An electrophysiological and kinematic model of Paramecium, the "swimming neuron".

Paramecium is a large unicellular organism that swims in fresh water using cilia. When stimulated by various means (mechanically, chemically, optically, thermally), it often swims backward then turns and swims forward again in a new direction: this is called the avoiding reaction. This reaction is triggered by a calcium-based action potential. For this reason, several authors have called Paramecium the "swimming neuron". Here we present an empirically constrained model of its action potential based on electrophysiology experiments on live immobilized paramecia, together with simultaneous measurement of ciliary beating using particle image velocimetry. Using these measurements and additional behavioral measurements of free swimming, we extend the electrophysiological model by coupling calcium concentration to kinematic parameters, turning it into a swimming model. In this way, we obtain a model of autonomously behaving Paramecium. Finally, we demonstrate how the modeled organism interacts with an environment, can follow gradients and display collective behavior. This work provides a modeling basis for investigating the physiological basis of autonomous behavior of Paramecium in ecological environments.

Neural excitability increases with axonal resistance between soma and axon initial segment.

The position of the axon initial segment (AIS) is thought to play a critical role in neuronal excitability. Previous experimental studies have found that a distal shift in AIS position correlates with a reduction in excitability. Yet theoretical work has suggested the opposite, because of increased electrical isolation. A distal shift in AIS position corresponds to an elevation of axial resistance Ra We therefore examined how changes in Ra at the axon hillock impact the voltage threshold (Vth) of the somatic action potential in L5 pyramidal neurons. Increasing Ra by mechanically pinching the axon between the soma and the AIS was found to lower Vth by ∼6 mV. Conversely, decreasing Ra by substituting internal ions with higher mobility elevated Vth All Ra -dependent changes in Vth could be reproduced in a Hodgkin-Huxley compartmental model. We conclude that in L5 pyramidal neurons, excitability increases with axial resistance and therefore with a distal shift of the AIS.

Does the present moment depend on the moments not lived?

Integrated information theory postulates that a conscious experience depends on a repertoire of hypothetical experiences (the axiom of information). This makes consciousness depend on the context that constrains the set of possibilities and on the scenarios imagined by the external observer, and not only on the system itself.

Electrical match between initial segment and somatodendritic compartment for action potential backpropagation in retinal ganglion cells.

The action potential of most vertebrate neurons initiates in the axon initial segment (AIS) and is then transmitted to the soma where it is regenerated by somatodendritic sodium channels. For successful transmission, the AIS must produce a strong axial current, so as to depolarize the soma to the threshold for somatic regeneration. Theoretically, this axial current depends on AIS geometry and Na+ conductance density. We measured the axial current of mouse retinal ganglion cells using whole cell recordings with post hoc AIS labeling. We found that this current is large, implying high Na+ conductance density, and carries a charge that covaries with capacitance so as to depolarize the soma by ∼30 mV. Additionally, we observed that the axial current attenuates strongly with depolarization, consistent with sodium channel inactivation, but temporally broadens so as to preserve the transmitted charge. Thus, the AIS appears to be organized so as to reliably backpropagate the axonal action potential.NEW & NOTEWORTHY We measured the axial current produced at spike initiation by the axon initial segment of mouse retinal ganglion cells. We found that it is a large current, requiring high sodium channel conductance density, which covaries with cell capacitance so as to ensure a ∼30 mV depolarization. During sustained depolarization the current attenuated, but it broadened to preserve somatic depolarization. Thus, properties of the initial segment are adjusted to ensure backpropagation of the axonal action potential.

A simple device to immobilize protists for electrophysiology and microinjection.

We present a simple device to mechanically immobilize motile cells such as ciliates. It can be used in particular for intracellular electrophysiology and microinjection. A transparent filter with holes smaller than the specimen is stretched over an outlet. A flow is induced by either a peristaltic pump or a depressurized tank, mechanically entraining cells to the bottom, where they are immobilized against the filter. The cells start swimming again as soon as the flow is stopped. We demonstrate the device by recording action potentials in Paramecium and injecting a fluorescent dye into the cytosol.

Anticipatory coadaptation of ankle stiffness and sensorimotor gain for standing balance.

External perturbation forces may compromise standing balance. The nervous system can intervene only after a delay greater than 100 ms, during which the body falls freely. With ageing, sensorimotor delays are prolonged, posing a critical threat to balance. We study a generic model of stabilisation with neural delays to understand how the organism should adapt to challenging balance conditions. The model suggests that ankle stiffness should be increased in anticipation of perturbations, for example by muscle co-contraction, so as to slow down body fall during the neural response delay. Increased ankle muscle co-contraction is indeed observed in young adults when standing in challenging balance conditions, and in older relative to young adults during normal stance. In parallel, the analysis of the model shows that increases in either stiffness or neural delay must be coordinated with decreases in spinal sensorimotor gains, otherwise the feedback itself becomes destabilizing. Accordingly, a decrease in spinal feedback is observed in challenging conditions, and with age-related increases in neural delay. These observations have been previously interpreted as indicating an increased reliance on cortical rather than spinal control of balance, despite the fact that cortical responses have a longer latency. Our analysis challenges this interpretation by showing that these observations are consistent with a functional coadaptation of spinal feedback gains to functional changes in stiffness and neural delay.

Covariation of axon initial segment location and dendritic tree normalizes the somatic action potential.

In mammalian neurons, the axon initial segment (AIS) electrically connects the somatodendritic compartment with the axon and converts the incoming synaptic voltage changes into a temporally precise action potential (AP) output code. Although axons often emanate directly from the soma, they may also originate more distally from a dendrite, the implications of which are not well-understood. Here, we show that one-third of the thick-tufted layer 5 pyramidal neurons have an axon originating from a dendrite and are characterized by a reduced dendritic complexity and thinner main apical dendrite. Unexpectedly, the rising phase of somatic APs is electrically indistinguishable between neurons with a somatic or a dendritic axon origin. Cable analysis of the neurons indicated that the axonal axial current is inversely proportional to the AIS distance, denoting the path length between the soma and the start of the AIS, and to produce invariant somatic APs, it must scale with the local somatodendritic capacitance. In agreement, AIS distance inversely correlates with the apical dendrite diameter, and model simulations confirmed that the covariation suffices to normalize the somatic AP waveform. Therefore, in pyramidal neurons, the AIS location is finely tuned with the somatodendritic capacitive load, serving as a homeostatic regulation of the somatic AP in the face of diverse neuronal morphologies.

Neural coding: The bureaucratic model of the brain.

The neural coding metaphor is so ubiquitous that we tend to forget its metaphorical nature. What do we mean when we assert that neurons encode and decode? What kind of causal and representational model of the brain does the metaphor entail? What lies beneath the neural coding metaphor, I argue, is a bureaucratic model of the brain.

Is coding a relevant metaphor for the brain?

"Neural coding" is a popular metaphor in neuroscience, where objective properties of the world are communicated to the brain in the form of spikes. Here I argue that this metaphor is often inappropriate and misleading. First, when neurons are said to encode experimental parameters, the neural code depends on experimental details that are not carried by the coding variable (e.g., the spike count). Thus, the representational power of neural codes is much more limited than generally implied. Second, neural codes carry information only by reference to things with known meaning. In contrast, perceptual systems must build information from relations between sensory signals and actions, forming an internal model. Neural codes are inadequate for this purpose because they are unstructured and therefore unable to represent relations. Third, coding variables are observables tied to the temporality of experiments, whereas spikes are timed actions that mediate coupling in a distributed dynamical system. The coding metaphor tries to fit the dynamic, circular, and distributed causal structure of the brain into a linear chain of transformations between observables, but the two causal structures are incongruent. I conclude that the neural coding metaphor cannot provide a valid basis for theories of brain function, because it is incompatible with both the causal structure of the brain and the representational requirements of cognition.

The world is complex, not just noisy.

To deny that human perception is optimal is not to claim that it is suboptimal. Rahnev & Denison (R&D) point out that optimality is often ill defined. The fundamental issue is framing perception as a statistical inference problem. Outside of the lab, the real perceptual challenge is to determine the lawful structure of the world, not variables of a predetermined statistical model.

Fast Learning with Weak Synaptic Plasticity.

New sensory stimuli can be learned with a single or a few presentations. Similarly, the responses of cortical neurons to a stimulus have been shown to increase reliably after just a few repetitions. Long-term memory is thought to be mediated by synaptic plasticity, but in vitro experiments in cortical cells typically show very small changes in synaptic strength after a pair of presynaptic and postsynaptic spikes. Thus, it is traditionally thought that fast learning requires stronger synaptic changes, possibly because of neuromodulation. Here we show theoretically that weak synaptic plasticity can, in fact, support fast learning, because of the large number of synapses N onto a cortical neuron. In the fluctuation-driven regime characteristic of cortical neurons in vivo, the size of membrane potential fluctuations grows only as √N, whereas a single output spike leads to potentiation of a number of synapses proportional to N. Therefore, the relative effect of a single spike on synaptic potentiation grows as √N. This leverage effect requires precise spike timing. Thus, the large number of synapses onto cortical neurons allows fast learning with very small synaptic changes. Significance statement: Long-term memory is thought to rely on the strengthening of coactive synapses. This physiological mechanism is generally considered to be very gradual, and yet new sensory stimuli can be learned with just a few presentations. Here we show theoretically that this apparent paradox can be solved when there is a tight balance between excitatory and inhibitory input. In this case, small synaptic modifications applied to the many synapses onto a given neuron disrupt that balance and produce a large effect even for modifications induced by a single stimulus. This effect makes fast learning possible with small synaptic changes and reconciles physiological and behavioral observations.

Slow feature analysis with spiking neurons and its application to audio stimuli.

Extracting invariant features in an unsupervised manner is crucial to perform complex computation such as object recognition, analyzing music or understanding speech. While various algorithms have been proposed to perform such a task, Slow Feature Analysis (SFA) uses time as a means of detecting those invariants, extracting the slowly time-varying components in the input signals. In this work, we address the question of how such an algorithm can be implemented by neurons, and apply it in the context of audio stimuli. We propose a projected gradient implementation of SFA that can be adapted to a Hebbian like learning rule dealing with biologically plausible neuron models. Furthermore, we show that a Spike-Timing Dependent Plasticity learning rule, shaped as a smoothed second derivative, implements SFA for spiking neurons. The theory is supported by numerical simulations, and to illustrate a simple use of SFA, we have applied it to auditory signals. We show that a single SFA neuron can learn to extract the tempo in sound recordings.

What is the most realistic single-compartment model of spike initiation?

A large variety of neuron models are used in theoretical and computational neuroscience, and among these, single-compartment models are a popular kind. These models do not explicitly include the dendrites or the axon, and range from the Hodgkin-Huxley (HH) model to various flavors of integrate-and-fire (IF) models. The main classes of models differ in the way spikes are initiated. Which one is the most realistic? Starting with some general epistemological considerations, I show that the notion of realism comes in two dimensions: empirical content (the sort of predictions that a model can produce) and empirical accuracy (whether these predictions are correct). I then examine the realism of the main classes of single-compartment models along these two dimensions, in light of recent experimental evidence.

On the variation of interaural time differences with frequency.

Interaural time difference (ITD) is a major cue to sound localization in humans and animals. For a given subject and position in space, ITD depends on frequency. This variation is analyzed here using a head related transfer functions (HRTFs) database collected from the literature and comprising human HRTFs from 130 subjects and animal HRTFs from six specimens of different species. For humans, the ITD is found to vary with frequency in a way that shows consistent differences with respect to a spherical head model. Maximal ITD values were found to be about 800 µs in low frequencies and 600 µs in high frequencies. The ITD variation with frequency (up to 200 µs for some positions) occurs within the frequency range where ITD is used to judge the lateral position of a sound source. In addition, ITD varies substantially within the bandwidth of a single auditory filter, leading to systematic differences between envelope and fine-structure ITDs. Because the frequency-dependent pattern of ITD does not display spherical symmetries, it potentially provides cues to elevation and resolves front/back confusion. The fact that the relation between position and ITDs strongly depends on the sound's spectrum in turn suggests that humans and animals make use of this relationship for the localization of sounds.

Spike-threshold adaptation predicted by membrane potential dynamics in vivo.

Neurons encode information in sequences of spikes, which are triggered when their membrane potential crosses a threshold. In vivo, the spiking threshold displays large variability suggesting that threshold dynamics have a profound influence on how the combined input of a neuron is encoded in the spiking. Threshold variability could be explained by adaptation to the membrane potential. However, it could also be the case that most threshold variability reflects noise and processes other than threshold adaptation. Here, we investigated threshold variation in auditory neurons responses recorded in vivo in barn owls. We found that spike threshold is quantitatively predicted by a model in which the threshold adapts, tracking the membrane potential at a short timescale. As a result, in these neurons, slow voltage fluctuations do not contribute to spiking because they are filtered by threshold adaptation. More importantly, these neurons can only respond to input spikes arriving together on a millisecond timescale. These results demonstrate that fast adaptation to the membrane potential captures spike threshold variability in vivo.

Sharpness of spike initiation in neurons explained by compartmentalization.

In cortical neurons, spikes are initiated in the axon initial segment. Seen at the soma, they appear surprisingly sharp. A standard explanation is that the current coming from the axon becomes sharp as the spike is actively backpropagated to the soma. However, sharp initiation of spikes is also seen in the input-output properties of neurons, and not only in the somatic shape of spikes; for example, cortical neurons can transmit high frequency signals. An alternative hypothesis is that Na channels cooperate, but it is not currently supported by direct experimental evidence. I propose a simple explanation based on the compartmentalization of spike initiation. When Na channels are placed in the axon, the soma acts as a current sink for the Na current. I show that there is a critical distance to the soma above which an instability occurs, so that Na channels open abruptly rather than gradually as a function of somatic voltage.

Effect of instantaneous frequency glides on interaural time difference processing by auditory coincidence detectors.

Detecting interaural time difference (ITD) is crucial for sound localization. The temporal accuracy required to detect ITD, and how ITD is initially encoded, continue to puzzle scientists. A fundamental question is whether the monaural inputs to the binaural ITD detectors differ only in their timing, when temporal and spectral tunings are largely inseparable in the auditory pathway. Here, we investigate the spectrotemporal selectivity of the monaural inputs to ITD detector neurons of the owl. We found that these inputs are selective for instantaneous frequency glides. Modeling shows that ITD tuning depends strongly on whether the monaural inputs are spectrotemporally matched, an effect that may generalize to mammals. We compare the spectrotemporal selectivity of monaural inputs of ITD detector neurons in vivo, demonstrating that their selectivity matches. Finally, we show that this refinement can develop through spike timing-dependent plasticity. Our findings raise the unexplored issue of time-dependent frequency tuning in auditory coincidence detectors and offer a unifying perspective.

Estimation of the low-frequency components of the head-related transfer functions of animals from photographs.

Reliable animal head-related transfer function (HRTF) estimation procedures are needed for several practical applications, for example, to investigate the neuronal mechanisms of sound localization using virtual acoustic spaces or to have a quantitative description of the different localization cues available to a given animal species. Here, two established techniques are combined to estimate an animal's HRTF from photographs by taking into account as much morphological detail as possible. The first step of the method consists in building a three-dimensional-model of the animal from pictures taken with a standard camera. The HRTFs are then estimated by means of a rapid boundary-element-method implementation. This combined method is validated on a taxidermist model of a cat by comparing binaural and monaural localization cues extracted from estimated and measured HRTFs. It is shown that it provides a reliable way to estimate low-frequency HRTF, which is difficult to obtain with standard acoustical measurements procedures because of reflections.

Predicting spike timing in highly synchronous auditory neurons at different sound levels.

A challenge for sensory systems is to encode natural signals that vary in amplitude by orders of magnitude. The spike trains of neurons in the auditory system must represent the fine temporal structure of sounds despite a tremendous variation in sound level in natural environments. It has been shown in vitro that the transformation from dynamic signals into precise spike trains can be accurately captured by simple integrate-and-fire models. In this work, we show that the in vivo responses of cochlear nucleus bushy cells to sounds across a wide range of levels can be precisely predicted by deterministic integrate-and-fire models with adaptive spike threshold. Our model can predict both the spike timings and the firing rate in response to novel sounds, across a large input level range. A noisy version of the model accounts for the statistical structure of spike trains, including the reliability and temporal precision of responses. Spike threshold adaptation was critical to ensure that predictions remain accurate at different levels. These results confirm that simple integrate-and-fire models provide an accurate phenomenological account of spike train statistics and emphasize the functional relevance of spike threshold adaptation.

Computing with neural synchrony.

Neurons communicate primarily with spikes, but most theories of neural computation are based on firing rates. Yet, many experimental observations suggest that the temporal coordination of spikes plays a role in sensory processing. Among potential spike-based codes, synchrony appears as a good candidate because neural firing and plasticity are sensitive to fine input correlations. However, it is unclear what role synchrony may play in neural computation, and what functional advantage it may provide. With a theoretical approach, I show that the computational interest of neural synchrony appears when neurons have heterogeneous properties. In this context, the relationship between stimuli and neural synchrony is captured by the concept of synchrony receptive field, the set of stimuli which induce synchronous responses in a group of neurons. In a heterogeneous neural population, it appears that synchrony patterns represent structure or sensory invariants in stimuli, which can then be detected by postsynaptic neurons. The required neural circuitry can spontaneously emerge with spike-timing-dependent plasticity. Using examples in different sensory modalities, I show that this allows simple neural circuits to extract relevant information from realistic sensory stimuli, for example to identify a fluctuating odor in the presence of distractors. This theory of synchrony-based computation shows that relative spike timing may indeed have computational relevance, and suggests new types of neural network models for sensory processing with appealing computational properties.