Conduction in heterogeneous systems in the low-frequency regime: variational principles and boundary integral equations.

The response of a homogeneous material to the presence of an external low-frequency oscillating electric field can be described by means of an effective complex conductivity. Low frequencies are characterized by negligible magnetic and radiative effects. The properties of heterogeneous systems, composed of multiple homogeneous regions, can be determined from those of the individual components and their geometric arrangement.

Electrical properties of tissues from a microscopic model of confined electrolytes.

. In the presence of oscillatory electric fields, the motion of electrolyte ions in biological tissues is often limited by the confinement created by cell and organelle walls. This confinement induces the organization of the ions into dynamic double layers.

Antigen receptor therapy in bone metastasis via optimal control for different human life stages.

In this work we propose a bone metastasis model using power law growth functions in order to describe the biochemical interactions between bone cells and cancer cells. Experimental studies indicate that bone remodeling cycles are different for human life stages: childhood, young adulthood, and adulthood. In order to include such differences in our study, we estimate the model parameter values for each human life stage via bifurcation analysis.

Pimples reduce and dimples enhance flat dielectric surface image repulsion.

In solid-liquid, or liquid-liquid, interfaces with dielectric contrast, charged particles interact with the induced polarization charge of the interface. These interactions contribute to an effective self-energy of the bulk ions and mediate ion-ion interactions. For flat interfaces, the self-energy and the mediated interactions are neatly constructed by the image charge method.

Strange attractors in discrete slow power-law models of bone remodeling.

Recently, a family of nonlinear mathematical discrete systems to describe biological interactions was considered. Such interactions are modeled by power-law functions where the exponents involve regulation processes. Considering exponent values giving rise to hyperbolic equilibria, we show that the systems exhibit irregular behavior characterized by strange attractors.

A simple model of immune and muscle cell crosstalk during muscle regeneration.

Muscle injury during aging predisposes skeletal muscles to increased damage due to reduced regenerative capacity. Some of the common causes of muscle injury are strains, while other causes are more complex muscle myopathies and other illnesses, and even excessive exercise can lead to muscle damage. We develop a new mathematical model based on ordinary differential equations of muscle regeneration.

Power Dissipation and Surface Charge in EEG: Application to Eigenvalue Structure of Integral Operators.

Objective: To demonstrate the role of surface charge and power dissipation in the analysis of EEG measurements.

Methods: The forward EEG problem is formulated in terms of surface charge density. Using bounds based on power dissipation, the integral equations for forward solutions are shown to satisfy bounds on their eigenvalue structure.

Asymmetric electrolytes near structured dielectric interfaces.

The ion distribution of electrolytes near interfaces with dielectric contrast has important consequences for electrochemical processes and many other applications. To date, most studies of such systems have focused on geometrically simple interfaces, for which dielectric effects are analytically solvable or computationally tractable. However, all real surfaces display nontrivial structure at the nanoscale and have, in particular, a nonuniform local curvature.

Bifurcations and limit cycles in cytosolic yeast calcium.

Calcium homeostasis is a fundamental cellular process in yeast. The regulation of the cytosolic calcium concentration is required for volume preservation and to regulate many vital calcium dependent processes such as mating and response to stress. The homeostatic mechanism is often studied by applying calcium pulses: sharply changing the calcium concentration in the yeast environment and observing the cellular response.

Control of Selective Ion Transfer across Liquid-Liquid Interfaces: A Rectifying Heterojunction Based on Immiscible Electrolytes.

The current rectification displayed by solid-state p-n semiconductor diodes relies on the abundance of electrons and holes near the interface between the p-n junction. In analogy to this electronic device, we propose here the construction of a purely ionic liquid-state electric rectifying heterojunction displaying an excess of monovalent cations and anions near the interface between two immiscible solvents with different dielectric properties. This system does not need any physical membrane or material barrier to show preferential ion transfer but relies on the ionic solvation energy between the two immiscible solvents.

Dynamics of coarsening in multicomponent lipid vesicles with non-uniform mechanical properties.

Multicomponent lipid vesicles are commonly used as a model system for the complex plasma membrane. One phenomenon that is studied using such model systems is phase separation. Vesicles composed of simple lipid mixtures can phase-separate into liquid-ordered and liquid-disordered phases, and since these phases can have different mechanical properties, this separation can lead to changes in the shape of the vesicle.

Generating true minima in constrained variational formulations via modified Lagrange multipliers.

Variational principles are important in the investigation of large classes of physical systems. They can be used both as analytical methods as well as starting points for the formulation of powerful computational techniques such as dynamical optimization methods. Systems with charged objects in dielectric media and systems with magnetically active particles are important examples.

Free-energy functionals of the electrostatic potential for Poisson-Boltzmann theory.

In simulating charged systems, it is often useful to treat some ionic components of the system at the mean-field level and solve the Poisson-Boltzmann (PB) equation to get their respective density profiles. The numerically intensive task of solving the PB equation at each step of the simulation can be bypassed using variational methods that treat the electrostatic potential as a dynamic variable. But such approaches require the access to a true free-energy functional: a functional that not only provides the correct solution of the PB equation upon extremization, but also evaluates to the true free energy of the system at its minimum.

A variational formulation of electrostatics in a medium with spatially varying dielectric permittivity.

In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it is important to take into account the spatial dependence of the permittivity of the medium. However, due to the ensuing theoretical and computational challenges, this inhomogeneous dielectric response of the medium is often ignored or excessively simplified.

Simulation of charged systems in heterogeneous dielectric media via a true energy functional.

For charged systems in heterogeneous dielectric media, a key obstacle for molecular dynamics (MD) simulations is the need to solve the Poisson equation in the media. This obstacle can be bypassed using MD methods that treat the local polarization charge density as a dynamic variable, but such approaches require access to a true free energy functional, one that evaluates to the equilibrium electrostatic energy at its minimum. In this Letter, we derive the needed functional.

Effects of interleaflet coupling on the morphologies of multicomponent lipid bilayer membranes.

We investigate dynamical and stationary compositional and surface morphologies in macroscopically phase-separating multicomponent lipid bilayer membranes using a computational model. We employ a phase-field method for the description of the coexisting phases and treat the two leaflets individually while including interleaflet interactions. The compositional evolution of the two leaflets is coupled to the shape evolution of the membrane via a Helfrich free energy with a composition-dependent spontaneous curvature.

Nematic liquid crystals on spherical surfaces: control of defect configurations by temperature, density, and rod shape.

Recent experiments have shown that defect conformations in spherical nematic liquid crystals can be controlled through variations of temperature, shell thickness, and other environmental parameters. These modifications can be understood as a result of the induced changes in the effective elastic constants of the system. To characterize the relation between defect conformations and elastic anisotropy, we carry out Monte Carlo simulations of a nematic on a spherical surface.

Conformation and mechanical properties of closed diblock fibers.

We analyze the conformations and mechanical properties of closed diblock fibers. In our model, the length fraction of each component and the total fiber length are controlled by tunable chemical potentials. Our formalism can describe fibers in which one block is a bare polymer while the other is an adsorbed protein-filament complex; these blocks maintain different bending rigidities and spontaneous curvatures.

Thermodynamics of ternary electrolytes: Enhanced adsorption of macroions as minority component to liquid interfaces.

We study the equilibrium thermodynamics between two ternary ionic systems in immiscible solvents characterized by different dielectric constants. We consider system geometries wherein the two phases of immiscible solvents occupy, respectively, semi-infinite regions of space separated by neutral and charged planar interfaces. Specifically we analyze the case where the ternary system is composed of a pair of symmetric ions plus a minority charged component of high valence.

Effects of linker length and flexibility on multivalent targeting.

Increasing valence can enhance the ability of molecular targeting constructs to bind specifically to targeted cells for drug delivery. Here, we mathematically model the length and flexibility of a linker used to conjoin two peptide ligands of a divalent targeting construct and investigate the influence both on binding avidity and specificity. Four different models are used to approximate varying degrees of linker flexibility (random coil, rigid rod, jointed rods, and combined rod-random coil) and for each linker a binding enhancement factor (VR) is derived that quantifies the increased rate of each construct's second binding event over the first.

Ion condensation on charged patterned surfaces.

We study ion condensation on a patterned surface with stripes of alternating charge. The competition between adsorbed ion-ion and adsorbed ion-surface interactions leads to the formation of different strongly correlated structures of condensed ions in the low-temperature limit (LTL). We consider two types of arrangements which have lowest energy in the LTL: (1) ions adsorbed onto the stripe center lines and (2) arrays of dipoles at the interfaces between charged domains.

Spontaneous chirality via long-range electrostatic forces.

We consider a model for periodic patterns of charges constrained over a cylindrical surface. In particular we focus on patterns of chiral helices, achiral rings, or vertical lamellae, with the constraint of global electroneutrality. We study the dependence of the patterns' size and pitch angle on the radius of the cylinder and salt concentration.

Charged particles on surfaces: coexistence of dilute phases and periodic structures at interfaces.

We consider a mixture of two immiscible oppositely charged molecules strongly adsorbed to an interface, with a neutral nonselective molecular background. We determine the coexistence between a high density ionic periodic phase and a dilute isotropic ionic phase. We use a strong segregation approach for the periodic phase and determine the one-loop free energy for the dilute phase.

Coupled composition-deformation phase-field method for multicomponent lipid membranes.

We present a method for modeling phase transitions and morphological evolution of binary lipid membranes with approximately planar geometries. The local composition and the shape of the membrane are coupled through composition-dependent spontaneous curvature in a Helfrich free energy. The evolution of the composition field is described by a Cahn-Hilliard-type equation, while shape changes are described by relaxation dynamics.