Dendritic synchrony and transient dynamics in a coupled oscillator model of the dopaminergic neuron

The physiology of coordination: self-resolving diverse affinities via the sparse order in relevant noise

Living systems at any given moment enact a very constrained set of end-directed and contextually appropriate actions that are self-initiated from among innumerable possible alternatives. However, these constrained actions are not necessarily because the system has reduced its sensitivities to themselves and their surroundings. Quite the contrary, living systems are continually open to novel and unanticipated stimulations that require a physiology of coordination. To address these competing demands, this paper offers a novel heuristic model informed by neuroscience, systems theory, biology and sign study to explain how organisms situated in diverse, complex and ever-changing environments might draw upon the sparse order made available by 'relevant noise'. This emergent order facilitates coordination, habituation and, ultimately, understanding of the world and its relevant affordances. Inspired by the burgeoning field of coordination dynamics and physiologist Denis Noble's concept of 'biological relativity', this model proposes a view of coordination on the neuronal level that is neither sequential nor stochastic, but instead implements a causal logic of phasic alignment, such that an organism's learned and inherited sets of diverse biological affinities and sympathies can be resolved into a continuous and complex range of patterns that will implement the kind of novel orientations and radical generativity required of such organisms to adaptively explore their environments and to learn from their experiences.

Resonance in the Mouse Ventral Tegmental Area Dopaminergic Network Induced by Regular and Poisson Distributed Optogenetic Stimulation in-vitro

Neurons in many brain regions exhibit spontaneous, intrinsic rhythmic firing activity. This rhythmic firing activity may determine the way in which these neurons respond to extrinsic synaptic inputs. We hypothesized that neurons should be most responsive to inputs at the frequency of the intrinsic oscillation frequency. We addressed this question in the ventral tegmental area (VTA), a dopaminergic nucleus in the midbrain. VTA neurons have a unique propensity to exhibit spontaneous intrinsic rhythmic activity in the 1-5 Hz frequency range, which persists in the in-vitro brain slice, and form a network of weakly coupled oscillators. Here, we combine in-vitro simultaneous recording of action potentials from a 60 channel multi-electrode-array with cell-type-specific optogenetic stimulation of the VTA dopamine neurons. We investigated how VTA neurons respond to wide-band stochastic (Poisson input) as well as regular laser pulses. Strong synchrony was induced between the laser input and the spike timing of the neurons, both for regular pulse trains and Poisson pulse trains. For rhythmically pulsed input, the neurons demonstrated resonant behavior with the strongest phase locking at their intrinsic oscillation frequency, but also at half and double the intrinsic oscillation frequency. Stochastic Poisson pulse stimulation provided a more effective stimulation of the entire population, yet we observed resonance at lower frequencies (approximately half the oscillation frequency) than the neurons' intrinsic oscillation frequency. The non-linear filter characteristics of dopamine neurons could allow the VTA to predict precisely timed future rewards based on past sensory inputs, a crucial component of reward prediction error signaling. In addition, these filter characteristics could contribute to a pacemaker role for the VTA in synchronizing activity with other regions like the prefrontal cortex and the hippocampus.

Mixed-mode oscillations and population bursting in the pre-Bötzinger complex

This study focuses on computational and theoretical investigations of neuronal activity arising in the pre-Bötzinger complex (pre-BötC), a medullary region generating the inspiratory phase of breathing in mammals. A progressive increase of neuronal excitability in medullary slices containing the pre-BötC produces mixed-mode oscillations (MMOs) characterized by large amplitude population bursts alternating with a series of small amplitude bursts. Using two different computational models, we demonstrate that MMOs emerge within a heterogeneous excitatory neural network because of progressive neuronal recruitment and synchronization. The MMO pattern depends on the distributed neuronal excitability, the density and weights of network interconnections, and the cellular properties underlying endogenous bursting. Critically, the latter should provide a reduction of spiking frequency within neuronal bursts with increasing burst frequency and a dependence of the after-burst recovery period on burst amplitude. Our study highlights a novel mechanism by which heterogeneity naturally leads to complex dynamics in rhythmic neuronal populations.

DOI:http://dx.doi.org/10.7554/eLife.13403.001

Each breath we take removes carbon dioxide from the body and exchanges it for oxygen. A structure called the brainstem, which connects the brain with the spinal cord, generates the breathing rhythm and controls its rate. While this process normally occurs automatically, we can also control our breathing voluntarily, such as when singing or speaking.

Within the brainstem, a group of neurons in the area known as the pre-Bötzinger complex is responsible for ensuring that an animal breathes in at regular intervals. Recordings of the electrical activity from slices of brainstem show that pre-Bötzinger neurons display rhythmic activity with characteristic patterns called “mixed-mode oscillations”. These rhythms consist of bursts of strong activity (“large amplitude bursts”), essential for triggering regular breathing, separated by a series of bursts of weak activity (“small amplitude bursts”). However, it is not clear how mixed-mode oscillations arise.

Bacak, Kim et al. now provide insights into this process by developing two computational models of the pre-Bötzinger complex. The first model consists of a diverse population of 100 neurons joined by a relatively small number of weak connections to form a network. The second model is a simplified version of the first, consisting of just three neurons. By manipulating the properties of the simulated networks, and analysing the data mathematically, Bacak, Kim et al. identify the properties of the neurons that allow them to generate mixed-mode oscillations and thus rhythmic breathing.

The models suggest that mixed-mode oscillations result from the synchronization of many neurons with different levels of activity (excitability). Neurons with low excitability have low bursting frequencies, but generate strong activity and recruit other neurons, ultimately producing large amplitude bursts that cause breathing.

Many parts of the nervous system are also made up of networks of neurons with diverse excitability. A challenge for future studies is thus to investigate whether other networks of neurons similar to the pre-Bötzinger complex generate rhythms that control other repetitive actions, such as walking and chewing.

DOI:http://dx.doi.org/10.7554/eLife.13403.002

Balance between the proximal dendritic compartment and the soma determines spontaneous firing rate in midbrain dopamine neurons

Midbrain dopamine (DA) neurons are slow intrinsic pacemakers that require the elaborate composition of many ion channels in the somatodendritic compartments. Understanding the major determinants of the spontaneous firing rate (SFR) of midbrain DA neurons is important because they determine the basal DA levels in target areas, including the striatum. As spontaneous firing occurs synchronously at the soma and dendrites, the electrical coupling between the soma and dendritic compartments has been regarded as a key determinant for the SFR. However, it is not known whether this somatodendritic coupling is served by the whole dendritic compartments or only parts of them. In the rat substantia nigra pars compacta (SNc) DA neurons, we demonstrate that the balance between the proximal dendritic compartment and the soma determines the SFR. Isolated SNc DA neurons showed a wide range of soma size and a variable number of primary dendrites but preserved a quite consistent SFR. The SFR was not correlated with soma size or with the number of primary dendrites, but it was strongly correlated with the area ratios of the proximal dendritic compartments to the somatic compartment. Tetrodotoxin puff and local Ca(2+) perturbation experiments, computer simulation, and local glutamate uncaging experiments suggest the importance of the proximal dendritic compartments in pacemaker activity. These data indicate that the proximal dendritic compartments, not the whole dendritic compartments, play a key role in the somatodendritic balance that determines the SFR in DA neurons.

Physiological phenotype and vulnerability in Parkinson's disease

This review will focus on the principles underlying the hypothesis that neuronal physiological phenotype-how a neuron generates and regulates action potentials-makes a significant contribution to its vulnerability in Parkinson's disease (PD) and aging. A cornerstone of this hypothesis is that the maintenance of ionic gradients underlying excitability can pose a significant energetic burden for neurons, particularly those that have sustained residence times at depolarized membrane potentials, broad action potentials, prominent Ca(2+) entry, and modest intrinsic Ca(2+) buffering capacity. This energetic burden is shouldered in neurons primarily by mitochondria, the sites of cellular respiration. Mitochondrial respiration increases the production of damaging superoxide and other reactive oxygen species (ROS) that have widely been postulated to contribute to cellular aging and PD. Many of the genetic mutations and toxins associated with PD compromise mitochondrial function, providing a mechanistic linkage between known risk factors and cellular physiology that could explain the pattern of pathology in PD. Because much of the mitochondrial burden created by this at-risk phenotype is created by Ca(2+) entry through L-type voltage-dependent channels for which there are antagonists approved for human use, a neuroprotective strategy to reduce this burden is feasible.

Regulation of firing frequency in a computational model of a midbrain dopaminergic neuron

Dopaminergic (DA) neurons of the mammalian midbrain exhibit unusually low firing frequencies in vitro. Furthermore, injection of depolarizing current induces depolarization block before high frequencies are achieved. The maximum steady and transient rates are about 10 and 20 Hz, respectively, despite the ability of these neurons to generate bursts at higher frequencies in vivo. We use a three-compartment model calibrated to reproduce DA neuron responses to several pharmacological manipulations to uncover mechanisms of frequency limitation. The model exhibits a slow oscillatory potential (SOP) dependent on the interplay between the L-type Ca(2+) current and the small conductance K(+) (SK) current that is unmasked by fast Na(+) current block. Contrary to previous theoretical work, the SOP does not pace the steady spiking frequency in our model. The main currents that determine the spontaneous firing frequency are the subthreshold L-type Ca(2+) and the A-type K(+) currents. The model identifies the channel densities for the fast Na(+) and the delayed rectifier K(+) currents as critical parameters limiting the maximal steady frequency evoked by a depolarizing pulse. We hypothesize that the low maximal steady frequencies result from a low safety factor for action potential generation. In the model, the rate of Ca(2+) accumulation in the distal dendrites controls the transient initial frequency in response to a depolarizing pulse. Similar results are obtained when the same model parameters are used in a multi-compartmental model with a realistic reconstructed morphology, indicating that the salient contributions of the dendritic architecture have been captured by the simpler model.

Electrical coupling promotes fidelity of responses in the networks of model neurons

We consider an integrate-and-fire element subject to randomly perturbed synaptic input and an electrically coupled ensemble of such elements. The latter is interpreted as either a model of electrically coupled population of neurons or a multicompartment model of a dendrite. Random fluctuations blur the input signal and cause false responses in the system dynamics. For instance, under the influence of noise, the system may respond with an action potential to a subthreshold stimulus. We show that the responses of the elements within the network are more reliable than the responses of the same elements in isolation. Specifically, we show that the variances of the stochastic processes generated by the coupled model can be made arbitrarily small (i.e., the network responses can be made arbitrarily accurate) by increasing the number of elements in the network and the strength of electrical coupling. Our results suggest that the organization of cells in electrically coupled groups on the network level, or the dendritic morphology on the cellular level, may be involved in the filtering noise and therefore may play an important role in the information processing mechanisms operating on the network or cellular level respectively.

The role of ongoing dendritic oscillations in single-neuron dynamics

The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as both temporally and spatially localized. Under this localist account, neurons compute near-instantaneous mappings from their current input to their current output, brought about by somatic summation of dendritic contributions that are generated in functionally segregated compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought; notably that local dendritic activity may be a mechanism for generating on-going whole-cell voltage oscillations.

A central issue in biology is how local processes yield global consequences. This is especially relevant for neurons since these spatially extended cells process local synaptic inputs to generate global action potential output. The dendritic tree of a neuron, which receives most of the inputs, expresses ion channels that can generate nonlinear dynamics. A prominent phenomenon resulting from such ion channels are voltage oscillations. The distribution of the active membrane channels throughout the cell is often highly non-uniform. This can turn the dendritic tree into a network of sparsely spaced local oscillators. Here we analyze whether local dendritic oscillators can produce cell-wide voltage oscillations. Our mathematical theory shows that indeed even when the dendritic oscillators are weakly coupled, they lock their phases and give global oscillations. We show how the biophysical properties of the dendrites determine the global locking and how it can be controlled by synaptic inputs. As a consequence of global locking, even individual synaptic inputs can affect the timing of action potentials. In fact, dendrites locking in synchrony can lead to sustained firing of the cell. We show that dendritic trees can be bistable, with dendrites locking in either synchrony or asynchrony, which may provide a novel mechanism for single cell-based memory.

Endogenous calcium buffering capacity of substantia nigral dopamine neurons

Dopamine (DA)-containing cells from the substantia nigra pars compacta (SNc) play a major role in the initiation of movement. Loss of these cells results in Parkinson's disease (PD). Changes in intracellular calcium ion concentration ([Ca(2+)](i)) elicit several events in DA cells, including spike afterhyperpolarizations (AHPs) and subthreshold oscillations underlying autonomous firing. Continuous Ca(2+) load due to Ca(2+)-dependent rhythmicity has been proposed to cause the death of DA cells in PD and normal aging. Because of the physiological and pathophysiological importance of [Ca(2+)](i) in DA cells, we characterized their intrinsic Ca(2+)-buffering capacity (K(S)) in brain slices. We introduced a fluorescent Ca(2+)-sensitive exogenous buffer (200 microM fura-2) and cells were tracked from break-in until steady state by stimulating with a single action potential (AP) every 30 s and measuring the Ca(2+) transient from the proximal dendrite. DA neurons filled exponentially with a tau of about 5-6 min. [Ca(2+)](i) was assumed to equilibrate between the endogenous Ca(2+) buffer and the exogenous Ca(2+) indicator buffer. Intrinsic buffering was estimated by extrapolating from the linear relationships between the amplitude or time constant of the Ca(2+) transients versus [fura-2]. Extrapolated Ca(2+)-transients in the absence of fura-2 had mean peak amplitudes of 293.7 +/- 65.3 nM and tau = 124 +/- 13 ms (postnatal day 13 [P13] to P17 animals). Intrinsic buffering increased with age in DA neurons. For cells from animals P13-P17, K(S) was estimated to be about 110 (n = 20). In older animals (P25-P32), the estimate was about 179 (n = 10). These relatively low values may reflect the need for rapid Ca(2+) signaling, e.g., to allow activation of sK channels, which shape autonomous oscillations and burst firing. Low intrinsic buffering may also make DA cells vulnerable to Ca(2+)-dependent pathology.

Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron

Mixed-mode dynamics is a complex type of dynamical behavior that has been observed both numerically and experimentally in numerous prototypical systems in the natural sciences. The compartmental Wilson-Callaway model for the dopaminergic neuron is an example of a system that exhibits a wide variety of mixed-mode patterns upon variation of a control parameter. One characteristic feature of this system is the presence of multiple time scales. In this article, we study the Wilson-Callaway model from a geometric point of view. We show that the observed mixed-mode dynamics is caused by a slowly varying canard structure. By appropriately transforming the model equations, we reduce them to an underlying three-dimensional canonical form that can be analyzed via a slight adaptation of the approach developed by M. Krupa, N. Popovic, and N. Kopell (unpublished).

Roles of subthreshold calcium current and sodium current in spontaneous firing of mouse midbrain dopamine neurons

We used a preparation of acutely dissociated neurons to quantify the ionic currents driving the spontaneous firing of substantia nigra pars compacta neurons, isolated from transgenic mice in which the tyrosine hydroxylase promoter drives expression of human placental alkaline phosphatase (PLAP) on the outer surface of the cell membrane. Dissociated neurons identified by fluorescent antibodies to PLAP showed firing properties similar to those of dopaminergic neurons in brain slice, including rhythmic spontaneous firing of broad action potentials and, in some cells, rhythmic oscillatory activity in the presence of tetrodotoxin (TTX). Spontaneous activity in TTX had broader, smaller spikes than normal pacemaking and was stopped by removal of external calcium. Normal pacemaking was also consistently silenced by replacement of external calcium by cobalt and was slowed by more specific calcium channel blockers. Nimodipine produced a slowing of pacemaking frequency. Pacemaking was also slowed by the P/Q-channel blocker omega-Aga-IVA, but the N-type channel blocker omega-conotoxin GVIA had no effect. In voltage-clamp experiments, using records of pacemaking as command voltage, cobalt-sensitive current and TTX-sensitive current were both sizeable at subthreshold voltages between spikes. Cobalt-sensitive current was consistently larger than TTX-sensitive current at interspike voltages from -70 to -50 mV, with TTX-sensitive current larger at voltages positive to -45 mV. These results support previous evidence for a major role of voltage-dependent calcium channels in driving pacemaking of midbrain dopamine neurons and suggest that multiple calcium channel types contribute to this function. The results also show a significant contribution of subthreshold TTX-sensitive sodium current.

GABAergic control of substantia nigra dopaminergic neurons

At least 70% of the afferents to substantia nigra dopaminergic neurons are GABAergic. The vast majority of these arise from the neostriatum, the external globus pallidus and the substantia nigra pars reticulata. Nigral dopaminergic neurons express both GABA(A) and GABA(B) receptors, and are inhibited by local application of GABA(A) or GABA(B) agonists in vivo and in vitro. However, in vivo, synaptic responses elicited by stimulation of neostriatal or pallidal afferents, or antidromic activation of nigral pars reticulata GABAergic projection neurons are mediated predominantly or exclusively by GABA(A) receptors. The clearest and most consistent role for the nigral GABA(B) receptor in vivo is as an inhibitory autoreceptor that presynaptically modulates GABA(A) synaptic responses that originate from all three principal GABAergic inputs. The firing pattern of dopaminergic neurons is also effectively modulated by GABAergic inputs in vivo. Local blockade of nigral GABA(A) receptors causes dopaminergic neurons to shift to a burst firing pattern regardless of the original firing pattern. This is accompanied by a modest increase in spontaneous firing rate. The GABAergic inputs from the axon collaterals of the pars reticulata projection neurons seem to be a particularly important source of a GABA(A) tone to the dopaminergic neurons, inhibition of which leads to burst firing. The globus pallidus exerts powerful control over the pars reticulata input, and through the latter, disynaptically over the dopaminergic neurons. Inhibition of pallidal output leads to a slight decrease in firing of the dopaminergic neurons due to disinhibition of the pars reticulata neurons whereas increased firing of pallidal neurons leads to burst firing in dopaminergic neurons that is associated with a modest increase in spontaneous firing rate and a significant increase in extracellular levels of dopamine in the neostriatum. The pallidal disynaptic disinhibitory control of the dopaminergic neurons dominates the monosynaptic inhibitory influence because of a differential sensitivity to GABA of the two nigral neuron types. Nigral GABAergic neurons are more sensitive to GABA(A)-mediated inhibition than dopaminergic neurons, in part due to a more hyperpolarized GABA(A) reversal potential. The more depolarized GABA(A) reversal potential in the dopaminergic neurons is due to the absence of KCC2, the chloride transporter responsible for setting up a hyperpolarizing Cl(-) gradient in most mature CNS neurons. The data reviewed in this chapter have made it increasingly clear that in addition to the effects that nigral GABAergic output neurons have on their target nuclei outside of the basal ganglia, local interactions between GABAergic projection neurons and dopaminergic neurons are crucially important to the functioning of the nigral dopaminergic neurons.

Transient high-frequency firing in a coupled-oscillator model of the mesencephalic dopaminergic neuron

Dopaminergic neurons of the midbrain fire spontaneously at rates <10/s and ordinarily will not exceed this range even when driven with somatic current injection. When driven at higher rates, these cells undergo spike failure through depolarization block. During spontaneous bursting of dopaminergic neurons in vivo, bursts related to reward expectation in behaving animals, and bursts generated by dendritic application of N-methyl-d-aspartate (NMDA) agonists, transient firing attains rates well above this range. We suggest a way such high-frequency firing may occur in response to dendritic NMDA receptor activation. We have extended the coupled oscillator model of the dopaminergic neuron, which represents the soma and dendrites as electrically coupled compartments with different natural spiking frequencies, by addition of dendritic AMPA (voltage-independent) or NMDA (voltage-dependent) synaptic conductance. Both soma and dendrites contain a simplified version of the calcium-potassium mechanism known to be the mechanism for slow spontaneous oscillation and background firing in dopaminergic cells. The compartments differ only in diameter, and this difference is responsible for the difference in natural frequencies. We show that because of its voltage dependence, NMDA receptor activation acts to amplify the effect on the soma of the high-frequency oscillation of the dendrites, which is normally too weak to exert a large influence on the overall oscillation frequency of the neuron. During the high-frequency oscillations that result, sodium inactivation in the soma is removed rapidly after each action potential by the hyperpolarizing influence of the dendritic calcium-dependent potassium current, preventing depolarization block of the spike mechanism, and allowing high-frequency spiking.

Computational model of electrically coupled, intrinsically distinct pacemaker neurons

Electrical coupling between neurons with similar properties is often studied. Nonetheless, the role of electrical coupling between neurons with widely different intrinsic properties also occurs, but is less well understood. Inspired by the pacemaker group of the crustacean pyloric network, we developed a multicompartment, conductance-based model of a small network of intrinsically distinct, electrically coupled neurons. In the pyloric network, a small intrinsically bursting neuron, through gap junctions, drives 2 larger, tonically spiking neurons to reliably burst in-phase with it. Each model neuron has 2 compartments, one responsible for spike generation and the other for producing a slow, large-amplitude oscillation. We illustrate how these compartments interact and determine the dynamics of the model neurons. Our model captures the dynamic oscillation range measured from the isolated and coupled biological neurons. At the network level, we explore the range of coupling strengths for which synchronous bursting oscillations are possible. The spatial segregation of ionic currents significantly enhances the ability of the 2 neurons to burst synchronously, and the oscillation range of the model pacemaker network depends not only on the strength of the electrical synapse but also on the identity of the neuron receiving inputs. We also compare the activity of the electrically coupled, distinct neurons with that of a network of coupled identical bursting neurons. For small to moderate coupling strengths, the network of identical elements, when receiving asymmetrical inputs, can have a smaller dynamic range of oscillation than that of its constituent neurons in isolation.

Stochastic multiresonance in the coupled relaxation oscillators

We study the noise-dependent dynamics in a chain of four very stiff excitable oscillators of the FitzHugh-Nagumo type locally coupled by inhibitor diffusion. We could demonstrate frequency- and noise-selective signal acceptance which is based on several noise-supported stochastic attractors that arise owing to slow variable diffusion between identical excitable elements. The attractors have different average periods distinct from that of an isolated oscillator and various phase relations between the elements. We explain the correspondence between the noise-supported stochastic attractors and the observed resonance peaks in the curves for the linear response versus signal frequency.