An ionic current model for medullary respiratory neurons

Theoretical perspectives on central chemosensitivity: CO2/H+-sensitive neurons in the locus coeruleus

Central chemoreceptors are highly sensitive neurons that respond to changes in pH and CO₂ levels. An increase in CO₂/H⁺ typically reflects a rise in the firing rate of these neurons, which stimulates an increase in ventilation. Here, we present an ionic current model that reproduces the basic electrophysiological activity of individual CO₂/H⁺-sensitive neurons from the locus coeruleus (LC). We used this model to explore chemoreceptor discharge patterns in response to electrical and chemical stimuli. The modeled neurons showed both stimulus-evoked activity and spontaneous activity under physiological parameters. Neuronal responses to electrical and chemical stimulation showed specific firing patterns of spike frequency adaptation, postinhibitory rebound, and post-stimulation recovery. Conversely, the response to chemical stimulation alone (based on physiological CO₂/H⁺ changes), in the absence of external depolarizing stimulation, showed no signs of postinhibitory rebound or post-stimulation recovery, and no depolarizing sag. A sensitivity analysis for the firing-rate response to the different stimuli revealed that the contribution of an applied stimulus current exceeded that of the chemical signals. The firing-rate response increased indefinitely with injected depolarizing current, but reached saturation with chemical stimuli. Our computational model reproduced the regular pacemaker-like spiking pattern, action potential shape, and most of the membrane properties that characterize CO₂/H⁺-sensitive neurons from the locus coeruleus. This validates the model and highlights its potential as a tool for studying the cellular mechanisms underlying the altered central chemosensitivity present in a variety of disorders such as sudden infant death syndrome, depression, and anxiety. In addition, the model results suggest that small external electrical signals play a greater role in determining the chemosensitive response to changes in CO₂/H⁺ than previously thought. This highlights the importance of considering electrical synaptic transmission in studies of intrinsic chemosensitivity.

The sensory mechanism by which changes in CO₂ and H⁺ levels are detected in the brain is known as central chemoreception. Altered chemoreception is common to a wide variety of clinical conditions, including sleep apnea, sudden infant death syndrome, hyperventilation, depression, anxiety and asthma. In addition, CO₂/H⁺-sensitive neurons are present in some regions of the brain that have been identified as drug targets for the treatment of anxiety and panic disorders. We are interested in understanding the cellular mechanisms that determine and modulate the behavior of these neurons. We previously investigated possible mechanisms underlying their behavior in rats to elucidate whether they respond to changes in intracellular or extracellular pH, CO₂, or a combination of these stimuli. To study the roles that signals and ion channel targets play in individual neurons we develop mathematical models that simulate their electrochemical behavior and their responses to hypercapnic and/or acidotic stimuli. Nowadays, we are focused on using computational tools to explore the firing pattern of such neurons in response to chemical (CO₂/H⁺) and electrical (synaptic) stimulation. Our results reveal significant effects of electrical stimulation on the responses of brainstem neurons and highlight the importance of considering synaptic transmission in experimental studies of chemosensitivity.

Multiscale model of dynamic neuromodulation integrating neuropeptide-induced signaling pathway activity with membrane electrophysiology

We developed a multiscale model to bridge neuropeptide receptor-activated signaling pathway activity with membrane electrophysiology. Typically, the neuromodulation of biochemical signaling and biophysics have been investigated separately in modeling studies. We studied the effects of Angiotensin II (AngII) on neuronal excitability changes mediated by signaling dynamics and downstream phosphorylation of ion channels. Experiments have shown that AngII binding to the AngII receptor type-1 elicits baseline-dependent regulation of cytosolic Ca(2+) signaling. Our model simulations revealed a baseline Ca(2+)-dependent response to AngII receptor type-1 activation by AngII. Consistent with experimental observations, AngII evoked a rise in Ca(2+) when starting at a low baseline Ca(2+) level, and a decrease in Ca(2+) when starting at a higher baseline. Our analysis predicted that the kinetics of Ca(2+) transport into the endoplasmic reticulum play a critical role in shaping the Ca(2+) response. The Ca(2+) baseline also influenced the AngII-induced excitability changes such that lower Ca(2+) levels were associated with a larger firing rate increase. We examined the relative contributions of signaling kinases protein kinase C and Ca(2+)/Calmodulin-dependent protein kinase II to AngII-mediated excitability changes by simulating activity blockade individually and in combination. We found that protein kinase C selectively controlled firing rate adaptation whereas Ca(2+)/Calmodulin-dependent protein kinase II induced a delayed effect on the firing rate increase. We tested whether signaling kinetics were necessary for the dynamic effects of AngII on excitability by simulating three scenarios of AngII-mediated KDR channel phosphorylation: (1), an increased steady state; (2), a step-change increase; and (3), dynamic modulation. Our results revealed that the kinetics emerging from neuromodulatory activation of the signaling network were required to account for the dynamical changes in excitability. In summary, our integrated multiscale model provides, to our knowledge, a new approach for quantitative investigation of neuromodulatory effects on signaling and electrophysiology.

Computational modeling of spike generation in serotonergic neurons of the dorsal raphe nucleus

Serotonergic neurons of the dorsal raphe nucleus, with their extensive innervation of limbic and higher brain regions and interactions with the endocrine system have important modulatory or regulatory effects on many cognitive, emotional and physiological processes. They have been strongly implicated in responses to stress and in the occurrence of major depressive disorder and other psychiatric disorders. In order to quantify some of these effects, detailed mathematical models of the activity of such cells are required which describe their complex neurochemistry and neurophysiology. We consider here a single-compartment model of these neurons which is capable of describing many of the known features of spike generation, particularly the slow rhythmic pacemaking activity often observed in these cells in a variety of species. Included in the model are 11 kinds of ion channels: a fast sodium current INa, a delayed rectifier potassium current IKDR, a transient potassium current IA, a slow non-inactivating potassium current IM, a low-threshold calcium current IT, two high threshold calcium currents IL and IN, small and large conductance potassium currents ISK and IBK, a hyperpolarization-activated cation current IH and a leak current ILeak. In Sections 3-8, each current type is considered in detail and parameters estimated from voltage clamp data where possible. Three kinds of model are considered for the BK current and two for the leak current. Intracellular calcium ion concentration Cai is an additional component and calcium dynamics along with buffering and pumping is discussed in Section 9. The remainder of the article contains descriptions of computed solutions which reveal both spontaneous and driven spiking with several parameter sets. Attention is focused on the properties usually associated with these neurons, particularly long duration of action potential, steep upslope on the leading edge of spikes, pacemaker-like spiking, long-lasting afterhyperpolarization and the ramp-like return to threshold after a spike. In some cases the membrane potential trajectories display doublets or have humps or notches as have been reported in some experimental studies. The computed time courses of IA and IT during the interspike interval support the generally held view of a competition between them in influencing the frequency of spiking. Spontaneous activity was facilitated by the presence of IH which has been found in these neurons by some investigators. For reasonable sets of parameters spike frequencies between about 0.6Hz and 1.2Hz are obtained, but frequencies as high as 6Hz could be obtained with special parameter choices. Topics investigated and compared with experiment include shoulders, notches, anodal break phenomena, the effects of noradrenergic input, frequency versus current curves, depolarization block, effects of cell size and the effects of IM. The inhibitory effects of activating 5-HT1A autoreceptors are also investigated. There is a considerable discussion of in vitro versus in vivo firing behavior, with focus on the roles of noradrenergic input, corticotropin-releasing factor and orexinergic inputs. Location of cells within the nucleus is probably a major factor, along with the state of the animal.

Hyperpolarization-activated current (I(h)) in vestibular calyx terminals: characterization and role in shaping postsynaptic events

Calyx afferent terminals engulf the basolateral region of type I vestibular hair cells, and synaptic transmission across the vestibular type I hair cell/calyx is not well understood. Calyces express several ionic conductances, which may shape postsynaptic potentials. These include previously described tetrodotoxin-sensitive inward Na(+) currents, voltage-dependent outward K(+) currents and a K(Ca) current. Here, we characterize an inwardly rectifying conductance in gerbil semicircular canal calyx terminals (postnatal days 3-45), sensitive to voltage and to cyclic nucleotides. Using whole-cell patch clamp, we recorded from isolated calyx terminals still attached to their type I hair cells. A slowly activating, noninactivating current (I(h)) was seen with hyperpolarizing voltage steps negative to the resting potential. External Cs(+) (1-5 mM) and ZD7288 (100 μM) blocked the inward current by 97 and 83 %, respectively, confirming that I(h) was carried by hyperpolarization-activated, cyclic nucleotide gated channels. Mean half-activation voltage of I(h) was -123 mV, which shifted to -114 mV in the presence of cAMP. Activation of I(h) was well described with a third order exponential fit to the current (mean time constant of activation, τ, was 190 ms at -139 mV). Activation speeded up significantly (τ=136 and 127 ms, respectively) when intracellular cAMP and cGMP were present, suggesting that in vivo I(h) could be subject to efferent modulation via cyclic nucleotide-dependent mechanisms. In current clamp, hyperpolarizing current steps produced a time-dependent depolarizing sag followed by either a rebound afterdepolarization or an action potential. Spontaneous excitatory postsynaptic potentials (EPSPs) became larger and wider when I(h) was blocked with ZD7288. In a three-dimensional mathematical model of the calyx terminal based on Hodgkin-Huxley type ionic conductances, removal of I(h) similarly increased the EPSP, whereas cAMP slightly decreased simulated EPSP size and width.

A model of the respiratory central pattern generator

We have developed a model of the mammalian respiratory central pattern generator (rCPG) to mimic the salient characteristics of its constituent medullary neurons. This model was designed as a network of Hodgkin-Huxley type medullary neurons under the hypothesis that synaptic and network effects predominate over ionic influences in determining the pattern of firing seen in individual neurons. After obtaining satisfactory mimicry of these patterns we validated the model to a different set of data in order to examine its robustness in the face of transient perturbations.

A model of the pacemaking neuron of the respiratory central pattern generator

We have developed a model of the mammalian respiratory central pattern generator (rCPG) to mimic the salient characteristics of its constituent medullary neurons. This model is designed as a network of Hodgkin-Huxley-type medullary neurons driven by a pacemaking neuron from the pre-Bötzinger complex. Here, we present the results of our model of this pacemaking neuron, based on available voltage clamp data. Implications for the behavior of the rCPG are discussed.

Respiratory-Like Rhythmic Activity Can Be Produced by an Excitatory Network of Non-Pacemaker Neuron Models

It is still unclear whether the respiratory-like rhythm observed in slice preparations containing the pre-Bötzinger complex is of pacemaker or network origin. The rhythm persists in the absence of inhibition, but blocking pacemaker activity did not always result in rhythm abolition. We developed a computational model of the slice to show that respiratory-like rhythm can emerge as a network property without pacemakers or synaptic inhibition. The key currents of our model cell are the low- and high-threshold calcium currents and the calcium-dependent potassium current. Depolarization of a single unit by current steps or by raising the external potassium concentration can induce periodic bursting activity. Gaussian stimulation increased the excitability of the model without evoking oscillatory activity, as indicated by autocorrelation analysis. In response to hyperpolarizing pulses, the model produces prolonged relative refractory periods. At the network level, an increase of external potassium concentration triggers rhythmic activity that can be attributed to cellular periodic bursting, network properties, or both, depending on different parameters. Gaussian stimulation also induces rhythmic activity that depends solely on network properties. In all cases, the calcium-dependent potassium current has a central role in burst termination and interburst duration. However, when periodic inhibition is considered, the activation of this current is responsible for the characteristic amplification ramp of the emerged rhythm. Our results may explain controversial results from studies blocking pacemakers in vitro and show a shift in the role of the calcium-dependent potassium current in the presence of network inhibition.

A model of the rat phrenic motor neuron

We have developed a model for the rat phrenic motor neuron (PMN) that robustly replicates many experimentally observed behaviors of PMNs in response to pharmacological, ionic, and electrical perturbations using a single set of parameters. Our model suggests that the after-depolarization (ADP) response seen in action potentials is a result of the slow deactivation of the fast sodium channel in the range of the ADP coupled with the activation of the L-type calcium channel (I(CaL)). This current and its interactions with the small and large conductance calcium-activated potassium currents (I(KCaSK) and I(KCaBK), respectively) is also important in the generation of spike frequency adaptation in the repetitive firing mode of activity. Other aspects of the model conform very well to experimental observations in both the action potential and repetitive firing mode of activity, including the role of I(KCaSK) in the medium after-hyperpolarization (AHP) and the role of I(KCaBK) in the fast AHP. We have made a number of predictions using the model, including the characterization of two putative sodium currents (fast and persistent), as well as functional roles for the N- and T-type calcium currents.