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Mandadapu, Kranthi K.

Publications and source records attributed to Mandadapu, Kranthi K..

7 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

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 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 ∼ 40 m / s , allowing faster ionic reorganization compared to bare diffusion. Together, our paper shows that transmembrane ionic fluxes induce transient long-ranged electric fields in electrolyte solutions, which may play hitherto unappreciated roles in biological signaling. Published by the American Physical Society 2025

Row, Hyeongjoo (ORCID:000000033623512X)↗
DOE OSTI2024

Emergent facilitation and glassy dynamics in supercooled liquids

In supercooled liquids, dynamical facilitation refers to a phenomenon where microscopic motion begets further motion nearby, resulting in spatially heterogeneous dynamics. This is central to the glassy relaxation dynamics of such liquids, which show super-Arrhenius growth of relaxation timescales with decreasing temperature. Despite the importance of dynamical facilitation, there is no theoretical understanding of how facilitation emerges and impacts relaxation dynamics. Here, we present a theory that explains the microscopic origins of dynamical facilitation. We show that dynamics proceeds by localized bond-exchange events, also known as excitations, resulting in the accumulation of elastic stresses with which new excitations can interact. At low temperatures, these elastic interactions dominate and facilitate the creation of new excitations near prior excitations. Using the theory of linear elasticity and Markov processes, we simulate a model, which reproduces multiple aspects of glassy dynamics observed in experiments and molecular simulations, including the stretched exponential decay of relaxation functions, the super-Arrhenius behavior of relaxation timescales as well as their two-dimensional finite-size effects. The model also predicts the subdiffusive behavior of the mean squared displacement (MSD) on short, intermediate timescales. Furthermore, we derive the phonon contributions to diffusion and relaxation, which when combined with the excitation contributions produce the two-step relaxation processes, and the ballistic–subdiffusive–diffusive crossover MSD behaviors commonly found in supercooled liquids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

(2 + δ)-dimensional theory of the electromechanics of lipid membranes: Electrostatics

The coupling of electric fields to the mechanics of lipid membranes gives rise to intriguing electromechanical behavior, as, for example, evidenced by the deformation of lipid vesicles in external electric fields. Electromechanical effects are relevant for many biological processes, such as the propagation of action potentials in axons and the activation of mechanically gated ion channels. Currently, a theoretical framework describing the electromechanical behavior of arbitrarily curved and deforming lipid membranes does not exist. Purely mechanical models commonly treat lipid membranes as two-dimensional surfaces, ignoring their finite thickness. While holding analytical and numerical merit, this approach cannot describe the coupling of lipid membranes to electric fields and is thus unsuitable for electromechanical models. In a sequence of articles, we derive an effective surface theory of the electromechanics of lipid membranes, called the (2 + δ)-dimensional theory, which has the advantages of surface descriptions while accounting for finite thickness effects. The present article proposes a generic dimension reduction procedure relying on low-order spectral expansions. This procedure is applied to the electrostatics of lipid membranes to obtain the (2 + δ)-dimensional theory that captures potential differences across and electric fields within lipid membranes. Finally, this model is tested on different geometries relevant for lipid membranes, showing good agreement with the corresponding three-dimensional electrostatics theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Inherent-state melting and the onset of glassy dynamics in two-dimensional supercooled liquids

Below the onset temperature T o , the equilibrium relaxation time of most glass-forming liquids exhibits glassy dynamics characterized by a super-Arrhenius temperature dependence. In this supercooled regime, the relaxation dynamics also proceeds through localized elastic excitations corresponding to hopping events between inherent states, i.e., potential-energy-minimizing configurations of the liquid. Despite its importance in distinguishing the supercooled regime from the high-temperature regime, the microscopic origin of T o is not yet known. Here, we construct a theory for the onset temperature in two dimensions and find that an inherent-state melting transition, described by the binding–unbinding transition of dipolar elastic excitations, delineates the supercooled regime from the high-temperature regime. The corresponding melting transition temperature is in good agreement with the onset temperature found in various two-dimensional (2D) atomistic models of glass formers and an experimental binary colloidal system confined to a water–air interface. Additionally, we find the predictions for the renormalized elastic moduli to agree with the experimentally observed values for the latter 2D colloidal system. We further discuss the predictions of our theory on the displacement and density correlations at supercooled conditions, which are consistent with observations of the Mermin–Wagner fluctuations in experiments and molecular simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Supervised learning and the finite-temperature string method for computing committor functions and reaction rates

A central object in the computational studies of rare events is the committor function. Though costly to compute, the committor function encodes complete mechanistic information of the processes involving rare events, including reaction rates and transition-state ensembles. Under the framework of transition path theory, Rotskoff et al. [Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, Proceedings of Machine Learning Research (PLMR, 2022), Vol. 145, pp. 757–780] proposes an algorithm where a feedback loop couples a neural network that models the committor function with importance sampling, mainly umbrella sampling, which collects data needed for adaptive training. Here, in this work, we show additional modifications are needed to improve the accuracy of the algorithm. The first modification adds elements of supervised learning, which allows the neural network to improve its prediction by fitting to sample-mean estimates of committor values obtained from short molecular dynamics trajectories. The second modification replaces the committor-based umbrella sampling with the finite-temperature string (FTS) method, which enables homogeneous sampling in regions where transition pathways are located. We test our modifications on low-dimensional systems with non-convex potential energy where reference solutions can be found via analytical or finite element methods, and show how combining supervised learning and the FTS method yields accurate computation of committor functions and reaction rates. We also provide an error analysis for algorithms that use the FTS method, using which reaction rates can be accurately estimated during training with a small number of samples. The methods are then applied to a molecular system in which no reference solution is known, where accurate computations of committor functions and reaction rates can still be obtained.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Absolute vs Convective Instabilities and Front Propagation in Lipid Membrane Tubes

Here we analyze the stability of biological membrane tubes, with and without a base flow of lipids. Membrane dynamics are completely specified by two dimensionless numbers: the well-known Föppl-von Kármán number Γ and the recently introduced Scriven-Love number SL, respectively quantifying the base tension and base flow speed. For unstable tubes, the growth rate of a local perturbation depends only on Γ, whereas SL governs the absolute versus convective nature of the instability. Furthermore, nonlinear simulations of unstable tubes reveal an initially localized disturbance result in propagating fronts, which leave a thin atrophied tube in their wake. Depending on the value of Γ, the thin tube is connected to the unperturbed regions via oscillatory or monotonic shape transitions-reminiscent of recent experimental observations on the retraction and atrophy of axons. We elucidate our findings through a weakly nonlinear analysis, which shows membrane dynamics may be approximated by a model of the class of extended Fisher-Kolmogorov equations. Our study sheds light on the pattern selection mechanism in axonal shapes by recognizing the existence of two Lifshitz points, at which the front dynamics undergo steady-to-oscillatory bifurcations.

59 BASIC BIOLOGICAL SCIENCES↗