A biophysical model explains the spontaneous bursting behavior in the developing retina

During early development, waves of activity propagate across the retina and play a key role in the proper wiring of the early visual system. During the stage II these waves are triggered by a transient network of neurons, called Starburst Amacrine Cells (SACs), showing a bursting activity which disappears upon further maturation. While several models have attempted to reproduce retinal waves, none of them is able to mimic the rhythmic autonomous bursting of individual SACs and reveal how these cells change their intrinsic properties during development. Here, we introduce a mathematical model, grounded on biophysics, which enables us to reproduce the bursting activity of SACs and to propose a plausible, generic and robust, mechanism that generates it. The core parameters controlling repetitive firing are fast depolarizing $V$-gated calcium channels and hyperpolarizing $V$-gated potassium channels. The quiescent phase of bursting is controlled by a slow after hyperpolarization (sAHP), mediated by calcium-dependent potassium channels. Based on a bifurcation analysis we show how biophysical parameters, regulating calcium and potassium activity, control the spontaneously occurring fast oscillatory activity followed by long refractory periods in individual SACs. We make a testable experimental prediction on the role of voltage-dependent potassium channels on the excitability properties of SACs and on the evolution of this excitability along development. We also propose an explanation on how SACs can exhibit a large variability in their bursting periods, as observed experimentally within a SACs network as well as across different species, yet based on a simple, unique, mechanism. As we discuss, these observations at the cellular level have a deep impact on the retinal waves description.Comment: 25 pages, 13 figures, submitte

Biophysical mechanisms of frequency-dependence and its neuromodulation in neurons in oscillatory networks

In response to oscillatory input, many isolated neurons exhibit a preferred frequency response in their voltage amplitude and phase shift. Membrane potential resonance (MPR), a maximum amplitude in a neuron’s input impedance at a non-zero frequency, captures the essential subthreshold properties of a neuron, which may provide a coordinating mechanism for organizing the activity of oscillatory neuronal networks around a given frequency. In the pyloric central pattern generator network of the crab Cancer borealis, for example, the pacemaker group pyloric dilator neurons show MPR at a frequency that is correlated with the network frequency. This dissertation uses the crab pyloric CPG to examine how, in one neuron type, interactions of ionic currents, even when expressed at different levels, can produce consistent MPR properties, how MPR properties are modified by neuromodulators and how such modifications may lead to distinct functional effects at different network frequencies. In the first part of this dissertation it is demonstrated that, despite the extensive variability of individual ionic currents in a neuron type such as PD, these currents can generate a consistent impedance profile as a function of input frequency and therefore result in stable MPR properties. Correlated changes in ionic current parameters are associated with the dependence of MPR on the membrane potential range. Synaptic inputs or neuromodulators that shift the membrane potential range can modify the interaction of multiple resonant currents and therefore shift the MPR frequency. Neuromodulators change the properties of voltage-dependent ionic currents. Since ionic current interactions are nonlinear, the modulation of excitability and the impedance profile may depend on all ionic current types expressed by the neuron. MPR is generated by the interaction of positive and negative feedback effects due to fast amplifying and slower resonant currents. Neuromodulators can modify existing MPR properties to generate antiresonance (a minimum amplitude response). In the second part of this dissertation, it is shown that the neuropeptide proctolin produces antiresonance in the follower lateral pyloric neuron, but not in the PD neuron. This finding is inconsistent with the known influences of proctolin. However, a novel proctolin-activated ionic current is shown to produce the antiresonance. Using linear models, antiresonance is then demonstrated to amplify MPR in synaptic partner neurons, indicating a potential function in the pyloric network. Neuromodulators are state dependent, so that their action may depend on the prior activity history of the network. It is shown that state-dependence may arise in part from the time-dependence of an inactivating inward current targeted by the neuromodulator proctolin. Due to the kinetics of inactivation, this current advances the burst phase and increases the duty cycle of the neuron, but mainly at higher network frequencies. These results demonstrate that the effect of neuromodulators on MPR in individual neuron types depends on the nonlinear interaction of modulator-activated and other ionic currents as well as the activation of currents with frequency-dependent properties. Consequently, the action of neuromodulators on the output of oscillatory networks may depend on the frequency of oscillations and be predictable from the MPR properties of the network neurons

Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity

It has become widely accepted that the most dangerous cardiac arrhythmias are due to re- entrant waves, i.e., electrical wave(s) that re-circulate repeatedly throughout the tissue at a higher frequency than the waves produced by the heart's natural pacemaker (sinoatrial node). However, the complicated structure of cardiac tissue, as well as the complex ionic currents in the cell, has made it extremely difficult to pinpoint the detailed mechanisms of these life-threatening reentrant arrhythmias. A simplified ionic model of the cardiac action potential (AP), which can be fitted to a wide variety of experimentally and numerically obtained mesoscopic characteristics of cardiac tissue such as AP shape and restitution of AP duration and conduction velocity, is used to explain many different mechanisms of spiral wave breakup which in principle can occur in cardiac tissue. Some, but not all, of these mechanisms have been observed before using other models; therefore, the purpose of this paper is to demonstrate them using just one framework model and to explain the different parameter regimes or physiological properties necessary for each mechanism (such as high or low excitability, corresponding to normal or ischemic tissue, spiral tip trajectory types, and tissue structures such as rotational anisotropy and periodic boundary conditions). Each mechanism is compared with data from other ionic models or experiments to illustrate that they are not model-specific phenomena. The fact that many different breakup mechanisms exist has important implications for antiarrhythmic drug design and for comparisons of fibrillation experiments using different species, electromechanical uncoupling drugs, and initiation protocols.Comment: 128 pages, 42 figures (29 color, 13 b&w

Pacemaker Neuron and Network Oscillations Depend on a Neuromodulator-Regulated Linear Current

Linear leak currents have been implicated in the regulation of neuronal excitability, generation of neuronal and network oscillations, and network state transitions. Yet, few studies have directly tested the dependence of network oscillations on leak currents or explored the role of leak currents on network activity. In the oscillatory pyloric network of decapod crustaceans neuromodulatory inputs are necessary for pacemaker activity. A large subset of neuromodulators is known to activate a single voltage-gated inward current IMI, which has been shown to regulate the rhythmic activity of the network and its pacemaker neurons. Using the dynamic clamp technique, we show that the crucial component of IMI for the generation of oscillatory activity is only a close-to-linear portion of the current-voltage relationship. The nature of this conductance is such that the presence or the absence of neuromodulators effectively regulates the amount of leak current and the input resistance in the pacemaker neurons. When deprived of neuromodulatory inputs, pyloric oscillations are disrupted; yet, a linear reduction of the total conductance in a single neuron within the pacemaker group recovers not only the pacemaker activity in that neuron, but also leads to a recovery of oscillations in the entire pyloric network. The recovered activity produces proper frequency and phasing that is similar to that induced by neuromodulators. These results show that the passive properties of pacemaker neurons can significantly affect their capacity to generate and regulate the oscillatory activity of an entire network, and that this feature is exploited by neuromodulatory inputs

Making Waves in the Brain: What Are Oscillations, and Why Modulating Them Makes Sense for Brain Injury.

Traumatic brain injury (TBI) can result in persistent cognitive, behavioral and emotional deficits. However, the vast majority of patients are not chronically hospitalized; rather they have to manage their disabilities once they are discharged to home. Promoting recovery to pre-injury level is important from a patient care as well as a societal perspective. Electrical neuromodulation is one approach that has shown promise in alleviating symptoms associated with neurological disorders such as in Parkinson's disease (PD) and epilepsy. Consistent with this perspective, both animal and clinical studies have revealed that TBI alters physiological oscillatory rhythms. More recently several studies demonstrated that low frequency stimulation improves cognitive outcome in models of TBI. Specifically, stimulation of the septohippocampal circuit in the theta frequency entrained oscillations and improved spatial learning following TBI. In order to evaluate the potential of electrical deep brain stimulation for clinical translation we review the basic neurophysiology of oscillations, their role in cognition and how they are changed post-TBI. Furthermore, we highlight several factors for future pre-clinical and clinical studies to consider, with the hope that it will promote a hypothesis driven approach to subsequent experimental designs and ultimately successful translation to improve outcome in patients with TBI

Bistable dynamics underlying excitability of ion homeostasis in neuron models

When neurons fire action potentials, dissipation of free energy is usually not directly considered, because the change in free energy is often negligible compared to the immense reservoir stored in neural transmembrane ion gradients and the long-term energy requirements are met through chemical energy, i.e., metabolism. However, these gradients can temporarily nearly vanish in neurological diseases, such as migraine and stroke, and in traumatic brain injury from concussions to severe injuries. We study biophysical neuron models based on the Hodgkin-Huxley (HH) formalism extended to include time-dependent ion concentrations inside and outside the cell and metabolic energy-driven pumps. We reveal the basic mechanism of a state of free energy-starvation (FES) with bifurcation analyses showing that ion dynamics is for a large range of pump rates bistable without contact to an ion bath. This is interpreted as a threshold reduction of a new fundamental mechanism of 'ionic excitability' that causes a long-lasting but transient FES as observed in pathological states. We can in particular conclude that a coupling of extracellular ion concentrations to a large glial-vascular bath can take a role as an inhibitory mechanism crucial in ion homeostasis, while the Na$^+$/K$^+$ pumps alone are insufficient to recover from FES. Our results provide the missing link between the HH formalism and activator-inhibitor models that have been successfully used for modeling migraine phenotypes, and therefore will allow us to validate the hypothesis that migraine symptoms are explained by disturbed function in ion channel subunits, Na$^+$/K$^+$ pumps, and other proteins that regulate ion homeostasis.Comment: 14 pages, 8 figures, 4 table

Intrinsic and synaptic membrane properties of neurons in the thalamic reticular nucleus

Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2004-2005Le noyau réticulaire thalamique (RE) est une structure qui engendre des fuseaux, une oscillation bioélectrique de marque pendant les stades précoces du sommeil. De multiples propriétés neuronales, intrinsèques et synaptiques, sont impliquées dans la génération, la propagation, le maintien et la terminaison des ondes en fuseaux. D’un autre côté, ce rythme constitue un état spécial de l’activité du réseau qui est généré par le réseau lui-même et affecte les propriétés cellulaires du noyau RE. Cette étude se concentre sur ces sujets: comment les propriétés cellulaires et les propriétés du réseau sont inter-reliées et interagissent pour engendrer les ondes fuseaux dans les neurones du RE et leurs cibles, les neurones thalamocorticaux. La présente thèse fournit de nouvelles évidences montrant le rôle fondamental joué par les neurones du noyau RE dans la genèse des ondes en fuseaux, dû aux synapses chimiques établies par ces neurones. La propagation et la synchronisation de l’activité sont modulées par les synapses électriques entre les neurones réticulaires thalamiques, mais aussi par les composantes dépolarisantes secondaires des réponses synaptiques évoquées par le cortex. De plus, la forme générale et la terminaison des oscillations thalamiques sont probablement contrôlées en grande partie par les neurones du RE, lesquels expriment une conductance intrinsèque leurs procurant une membrane avec un comportement bistable. Finalement, les oscillations thalamiques en fuseaux sont aussi capables de moduler les propriétés membranaires et l’activité des neurones individuels du RE.The thalamic reticular nucleus (RE) is a key structure related to spindles, a hallmark bioelectrical oscillation during early stages of sleep. Multiple neuronal properties, both intrinsic and synaptic, are implicated in the generation, propagation, maintenance and termination of spindle waves. On the other hand, this rhythm constitutes a special state of network activity, which is generated within, and affects single-cell properties of the RE nucleus. This study is focused on these topics: how cellular and network properties are interrelated and interact to generate spindle waves in the pacemaking RE neurons and their targets, thalamocortical neurons. The present thesis provides new evidence showing the fundamental role played by the RE nucleus in the generation of spindle waves, due to chemical synapses established by its neurons. The propagation and synchronization of activity is modulated by electrical synapses between thalamic reticular neurons, but also by the secondary depolarizing component of cortically-evoked synaptic responses. Additionally, the general shaping and probably the termination of thalamic oscillations could be controlled to a great extent by RE neurons, which express an intrinsic conductance endowing them with membrane bistable behaviour. Finally, thalamic spindle oscillations are also able to modulate the membrane properties and activities of individual RE neurons

The role of inhibitory feedback for information processing in thalamocortical circuits

The information transfer in the thalamus is blocked dynamically during sleep, in conjunction with the occurence of spindle waves. As the theoretical understanding of the mechanism remains incomplete, we analyze two modeling approaches for a recent experiment by Le Masson {\sl et al}. on the thalamocortical loop. In a first step, we use a conductance-based neuron model to reproduce the experiment computationally. In a second step, we model the same system by using an extended Hindmarsh-Rose model, and compare the results with the conductance-based model. In the framework of both models, we investigate the influence of inhibitory feedback on the information transfer in a typical thalamocortical oscillator. We find that our extended Hindmarsh-Rose neuron model, which is computationally less costly and thus siutable for large-scale simulations, reproduces the experiment better than the conductance-based model. Further, in agreement with the experiment of Le Masson {\sl et al}., inhibitory feedback leads to stable self-sustained oscillations which mask the incoming input, and thereby reduce the information transfer significantly.Comment: 16 pages, 15eps figures included. To appear in Physical Review