Control of the firing patterns of vibrissa motoneurons by modulatory and phasic synaptic inputs: a modeling study

Theory of hierarchically organized neuronal oscillator dynamics that mediate rodent rhythmic whisking

Rodents explore their environment through coordinated orofacial motor actions, including whisking. Whisking can free-run via an oscillator of inhibitory neurons in the medulla and can be paced by breathing. Yet, the mechanics of the whisking oscillator and its interaction with breathing remain to be understood. We formulate and solve a hierarchical model of the whisking circuit. The first whisk within a breathing cycle is generated by inhalation, which resets a vibrissa oscillator circuit, while subsequent whisks are derived from the oscillator circuit. Our model posits, consistent with experiment, that there are two subpopulations of oscillator neurons. Stronger connections between the subpopulations support rhythmicity, while connections within each subpopulation induce variable spike timing that enhances the dynamic range of rhythm generation. Calculated cycle-to-cycle changes in whisking are consistent with experiment. Our model provides a computational framework to support longstanding observations of concurrent autonomous and driven rhythmic motor actions that comprise behaviors.

The role of relative membrane capacitance and time delay in cerebellar Purkinje cells

The membrane capacitance of a neuron can influence the synaptic efficacy and the speed of electrical signal propagation. Exploring the role of membrane capacitance will help facilitate a deeper understanding of the electrical properties of neurons. Thus, in this paper, we investigated the neuronal firing behaviors of a two-compartment model in Purkinje cells. We evaluated the influence of membrane capacitance under two different circumstances: in the absence of time delay and in the presence of time delay. Firstly, we separately studied the influence of somatic membrane capacitance Cs and dendritic membrane capacitance Cd on neuronal firing patterns. Through numerical simulation, we observed that they had two different types of period-adding scenarios, i.e. with and without chaotic bursting. Secondly, our results indicated that when the time delay was included in the model, periodic motions were more inclined to be destroyed, while at the same time, corresponding new chaotic motions were induced. These findings suggested that membrane capacitance and time delay play a pivotal functional role in modulating dynamical firing properties of neurons, especially aspects which lead to behaviors which result in changes to bursting patterns.

Spiking resonances in models with the same slow resonant and fast amplifying currents but different subthreshold dynamic properties

The generation of spiking resonances in neurons (preferred spiking responses to oscillatory inputs) requires the interplay of the intrinsic ionic currents that operate at the subthreshold voltage level and the spiking mechanisms. Combinations of the same types of ionic currents in different parameter regimes may give rise to different types of nonlinearities in the voltage equation (e.g., parabolic- and cubic-like), generating subthreshold (membrane potential) oscillations patterns with different properties. These nonlinearities are not apparent in the model equations, but can be uncovered by plotting the voltage nullclines in the phase-plane diagram. We investigate the spiking resonant properties of conductance-based models that are biophysically equivalent at the subthreshold level (same ionic currents), but dynamically different (parabolic- and cubic-like voltage nullclines). As a case study we consider a model having a persistent sodium and a hyperpolarization-activated (h-) currents, which exhibits subthreshold resonance in the theta frequency band. We unfold the concept of spiking resonance into evoked and output spiking resonance. The former focuses on the input frequencies that are able to generate spikes, while the latter focuses on the output spiking frequencies regardless of the input frequency that generated these spikes. A cell can exhibit one or both types of resonances. We also measure spiking phasonance, which is an extension of subthreshold phasonance (zero-phase-shift response to oscillatory inputs) to the spiking regime. The subthreshold resonant properties of both types of models are communicated to the spiking regime for low enough input amplitudes as the voltage response for the subthreshold resonant frequency band raises above threshold. For higher input amplitudes evoked spiking resonance is no longer present in these models, but output spiking resonance is present primarily in the parabolic-like model due to a cycle skipping mechanism (involving mixed-mode oscillations), while the cubic-like model shows a better 1:1 entrainment. We use dynamical systems tools to explain the underlying mechanisms and the mechanistic differences between the resonance types. Our results demonstrate that the effective time scales that operate at the subthreshold regime to generate intrinsic subthreshold oscillations, mixed-mode oscillations and subthreshold resonance do not necessarily determine the existence of a preferred spiking response to oscillatory inputs in the same frequency band. The results discussed in this paper highlight both the complexity of the suprathreshold responses to oscillatory inputs in neurons having resonant and amplifying currents with different time scales and the fact that the identity of the participating ionic currents is not enough to predict the resulting patterns, but additional dynamic information, captured by the geometric properties of the phase-space diagram, is needed.

The shaping of intrinsic membrane potential oscillations: positive/negative feedback, ionic resonance/amplification, nonlinearities and time scales

The generation of intrinsic subthreshold (membrane potential) oscillations (STOs) in neuronal models requires the interaction between two processes: a relatively fast positive feedback that favors changes in voltage and a slower negative feedback that opposes these changes. These are provided by the so-called resonant and amplifying gating variables associated to the participating ionic currents. We investigate both the biophysical and dynamic mechanisms of generation of STOs and how their attributes (frequency and amplitude) depend on the model parameters for biophysical (conductance-based) models having qualitatively different types of resonant currents (activating and inactivating) and an amplifying current. Combinations of the same types of ionic currents (same models) in different parameter regimes give rise to different types of nonlinearities in the voltage equation: quasi-linear, parabolic-like and cubic-like. On the other hand, combinations of different types of ionic currents (different models) may give rise to the same type of nonlinearities. We examine how the attributes of the resulting STOs depend on the combined effect of these resonant and amplifying ionic processes, operating at different effective time scales, and the various types of nonlinearities. We find that, while some STO properties and attribute dependencies on the model parameters are determined by the specific combinations of ionic currents (biophysical properties), and are different for models with different such combinations, others are determined by the type of nonlinearities and are common for models with different types of ionic currents. Our results highlight the richness of STO behavior in single cells as the result of the various ways in which resonant and amplifying currents interact and affect the generation and termination of STOs as control parameters change. We make predictions that can be tested experimentally and are expected to contribute to the understanding of how rhythmic activity in neuronal networks emerge from the interplay of the intrinsic properties of the participating neurons and the network connectivity.

Emergent exploration via novelty management

When encountering novel environments, animals perform complex yet structured exploratory behaviors. Despite their typical structuring, the principles underlying exploratory patterns are still not sufficiently understood. Here we analyzed exploratory behavioral data from two modalities: whisking and locomotion in rats and mice. We found that these rodents maximized novelty signal-to-noise ratio during each exploration episode, where novelty is defined as the accumulated information gain. We further found that these rodents maximized novelty during outbound exploration, used novelty-triggered withdrawal-like retreat behavior, and explored the environment in a novelty-descending sequence. We applied a hierarchical curiosity model, which incorporates these principles, to both modalities. We show that the model captures the major components of exploratory behavior in multiple timescales: single excursions, exploratory episodes, and developmental timeline. The model predicted that novelty is managed across exploratory modalities. Using a novel experimental setup in which mice encountered a novel object for the first time in their life, we tested and validated this prediction. Further predictions, related to the development of brain circuitry, are described. This study demonstrates that rodents select exploratory actions according to a novelty management framework and suggests a plausible mechanism by which mammalian exploration primitives can be learned during development and integrated in adult exploration of complex environments.

Mechanism and function of mixed-mode oscillations in vibrissa motoneurons

Vibrissa motoneurons in the facial nucleus innervate the intrinsic and extrinsic muscles that move the whiskers. Their intrinsic properties affect the way they process fast synaptic input from the vIRT and Bötzinger nuclei together with serotonergic neuromodulation. In response to constant current (I_app) injection, vibrissa motoneurons may respond with mixed mode oscillations (MMOs), in which sub-threshold oscillations (STOs) are intermittently mixed with spikes. This study investigates the mechanisms involved in generating MMOs in vibrissa motoneurons and their function in motor control. It presents a conductance-based model that includes the M-type K⁺ conductance, g_M, the persistent Na⁺ conductance, g_NaP, and the cationic h conductance, g_h. For g_h = 0 and moderate values of g_M and g_NaP, the model neuron generates STOs, but not MMOs, in response to I_app injection. STOs transform abruptly to tonic spiking as the current increases. In addition to STOs, MMOs are generated for g_h>0 for larger values of I_app; the I_app range in which MMOs appear increases linearly with g_h. In the MMOs regime, the firing rate increases with I_app like a Devil's staircase. Stochastic noise disrupts the temporal structure of the MMOs, but for a moderate noise level, the coefficient of variation (CV) is much less than one and varies non-monotonically with I_app. Furthermore, the estimated time period between voltage peaks, based on Bernoulli process statistics, is much higher in the MMOs regime than in the tonic regime. These two phenomena do not appear when moderate noise generates MMOs without an intrinsic MMO mechanism. Therefore, and since STOs do not appear in spinal motoneurons, the analysis can be used to differentiate different MMOs mechanisms. MMO firing activity in vibrissa motoneurons suggests a scenario in which moderate periodic inputs from the vIRT and Bötzinger nuclei control whisking frequency, whereas serotonergic neuromodulation controls whisking amplitude.

Activation and measurement of free whisking in the lightly anesthetized rodent

The rodent vibrissa system is a widely used experimental model of active sensation and motor control. Vibrissa-based touch in rodents involves stereotypic, rhythmic sweeping of the vibrissae as the animal explores its environment. Although pharmacologically induced rhythmic movements have long been used to understand the neural circuitry that underlies a variety of rhythmic behaviors, including locomotion, digestion and ingestion, these techniques have not been available for active sensory movements such as whisking. However, recent work that delineated the location of the central pattern generator for whisking has enabled pharmacological control over this behavior. Here we specify a protocol for the pharmacological induction of rhythmic vibrissa movements that mimic exploratory whisking. The rhythmic vibrissa movements are induced by local injection of a glutamatergic agonist, kainic acid. This protocol produces coordinated rhythmic vibrissa movements that are sustained for several hours in the anesthetized mouse or rat and thus provides unprecedented experimental control in studies related to vibrissa-based neuronal circuitry.

How the brainstem controls orofacial behaviors comprised of rhythmic actions

Mammals perform a multitude of well-coordinated orofacial behaviors such as breathing, sniffing, chewing, licking, swallowing, vocalizing, and in rodents, whisking. The coordination of these actions must occur without fault to prevent fatal blockages of the airway. Deciphering the neuronal circuitry that controls even a single action requires understanding the integration of sensory feedback and executive commands. A far greater challenge is to understand the coordination of multiple actions. Here, we focus on brainstem circuits that drive rhythmic orofacial actions. We discuss three neural computational mechanisms that may enable circuits for different actions to operate without interfering with each other. We conclude with proposed experimental programs for delineating the neural control principles that have evolved to coordinate orofacial behaviors.

Learning and control of exploration primitives

Animals explore novel environments in a cautious manner, exhibiting alternation between curiosity-driven behavior and retreats. We present a detailed formal framework for exploration behavior, which generates behavior that maintains a constant level of novelty. Similar to other types of complex behaviors, the resulting exploratory behavior is composed of exploration motor primitives. These primitives can be learned during a developmental period, wherein the agent experiences repeated interactions with environments that share common traits, thus allowing transference of motor learning to novel environments. The emergence of exploration motor primitives is the result of reinforcement learning in which information gain serves as intrinsic reward. Furthermore, actors and critics are local and ego-centric, thus enabling transference to other environments. Novelty control, i.e. the principle which governs the maintenance of constant novelty, is implemented by a central action-selection mechanism, which switches between the emergent exploration primitives and a retreat policy, based on the currently-experienced novelty. The framework has only a few parameters, wherein time-scales, learning rates and thresholds are adaptive, and can thus be easily applied to many scenarios. We implement it by modeling the rodent's whisking system and show that it can explain characteristic observed behaviors. A detailed discussion of the framework's merits and flaws, as compared to other related models, concludes the paper.

Hierarchy of orofacial rhythms revealed through whisking and breathing

Whisking and sniffing are predominant aspects of exploratory behaviour in rodents. Yet the neural mechanisms that generate and coordinate these and other orofacial motor patterns remain largely uncharacterized. Here we use anatomical, behavioural, electrophysiological and pharmacological tools to show that whisking and sniffing are coordinated by respiratory centres in the ventral medulla. We delineate a distinct region in the ventral medulla that provides rhythmic input to the facial motor neurons that drive protraction of the vibrissae. Neuronal output from this region is reset at each inspiration by direct input from the pre-Bötzinger complex, such that high-frequency sniffing has a one-to-one relationship with whisking, whereas basal respiration is accompanied by intervening whisks that occur between breaths. We conjecture that the respiratory nuclei, which project to other premotor regions for oral and facial control, function as a master clock for behaviours that coordinate with breathing.

θ-Frequency resonance at the cerebellum input stage improves spike timing on the millisecond time-scale

The neuronal circuits of the brain are thought to use resonance and oscillations to improve communication over specific frequency bands (Llinas, 1988; Buzsaki, 2006). However, the properties and mechanism of these phenomena in brain circuits remain largely unknown. Here we show that, at the cerebellum input stage, the granular layer (GRL) generates its maximum response at 5-7 Hz both in vivo following tactile sensory stimulation of the whisker pad and in acute slices following mossy fiber bundle stimulation. The spatial analysis of GRL activity performed using voltage-sensitive dye (VSD) imaging revealed 5-7 Hz resonance covering large GRL areas. In single granule cells, resonance appeared as a reorganization of output spike bursts on the millisecond time-scale, such that the first spike occurred earlier and with higher temporal precision and the probability of spike generation increased. Resonance was independent from circuit inhibition, as it persisted with little variation in the presence of the GABAA receptor blocker, gabazine. However, circuit inhibition reduced the resonance area more markedly at 7 Hz. Simulations with detailed computational models suggested that resonance depended on intrinsic granule cells ionic mechanisms: specifically, K slow (M-like) and KA currents acted as resonators and the persistent Na current and NMDA current acted as amplifiers. This form of resonance may play an important role for enhancing coherent spike emission from the GRL when theta-frequency bursts are transmitted by the cerebral cortex and peripheral sensory structures during sensory-motor processing, cognition, and learning.

Pre-neuronal morphological processing of object location by individual whiskers

In the vibrissal system, touch information is conveyed by a receptorless whisker hair to follicle mechanoreceptors, which then provide input to the brain. We examined whether any processing, that is, meaningful transformation, occurs in the whisker itself. Using high-speed videography and tracking the movements of whiskers in anesthetized and behaving rats, we found that whisker-related morphological phase planes, based on angular and curvature variables, can represent the coordinates of object position after contact in a reliable manner, consistent with theoretical predictions. By tracking exposed follicles, we found that the follicle-whisker junction is rigid, which enables direct readout of whisker morphological coding by mechanoreceptors. Finally, we found that our behaving rats pushed their whiskers against objects during localization in a way that induced meaningful morphological coding and, in parallel, improved their localization performance, which suggests a role for pre-neuronal morphological computation in active vibrissal touch.

Fast feedback in active sensing: touch-induced changes to whisker-object interaction

Whisking mediated touch is an active sense whereby whisker movements are modulated by sensory input and behavioral context. Here we studied the effects of touching an object on whisking in head-fixed rats. Simultaneous movements of whiskers C1, C2, and D1 were tracked bilaterally and their movements compared. During free-air whisking, whisker protractions were typically characterized by a single acceleration-deceleration event, whisking amplitude and velocity were correlated, and whisk duration correlated with neither amplitude nor velocity. Upon contact with an object, a second acceleration-deceleration event occurred in about 25% of whisk cycles, involving both contacting (C2) and non-contacting (C1, D1) whiskers ipsilateral to the object. In these cases, the rostral whisker (C2) remained in contact with the object throughout the double-peak phase, which effectively prolonged the duration of C2 contact. These “touch-induced pumps” (TIPs) were detected, on average, 17.9 ms after contact. On a slower time scale, starting at the cycle following first touch, contralateral amplitude increased while ipsilateral amplitude decreased. Our results demonstrate that sensory-induced motor modulations occur at various timescales, and directly affect object palpation.

Reinforcement active learning in the vibrissae system: optimal object localization

Rats move their whiskers to acquire information about their environment. It has been observed that they palpate novel objects and objects they are required to localize in space. We analyze whisker-based object localization using two complementary paradigms, namely, active learning and intrinsic-reward reinforcement learning. Active learning algorithms select the next training samples according to the hypothesized solution in order to better discriminate between correct and incorrect labels. Intrinsic-reward reinforcement learning uses prediction errors as the reward to an actor-critic design, such that behavior converges to the one that optimizes the learning process. We show that in the context of object localization, the two paradigms result in palpation whisking as their respective optimal solution. These results suggest that rats may employ principles of active learning and/or intrinsic reward in tactile exploration and can guide future research to seek the underlying neuronal mechanisms that implement them. Furthermore, these paradigms are easily transferable to biomimetic whisker-based artificial sensors and can improve the active exploration of their environment.

Mixed mode oscillations in mouse spinal motoneurons arise from a low excitability state

We explain the mechanism that elicits the mixed mode oscillations (MMOs) and the subprimary firing range that we recently discovered in mouse spinal motoneurons. In this firing regime, high-frequency subthreshold oscillations appear a few millivolts below the spike voltage threshold and precede the firing of a full blown spike. By combining intracellular recordings in vivo (including dynamic clamp experiments) in mouse spinal motoneurons and modeling, we show that the subthreshold oscillations are due to the spike currents and that MMOs appear each time the membrane is in a low excitability state. Slow kinetic processes largely contribute to this low excitability. The clockwise hysteresis in the I-F relationship, frequently observed in mouse motoneurons, is mainly due to a substantial slow inactivation of the sodium current. As a consequence, less sodium current is available for spiking. This explains why a large subprimary range with numerous oscillations is present in motoneurons displaying a clockwise hysteresis. In motoneurons whose I-F curve exhibits a counterclockwise hysteresis, it is likely that the slow inactivation operates on a shorter time scale and is substantially reduced by the de-inactivating effect of the afterhyperpolarization (AHP) current, thus resulting in a more excitable state. This accounts for the short subprimary firing range with only a few MMOs seen in these motoneurons. Our study reveals a new role for the AHP current that sets the membrane excitability level by counteracting the slow inactivation of the sodium current and allows or precludes the appearance of MMOs.

Temporal and spatial characteristics of vibrissa responses to motor commands

A mechanistic description of the generation of whisker movements is essential for understanding the control of whisking and vibrissal active touch. We explore how facial-motoneuron spikes are translated, via an intrinsic muscle, to whisker movements. This is achieved by constructing, simulating, and analyzing a computational, biomechanical model of the motor plant, and by measuring spiking to movement transformations at small and large angles using high-precision whisker tracking in vivo. Our measurements revealed a supralinear summation of whisker protraction angles in response to consecutive motoneuron spikes with moderate interspike intervals (5 ms < Deltat < 30 ms). This behavior is explained by a nonlinear transformation from intracellular changes in Ca(2+) concentration to muscle force. Our model predicts the following spatial constraints: (1) Contraction of a single intrinsic muscle results in movement of its two attached whiskers with different amplitudes; the relative amplitudes depend on the resting angles and on the attachment location of the intrinsic muscle on the anterior whisker. Counterintuitively, for a certain range of resting angles, activation of a single intrinsic muscle can lead to a retraction of one of its two attached whiskers. (2) When a whisker is pulled by its two adjacent muscles with similar forces, the protraction amplitude depends only weakly on the resting angle. (3) Contractions of two adjacent muscles sums up linearly for small amplitudes and supralinearly for larger amplitudes. The model provides a direct translation from motoneuron spikes to whisker movements and can serve as a building block in closed-loop motor-sensory models of active touch.