Hydropathicity-based prediction of pain-causing NaV1.7 variants

Background Mutation-induced variations in the functional architecture of the NaV1.7 channel protein are causally related to a broad spectrum of human pain disorders. Predicting in silico the phenotype of NaV1.7 variant is of major clinical importance; it can aid in reducing costs of in vitro pathophysiological characterization of NaV1.7 variants, as well as, in the design of drug agents for counteracting pain-disease symptoms. Results In this work, we utilize spatial complexity of hydropathic effects toward predicting which NaV1.7 variants cause pain (and which are neutral) based on the location of corresponding mutation sites within the NaV1.7 structure. For that, we analyze topological and scaling hydropathic characteristics of the atomic environment around NaV1.7’s pore and probe their spatial correlation with mutation sites. We show that pain-related mutation sites occupy structural locations in proximity to a hydrophobic patch lining the pore while clustering at a critical hydropathic-interactions distance from the selectivity filter (SF). Taken together, these observations can differentiate pain-related NaV1.7 variants from neutral ones, i.e., NaV1.7 variants not causing pain disease, with 80.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}% sensitivity and 93.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document}% specificity [area under the receiver operating characteristics curve = 0.872]. Conclusions Our findings suggest that maintaining hydrophobic NaV1.7 interior intact, as well as, a finely-tuned (dictated by hydropathic interactions) distance from the SF might be necessary molecular conditions for physiological NaV1.7 functioning. The main advantage for using the presented predictive scheme is its negligible computational cost, as well as, hydropathicity-based biophysical rationalization. Supplementary Information The online version contains supplementary material available at 10.1186/s12859-021-04119-2.

: Superposition of heavy-atom NaV1.7 structures. (a), Cartoon illustration of a structural superposition of the 6J8J NaV1.7 structure [1] upon the NaV1.7 plemented by Mustang algorithm [2]. The 6J8J NaV1.7 structure is shown in red color. 30 The NaV1.7 structural model in use throughout this study is illustrated in yellow color. 31 The residue sequence F1462:K1484 which is part of the DIII-DIV intracellular linker 32 is highlighted in blue color in the 6J8J NaV1.7 structure. 33 Section S2. Navigating through NaV1.7's pore 34 The HOLE routine was called n = 100 times. During each call, HOLE control 35 parameters are fixed but the searching path is randomly reset according to the 36 rule RASEED = i·1000 with i = 1, 2.., n (see Table S1). At the end of each call 37 we obtain a set of points navigating through the pore where each navigation 38 point, q i = (q x,i , q y,i , q z,i ) ∈ Q, is located on a membrane-parallel plane. The 39 distance between subsequent membrane-parallel planes is set to 0.1Å (see Table   40 S1). After the completion of all the calls, we collected all the membrane-parallel 41 planes with each of them containing n navigation points and, under the Gaussian 42 assumption, the geometrical location of a pore point was approximated by q z,i ) ∈ P (S1) where P contains N p = 920 pore points (note that N p depends on the choice 44 of HOLE parameters (see Table S1)). Due to the skewness of the pore, x and 45 y coordinates of pore points are non-zero. Hence, pore points are radially dis-46 placed from the z-axis with an average offset of 3.13±4.63Å.  pected to decrease in relation to its axial counterpart as the median-statistical from pore walls of thickness l α=47 (p) ≈ 9.5Å cannot be neglected. However, 71 their contribution to the structural stability of the NaV1.7 structural model 72 under scrutiny is expected to be rather marginal for scales larger than l α=47 (p) 73 as macroscopically, i.e., for l α (p) → L(p), || h xy (p, l α (p))||/|| h z (p, l α (p))|| α 74 drops below 0.16 (see inset figure). field descriptor (MSFD) || hxy(p, lα(p))||/|| hz(p, lα(p))|| α for α = 1, 2, .., 800 is il- condition f (p , l α (p ))·f (p, l α (p)) < 0 is satisfied, extract the four-dimensional that represents a zero-crossing point of f (p, l α (p)) along p-direction with | · | 98 returning the absolute values of f , and s approximated via linear interpolation.

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The set of all detected zero-crossing points of f (p, l α (p)) along p-direction for 100 a given scaling index α is represented as ω(α) so that hydropathic topological

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The discretized RDF of N (p, l α (p)) atoms around p reads Kα is the thickness of a spherical shell around p, ∆N (p, l α (p)) = 147 N (p, l α (p)) − N (p, l α (p)) is the number of atoms found within the spherical 148 shell of thickness ∆l α (p) centered at p and ρ(p) = Nc V (p) = Nc 4 3 ·π·(L(p)−R(p)) 3 is the 149 average atomic density around p.

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Using equation S4 we approximated the RDFs of the PM and VS atoms

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In order to obtain a relative measure of how the RDF of PM atoms varies with respect to the RDF of VS atoms, and vice versa, we used the PMs-VSs where sm(·) implements the Nadaraya-Watson kernel regression R-function is of interest here is the sign-change behavior of e(p, l α (p) for increasing l α (p). 165 We investigated it by detecting for every p the pair {l α (p), l α (p)} for which the 166 sign-change condition e(p, l α (p))·e(p, l α (p)) < 0 is satisfied and approximating 167 with linear interpolation the root location where e(p, l α (p)) changes sign along l α (p)-direction.  in vitro observations (see caption of Table S3).

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What is of interest for this study is the location of the mutated residue (i.e., 202 mutation site) within the NaV1.7 structure which is calculated by nres. i is the total residue mass, and n res. is the 205 total number of atoms forming the residue.

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The mutation structural location is mapped on two dimensions by rounding 207 its z-coordinate, v z , to SAMPLE accuracy (see Table S1) so that it can be as-    The distance between a mutation structural location, v, and the HP's bound-  Section S11. Classification of SCN9A-gene mutations based on a 301 weighted topological-distance average measure 302 We calculated the weighted topological-distance average w HP ·D HP (v)+w ξ · 303 D ξ(p crit. ) (v), where w HP and w ξ are weights, for all the pain-related and neutral 304 mutation structural locations, and fed retrieved distances into a binary classifier.

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The quality of retrieved classifications is demonstrated in Figure S5 in terms of 306 the area under the ROC curve for w ξ = 1 − w HP = i · 0.001, i = 0, 1, .., 1000.

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The linear combination of D HP (v) with D ξ(p crit. ) (v) which maximized the area 308 under the ROC curve corresponds to w ξ = 0.618 and w HP = 0.382 ( Figure S5).
and D ξ(p crit. ) (v) are given by equations S10 and S11, respectively. The study was partly funded by the European Union 7th Framework Pro-329 gramme (grant n602273).