arXiv subjects

Karthik Shekhar

Publications and source records attributed to Karthik Shekhar.

7 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

Thickness effects in the electromechanical stability of charged biological membranes

Understanding how electric fields destabilize biological membranes is important for electroporation-based technologies and bioelectronic interfaces. However, theoretical descriptions of this phenomenon remain fragmented. Existing theories treat either electrostatics in membranes of finite thickness or electrohydrodynamic flows at idealized zero-thickness interfaces, leaving unresolved a unified description that simultaneously incorporates finite membrane thickness, surface charge, and bulk electrohydrodynamics. Here, we apply a recently-developed, dimension-reduction framework that captures the coupled electrohydrodynamic and mechanical effects governing height fluctuations of a charged lipid bilayer of thickness $δ$ in an electrolyte characterized by Debye screening length $λ$. We derive voltage- and charge-dependent renormalizations of the effective surface tension and bending rigidity, along with a dispersion relation governing undulatory instabilities. A wide range of prior theoretical results arise as limiting cases of our more general theory when finite-thickness effects are neglected or screening is asymptotically strong. The key new contribution arises from traction moments generated across the finite membrane thickness, which are absent in zero-thickness descriptions. Under physiological screening ($δ/λ\sim 4$), these contributions account for more than $>70\%$ of the total electrostatic correction to both surface tension and bending rigidity. The theory further reveals that surface charges can stabilize the membrane at physiological ionic strengths, increasing the effective tension and shifting electroporation thresholds in a manner that depends on charge asymmetry between the leaflets.

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

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

Odd Viscodiffusive Fluids

We introduce a theory of "odd viscodiffusive fluids," which exhibit three-dimensional odd transport phenomena through the coupling of viscous and diffusive transport. In these fluids, diffusive fluxes may arise from orthogonal velocity gradients and, reciprocally, stresses may arise from concentration gradients. We examine microscopic fluctuations using the recently proposed "flux hypothesis" to derive Green-Kubo and reciprocal relations for the governing transport coefficients. These relations suggest that only parity symmetry, and not time-reversal symmetry, must be broken at the microscopic scale to observe these couplings. Chiral liquids, whether passive or active, are therefore a natural choice as viscodiffusive fluids. We then introduce two analytically tractable model systems, namely a generator and a corresponding reciprocal engine, which illustrate the nature of viscodiffusive cross-coupling in chiral matter and enable the experimental measurement of the novel transport coefficients. Finally, we make the case for chiral bacterial suspensions to be odd viscodiffusive fluids, and use our theory to predict the behaviors exhibited in prior experimental microfluidic studies involving bacterial migration in response to shearing flows.

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↗

arXiv2013

Spin models inferred from patient data faithfully describe HIV fitness landscapes and enable rational vaccine design

Mutational escape from vaccine induced immune responses has thwarted the development of a successful vaccine against AIDS, whose causative agent is HIV, a highly mutable virus. Knowing the virus' fitness as a function of its proteomic sequence can enable rational design of potent vaccines, as this information can focus vaccine induced immune responses to target mutational vulnerabilities of the virus. Spin models have been proposed as a means to infer intrinsic fitness landscapes of HIV proteins from patient-derived viral protein sequences. These sequences are the product of non-equilibrium viral evolution driven by patient-specific immune responses, and are subject to phylogenetic constraints. How can such sequence data allow inference of intrinsic fitness landscapes? We combined computer simulations and variational theory á la Feynman to show that, in most circumstances, spin models inferred from patient-derived viral sequences reflect the correct rank order of the fitness of mutant viral strains. Our findings are relevant for diverse viruses.

physics.bio-ph↗