Modeling Microtubule Counterion Distributions and Conductivity Using the Poisson-Boltzmann Equation

Motorless transport of microtubules along tubulin, RanGTP, and salt gradients

Microtubules are dynamic filaments that assemble spindles for eukaryotic cell division. As the concentration profiles of soluble tubulin and regulatory proteins are non-uniform during spindle assembly, we asked if diffusiophoresis - motion of particles under solute gradients - can act as a motorless transport mechanism for microtubules. We identify the migration of stable microtubules along cytoplasmic and higher concentration gradients of soluble tubulin, MgCl2, Mg-ATP, Mg-GTP, and RanGTP at speeds O(100) nm/s, validating the diffusiophoresis hypothesis. Using two buffers (BRB80 and CSF-XB), microtubule behavior under MgCl2 gradients is compared with negatively charged particles and analyzed with a multi-ion diffusiophoresis and diffusioosmosis model. Microtubule diffusiophoresis under gradients of tubulin and RanGTP is also compared with the charged particles and analyzed with a non-electrolyte diffusiophoresis model. Further, we find that tubulin and RanGTP display concentration dependent cross-diffusion that influences microtubule diffusiophoresis. Finally, using Xenopus laevis egg extract, we show that diffusiophoretic transport occurs in an active cytoplasmic environment.

Measurement and Characterization of the Electrical Properties of Actin Filaments

Actin filaments, as key components of the cytoskeleton, have aroused great interest due to their numerous functional roles in eukaryotic cells, including intracellular electrical signaling. The aim of this research is to characterize the alternating current (AC) conduction characteristics of both globular and polymerized actin and quantitatively compare their values to those theoretically predicted earlier. Actin filaments have been demonstrated to act as conducting bionanowires, forming a signaling network capable of transmitting ionic waves in cells. We performed conductivity measurements for different concentrations of actin, considering both unpolymerized and polymerized actin to identify potential differences in their electrical properties. These measurements revealed two relevant characteristics: first, the polymerized actin, arranged in filaments, has a lower impedance than its globular counterpart; second, an increase in the actin concentration leads to higher conductivities. Furthermore, from the data collected, we developed a quantitative model to represent the electrical properties of actin in a buffer solution. We hypothesize that actin filaments can be modeled as electrical resistor-inductor-capacitor (RLC) circuits, where the resistive contribution is due to the viscous ion flows along the filaments; the inductive contribution is due to the solenoidal flows along and around the helix-shaped filament and the capacitive contribution is due to the counterion layer formed around each negatively charged filament.

Modeling non-genetic information dynamics in cells using reservoir computing

Virtually all cells use energy-driven, ion-specific membrane pumps to maintain large transmembrane gradients of Na+, K+, Cl-, Mg++, and Ca++, but the corresponding evolutionary benefit remains unclear. We propose that these gradients enable a dynamic and versatile biological system that acquires, analyzes, and responds to environmental information. We hypothesize that environmental signals are transmitted into the cell by ion fluxes along pre-existing gradients through gated ion-specific membrane channels. The consequent changes in cytoplasmic ion concentration can generate a local response or orchestrate global/regional cellular dynamics through wire-like ion fluxes along pre-existing and self-assembling cytoskeleton to engage the endoplasmic reticulum, mitochondria, and nucleus.

On the role of calcium diffusion and its rapid buffering in intraflagellar signaling

We have considered the realistic mechanism of rapid Ca2+ (calcium ion) buffering within the wave of calcium ions progressing along the flagellar axoneme. This buffering is an essential part of the Ca2+ signaling pathway aimed at controlling the bending dynamics of flagella. It is primarily achieved by the mobile region of calmodulin molecules and by stationary calaxin, as well as by the part of calmodulin bound to calcium/calmodulin-dependent kinase II and kinase C. We derived and elaborated a model of Ca2+ diffusion within a signaling wave in the presence of these molecules which rapidly buffer Ca2+. This approach has led to a single nonlinear transport equation for the Ca2+ wave that contains the effects brought about by both as necessary buffers for signaling. The presence of mobile buffer calmodulin gives rise to a transport equation that is not strictly diffusive but also exhibits a sink-like effect. We solved straightforwardly the final transport equation in an analytical framework and obtained the implied function of calcium concentration. The effective diffusion coefficient depends on local Ca2+ concentration. It is plausible that these buffers' presence can impact Ca2+ wave speed and shape, which are essential for decoding Ca2+ signaling in flagella. We present the solution of the transport equation for a few specified cases with physiologically reasonable sets of parameters involved.

Calcium messages in flagella are faster than messenger particles

Calcium is one of the most versatile messengers for intracellular signaling. In the case of cilia and flagella calcium has the central role in transfer of communications between extracellular stimuli and intracellular formation of frequency modulated signal and their deciphering by target proteins. In this paper, the diffusion of fluorescently or otherwise tagged and un-tagged Ca2＋ particles is analyzed by solving the system of pertaining reaction-diffusion equations. We used Fourier transform tools to get asymptotic eigenfunctions for tagged (un-tagged) free and buffered Ca2＋ ions. We made some numerical estimations for diffusion coefficients corroborating the fact that messages diffuse faster than Ca2＋ messengers. From the best of our knowledge, this is the first time that Ca2＋ signaling in living cells is biophysically elaborated within the framework of model presented here. We suggest the experimental assay on the basis of radioactive Ca2＋ as tagged probe.

Mathematical modeling of microscale biology: Ion pairing, spatially varying permittivity, and Born energy in glycosaminoglycan brushes

Biological macromolecules including nucleic acids, proteins, and glycosaminoglycans are typically anionic and can span domains of up to hundreds of nanometers and even micron length scales. The structures exist in crowded environments that are dominated by multivalent electrostatic interactions that can be modeled using mean-field continuum approaches that represent underlying molecular nanoscale biophysics. We develop such models for glycosaminoglycan brushes using steady state modified Poisson-Boltzmann models that incorporate important ion-specific (Hofmeister) effects. The results quantify how electroneutrality is attained through ion electrophoresis, spatially-varying permittivity hydration forces, and ion-specific pairing. Brush-salt interfacial profiles of the electrostatic potential as well as bound and unbound ions are characterized for imposed jump conditions across the interface. The models should be applicable to many intrinsically-disordered biophysical environments and are anticipated to provide insight into the design and development of therapeutics and drug-delivery vehicles to improve human health.

The distinguishing electrical properties of cancer cells

In recent decades, medical research has been primarily focused on the inherited aspect of cancers, despite the reality that only 5-10% of tumours discovered are derived from genetic causes. Cancer is a broad term, and therefore it is inaccurate to address it as a purely genetic disease. Understanding cancer cells' behaviour is the first step in countering them. Behind the scenes, there is a complicated network of environmental factors, DNA errors, metabolic shifts, and electrostatic alterations that build over time and lead to the illness's development. This latter aspect has been analyzed in previous studies, but how the different electrical changes integrate and affect each other is rarely examined. Every cell in the human body possesses electrical properties that are essential for proper behaviour both within and outside of the cell itself. It is not yet clear whether these changes correlate with cell mutation in cancer cells, or only with their subsequent development. Either way, these aspects merit further investigation, especially with regards to their causes and consequences. Trying to block changes at various levels of occurrence or assisting in their prevention could be the key to stopping cells from becoming cancerous. Therefore, a comprehensive understanding of the current knowledge regarding the electrical landscape of cells is much needed. We review four essential electrical characteristics of cells, providing a deep understanding of the electrostatic changes in cancer cells compared to their normal counterparts. In particular, we provide an overview of intracellular and extracellular pH modifications, differences in ionic concentrations in the cytoplasm, transmembrane potential variations, and changes within mitochondria. New therapies targeting or exploiting the electrical properties of cells are developed and tested every year, such as pH-dependent carriers and tumour-treating fields. A brief section regarding the state-of-the-art of these therapies can be found at the end of this review. Finally, we highlight how these alterations integrate and potentially yield indications of cells' malignancy or metastatic index.

Orientation dependence of R2 relaxation in the newborn brain

In MRI the transverse relaxation rate, R₂ = 1/T₂^, shows dependence on the orientation of ordered tissue relative to the main magnetic field. In previous studies, orientation effects of R₂ relaxation in the mature brain's white matter have been found to be described by a susceptibility-based model of diffusion through local magnetic field inhomogeneities created by the diamagnetic myelin sheaths. Orientation effects in human newborn white matter have not yet been investigated. The newborn brain is known to contain very little myelin and is therefore expected to exhibit a decrease in orientation dependence driven by susceptibility-based effects. We measured R₂ orientation dependence in the white matter of human newborns. R₂ data were acquired with a 3D Gradient and Spin Echo (GRASE) sequence and fiber orientation was mapped with diffusion tensor imaging (DTI). We found orientation dependence in newborn white matter that is not consistent with the susceptibility-based model and is best described by a model of residual dipolar coupling. In the near absence of myelin in the newborn brain, these findings suggest the presence of residual dipolar coupling between rotationally restricted water molecules. This has important implications for quantitative imaging methods such as myelin water imaging, and suggests orientation dependence of R₂ as a potential marker in early brain development.

Computational Investigation of the Ordered Water System Around Microtubules: Implications for Protein Interactions

The existence of an exclusion zone in which particles of a colloidal suspension in water are repelled from hydrophilic surfaces has been experimentally demonstrated in numerous studies, especially in the case of Nafion surfaces. Various explanations have been proposed for the origin of this phenomenon, which is not completely understood yet. In particular, the existence of a fourth phase of water has been proposed by G. Pollack and if this theory is proven correct, its implications on our understanding of the properties of water, especially in biological systems, would be profound and could give rise to new medical therapies. Here, a simple approach based on the linearized Poisson-Boltzmann equation is developed in order to study the repulsive forces mediated by ordered water and involving the following interacting biomolecules: 1) microtubule and a tubulin dimer, 2) two tubulin dimers and 3) a tubulin sheet and a tubulin dimer. The choice of microtubules in this study is motivated because they could be a good candidate for the generation of an exclusion zone in the cell and these models could be a starting point for detailed experimental investigations of this phenomenon.

A Nanometric Probe of the Local Proton Concentration in Microtubule-Based Biophysical Systems

We show a double-functional fluorescence sensing paradigm that can retrieve nanometric pH information on biological structures. We use this method to measure the extent of protonic condensation around microtubules, which are protein polymers that play many roles crucial to cell function. While microtubules are believed to have a profound impact on the local cytoplasmic pH, this has been hard to show experimentally due to the limitations of conventional sensing techniques. We show that subtle changes in the local electrochemical surroundings cause a double-functional sensor to transform its spectrum, thus allowing a direct measurement of the protonic concentration at the microtubule surface. Microtubules concentrate protons by as much as one unit on the pH scale, indicating a charge storage role within the cell via the localized ionic condensation. These results confirm the bioelectrical significance of microtubules and reveal a sensing concept that can deliver localized biochemical information on intracellular structures.

A New Antiport Mechanism Using the Abnormal Adsorption of Ions

Ion pumps are crucial in many biological and nonbiological systems, but their mechanisms have not yet been completely elucidated. Generally, it is understood that ion pumps are implemented by functional proteins. In this investigation, we have proposed a new model for the antiport process, which does not involve a "lever molecule". In this model, abnormal adsorption of the ions occurs in charged nanopores, which can adsorb more transport ions in the lower concentration phase than the higher one. The classical density functional theory (CDFT) confirms the existence of this abnormal adsorption, and the density profiles indicate that it is due to the competition between the transport and background ions. This antiport mechanism thus provides new insights into the function and design of ion pumps.