arXiv subjects

Joshua B. Fernandes

Publications and source records attributed to Joshua B. Fernandes.

6 recordsLinked to original sources

arXiv2026

Voltage dynamics of spherical membranes from single ion channel currents

Ion channels and pumps drive ion-selective currents through cell membranes at localized sites, yet a cell's electrical state is routinely summarized by a single transmembrane voltage. Combining theory and numerical simulations, we resolve the spatiotemporal dynamics of charge reorganization driven by a localized current on a spherical membrane vesicle. At early times, the response is insensitive to membrane geometry: as in the case of a flat membrane (arXiv:2407.11947; arXiv:2508.14001), the transmembrane voltage decays in a monopolar fashion, varying inversely with distance from the source, and crosses over to a dipolar tail that scales as the inverse cube of distance. Under sustained current, this monopolar response spreads outward from the source. Because the vesicle is closed, this response cannot persist indefinitely; once the monopolar front traverses the entire vesicle, the subsequent charging dynamics is dominated by a spatially uniform mode corresponding to capacitive charging of the membrane. We further decompose the bulk potentials into an electrostatic image-charge component that generates the bulk electric fields and a spatially uniform capacitive mode that can be represented as an equivalent circuit. We also derive a nonlocal cable equation governing the transmembrane voltage dynamics and show that the uniform mode is its long-time solution. This work provides a first-principles basis for the electrophysiological simplification of an electrotonically compact cell.

cond-mat.soft↗

arXiv2026

Interfacial mass transfer resistance at fluid-fluid interfaces

Complex chemistry in nano- and microscale compartments is often governed by how quickly reagents transit a fluid-fluid interface. Mass transport across interfaces is commonly modeled by assuming local equilibrium, enforcing continuity of chemical potential across the interface. While adequate at large scales, this approximation may break down at the microscale, where interfacial processes can become rate-limiting. Here, we extend linear irreversible thermodynamics to describe nonequilibrium interfacial mass transport. We identify an interface-limited regime, in which transport is governed by interfacial resistance and exhibits exponential relaxation. Combining microfluidic and spectroscopic techniques, we introduce an experimental technique that explores this regime and provides a direct measurement of the interfacial mass transfer coefficient. For a model system consisting of acetonitrile transport across a surfactant-stabilized water-oil interface, we obtain an interfacial transport coefficient ${M \sim 7\,{\rm nm/s}}$. These results establish interfacial mass transfer resistance as a governing mechanism in microscale transport and provide a framework to predict, control and measure mass transport in multiphase systems at microscale.

cond-mat.soft↗

arXiv2025

Electrochemical response of biological membranes to localized currents and external electric fields

Electrochemical phenomena in biology often unfold in confined geometries where micrometer- to millimeter-scale domains coexist with nanometer-scale interfacial diffuse charge layers. We analyze a model lipid membrane-electrolyte system where an ion channel-like current flows across the membrane while parallel electrodes simultaneously apply a step voltage, emulating an extrinsic electric field. Matched asymptotic expansions of the Poisson-Nernst-Planck equations show that, under physiological conditions, the diffuse charge layers rapidly reach a quasi-steady state, and the bulk electrolyte remains electroneutral. As a result, all free charge is confined to the nanometer-scale screening layers at the membrane and electrode interfaces. The bulk electric potential satisfies Laplace's equation, and is dynamically coupled to the interfacial layers through time-dependent boundary conditions. This multiscale coupling partitions the space-time response into distinct regimes. At sufficiently long times, we show that the system can be represented by an equivalent circuit analogous to those used in classical cable theory. We derive closed-form expressions of the transmembrane potential within each regime, and verify them against nonlinear numerical simulations. Our results show how electrode-induced screening and confinement effects influence the electrochemical response over multiple length and time scales in biological systems.

cond-mat.soft↗

arXiv2025

A Hereditary Integral, Transient Network Approach to Modeling Permanent Set and Viscoelastic Response in Polymers

An efficient numerical framework is presented for modeling viscoelasticity and permanent set of polymers. It is based on the hereditary integral form of transient network theory, in which polymer chains belong to distinct networks each with different natural equilibrium states. Chains continually detach from previously formed networks and reattach to new networks in a state of zero stress. The free energy of these networks is given in terms of the deformation gradient relative to the configuration at which the network was born. A decomposition of the kernel for various free energies allows for a recurrence relationship to be established, bypassing the need to integrate over all time history. The technique is established for both highly compressible and nearly incompressible materials through the use of neo-Hookean, Blatz-Ko, Yeoh, and Ogden-Hill material models. Multiple examples are presented showing the ability to handle rate-dependent response and residual strains under complex loading histories.

cs.CE↗

arXiv2025

Capacitive response of biological membranes

We present a minimal model to analyze the capacitive response of a biological membrane subjected to a step voltage via blocking electrodes. Through a perturbative analysis of the underlying electrolyte transport equations, we show that the leading-order relaxation of the transmembrane potential is governed by a capacitive timescale, ${τ_{\rm C} =\dfrac{λ_{\rm D}L}{D}\left(\dfrac{2+Γδ^{\rm M}/L}{4+Γδ^{\rm M}/λ_{\rm D}}\right)}$, where $λ_{\rm D}$ is the Debye screening length, $L$ is the electrolyte width, $Γ$ is the ratio of the dielectric permittivity of the electrolyte to the membrane, $δ^{\rm M}$ is the membrane thickness, and $D$ is the ionic diffusivity. This timescale is considerably shorter than the traditional RC timescale ${λ_{\rm D} L / D}$ for a bare electrolyte due to the membrane's low dielectric permittivity and finite thickness. Beyond the linear regime, however, salt diffusion in the bulk electrolyte drives a secondary, nonlinear relaxation process of the transmembrane potential over a longer timescale ${τ_{\rm L} =L^2/4π^2 D}$. A simple equivalent-circuit model accurately captures the linear behavior, and the perturbation expansion remains applicable across the entire range of observed physiological transmembrane potentials. Together, these findings underscore the importance of the faster capacitive timescale and nonlinear effects on the bulk diffusion timescale in determining transmembrane potential dynamics for a range of biological systems.

cond-mat.soft↗

arXiv2024

Spatiotemporal dynamics of ionic reorganization near biological membrane interfaces

Electrical signals in excitable cells involve spatially localized ionic fluxes through ion channels and pumps on cellular lipid membranes. Common approaches to understand how these localized fluxes spread assume that the membrane and the surrounding electrolyte comprise an equivalent circuit of capacitors and resistors, which ignores the localized nature of transmembrane ion transport, the resulting ionic gradients and electric fields, and their spatiotemporal relaxation. Here, we consider a model of localized ion pumping across a lipid membrane, and use theory and simulation to investigate how the electrochemical signal propagates spatiotemporally in- and out-of-plane along the membrane. The localized pumping generates long-ranged electric fields with three distinct scaling regimes along the membrane: a constant potential near-field region, an intermediate "monopolar" region, and a far-field "dipolar" region. Upon sustained pumping, the monopolar region expands radially in-plane with a steady speed that is enhanced by the dielectric mismatch and the finite thickness of the lipid membrane. For unmyelinated lipid membranes in physiological settings, we find remarkably fast propagation speeds of $\sim\!40 \, \mathrm{m/s}$, allowing faster ionic reorganization compared to bare diffusion. Together, our work shows that transmembrane ionic fluxes induce transient long-ranged electric fields in electrolyte solutions, which may play hitherto unappreciated roles in biological signaling.

cond-mat.soft↗