Oscillatory behavior of neutrophils under opposing chemoattractant gradients supports a winner-take-all mechanism.

Neutrophils constitute the largest class of white blood cells and are the first responders in the innate immune response. They are able to sense and migrate up concentration gradients of chemoattractants in search of primary sites of infection and inflammation through a process known as chemotaxis. These chemoattractants include formylated peptides and various chemokines. While much is known about chemotaxis to individual chemoattractants, far less is known about chemotaxis towards many. Previous studies have shown that in opposing gradients of intermediate chemoattractants (interleukin-8 and leukotriene B4), neutrophils preferentially migrate toward the more distant source. In this work, we investigated neutrophil chemotaxis in opposing gradients of chemoattractants using a microfluidic platform. We found that primary neutrophils exhibit oscillatory motion in opposing gradients of intermediate chemoattractants. To understand this behavior, we constructed a mathematical model of neutrophil chemotaxis. Our results suggest that sensory adaptation alone cannot explain the observed oscillatory motion. Rather, our model suggests that neutrophils employ a winner-take-all mechanism that enables them to transiently lock onto sensed targets and continuously switch between the intermediate attractant sources as they are encountered. These findings uncover a previously unseen behavior of neutrophils in opposing gradients of chemoattractants that will further aid in our understanding of neutrophil chemotaxis and the innate immune response. In addition, we propose a winner-take-all mechanism allows the cells to avoid stagnation near local chemical maxima when migrating through a network of chemoattractant sources.

A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore.

The conventional Poisson-Nernst-Planck equations do not account for the finite size of ions explicitly. This leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials, in particular, near highly charged surfaces. A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion concentrations. Here, we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a nanopore. We describe a novel, robust finite element solver that combines the applications of the Newton's method to the nonlinear Galerkin form of the equations, augmented with stabilization terms to appropriately handle the drift-diffusion processes. To make direct comparison with particle-based simulations possible, our method is specifically designed to produce solutions under periodic boundary conditions and to conserve the number of ions in the solution domain. We test our finite element solver on a set of challenging numerical experiments that include calculations of the ion distribution in a volume confined between two charged plates, calculations of the ionic current though a nanopore subject to an external electric field, and modeling the effect of a DNA molecule on the ion concentration and nanopore current.

A first-order system least-squares finite element method for the Poisson-Boltzmann equation.

The Poisson-Boltzmann equation is an important tool in modeling solvent in biomolecular systems. In this article, we focus on numerical approximations to the electrostatic potential expressed in the regularized linear Poisson-Boltzmann equation. We expose the flux directly through a first-order system form of the equation. Using this formulation, we propose a system that yields a tractable least-squares finite element formulation and establish theory to support this approach. The least-squares finite element approximation naturally provides an a posteriori error estimator and we present numerical evidence in support of the method. The computational results highlight optimality in the case of adaptive mesh refinement for a variety of molecular configurations. In particular, we show promising performance for the Born ion, Fasciculin 1, methanol, and a dipole, which highlights robustness of our approach.