Computational implications of biophysical diversity and multiple timescales in neurons and synapses for circuit performance

Despite advances in experimental and theoretical neuroscience, we are still trying to identify key biophysical details that are important for characterizing the operation of brain circuits. Biological mechanisms at the level of single neurons and synapses can be combined as ‘building blocks’ to generate circuit function. We focus on the importance of capturing multiple timescales when describing these intrinsic and synaptic components. Whether inherent in the ionic currents, the neuron’s complex morphology, or the neurotransmitter composition of synapses, these multiple timescales prove crucial for capturing the variability and richness of circuit output and enhancing the information-carrying capacity observed across nervous systems

Computational Properties of Cerebellar Nucleus Neurons: Effects of Stochastic Ion Channel Gating and Input Location

The function of the nervous system is shaped by the refined integration of synaptic inputs taking place at the single neuron level. Gain modulation is a computational principle that is widely used across the brain, in which the response of a neuronal unit to a set of inputs is affected in a multiplicative fashion by a second set of inputs, but without any effect on its selectivity. The arithmetic operations performed by pyramidal cells in cortical brain areas have been well characterised, along with the underlying mechanisms at the level of networks and cells, for instance background synaptic noise and dendritic saturation. However, in spite of the vast amount of research on the cerebellum and its function, little is known about neuronal computations carried out by its cellular components. A particular area of interest are the cerebellar nuclei, the main output gate of the cerebellum to the brain stem and cortical areas. The aim of this thesis is to contribute to an understanding of the arithmetic operations performed by neurons in the cerebellar nuclei. Focus is placed on two putative determinants, the location of the synaptic input and the presence of channel noise. To analyse the effect of channel noise, the known voltage-gated ion channels of a cerebellar nucleus neuron model are translated to stochastic Markov formalisms and their electrophysiologial behaviour is compared to their deterministic Hodgkin-Huxley counterparts. The findings demonstrate that in most cases, the behaviour of stochastic channels matches the reference deterministic models, with the notable exception of voltage-gated channels with fast kinetics. Two potential explanations are suggested for this discrepancy. Firstly, channels with fast kinetics are strongly affected by the artefactual loss of gating events in the simulation that is caused by the use of a finite-length time step. While this effect can be mitigated, in part, by using very small time steps, the second source of simulation artefacts is the rectification of the distribution of open channels, when channel kinetics characteristics allow the generation of a window current, with an temporal-averaged equilibrium close to zero. Further, stochastic gating is implemented in a realistic cerebellar nucleus neuronal model. The resulting stochastic model exhibits probabilistic spiking and a similar output rate as the corresponding deterministic cerebellar nucleus neuronal model. However, the outcomes of this thesis indicate the computational properties of the cerebellar nucleus neuronal model are independent of the presence of ion channel noise. The main result of this thesis is that the synaptic input location determines the single neuron computational properties, both in the cerebellar nucleus and layer Vb pyramidal neuronal models. The extent of multiplication increases systematically with the distance from the soma, for the cerebellar nucleus, but not for the layer Vb pyramidal neuron, where it is smaller than it would be expected for the distance from the soma. For both neurons, the underlying mechanism is related to the combined effect of nonlinearities introduced by dendritic saturation and the synaptic input noise. However, while excitatory inputs in the perisomatic areas in the cerebellar nucleus undergo additive operations and the distal areas multiplicative, in the layer Vb pyramidal neuron the integration of the excitatory driving input is always multiplicative. In addition, the change in gain is sensitive to the synchronicity of the excitatory synaptic input in the layer Vb pyramidal neuron, but not in the cerebellar nucleus neuron. These observations indicate that the same gain control mechanism might be utilized in distinct ways, in different computational contexts and across different areas, based on the neuronal type and its function

Spike timing in pyramidal cells of the dorsal cochlear nucleus

The cochlear nucleus is the termination point for all axons of the auditory nerve. In addition to input from the auditory nerve, the dorsal cochlear nucleus (DCN) receives input from other sensory systems. The principal neurons of the DCN, the pyramidal cells, process information from both the auditory and non-auditory inputs and relay this information to the inferior colliculus. While it is known that pyramidal cells can use spike timing to encode some auditory information such as frequency modulation, these neurons are usually described in terms of average rate. This study examines the spike timing characteristics of DCN pyramidal cells. We first investigated the spike timing characteristics of pyramidal cells by presenting the cells with Gaussian distributed white noise currents. In response to such stimuli, pyramidal cells fired trains of action potentials with precisely timed spikes. In addition, when an inhibitory event, such as an IPSP was added at the midpoint of the stimulus, the spike times became more precise after the IPSP than they were without the inhibitory event. Intrinsic conductances can shape the output of neurons. One important conductance is a transient outward current known as an A-current. A-currents arise from potassium channels such as Kv1.4, Kv3.4 and the entire Kv4 family. It has been hypothesized that an A-current leads to the build-up response pattern in pyramidal cells, which is characterized by a long latency to the first spike. Using heteropodatoxin-2, a specific blocker of Kv4 channels, we determined that Kv4 channels are responsible for the long delay to the first spike after a hyperpolarizing pre-pulse. To confirm this result, we also subtracted a model of the Acurrent using dynamic clamp and observed the same effect. Finally, the identity of this potassium current was determined using in situ hybridization and immunofluoresence. Pyramidal cells were labeled by injecting a retrograde dye into the inferior colliculus. Labeled pyramidal cells expressed Kv4.3 but not Kv4.2 potassium channels. From these results we concluded that Kv4.3 is essential for the characteristic response patterns observed in DCN pyramidal cells

Long-Distance Modulation of Sensory Encoding via Axonal Neuromodulation

The neuromodulatory system plays a critical role in sensorimotor system function and animal behavior. Its influence on axons, however, remains enigmatic although axons possess receptors for a plethora of modulators, and pathologies of the neuromodulatory system impair neuronal communication. The most dramatic neuromodulatory effect on axons is ectopic spiking, a process common to many systems and neurons during which action potentials are elicited in the axon trunk and travel antidromically towards the site of sensory transduction. We argue that ectopic action potentials modify sensory encoding by invading the primary spike initiation zone in the periphery. This is a particularly intriguing concept, since it allows the modulatory system to alter sensory information processing. We demonstrate that aminergic modulation of a proprioceptive axon that elicits spontaneous ectopic action potentials changes spike frequency, which determines the burst behavior of the proprioceptor. Increasing ectopic spike frequency delayed the peripheral burst, caused reductions in spike number and burst duration, and changes in sensory firing frequency. Computational models show these effects depend on slow ionic conductances to modulate membrane excitability. Thus, axonal neuromodulation provides a means to rapidly influence sensory encoding without directly or locally affecting the sites of stimulus reception and spike initiation

Synaptic and circuit mechanisms promoting broadband transmission of olfactory stimulus dynamics

Sensory stimuli fluctuate on many timescales. However, short-term plasticity causes synapses to act as temporal filters, limiting the range of frequencies they can transmit. How synapses in vivo might transmit a range of frequencies in spite of short-term plasticity is poorly understood. The first synapse in the Drosophila olfactory system exhibits short-term depression, and yet can transmit broadband signals. Here we describe two mechanisms that broaden the frequency characteristics of this synapse. First, two distinct excitatory postsynaptic currents transmit signals on different timescales. Second, presynaptic inhibition dynamically updates synaptic properties to promote accurate transmission of signals across a wide range of frequencies. Inhibition is transient but grows slowly, and simulations show that these two features of inhibition promote broadband synaptic transmission. Dynamic inhibition is often thought to restrict the temporal patterns that a neuron responds to, but our results illustrate a different idea: inhibition can expand the bandwidth of neural coding

Spiking Models for Level-Invariant Encoding

Levels of ecological sounds vary over several orders of magnitude, but the firing rate and membrane potential of a neuron are much more limited in range. In binaural neurons of the barn owl, tuning to interaural delays is independent of level differences. Yet a monaural neuron with a fixed threshold should fire earlier in response to louder sounds, which would disrupt the tuning of these neurons. How could spike timing be independent of input level? Here I derive theoretical conditions for a spiking model to be insensitive to input level. The key property is a dynamic change in spike threshold. I then show how level invariance can be physiologically implemented, with specific ionic channel properties. It appears that these ingredients are indeed present in monaural neurons of the sound localization pathway of birds and mammals

Neuronal behaviors: A control perspective

The purpose of this tutorial is to introduce and analyze models of neurons from a control perspective and to show how recently developed analytical tools help to address important biological questions. A first objective is to review the basic modeling principles of neurophysiology in which neurons are modeled as equivalent nonlinear electrical circuits that capture their excitable properties. The specific architecture of the models is key to the tractability of their analysis: in spite of their high-dimensional and nonlinear nature, the model properties can be understood in terms of few canonical positive and negative feedback motifs localized in distinct timescales. We use this insight to shed light on a key problem in experimental neurophysiology, the challenge of understanding the sensitivity of neuronal behaviors to underlying parameters in empirically-derived models. Finally, we show how sensitivity analysis of neuronal excitability relates to robustness and regulation of neuronal behaviors.This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. G.D. is a Marie-Curie COFUND postdoctoral fellow at the University of Liege. Co-funded by the European Union. J.D. is supported by the F.R.S.-FNRS (Belgian Fund for Scientific Research. The scientific responsibility rests with its authors.This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/CDC.2015.740249

Implications of Potassium Channel Heterogeneity for Model Vestibulo-Ocular Reflex Response Fidelity

The Vestibulo-Ocular Reflex (VOR) produces compensatory eye movements in response to head and body rotations movements, over a wide range of frequencies and in a variety of dimensions. The individual components of the VOR are separated into parallel pathways, each dealing with rotations or movements in individual planes or axes. The Horizontal VOR (hVOR) compensates for eye movements in the Horizontal plane, and comprises a linear and non-linear pathway. The linear pathway of the hVOR provides fast and accurate compensation for rotations, the response being produced through 3-neuron arc, producing a direct translation of detected head velocity to compensatory eye velocity. However, single neurons involved in the middle stage of this 3-neuron arc cannot account for the wide frequency over which the reflex compensates, and the response is produced through the population response of the Medial Vestibular Nucleus (MVN) neurons involved. Population Heterogeneity likely plays a role in the production of high fidelity population response, especially for high frequency rotations. Here we present evidence that, in populations of bio-physical compartmental models of the MVN neurons involved, Heterogeneity across the population, in the form of diverse spontaneous firing rates, improves the response fidelity of the population over Homogeneous populations. Further, we show that the specific intrinsic membrane properties that give rise to this Heterogeneity may be the diversity of certain slow voltage activated Potassium conductances of the neurons. We show that Heterogeneous populations perform significantly better than Homogeneous populations, for a wide range of input amplitudes and frequencies, producing a much higher fidelity response. We propose that variance of Potassium conductances provides a plausible biological means by which Heterogeneity arises, and that the Heterogeneity plays an important functional role in MVN neuron population responses. We discuss our findings in relation to the specific mechanism of Desynchronisation through which the benfits of Heterogeneity may arise, and place those findings in the context of previous work on Heterogeneity both in general neural processing, and the VOR in particular. Interesting findings regarding the emergence of phase leads are also discussed, as well as suggestions for future work, looking further at Heterogeneity of MVN neuron populations

Control by neuromodulation: A tutorial

This tutorial provides an introduction to the topic of neuromodulation as an important control paradigm for natural and artificial neuronal networks. We review how neuromodulation modulates excitability, and how neuromodulation interacts with homeostasis. We stress how modulating nodal excitability provides a robust and versatile control principle to dynamically reconfigure the connectivity of rhythmic circuits and to shape the spatio-temporal synchrony of large populations.ER