A Threshold Equation for Action Potential Initiation

In central neurons, the threshold for spike initiation can depend on the stimulus and varies between cells and between recording sites in a given cell, but it is unclear what mechanisms underlie this variability. Properties of ionic channels are likely to play a role in threshold modulation. We examined in models the influence of Na channel activation, inactivation, slow voltage-gated channels and synaptic conductances on spike threshold. We propose a threshold equation which quantifies the contribution of all these mechanisms. It provides an instantaneous time-varying value of the threshold, which applies to neurons with fluctuating inputs. We deduce a differential equation for the threshold, similar to the equations of gating variables in the Hodgkin-Huxley formalism, which describes how the spike threshold varies with the membrane potential, depending on channel properties. We find that spike threshold depends logarithmically on Na channel density, and that Na channel inactivation and K channels can dynamically modulate it in an adaptive way: the threshold increases with membrane potential and after every action potential. Our equation was validated with simulations of a previously published multicompartemental model of spike initiation. Finally, we observed that threshold variability in models depends crucially on the shape of the Na activation function near spike initiation (about −55 mV), while its parameters are adjusted near half-activation voltage (about −30 mV), which might explain why many models exhibit little threshold variability, contrary to experimental observations. We conclude that ionic channels can account for large variations in spike threshold

Expanded Prader-Willi Syndrome due to an Unbalanced de novo Translocation t(14;15): Report and Review of the Literature

In the present study, we report a case of a female infant with a de novo unbalanced t(14;15) translocation resulting in a 14-Mb deletion of the 15q11.1q14 region. The deletion includes the 15q11.2q13 Prader-Willi syndrome (PWS) critical region, while no known deleted genes are found in the 14qter region. According to literature review, patients with similar or larger deletions in the 15q region exhibit an expanded phenotype of PWS with case-specific atypical features such as severe retardation, absence of speech, microcephaly, retrognathia, bifid uvula, ear malformations, and heart defects in addition to typical features of PWS. Our proband exhibited increased deep tendon reflexes, an atypical feature which is not reported in the reviewed literature. The severity of the phenotype is not directly associated with the size of the deletion; however, using a combination of methods, the identification of breakpoints and the deleted genes can be helpful for the prognostication in patients with atypical PWS deletions. © 2019 S. Karger AG, Basel. All rights reserved