Abstract
An accurate and efficient characterization of the polyelectrolyte properties for cytoskeleton filaments are key to the molecular understanding of electrical signal propagation, bundle and network formation, as well as their potential nanotechnological applications. In this article, we introduce an innovative multi-scale approach able to account for the atomistic details of a protein molecular structure, its biological environment, and their impact on electrical impulses propagating along wild type actin filaments. The formulation includes non-trivial contributions to the ionic electrical conductivity and capacitance coming from the diffuse part of the electrical double layer of G-actins. We utilize this monomer characterization in a non-linear inhomogeneous transmission line prototype model to account for the monomer–monomer interactions, dissipation and damping perturbations along the filament length. A novel, simple, accurate, approximate analytic expression has been obtained for the transmission line model. Our results reveal the propagation of electrical signal impulses in the form of solitons for the range of voltage stimulus and electrolyte solutions typically present for intracellular and in vitro conditions. The approach predicts a lower electrical conductivity with higher linear capacitance and non-linear accumulation of charge for intracellular conditions. Our results show a significant influence of the voltage input on the electrical impulse shape, attenuation and kern propagation velocity. The filament is able to sustain the soliton propagation at almost constant kern velocity for the in vitro condition, whereas the intracellular condition displays a remarkable deceleration. Additionally, the solitons are narrower and travel faster at higher voltage input. As a unique feature, this multi-scale theory is able to account for molecular structure conformation (mutation) and biological environment (protonations/deprotonations) changes often present in pathological conditions. It is also applicable to other highly charged rod-like polyelectrolytes with relevance in biomedicine and biophysics.
Highlights
Actin laments (F-actin) are long charged rod-like cytoskeleton polymers, which carry out many important biological activities in eukaryotic cells.[1,2] These micro laments have recently gained wide notoriety for their fascinating polyelectrolyte properties.[3]
Under the conditions considered in this article, the Debye length reveals a wider electrical double layer formation in the intracellular condition than in vitro condition, namely lD
We introduced an innovative multi-scale approach which accounts for the atomistic details on the protein molecular structure and biological environment, as well as their impact on electrical impulses propagating in the form of micron solitons along wild type actin laments
Summary
All of these observations provide strong evidence on the polyelectrolyte nature of F-actin, which provides unique, yet still poorly understood, conducting and bundling formation properties in a variety of neuron activities including intracellular information processing, regulating developmental plasticity, and mediating transport. Actin polymers may serve as “electrical nanobiowires” whom can be modeled as non-linear inhomogeneous transmission lines known to propagate non-linear dispersive solitary waves.[18] These waves can take the form of localized electrical signal impulses.[19,20,21] this basic understanding about the electrical impulses propagating along actin laments does not account for all conductance properties of micro lament bundles.[22] More recent approaches, based on Gouy-Chapman electrical double layer type models and mean- eld PoissonBoltzmann (PB) theories, provide further insight into the ionic equilibrium distributions and electric potential properties near the polymer surface, which arise from the charged polyelectrolyte surface, continuum solvent dielectric medium, and mean electrostatic potential energy generated by mixed salts comprised of point-like ions.[23,24,25,26,27] These methods are shown to break down for cytoskeleton laments under certain situations, because they entail several approximations in their treatment of the ions and solvent molecules. A novel approximate analytic solution is obtained for this model and utilized in section IV to characterize the electrical impulse peak, width, and velocity of propagation under several voltage stimulus and electrolyte conditions
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