Voltage-gated sodium channels play a critical role in cellular excitability, amplifying small membrane depolarizations into action potentials. Interactions with auxiliary subunits and other factors modify the intrinsic kinetic mechanism to result in new molecular and cellular functionality. We show here that sodium channels can implement a molecular leaky integrator, where the input signal is the membrane potential and the output is the occupancy of a long-term inactivated state. Through this mechanism, sodium channels effectively measure the frequency of action potentials and convert it into Na+ current availability. In turn, the Na+ current can control neuronal firing frequency in a negative feedback loop. Consequently, neurons become less sensitive to changes in excitatory input and maintain a lower firing rate. We present these ideas in the context of rat serotonergic raphe neurons, which fire spontaneously at low frequency and provide critical neuromodulation to many autonomous and cognitive brain functions.
The rhythmic pattern of breathing depends on the pre-Bötzinger complex (preBötC) in the brainstem, a vital circuit that contains a population of neurons with intrinsic oscillatory bursting behavior. Here, we investigate the specific kinetic properties that enable voltage-gated sodium channels to establish oscillatory bursting in preBötC inspiratory neurons, which exhibit an unusually large persistent Na+ current (INaP). We first characterize the kinetics of INaP in neonatal rat brainstem slices in vitro, using whole-cell patch-clamp and computational modeling, and then test the contribution of INaP to rhythmic bursting in live neurons, using the dynamic clamp technique. We provide evidence that subthreshold activation, persistence at suprathreshold potentials, slow inactivation, and slow recovery from inactivation are kinetic features of INaP that regulate all aspects of intrinsic rhythmic bursting in preBötC neurons. The slow and cumulative inactivation of INaP during the burst active phase controls burst duration and termination, while the slow recovery from inactivation controls the duration of the interburst interval. To demonstrate this mechanism, we develop a Markov state model of INaP that explains a comprehensive set of voltage clamp data. By adding or subtracting a computer-generated INaP from a live neuron via dynamic clamp, we are able to convert nonbursters into intrinsic bursters, and vice versa. As a control, we test a model with inactivation features removed. Adding noninactivating INaP into nonbursters results in a pattern of random transitions between sustained firing and quiescence. The relative amplitude of INaP is the key factor that separates intrinsic bursters from nonbursters and can change the fraction of intrinsic bursters in the preBötC. INaP could thus be an important target for regulating network rhythmogenic properties.
New mathematical tools are needed to incorporate existing knowledge into kinetic models of ion channels and other proteins. Salari et al. describe an algebraic transformation that can enforce linearly interdependent parameters into kinetic models in order to test new hypotheses.
In their preceding paper, Salari et al. describe a formalism that allows existing knowledge to be enforced into kinetic models. Here, Navarro et al. present a penalty-based optimization mechanism to incorporate arbitrary parameter relationships and constraints that quantify the behavior of the model.
Synaptic and intrinsic properties interact to sculpt neuronal output. Kisspeptin neurons in the hypothalamic arcuate nucleus help convey homeostatic estradiol feedback to central systems controlling fertility. Estradiol increases membrane depolarization induced by GABA A receptor activation in these neurons. We hypothesized that the mechanisms underlying estradiol-induced alterations in postsynaptic response to GABA, and also AMPA, receptor activation include regulation of voltage-gated potassium currents. Whole-cell recordings of arcuate kisspeptin neurons in brain slices from ovariectomized (OVX) and OVXϩestradiol (OVXϩE) female mice during estradiol negative feedback revealed that estradiol reduced capacitance, reduced transient and sustained potassium currents, and altered voltage dependence and kinetics of transient currents. Consistent with these observations, estradiol reduced rheobase and action potential latency. To study more directly interactions between synaptic and active intrinsic estradiol feedback targets, dynamic clamp was used to simulate GABA and AMPA conductances. Both GABA and AMPA dynamic clamp-induced postsynaptic potentials (PSPs) were smaller in neurons from OVX than OVXϩE mice; blocking transient potassium currents eliminated this difference. To interrogate the role of the estradiol-induced changes in passive intrinsic properties, different Markov model structures based on the properties of the transient potassium current in cells from OVX or OVXϩE mice were combined in silico with passive properties reflecting these two endocrine conditions. Some of tested models reproduced the effect on PSPs in silico, revealing that AMPA PSPs were more sensitive to changes in capacitance. These observations support the hypothesis that PSPs in arcuate kisspeptin neurons are regulated by estradiol-sensitive mechanisms including potassium conductances and membrane properties.
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