Fig. 1

Atom-packing around NaV1.7’s pore. a Cartoon illustration of the NaV1.7 structural model (side view). b Cartoon illustration of the NaV1.7 structural model (intracellular-to-extracellular view). The atomic environment around every pore point \({\mathbf{p}}\in P\) is partitioned into three consecutive atom-packing domains; a lag domain realized for \(l_{\alpha }({\mathbf{p}})\le s({\mathbf{p}})\), an inflection domain consisting of two parts realized for \(s({\mathbf{p}})<l_{\alpha }({\mathbf{p}})\le \xi ({\mathbf{p}})\) and \(\xi ({\mathbf{p}})<l_{\alpha }({\mathbf{p}})\le o({\mathbf{p}})\), respectively, and an asymptote domain realized for \(l_{\alpha }({\mathbf{p}})>o({\mathbf{p}})\) (see “Methods” section). \(s({\mathbf{p}})\), \(\xi ({\mathbf{p}})\) and \(o({\mathbf{p}})\) are represented in b in terms of \(\langle s({\mathbf{p}}) \rangle\), \(\langle \xi ({\mathbf{p}}) \rangle\), and \(\langle o({\mathbf{p}}) \rangle\), respectively, roughly indicating the median-statistical value of the radial distance from \({\mathbf{p}}\) at which the transition among subsequent domains takes place. The median-statistical value of the radial distance from \({\mathbf{p}}\) at which the PMs-to-VSs transition, \(\langle \nu ({\mathbf{p}}) \rangle\), takes place is also illustrated. Note that \(\langle \nu ({\mathbf{p}}) \rangle\) and \(\langle \xi ({\mathbf{p}}) \rangle\) are almost indistinguishable, i.e., \(\langle \nu ({\mathbf{p}}) \rangle \approx \langle \xi ({\mathbf{p}}) \rangle\). c Traces of statistical descriptors of the normalized (with respect to \(N_{c}\)) atomic CDF, \(\langle \bar{N}({\mathbf{p}},l_{\alpha }({\mathbf{p}}))\rangle _{\alpha }\), and of its best-fitted Richards model \(\langle n({\mathbf{p}},l_{\alpha }({\mathbf{p}}))\rangle _{\alpha }\) are plotted in log-scale with shaded areas around \(\langle N({\mathbf{p}},l_{\alpha }({\mathbf{p}}))\rangle _{\alpha }\) indicative of 95\(\%\) confidence intervals. \(s({\mathbf{p}})\), \(\xi ({\mathbf{p}})\), and \(o({\mathbf{p}})\) are represented in c in terms of statistical descriptors \(\langle \alpha _{s} \rangle\), \(\langle \alpha _{\xi } \rangle \approx \langle \alpha _{\nu } \rangle\), and \(\langle \alpha _{o} \rangle\), respectively, returning the median-statistical value of corresponding scaling indices \(\alpha\). All statistical descriptors correspond to median values and are calculated according to the scheme presented in Additional file 1: S7