Nonlinear electrokinetics of the bacterial cell envelope for applications in biomicrofluidics

Abstract

Mathematical modeling is a powerful tool to improve the fundamental understanding in life sciences and to guide experiments. In this thesis, we primarily focus on developing a modeling platform for the electrokinetic ion transport around bacterial cell envelope under the influence of externally applied electric fields. The ability to understand the physics of this ion transport has experimental applications in cell envelope phenotyping of bacteria, cell sorting, intracellular delivery of nucleic acids for genetic engineering, and cell-cycle arrest for controlling antibiotic resistant bacteria. In the first part of my thesis we model the direct current (DC) electric field polarizability of two strains of Streptococcus Salivarius bacteria - fibrillated and unfibrillated, which differ in their cell envelope appendage (soft layer) properties. Using the Poisson-Nernst-Planck equations for ion transport and Stokes equation for fluid flow, we model the electric double layer polarization within and outside the soft layers to calculate the polarizability for these two strains. Firstly, we demonstrate that soft layers have significant influence on the polarizability of bacteria, especially when the soft layer conductivity is much higher than the buffer conductivity (high soft layer Dukhin number). Secondly, we demonstrate a significant difference in the polarizability of these two strains in the high soft layer Dukhin number regime, highlighting the potential use of polarizability based separation (using dielectrophoresis) of two very similar strains of bacteria. We have extended our model to alternating current (AC) fields and demonstrated a transition from cell envelope dominated polarizability at low frequencies (-kHz) to intracellular polarizability at high frequencies (-MHz). The model agrees qualitatively with the experimental literature on AC field polarizability. In the second part of my thesis, we perform finite-element simulations to model the influence of soft layer electrokinetics on bacterial electroporation. Electroporation is a biotechnological tool for intracellular delivery of external molecules by generating pores on the cell membrane using strong but brief pulsed electric fields (~1 ms duration). The pore creation in the bacterial plasma membrane is modeled using Krassowska's mammalian cell electroporation formalism. We used a rubber elasticity based approach to include the effect of peptidoglycan layer elasticity on the pore formation in the plasma membrane. We show that soft layer electrokinetics significantly alters the transmembrane voltage across the plasma membrane and hence the pore characteristics. Our numerical simulations suggest that at low buffer concentrations (less than 0.1 mM) surface conduction significantly lowers the number pores in the plasma membrane, which is a critical parameter for successful genetic engineering of cells. This is consistent with the experimental studies that show that gram-positive bacteria are, in general, have low transformation efficiencies compared to gram-negative species (which have much thinner soft layers of the order of few nanometers). In addition, medium with high osmolarity has been observed to improve gram positive bacteria transformation efficiency. Based on our studies, we hypothesize that in addition to improving cell survivability, keeping the buffer concentration above ~1 mM also reduces concentration polarization around the cell envelope, thereby improving the transformation efficiency. This theoretical study is intended to inform the design of optimized electroporation protocols for bacterial strains and enable the prediction of electroporation conditions for bacteria previously considered to be intractable or difficult-to-transfect with electroporation. In the final part of my thesis, we perform finite element simulations to model the particle trajectories near insulating microfluidic constrictions under AC electric fields. The fluid flow near insulating constrictions at high electric fields can result from two nonlinear electrohydrodynamic effects - induced charge electroosmosis (ICEO) and electrothermal flow. We develop closed form analytical expressions using scaling arguments to get estimates of the fluid flow resulting from these two nonlinear effects, without resorting to computationally intensive numerical simulations. Using these expressions, we demonstrate an interplay between these two effects with ICEO dominated flow at low concentrations (< 0.1 mM) and electrothermal dominated flow at medium to high concentrations (> 1 mM). In the electrothermal flow dominated regime we have validated the model with experimentally measured temperature profiles for two channel geometries - 1:10 constriction ratio (ratio of minimum to maximum channel cross section area) and 1:20 constriction ratio. Contrary to intuition, we find that the temperature-rise in the 1:20 channel is not significantly higher than the 1:10 channel due to temperature-induced increase in the fluid conductivity, which in turn lowers the electric field near the constriction. The insights from this study will enable optimal channel design for insulator dielectrophoresis based particle manipulation.