The resurgent component of the voltage-gated sodium current (INaR) is a depolarizing conductance, revealed on membrane hyperpolarizations following brief depolarizing voltage steps, which has been shown to contribute to regulating the firing properties of numerous neuronal cell types throughout the central and peripheral nervous systems. Although mediated by the same voltage-gated sodium (Nav) channels that underlie the transient and persistent Nav current components, the gating mechanisms that contribute to the generation of INaR remain unclear. Here, we characterized Nav currents in mouse cerebellar Purkinje neurons, and used tailored voltage-clamp protocols to define how the voltage and the duration of the initial membrane depolarization affect the amplitudes and kinetics of INaR. Using the acquired voltage-clamp data, we developed a novel Markov kinetic state model with parallel (fast and slow) inactivation pathways and, we show that this model reproduces the properties of the resurgent, as well as the transient and persistent, Nav currents recorded in (mouse) cerebellar Purkinje neurons. Based on the acquired experimental data and the simulations, we propose that resurgent Na+ influx occurs as a result of fast inactivating Nav channels transitioning into an open/conducting state on membrane hyperpolarization, and that the decay of INaR reflects the slow accumulation of recovered/opened Nav channels into a second, alternative and more slowly populated, inactivated state. Additional simulations reveal that extrinsic factors that affect the kinetics of fast or slow Nav channel inactivation and/or impact the relative distribution of Nav channels in the fast- and slow-inactivated states, such as the accessory Navβ4 channel subunit, can modulate the amplitude of INaR.

Over 75% of abdominal aortic aneurysms harbor an intraluminal thrombus, and increasing evidence suggests that biologically active thrombus contributes to the natural history of these potentially lethal lesions. Thrombus formation depends on the local hemodynamics, which in turn depends on morphological features of the aneurysm and near vasculature. We previously presented a hemodynamically motivated “thrombus formation potential” that predicts where and when thrombus might form. Herein, we combine detailed studies of the three-dimensional hemodynamics with methods of sparse grid collocation and interpolation via kriging to examine roles of five key morphological features of aneurysms on thrombus formation: lesion diameter, axial position, length, curvature, and renal artery position. Computational simulations suggest that maximum diameter is a key determinant of thrombogenicity, but other morphological features modulate this dependence. More distally located lesions tend to have a higher thrombus formation potential and shorter lesions tend to have a higher potential than longer lesions, given the same aneurysmal dilatation. Finally, movement of vortical structures through the infrarenal aorta and lesion can significantly affect thrombogenicity. Formation of intraluminal thrombus within an evolving abdominal aortic aneurysm thus depends on coupled morphological features, not all intuitive, and computational simulations can be useful for predicting thrombogenesis.

Markov models of ion channel dynamics have evolved as experimental advances have improved our understanding of channel function. Past studies have examined limited sets of various topologies for Markov models of channel dynamics. We present a systematic method for identification of all possible Markov model topologies using experimental data for two types of native voltage-gated ion channel currents: mouse atrial sodium currents and human left ventricular fast transient outward potassium currents. Successful models identified with this approach have certain characteristics in common, suggesting that aspects of the model topology are determined by the experimental data. Incorporating these channel models into cell and tissue simulations to assess model performance within protocols that were not used for training provided validation and further narrowing of the number of acceptable models. The success of this approach suggests a channel model creation pipeline may be feasible where the structure of the model is not specified a priori.

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Markov models of ion channel dynamics have evolved as experimental advances have improved our understanding of channel function. Past studies have examined various topologies for Markov models of channel dynamics. We present a systematic method for identification of all possible Markov model topologies using experimental data for two types of native voltage-gated ion channel currents: mouse atrial sodium and human left ventricular fast transient outward potassium currents. In addition to optional biophysically inspired restrictions on the number of connections from a state and elimination of long-range connections, this study further suggests successful models have more than minimum number of connections for set number of states. When working with topologies with more than the minimum number of connections, the topologies with three and four connections to the open state tend to serve well as Markov models of ion channel dynamics.