John C. Neu

Vortices in complex scalar fields

Abstract Consider a spatially extended field which evolves in time according to a PDE. The solutions contain particle-like defects whose motions are parts of the full dynamics. We inquire into the formulation of an asymptotic “particle + field” defect dynamics which derives from the full PDE. We carry out this program for two complex scalar field equations in two space dimensions, the nonlinear Schrodinger equation and the nonlinear heat equation. The topological defects are zeros of the complex scalar field with nonzero integer winding numbers, called vortices . Vortices evolving under the nonlinear Schrodinger equation behave like point vortices in ideal fluid. Pairs of vortices evolving under the nonlinear heat equation with like (opposite) winding numbers undergo a repulsive (attractive) interaction.

Model of Creation and Evolution of Stable Electropores for DNA Delivery

Electroporation, in which electric pulses create transient pores in the cell membrane, is becoming an important technique for gene therapy. To enable entry of supercoiled DNA into cells, the pores should have sufficiently large radii (>10 nm), remain open long enough for the DNA chain to enter the cell (milliseconds), and should not cause membrane rupture. This study presents a model that can predict such macropores. The distinctive features of this model are the coupling of individual pores through membrane tension and the electrical force on the pores, which is applicable to pores of any size. The model is used to explore the process of pore creation and evolution and to determine the number and size of pores as a function of the pulse magnitude and duration. Next, our electroporation model is combined with a heuristic model of DNA uptake and used to predict the dependence of DNA uptake on pulsing parameters. Finally, the model is used to examine the mechanism of a two-pulse protocol, which was proposed specifically for gene delivery. The comparison between experimental results and the model suggests that this model is well-suited for the investigation of electroporation-mediated DNA delivery.

Curvature-Mediated Interactions Between Membrane Proteins

Membrane proteins can deform the lipid bilayer in which they are embedded. If the bilayer is treated as an elastic medium, then these deformations will generate elastic interactions between the proteins. The interaction between a single pair is repulsive. However, for three or more proteins, we show that there are nonpairwise forces whose magnitude is similar to the pairwise forces. When there are five or more proteins, we show that the nonpairwise forces permit the existence of stable protein aggregates, despite their pairwise repulsions.

Effective boundary conditions for syncytial tissues

This study derives effective boundary conditions for potentials and currents on the interface between syncytial tissue and a surrounding volume conductor. The derivation is based on an idealized representation of the syncytium as a network of interconnected cells arranged periodically in space. The microscopic model of an interface assumes that the extracellular fluid is in direct contact with the outside volume conductor and that the inside of the cells is separated from the outside by the membrane. From this microscopic model, a homogenization process and boundary layer analysis derive effective boundary conditions applicable to macroscopic volume-averaged potentials. These effective boundary conditions call for the extracellular potential and current density to be continuous with the potential and current density in the volume conductor, and for the intracellular current to vanish. Hence, the long-debated appropriate boundary conditions for the bidomain model are established.<<ETX>>

Response of a single cell to an external electric field

The response of a cell to an external electric field is investigated using dimensional analysis and singular perturbation. The results demonstrate that the response of a cell is a two-stage process consisting of the initial polarization that proceeds with the cellular time constant (< 1 microseconds), and of the actual change of physiological state that proceeds with the membrane time constant (several milliseconds). The second stage is governed by an ordinary differential equation similar to that of a space-clamped membrane patch but formulated in terms of intracellular rather than transmembrane potential. Therefore, it is meaningful to analyze the physiological state and the dynamics of a cell as a whole instead of the physiological states and the dynamics of the underlying membrane patches. This theoretical result is illustrated with an example of an excitation of a cylindrical cell by a transverse electric field.

Myxobacteria gliding motility requires cytoskeleton rotation powered by proton motive force

Myxococcus xanthus is a Gram-negative bacterium that glides over surfaces without the aid of flagella. Two motility systems are used for locomotion: social-motility, powered by the retraction of type IV pili, and adventurous (A)-motility, powered by unknown mechanism(s). We have shown that AgmU, an A-motility protein, is part of a multiprotein complex that spans the inner membrane and periplasm of M. xanthus. In this paper, we present evidence that periplasmic AgmU decorates a looped continuous helix that rotates clockwise as cells glide forward, reversing its rotation when cells reverse polarity. Inhibitor studies showed that the AgmU helix rotation is driven by proton motive force (PMF) and depends on actin-like MreB cytoskeletal filaments. The AgmU motility complex was found to interact with MotAB homologs. Our data are consistent with a mechanochemical model in which PMF-driven motors, similar to bacterial flagella stator complexes, run along an endless looped helical track, driving rotation of the track; deformation of the cell surface by the AgmU-associated proteins creates pressure waves in the slime, pushing cells forward.

COUPLED CHEMICAL OSCILLATORS

We analyze the interaction between a pair of coupled chemical oscillators. Using singular perturbation techniques, we derive an equation that governs the time evolution of the phase shift, which is a measure of how much the oscillators are out of phase. This result is the key to understanding experimental observations on coupled reactor systems. In particular, our model accounts for synchronization, and its bifurcation into rhythm splitting.

ROTATING SPIRAL WAVE SOLUTIONS OF REACTION-DIFFUSION EQUATIONS*

We resolve the question of existence of regular rotating spiral waves as a consequence of only the processes of chemical reaction and molecular diffusion. We prove rigorously the existence of these waves as solutions of reaction-diffusion equations, and we exhibit them by means of numerical computations in several concrete cases. Existence is proved via the Schauder fixed point theorem applied to a class of functions with sufficient structure that, in fact, important constructive properties such as asymptotic representations and frequency of rotation are obtained.

Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators

A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution isbimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and theirnonlinear stability properties ascertained.

The dynamics of a columnar vortex in an imposed strain

Exact solutions of the time‐dependent Euler equations are presented which correspond to uniform columnar vortices with elliptical cross sections undergoing rotation and deformation in a uniform three‐dimensional straining flow. In this work, the recent solutions of Kida [J. Phys. Soc. Jpn. 50, 3517 (1981)] are generalized to include the effect of a strain component along the axis of the vortex which results in its stretching. The time‐dependent solutions should play a very useful role in modeling time‐dependent vortex interactions in more complicated flows such as the mixing layer.