[Paper Review] Profiles for voltage-activated currents are multiphasic, not curvilinear

P. Nissen|arXiv (Cornell University)|Mar 16, 2016

Ion channel regulation and function7 references3 citations

TL;DR

This paper challenges the conventional use of Boltzmann (curvilinear) fits for voltage-activated ion channel currents, demonstrating instead that multiphasic profiles—composed of discontinuous, straight-line segments with abrupt transitions—provide vastly superior fits to experimental data. The authors show that Boltzmann fits produce significantly larger deviations and uneven residual distributions, with statistical significance (p < 0.001), indicating that the true activation profile is better described by non-continuous, phase-like transitions rather than smooth curves.

ABSTRACT

Data for voltage-activation of a potassium channel (Matulef et al. Proc Natl Acad Sci USA 110: 17886-17891. 2013) were, as conventionally done, fitted by the authors by a Boltzmann function, i.e. by a curvilinear profile. Reanalysis of the data reveals however that this interpretation must be rejected in favor of a multiphasic profile, a series of straight lines separated by discontinuous transitions, quite often in the form of noncontiguities (jumps). In contrast to the generally very poor fits to the Boltzmann profiles, the fits to multiphasic profiles are very good. (For the four replicates, the average deviations from the Boltzmann curves were 10- to 100-fold larger than the deviations from the multiphasic profiles.) The difference in the median values was statistically highly significant, P&lt;0.001 in most cases. For the mean values the deviations from the Boltzmann curve were 20-fold larger than the deviations from the multiphasic profile, and the difference in the median values was also highly significant. The curvilinear interpretation must be rejected also because of the uneven distribution of the points around the Boltzmann curves. The combined probability for the four replicates that this uneven distribution is due to chance is less than 0.002. In addition to activation of ion channels, a wide variety of biological as well as non-biological processes and phenomena involving binding, pH, folding/unfolding and effect of chain length can be well represented by multiphasic profiles (Nissen 2015a,b. Posted on arXiv.org with Paper ID arXiv: 1511.06601 and 1512.02561).

Motivation & Objective

• To reevaluate the standard practice of fitting voltage-activated ion channel current-voltage relationships using Boltzmann functions.
• To test whether the observed data from Matulef et al. (2013) better conform to a multiphasic profile than a curvilinear Boltzmann model.
• To assess the statistical and quantitative validity of Boltzmann fitting in light of residual distribution and fit deviation metrics.
• To demonstrate that multiphasic profiles, including noncontiguous jumps, provide a more accurate representation of voltage-activation phenomena.
• To extend the applicability of multiphasic modeling to other biological and physical processes involving binding, folding, and conformational transitions.

Proposed method

• Reanalysis of experimental voltage-activation data from Matulef et al. (2013) on potassium channels using both Boltzmann and multiphasic fitting models.
• Application of multiphasic profiles consisting of segmented straight lines with discontinuous transitions (jumps) to fit the data.
• Quantitative comparison of fit quality using average and median deviations between data and fitted curves.
• Statistical assessment of residual distribution using combined probability to evaluate randomness of deviations from Boltzmann fits.
• Use of established multiphasic modeling frameworks previously published by the author (Nissen, 2015a,b) on arXiv.
• Evaluation of goodness-of-fit through residual analysis and significance testing (p-values) across four biological replicates.

Experimental results

Research questions

• RQ1 Does the Boltzmann function provide an accurate description of voltage-activation profiles in potassium channels?
• RQ2 Are the deviations between experimental data and Boltzmann fits significantly larger than those from multiphasic profiles?
• RQ3 Is the distribution of residuals around Boltzmann curves randomly distributed, or does it indicate systematic misfit?
• RQ4 Can multiphasic profiles with discontinuous transitions better represent voltage-activation data than smooth curvilinear models?
• RQ5 Is the multiphasic model statistically superior to the Boltzmann model in describing voltage-activated currents?

Key findings

• The average deviation from Boltzmann curves was 10- to 100-fold larger than from multiphasic profiles across four replicates.
• For mean values, deviations from the Boltzmann curve were 20-fold larger than from the multiphasic profile.
• The difference in median values between data and Boltzmann fits was statistically significant (p < 0.001) in most cases.
• The combined probability that the uneven residual distribution around Boltzmann curves is due to chance is less than 0.002.
• Multiphasic profiles, including noncontiguous jumps, provided significantly better fits than curvilinear models.
• The results support rejecting the curvilinear Boltzmann interpretation in favor of a multiphasic, discontinuous activation mechanism.