A male spider׳s ornamentation polymorphism maintained by opposing selection with two niches

Deng, Bo; Estes, Alex; Grieb, Brett; Richard, Douglas; Hinds, Brittney; Hebets, Eileen A.

doi:10.1016/j.jtbi.2014.05.001

Cited by 6 publications

(2 citation statements)

References 43 publications

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“…The HHAxon17 data was obtained by Hodgkin and Huxley by an instantaneous depolariza- A best fit of the model to the data is done by Newton's line search method (c.f. [20,21]). the error function is defined to be…”

Section: Voltage-gatingmentioning

confidence: 99%

Mechanistic Model to Replace Hodgkin-Huxley Equations

Deng¹

2015

Preprint

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In this paper we construct a mathematical model for excitable membranes by introducing circuit characteristics for ion pump, ion current activation, and voltage-gating. The model is capable of reestablishing the Nernst resting potentials, all-or-nothing action potentials, absolute refraction, anode break excitation, and spike bursts. We propose to replace the Hodgkin-Huxley model by our model as the basis template for neurons and excitable membranes.1. Introduction. When Hodgkin and Huxley constructed their model for the squid giant axon ([1]) they were fully aware of their model's drawbacks because it was only a phenomenological fit to their experimental data. They commented specifically that different empirical forms should fit the same data or even better. They were right and other researchers saw the same problem too [2,3,4]. Alternative models were concocted ([2]) but never gained any traction because there was no point to replace one ad hoc model by another arbitrary one. However, replacing a phenomenological model by a mechanistic one is a different matter entirely.By mechanistic it is meant for a model to have as few hypotheses as possible that apply to physical processes or objects of a same type. Newton's inverse-distance-squared law for gravitation is the first and one perfect example of mechanistic modeling because it applies to all macroscopic bodies of mass. Goldman's derivation ([5]) of Nernst potentials across cell membranes is mechanistic because it applies to all ion species. In contrast Hodgkin and Huxley's individual treatments of the sodium and the potassium currents are not mechanistic because their hypothesis for the sodium ion does not apply to the potassium ion or vice versa. Researchers must have tried but failed because other than various variations of the HH model no mechanistic model can be found in the literature.The purpose of this paper is to fill this literature gap. The idea is to model the membrane as a circuit of devices each is defined by a current-voltage characteristics. We will model the sodium-potassium ion exchanger pump by the IV -characteristics that the time-rate of change of the current is proportional to the power of the pump. We will model the ion channel activation and the voltage-gating by one unified IV -characteristics that the voltage-rate of change of the conductance is proportional to the conductance. We will demonstrate that the resulting conductance-adaptation model is capable of reproducing all known phenomena of the HH model and much more, and hence provides a mechanistic alternative to the HH model and a model template for other types of excitable membranes in general.

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Section: Voltage-gatingmentioning

confidence: 99%

Mechanistic Model to Replace Hodgkin-Huxley Equations

Deng¹

2015

Preprint

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“…Conspicuous courtship displays and secondary sexual ornaments of male wolf spiders have been well studied in the context of female mate choice (Stratton & Uetz 1986;McClintock & Uetz 1996;Scheffer et al 1996;Parri et al 1997;Hebets & Uetz 1999, 2000Deng et al 2014), while the possible presence or function of concurrent male silk deposition during these displays remains relatively understudied (Richter & Van der Kraan 1970;Aisenberg et al 2010;Plunkett 2010). Male silk deposition may well be an integral part of multi-modal courtship displays and convey important information to females about body condition, genetic quality, or the motivation to mate.…”

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FemalePardosa milvinawolf spiders increase silk advertisements when in the presence of silk from courting males

Khan¹,

Persons²

2015

Journal of Arachnology

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Alternative Models to Hodgkin–Huxley Equations

Deng

2017

Bull Math Biol

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The Hodgkin and Huxley equations have served as the benchmark model in electrophysiology since 1950s. But it suffers from four major drawbacks. Firstly, it is only phenomenological not mechanistic. Secondly, it fails to exhibit the all-or-nothing firing mechanism for action potential generation. Thirdly, it lacks a theory for ion channel opening and closing activation across the cell membrane. Fourthly, it does not count for the phenomenon of voltage-gating which is vitally important for action potential generation. In this paper, a mathematical model for excitable membranes is constructed by introducing circuit characteristics for ion pump exchange, ion channel activation, and voltage-gating. It is demonstrated that the model is capable of re-establishing the Nernst resting potentials, explicitly exhibiting the all-or-nothing firing mechanism, and most important of all, filling the long-lasting theoretical gap by a unified theory on ion channel activation and voltage-gating. It is also demonstrated that the new model has one half fewer parameters but fits significantly better to experiment than the HH model does. The new model can be considered as an alternative template for neurons and excitable membranes when one looks for simpler models for mathematical studies and for forming large networks with fewer parameters.

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A male spider׳s ornamentation polymorphism maintained by opposing selection with two niches

Cited by 6 publications

References 43 publications

Mechanistic Model to Replace Hodgkin-Huxley Equations

Mechanistic Model to Replace Hodgkin-Huxley Equations

FemalePardosa milvinawolf spiders increase silk advertisements when in the presence of silk from courting males

Alternative Models to Hodgkin–Huxley Equations

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