73 research outputs found
Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States
The phenomena that emerge from the interaction of the stochastic opening and
closing of ion channels (channel noise) with the non-linear neural dynamics are
essential to our understanding of the operation of the nervous system. The
effects that channel noise can have on neural dynamics are generally studied
using numerical simulations of stochastic models. Algorithms based on discrete
Markov Chains (MC) seem to be the most reliable and trustworthy, but even
optimized algorithms come with a non-negligible computational cost. Diffusion
Approximation (DA) methods use Stochastic Differential Equations (SDE) to
approximate the behavior of a number of MCs, considerably speeding up
simulation times. However, model comparisons have suggested that DA methods did
not lead to the same results as in MC modeling in terms of channel noise
statistics and effects on excitability. Recently, it was shown that the
difference arose because MCs were modeled with coupled activation subunits,
while the DA was modeled using uncoupled activation subunits. Implementations
of DA with coupled subunits, in the context of a specific kinetic scheme,
yielded similar results to MC. However, it remained unclear how to generalize
these implementations to different kinetic schemes, or whether they were faster
than MC algorithms. Additionally, a steady state approximation was used for the
stochastic terms, which, as we show here, can introduce significant
inaccuracies. We derived the SDE explicitly for any given ion channel kinetic
scheme. The resulting generic equations were surprisingly simple and
interpretable - allowing an easy and efficient DA implementation. The algorithm
was tested in a voltage clamp simulation and in two different current clamp
simulations, yielding the same results as MC modeling. Also, the simulation
efficiency of this DA method demonstrated considerable superiority over MC
methods.Comment: 32 text pages, 10 figures, 1 supplementary text + figur
Na+ imaging reveals little difference in action potentialâevoked Na+ influx between axon and soma
Author Posting. © The Authors, 2010. This is the author's version of the work. It is posted here by permission of Nature Publishing Group for personal use, not for redistribution. The definitive version was published in Nature Neuroscience 13 (2010): 852-860, doi:10.1038/nn.2574.In cortical pyramidal neurons, the axon initial segment (AIS) plays a pivotal role in synaptic
integration. It has been asserted that this property reflects a high density of Na+ channels in AIS.
However, we here report that APâassociated Na+ flux, as measured by highâspeed fluorescence
Na+ imaging, is about 3 times larger in the rat AIS than in the soma. Spike evoked Na+ flux in
the AIS and the first node of Ranvier is about the same, and in the basal dendrites it is about 8
times lower. At near threshold voltages persistent Na+ conductance is almost entirely axonal.
Finally, we report that on a time scale of seconds, passive diffusion and not pumping is
responsible for maintaining transmembrane Na+ gradients in thin axons during high frequency
AP firing. In computer simulations, these data were consistent with the known features of AP
generation in these neurons.Supported by USâ
Israel BSF Grant (2003082), Grass Faculty Grant from the MBL, NIH Grant (NS16295),
Multiple Sclerosis Society Grant (PP1367), and a fellowship from the Gruss Lipper Foundation
Characterization of Voltage-Gated Ca2+ Conductances in Layer 5 Neocortical Pyramidal Neurons from Rats
Neuronal voltage-gated Ca2+ channels are involved in electrical signalling and in converting these signals into cytoplasmic calcium changes. One important function of voltage-gated Ca2+ channels is generating regenerative dendritic Ca2+ spikes. However, the Ca2+ dependent mechanisms used to create these spikes are only partially understood. To start investigating this mechanism, we set out to kinetically and pharmacologically identify the sub-types of somatic voltage-gated Ca2+ channels in pyramidal neurons from layer 5 of rat somatosensory cortex, using the nucleated configuration of the patch-clamp technique. The activation kinetics of the total Ba2+ current revealed conductance activation only at medium and high voltages suggesting that T-type calcium channels were not present in the patches. Steady-state inactivation protocols in combination with pharmacology revealed the expression of R-type channels. Furthermore, pharmacological experiments identified 5 voltage-gated Ca2+ channel sub-types â L-, N-, R- and P/Q-type. Finally, the activation of the Ca2+ conductances was examined using physiologically derived voltage-clamp protocols including a calcium spike protocol and a mock back-propagating action potential (mBPAP) protocol. These experiments enable us to suggest the possible contribution of the five Ca2+ channel sub-types to Ca2+ current flow during activation under physiological conditions
Calmodulin Activation by Calcium Transients in the Postsynaptic Density of Dendritic Spines
The entry of calcium into dendritic spines can trigger a sequence of biochemical reactions that begins with the activation of calmodulin (CaM) and ends with long-term changes to synaptic strengths. The degree of activation of CaM can depend on highly local elevations in the concentration of calcium and the duration of transient increases in calcium concentration. Accurate measurement of these local changes in calcium is difficult because the spaces are so small and the numbers of molecules are so low. We have therefore developed a Monte Carlo model of intracellular calcium dynamics within the spine that included calcium binding proteins, calcium transporters and ion channels activated by voltage and glutamate binding. The model reproduced optical recordings using calcium indicator dyes and showed that without the dye the free intracellular calcium concentration transient was much higher than predicted from the fluorescent signal. Excitatory postsynaptic potentials induced large, long-lasting calcium gradients across the postsynaptic density, which activated CaM. When glutamate was released at the synapse 10 ms before an action potential occurred, simulating activity patterns that strengthen hippocampal synapses, the calcium gradient and activation of CaM in the postsynaptic density were much greater than when the order was reversed, a condition that decreases synaptic strengths, suggesting a possible mechanism underlying the induction of long-term changes in synaptic strength. The spatial and temporal mechanisms for selectivity in CaM activation demonstrated here could be used in other signaling pathways
Computing Highly Correlated Positions Using Mutual Information and Graph Theory for G Protein-Coupled Receptors
G protein-coupled receptors (GPCRs) are a superfamily of seven transmembrane-spanning proteins involved in a wide array of physiological functions and are the most common targets of pharmaceuticals. This study aims to identify a cohort or clique of positions that share high mutual information. Using a multiple sequence alignment of the transmembrane (TM) domains, we calculated the mutual information between all inter-TM pairs of aligned positions and ranked the pairs by mutual information. A mutual information graph was constructed with vertices that corresponded to TM positions and edges between vertices were drawn if the mutual information exceeded a threshold of statistical significance. Positions with high degree (i.e. had significant mutual information with a large number of other positions) were found to line a well defined inter-TM ligand binding cavity for class A as well as class C GPCRs. Although the natural ligands of class C receptors bind to their extracellular N-terminal domains, the possibility of modulating their activity through ligands that bind to their helical bundle has been reported. Such positions were not found for class B GPCRs, in agreement with the observation that there are not known ligands that bind within their TM helical bundle. All identified key positions formed a clique within the MI graph of interest. For a subset of class A receptors we also considered the alignment of a portion of the second extracellular loop, and found that the two positions adjacent to the conserved Cys that bridges the loop with the TM3 qualified as key positions. Our algorithm may be useful for localizing topologically conserved regions in other protein families
Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs
International Consensus Statement on Rhinology and Allergy: Rhinosinusitis
Background: The 5 years since the publication of the first International Consensus Statement on Allergy and Rhinology: Rhinosinusitis (ICARâRS) has witnessed foundational progress in our understanding and treatment of rhinologic disease. These advances are reflected within the more than 40 new topics covered within the ICARâRSâ2021 as well as updates to the original 140 topics. This executive summary consolidates the evidenceâbased findings of the document. Methods: ICARâRS presents over 180 topics in the forms of evidenceâbased reviews with recommendations (EBRRs), evidenceâbased reviews, and literature reviews. The highest grade structured recommendations of the EBRR sections are summarized in this executive summary. Results: ICARâRSâ2021 covers 22 topics regarding the medical management of RS, which are grade A/B and are presented in the executive summary. Additionally, 4 topics regarding the surgical management of RS are grade A/B and are presented in the executive summary. Finally, a comprehensive evidenceâbased management algorithm is provided. Conclusion: This ICARâRSâ2021 executive summary provides a compilation of the evidenceâbased recommendations for medical and surgical treatment of the most common forms of RS
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