The role of gap junctions between midbrain dopamine (DA) neurons in mechanisms of firing pattern ... more The role of gap junctions between midbrain dopamine (DA) neurons in mechanisms of firing pattern generation and synchronization has not been well characterized experimentally. We modified a multi-compartment model of DA neuron by adding a spike-generating mechanism and electrically coupling the dendrites of two such neurons through gap junctions. The burst-generating mechanism in the model neuron results from the interaction of a N-methyl-D-aspartate (NMDA)-induced current and the sodium pump. The firing patterns exhibited by the two model neurons included low frequency (2-7 Hz) spiking, high-frequency (13-20 Hz) spiking, irregular spiking, regular bursting, irregular bursting, and leader/follower bursting, depending on the parameter values used for the permeability for NMDA-induced current and the conductance for electrical coupling. All of these firing patterns have been observed in physiological neurons, but a systematic dependence of the firing pattern on the covariation of these two parameters has not been established experimentally. Our simulations indicate that electrical coupling facilitates NMDA-induced burst firing via two mechanisms. The first can be observed in a pair of identical cells. At low frequencies (low NMDA), as coupling strength was increased, only a transition from asynchronous to synchronous single-spike firing was observed. At high frequencies (high NMDA), increasing the strength of the electrical coupling in an identical pair resulted in a transition from high-frequency single-spike firing to burst firing, and further increases led to synchronous high-frequency spiking. Weak electrical coupling destabilizes the synchronous solution of the fast spiking subsystems, and in the presence of a slowly varying sodium concentration, the desynchronized spiking solution leads to bursts that are approximately in phase with spikes that are not in phase. Thus this transitional mechanism depends critically on action potential dynamics. The second mechanism for the induction of burst firing requires a heterogeneous pair that is, respectively, too depolarized and too hyperpolarized to burst. The net effect of the coupling is to bias at least one cell into an endogenously burst firing regime. In this case, action potential dynamics are not critical to the transitional mechanism. If electrical coupling is indeed more prominent in vivo due to basal level of modulation of gap junctions in vivo, these results may indicate why NMDA-induced burst firing is easier to observe in vivo as compared in vitro.
Midbrain dopaminergic (DA) neurons in vivo exhibit two major firing patterns: single-spike firing... more Midbrain dopaminergic (DA) neurons in vivo exhibit two major firing patterns: single-spike firing and burst firing. The firing pattern expressed is dependent on both the intrinsic properties of the neurons and their excitatory and inhibitory synaptic inputs. Experimental data suggest that the activation of N-methyl-D-aspartate (NMDA) and GABAA receptors is a crucial contributor to the initiation and suppression of burst firing, respectively, and that blocking Ca(2+)-activated potassium SK channels can facilitate burst firing. A multi-compartmental model of a DA neuron with a branching structure was developed and calibrated based on in vitro experimental data to explore the effects of different levels of activation of NMDA and GABAA receptors as well as the modulation of the SK current on the firing activity. The simulated tonic activation of GABAA receptors was calibrated by taking into account the difference in the electrotonic properties in vivo versus in vitro. Although NMDA-evoked currents are required for burst generation in the model, currents evoked by GABAA-receptor activation can also regulate the firing pattern. For example, the model predicts that increasing the level of NMDA receptor activation can produce excessive depolarization that prevents burst firing, but a concurrent increase in the activation of GABAA receptors can restore burst firing. Another prediction of the model is that blocking the SK channel current in vivo will facilitate bursting, but not as robustly as blocking the GABAA receptors.
Serotonergic modulation of the sensory neurons that mediate the gill- and tail-withdrawal reflexe... more Serotonergic modulation of the sensory neurons that mediate the gill- and tail-withdrawal reflexes of Aplysia is a useful model system for studies of neuronal plasticity that contributes to learning and memory. The effects of serotonin (5-HT) are mediated, in part, via two protein kinases (protein kinase A, PKA, and protein kinase C, PKC), which in turn, modulate at least four membrane currents, including a S ("serotonin-sensitive") K(+) current (I(K, S)), a steeply voltage-dependent K(+) current (I(K-V)), a slow component of the Ca(2+)-activated K(+) current (I(K,Ca-S)), and a L-type Ca(2+) current (I(Ca-L)). The present study investigated how the modulation of these currents altered the spike duration and excitability of sensory neurons and examined the relative contributions of PKA- and PKC-mediated effects to the actions of 5-HT. A Hodgkin-Huxley type model was developed that described the ionic conductances in the somata of sensory neurons. The descriptions of these currents and their modulation were based largely on voltage-clamp data from sensory neurons. Simulations were preformed with the program SNNAP (Simulator for Neural Networks and Action Potentials). The model was sufficient to replicate empirical data that describes the membrane currents, action potential waveform and excitability as well as their modulation by application of 5-HT, increased levels of adenosine cyclic monophosphate or application of active phorbol esters. In the model, modulation of I(K-V) by PKC played a dominate role in 5-HT-induced spike broadening, whereas the concurrent modulation of I(K,S) and I(K,Ca-S) by PKA primarily accounted for 5-HT-induced increases in excitability. Finally, simulations indicated that a PKC-induced increase in excitability resulted from decreases of I(K,S) and I(K,Ca-S), which was likely the indirect result of cross-talk between the PKC and PKA systems. The results provide several predictions that warrant additional experimental investigation and illustrate the importance of considering indirect as well as direct effects of modulatory agents on the modulation of membrane currents.
Network Computation in Neural Systems, Feb 26, 2014
Cross-frequency coupling is hypothesized to play a functional role in neural computation. We appl... more Cross-frequency coupling is hypothesized to play a functional role in neural computation. We apply phase resetting theory to two types of cross-frequency coupling that can occur when a slower oscillator periodically forces one or more oscillators: phase-phase coupling, in which the two oscillations are phase-locked, and phase-amplitude coupling, in which the amplitude of the driven oscillation is modulated. Our first result is that the shape of the phase resetting curve predicts the tightness of locking to a pulsatile forcing periodic input at any ratio of forced to intrinsic period; the tightness of the locking decreases as the ratio increases. Theoretical expressions were obtained for the probability density of the phases for a population of heterogeneous oscillators or a noisy single oscillator. Results were confirmed using two types of simulated networks and experiments on hippocampal CA1 neurons. Theoretical expressions were also obtained and confirmed for the probability density of N spike times within a single cycle of low frequency forcing. The second result is a suggested mechanism for phase-amplitude coupling in which progressive desynchronization leads to decreasing amplitude during a low frequency forcing cycle. Network simulations confirmed the theoretical viability of this mechanism, and that it generalizes to more diffuse input.
Phase response curves (PRCs) for a single neuron are often used to predict the synchrony of mutua... more Phase response curves (PRCs) for a single neuron are often used to predict the synchrony of mutually coupled neurons. Previous theoretical work on pulse coupled oscillators used single pulse perturbations. We propose an alternate method in which functional PRCs (FPRCs) are generated using a train of pulses applied at a fixed delay after a spike. Experimental FPRCs in Aplysia pacemaker
We address how feedback to a bursting biological pacemaker with intrinsic variability in cycle le... more We address how feedback to a bursting biological pacemaker with intrinsic variability in cycle length can affect that variability. Specifically we examine a hybrid circuit constructed of an isolated crab AB/PD pyloric pacemaker receiving virtual feedback via Dynamic Clamp. This virtual feedback generates artificial synaptic input to PD with timing determined by adjustable phase response dynamics that mimic average burst intervals generated by LP in the intact pyloric network. Using this system we measure network period variability dependence on the feedback element's phase response dynamics, and find that a constant response interval confers minimum variability. We further find that these optimal dynamics are characteristic of the biological pyloric network. Building upon our previous theoretical work mapping the firing intervals in one cycle onto the firing intervals in the next cycle, we create a theoretical map of the distribution of all firing intervals in one cycle to the distribution of firing intervals in the next cycle. We then obtain an integral equation for a stationary self-consistent distribution of the network periods of the hybrid circuit, which can be solved numerically given the uncoupled pacemaker's distribution of intrinsic periods, nature of the network's feedback, and phase resetting characteristics of the pacemaker. The stationary distributions obtained in this manner are strongly predictive of the experimentally observed distributions of hybrid network period. This theoretical framework can provide insight into optimal feedback schemes for minimizing variability to increase reliability or maximizing variability to increase flexibility in central pattern generators driven by pacemakers with feedback.
The role of gap junctions between midbrain dopamine (DA) neurons in mechanisms of firing pattern ... more The role of gap junctions between midbrain dopamine (DA) neurons in mechanisms of firing pattern generation and synchronization has not been well characterized experimentally. We modified a multi-compartment model of DA neuron by adding a spike-generating mechanism and electrically coupling the dendrites of two such neurons through gap junctions. The burst-generating mechanism in the model neuron results from the interaction of a N-methyl-D-aspartate (NMDA)-induced current and the sodium pump. The firing patterns exhibited by the two model neurons included low frequency (2-7 Hz) spiking, high-frequency (13-20 Hz) spiking, irregular spiking, regular bursting, irregular bursting, and leader/follower bursting, depending on the parameter values used for the permeability for NMDA-induced current and the conductance for electrical coupling. All of these firing patterns have been observed in physiological neurons, but a systematic dependence of the firing pattern on the covariation of these two parameters has not been established experimentally. Our simulations indicate that electrical coupling facilitates NMDA-induced burst firing via two mechanisms. The first can be observed in a pair of identical cells. At low frequencies (low NMDA), as coupling strength was increased, only a transition from asynchronous to synchronous single-spike firing was observed. At high frequencies (high NMDA), increasing the strength of the electrical coupling in an identical pair resulted in a transition from high-frequency single-spike firing to burst firing, and further increases led to synchronous high-frequency spiking. Weak electrical coupling destabilizes the synchronous solution of the fast spiking subsystems, and in the presence of a slowly varying sodium concentration, the desynchronized spiking solution leads to bursts that are approximately in phase with spikes that are not in phase. Thus this transitional mechanism depends critically on action potential dynamics. The second mechanism for the induction of burst firing requires a heterogeneous pair that is, respectively, too depolarized and too hyperpolarized to burst. The net effect of the coupling is to bias at least one cell into an endogenously burst firing regime. In this case, action potential dynamics are not critical to the transitional mechanism. If electrical coupling is indeed more prominent in vivo due to basal level of modulation of gap junctions in vivo, these results may indicate why NMDA-induced burst firing is easier to observe in vivo as compared in vitro.
Midbrain dopaminergic (DA) neurons in vivo exhibit two major firing patterns: single-spike firing... more Midbrain dopaminergic (DA) neurons in vivo exhibit two major firing patterns: single-spike firing and burst firing. The firing pattern expressed is dependent on both the intrinsic properties of the neurons and their excitatory and inhibitory synaptic inputs. Experimental data suggest that the activation of N-methyl-D-aspartate (NMDA) and GABAA receptors is a crucial contributor to the initiation and suppression of burst firing, respectively, and that blocking Ca(2+)-activated potassium SK channels can facilitate burst firing. A multi-compartmental model of a DA neuron with a branching structure was developed and calibrated based on in vitro experimental data to explore the effects of different levels of activation of NMDA and GABAA receptors as well as the modulation of the SK current on the firing activity. The simulated tonic activation of GABAA receptors was calibrated by taking into account the difference in the electrotonic properties in vivo versus in vitro. Although NMDA-evoked currents are required for burst generation in the model, currents evoked by GABAA-receptor activation can also regulate the firing pattern. For example, the model predicts that increasing the level of NMDA receptor activation can produce excessive depolarization that prevents burst firing, but a concurrent increase in the activation of GABAA receptors can restore burst firing. Another prediction of the model is that blocking the SK channel current in vivo will facilitate bursting, but not as robustly as blocking the GABAA receptors.
Serotonergic modulation of the sensory neurons that mediate the gill- and tail-withdrawal reflexe... more Serotonergic modulation of the sensory neurons that mediate the gill- and tail-withdrawal reflexes of Aplysia is a useful model system for studies of neuronal plasticity that contributes to learning and memory. The effects of serotonin (5-HT) are mediated, in part, via two protein kinases (protein kinase A, PKA, and protein kinase C, PKC), which in turn, modulate at least four membrane currents, including a S ("serotonin-sensitive") K(+) current (I(K, S)), a steeply voltage-dependent K(+) current (I(K-V)), a slow component of the Ca(2+)-activated K(+) current (I(K,Ca-S)), and a L-type Ca(2+) current (I(Ca-L)). The present study investigated how the modulation of these currents altered the spike duration and excitability of sensory neurons and examined the relative contributions of PKA- and PKC-mediated effects to the actions of 5-HT. A Hodgkin-Huxley type model was developed that described the ionic conductances in the somata of sensory neurons. The descriptions of these currents and their modulation were based largely on voltage-clamp data from sensory neurons. Simulations were preformed with the program SNNAP (Simulator for Neural Networks and Action Potentials). The model was sufficient to replicate empirical data that describes the membrane currents, action potential waveform and excitability as well as their modulation by application of 5-HT, increased levels of adenosine cyclic monophosphate or application of active phorbol esters. In the model, modulation of I(K-V) by PKC played a dominate role in 5-HT-induced spike broadening, whereas the concurrent modulation of I(K,S) and I(K,Ca-S) by PKA primarily accounted for 5-HT-induced increases in excitability. Finally, simulations indicated that a PKC-induced increase in excitability resulted from decreases of I(K,S) and I(K,Ca-S), which was likely the indirect result of cross-talk between the PKC and PKA systems. The results provide several predictions that warrant additional experimental investigation and illustrate the importance of considering indirect as well as direct effects of modulatory agents on the modulation of membrane currents.
Network Computation in Neural Systems, Feb 26, 2014
Cross-frequency coupling is hypothesized to play a functional role in neural computation. We appl... more Cross-frequency coupling is hypothesized to play a functional role in neural computation. We apply phase resetting theory to two types of cross-frequency coupling that can occur when a slower oscillator periodically forces one or more oscillators: phase-phase coupling, in which the two oscillations are phase-locked, and phase-amplitude coupling, in which the amplitude of the driven oscillation is modulated. Our first result is that the shape of the phase resetting curve predicts the tightness of locking to a pulsatile forcing periodic input at any ratio of forced to intrinsic period; the tightness of the locking decreases as the ratio increases. Theoretical expressions were obtained for the probability density of the phases for a population of heterogeneous oscillators or a noisy single oscillator. Results were confirmed using two types of simulated networks and experiments on hippocampal CA1 neurons. Theoretical expressions were also obtained and confirmed for the probability density of N spike times within a single cycle of low frequency forcing. The second result is a suggested mechanism for phase-amplitude coupling in which progressive desynchronization leads to decreasing amplitude during a low frequency forcing cycle. Network simulations confirmed the theoretical viability of this mechanism, and that it generalizes to more diffuse input.
Phase response curves (PRCs) for a single neuron are often used to predict the synchrony of mutua... more Phase response curves (PRCs) for a single neuron are often used to predict the synchrony of mutually coupled neurons. Previous theoretical work on pulse coupled oscillators used single pulse perturbations. We propose an alternate method in which functional PRCs (FPRCs) are generated using a train of pulses applied at a fixed delay after a spike. Experimental FPRCs in Aplysia pacemaker
We address how feedback to a bursting biological pacemaker with intrinsic variability in cycle le... more We address how feedback to a bursting biological pacemaker with intrinsic variability in cycle length can affect that variability. Specifically we examine a hybrid circuit constructed of an isolated crab AB/PD pyloric pacemaker receiving virtual feedback via Dynamic Clamp. This virtual feedback generates artificial synaptic input to PD with timing determined by adjustable phase response dynamics that mimic average burst intervals generated by LP in the intact pyloric network. Using this system we measure network period variability dependence on the feedback element's phase response dynamics, and find that a constant response interval confers minimum variability. We further find that these optimal dynamics are characteristic of the biological pyloric network. Building upon our previous theoretical work mapping the firing intervals in one cycle onto the firing intervals in the next cycle, we create a theoretical map of the distribution of all firing intervals in one cycle to the distribution of firing intervals in the next cycle. We then obtain an integral equation for a stationary self-consistent distribution of the network periods of the hybrid circuit, which can be solved numerically given the uncoupled pacemaker's distribution of intrinsic periods, nature of the network's feedback, and phase resetting characteristics of the pacemaker. The stationary distributions obtained in this manner are strongly predictive of the experimentally observed distributions of hybrid network period. This theoretical framework can provide insight into optimal feedback schemes for minimizing variability to increase reliability or maximizing variability to increase flexibility in central pattern generators driven by pacemakers with feedback.
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