlinear correlations. For the special case of a Gaussian output variable with nonlinear signal dependencies of mean and variance we also derive an exact integral formula for the full mutual information. In our numerical analysis, we first compare the linear and nonlinear lower bounds and the exact integral formula for two different Gaussian models and show under which conditions the nonlinear lower bound provides a significant improvement to the linear approximation. We then inspect two neuron models, the leaky integrate-and-fire model with white Gaussian noise and the Na-K model with channel noise. We show that for certain firing regimes and for intermediate signal strengths the nonlinear lower bound can provide a substantial improvement compared to the linear lower bound. Our results demonstrate the importance of nonlinear input-output correlations for neural information transmission and provide a simple nonlinear approximation for the mutual information that can be applied to more complicated neuron models as well as to experimental data.

An axon initial segment is required for temporal precision in action potential encoding by neuronal populations

Central neurons initiate action potentials (APs) in the axon initial segment (AIS), a compartment characterized by a high concentration of voltage-dependent ion channels and specialized cytoskeletal anchoring proteins arranged in a regular nanoscale pattern. Although the AIS was a key evolutionary innovation in neurons, the functional benefits it confers are not clear. Using a mutation of the AIS cytoskeletal protein βIV-spectrin, we here establish an in vitro model of neurons with a perturbed AIS architecture that retains nanoscale order but loses the ability to maintain a high Na_V density. Combining experiments and simulations, we show that a high Na_V density in the AIS is not required for axonal AP initiation; it is, however, crucial for a high bandwidth of information encoding and AP timing precision. Our results provide the first experimental demonstration of axonal AP initiation without high axonal channel density and suggest that increasing the bandwidth of the neuronal code and, hence, the computational efficiency of network function, was a major benefit of the evolution of the AIS.

Pyramidal Cell-Interneuron Circuit Architecture and Dynamics in Hippocampal Networks

Excitatory control of inhibitory neurons is poorly understood due to the difficulty of studying synaptic connectivity in vivo. We inferred such connectivity through analysis of spike timing and validated this inference using juxtacellular and optogenetic control of presynaptic spikes in behaving mice. We observed that neighboring CA1 neurons had stronger connections and that superficial pyramidal cells projected more to deep interneurons. Connection probability and strength were skewed, with a minority of highly connected hubs. Divergent presynaptic connections led to synchrony between interneurons. Synchrony of convergent presynaptic inputs boosted postsynaptic drive. Presynaptic firing frequency was read out by postsynaptic neurons through short-term depression and facilitation, with individual pyramidal cells and interneurons displaying a diversity of spike transmission filters. Additionally, spike transmission was strongly modulated by prior spike timing of the postsynaptic cell. These results bridge anatomical structure with physiological function.

Evoking prescribed spike times in stochastic neurons

Single cell stimulation in vivo is a powerful tool to investigate the properties of single neurons and their functionality in neural networks. We present a method to determine a cell-specific stimulus that reliably evokes a prescribed spike train with high temporal precision of action potentials. We test the performance of this stimulus in simulations for two different stochastic neuron models. For a broad range of parameters and a neuron firing with intermediate firing rates (20-40 Hz) the reliability in evoking the prescribed spike train is close to its theoretical maximum that is mainly determined by the level of intrinsic noise.

Exact analytical results for integrate-and-fire neurons driven by excitatory shot noise

A neuron receives input from other neurons via electrical pulses, so-called spikes. The pulse-like nature of the input is frequently neglected in analytical studies; instead, the input is usually approximated to be Gaussian. Recent experimental studies have shown, however, that an assumption underlying this approximation is often not met: Individual presynaptic spikes can have a significant effect on a neuron's dynamics. It is thus desirable to explicitly account for the pulse-like nature of neural input, i.e. consider neurons driven by a shot noise - a long-standing problem that is mathematically challenging. In this work, we exploit the fact that excitatory shot noise with exponentially distributed weights can be obtained as a limit case of dichotomous noise, a Markovian two-state process. This allows us to obtain novel exact expressions for the stationary voltage density and the moments of the interspike-interval density of general integrate-and-fire neurons driven by such an input. For the special case of leaky integrate-and-fire neurons, we also give expressions for the power spectrum and the linear response to a signal. We verify and illustrate our expressions by comparison to simulations of leaky-, quadratic- and exponential integrate-and-fire neurons.

Temporally precise control of single-neuron spiking by juxtacellular nanostimulation

Temporal patterns of action potentials influence a variety of activity-dependent intra- and intercellular processes and play an important role in theories of neural coding. Elucidating the mechanisms underlying these phenomena requires imposing spike trains with precisely defined patterns, but this has been challenging due to the limitations of existing stimulation techniques. Here we present a new nanostimulation method providing control over the action potential output of individual cortical neurons. Spikes are elicited through the juxtacellular application of short-duration fluctuating currents ("kurzpulses"), allowing for the sub-millisecond precise and reproducible induction of arbitrary patterns of action potentials at all physiologically relevant firing frequencies (<120 Hz), including minute-long spike trains recorded in freely moving animals. We systematically compared our method to whole cell current injection, as well as optogenetic stimulation, and show that nanostimulation performance compares favorably with these techniques. This new nanostimulation approach is easily applied, can be readily performed in awake behaving animals, and thus promises to be a powerful tool for systematic investigations into the temporal elements of neural codes, as well as the mechanisms underlying a wide variety of activity-dependent cellular processes.NEW & NOTEWORTHY Assessing the impact of temporal features of neuronal spike trains requires imposing arbitrary patterns of spiking on individual neurons during behavior, but this has been difficult to achieve due to limitations of existing stimulation methods. We present a technique that overcomes these limitations by using carefully designed short-duration fluctuating juxtacellular current injections, which allow for the precise and reliable evocation of arbitrary patterns of neuronal spikes in single neurons in vivo.