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Register a new userElucidating distinct ion channel populations on the surface of hippocampal neurons via single-particle tracking recurrence analysis
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Protein and lipid nanodomains are prevalent on the surface of mammalian cells. In particular, it has been recently recognized that ion channels assemble into surface nanoclusters in the soma of cultured neurons. However, the interactions of these molecules with surface nanodomains display a considerable degree of heterogeneity. Here, we investigate this heterogeneity and develop statistical tools based on the recurrence of individual trajectories to identify subpopulations within ion channels in the neuronal surface. We specifically study the dynamics of the K$^+$ channel Kv1.4 and the Na$^+$ channel Nav1.6 on the surface of cultured hippocampal neurons at the single-molecule level. We find that both these molecules are expressed in two different forms with distinct kinetics with regards to surface interactions, emphasizing the complex proteomic landscape of the neuronal surface. Further, the tools presented in this work provide new methods for the analysis of membrane nanodomains, transient confinement, and identification of populations within single-particle trajectories.
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Voltage-gated sodium (Na$_mathrm{v}$) channels are responsible for the depolarizing phase of the action potential in most nerve cells, and Na$_mathrm{v}$ channel localization to the axon initial segment is vital to action potential initiation. Na$_mathrm{v}$ channels in the soma play a role in the transfer of axonal output information to the rest of the neuron and in synaptic plasticity, although little is known about Na$_mathrm{v}$ channel localization and dynamics within this neuronal compartment. This study uses single-particle tracking and photoactivation localization microscopy to analyze cell-surface Na$_mathrm{v}$1.6 within the soma of cultured hippocampal neurons. Mean-square displacement analysis of individual trajectories indicated that half of the somatic Na$_mathrm{v}$1.6 channels localized to stable nanoclusters $sim$230 nm in diameter. Strikingly, these domains were stabilized at specific sites on the cell membrane for >30 min, notably via an ankyrin-independent mechanism, indicating that the means by which Na$_mathrm{v}$1.6 nanoclusters are maintained in the soma is biologically different from axonal localization. Nonclustered Na$_mathrm{v}$1.6 channels showed anomalous diffusion, as determined by mean-square-displacement analysis. High-density single-particle tracking of Na$_mathrm{v}$ channels labeled with photoactivatable fluorophores in combination with Bayesian inference analysis was employed to characterize the surface nanoclusters. A subpopulation of mobile Na$_mathrm{v}$1.6 was observed to be transiently trapped in the nanoclusters. Somatic Na$_mathrm{v}$1.6 nanoclusters represent a new, to our knowledge, type of Na$_mathrm{v}$ channel localization, and are hypothesized to be sites of localized channel regulation.
An extensive comparison of the path uncertainty in single particle tracking systems for ion imaging was carried out based on Monte Carlo simulations. The spatial resolution as function of system parameters such as geometry, detector properties and the energy of proton and helium beams was investigated to serve as a guideline for hardware developments. Primary particle paths were sampled within a water volume and compared to the most likely path estimate obtained from detector measurements, yielding a depth-dependent uncertainty envelope. The maximum uncertainty along this curve was converted to a conservative estimate of the minimal radiographic pixel spacing for a single set of parameter values. Simulations with various parameter settings were analysed to obtain an overview of the reachable pixel spacing as function of system parameters. The results were used to determine intervals of detector material budget and position resolution that yield a pixel spacing small enough for clinical dose calculation. To ensure a pixel spacing below 2 mm, the material budget of a detector should remain below 0.25 % for a position resolution of 200 $mathrm{mu m}$ or below 0.75 % for a resolution of 10 $mathrm{mu m}$. Using protons, a sub-millimetre pixel size could not be achieved for a phantom size of 300 mm or at a large clearance. With helium ions, a sub-millimetre pixel spacing could be achieved even for a large phantom size and clearance, provided the position resolution was less than 100 $mathrm{mu m}$ and material budget was below 0.75 %.
Membrane protein transporters alternate their substrate-binding sites between the extracellular and cytosolic side of the membrane according to the alternating access mechanism. Inspired by this intriguing mechanism devised by nature, we study particle transport through a channel coupled with an energy well that oscillates its position between the two entrances of the channel. We optimize particle transport across the channel by adjusting the oscillation frequency. At the optimal oscillation frequency, the translocation rate through the channel is a hundred times higher with respect to free diffusion across the channel. Our findings reveal the effect of time dependent potentials on particle transport across a channel and will be relevant for membrane transport and microfluidics application.
In this paper, we proposed and validated a fully automatic pipeline for hippocampal surface generation via 3D U-net coupled with active shape modeling (ASM). Principally, the proposed pipeline consisted of three steps. In the beginning, for each magnetic resonance image, a 3D U-net was employed to obtain the automatic hippocampus segmentation at each hemisphere. Secondly, ASM was performed on a group of pre-obtained template surfaces to generate mean shape and shape variation parameters through principal component analysis. Ultimately, hybrid particle swarm optimization was utilized to search for the optimal shape variation parameters that best match the segmentation. The hippocampal surface was then generated from the mean shape and the shape variation parameters. The proposed pipeline was observed to provide hippocampal surfaces at both hemispheres with high accuracy, correct anatomical topology, and sufficient smoothness.
The random transitions of ion channels between conducting and non-conducting states generate a source of internal fluctuations in a neuron, known as channel noise. The standard method for modeling fluctuations in the states of ion channels uses continuous-time Markov chains nonlinearly coupled to a differential equation for voltage. Beginning with the work of Fox and Lu, there have been attempts to generate simpler models that use stochastic differential equation (SDEs) to approximate the stochastic spiking activity produced by Markov chain models. Recent numerical investigations, however, have raised doubts that SDE models can preserve the stochastic dynamics of Markov chain models. We analyze three SDE models that have been proposed as approximations to the Markov chain model: one that describes the states of the ion channels and two that describe the states of the ion channel subunits. We show that the former channel-based approach can capture the distribution of channel noise and its effect on spiking in a Hodgkin-Huxley neuron model to a degree not previously demonstrated, but the latter two subunit-based approaches cannot. Our analysis provides intuitive and mathematical explanations for why this is the case: the temporal correlation in the channel noise is determined by the combinatorics of bundling subunits into channels, and the subunit-based approaches do not correctly account for this structure. Our study therefore confirms and elucidates the findings of previous numerical investigations of subunit-based SDE models. Moreover, it presents the first evidence that Markov chain models of the nonlinear, stochastic dynamics of neural membranes can be accurately approximated by SDEs. This finding opens a door to future modeling work using SDE techniques to further illuminate the effects of ion channel fluctuations on electrically active cells.
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