Dynamics of ionic flows via Poisson-Nernst-Planck systems with local hard-sphere potentials: Competition between cations.

We study a quasi-one-dimensional steady-state Poisson-Nernst-Planck type model for ionic flows through a membrane channel with three ion species, two positively charged with the same valence and one negatively charged. Bikerman's local hard-sphere potential is included in the model to account for ion sizes. The problem is treated as a boundary value problem of a singularly perturbed differential system. Under the framework of a geometric singular perturbation theory, together with specific structures of this concrete model, the existence and uniqueness of solutions to the boundary value problem for small ion sizes is established. Furthermore, treating the ion sizes as small parameters, we derive an approximation of individual fluxes, from which one can further study the qualitative properties of ionic flows and extract concrete information directly related to biological measurements. Of particular interest is the competition between two cations due to the nonlinear interplay between finite ion sizes, diffusion coefficients and boundary conditions, which is closely related to selectivity phenomena of open ion channels with given protein structures. Furthermore, we are able to characterize the distinct effects of the nonlinear interplays between these physical parameters. Numerical simulations are performed to identify some critical potentials which play critical roles in examining properties of ionic flows in our analysis.

Variational approach for nonpolar solvation analysis.

Solvation analysis is one of the most important tasks in chemical and biological modeling. Implicit solvent models are some of the most popular approaches. However, commonly used implicit solvent models rely on unphysical definitions of solvent-solute boundaries. Based on differential geometry, the present work defines the solvent-solute boundary via the variation of the nonpolar solvation free energy. The solvation free energy functional of the system is constructed based on a continuum description of the solvent and the discrete description of the solute, which are dynamically coupled by the solvent-solute boundaries via van der Waals interactions. The first variation of the energy functional gives rise to the governing Laplace-Beltrami equation. The present model predictions of the nonpolar solvation energies are in an excellent agreement with experimental data, which supports the validity of the proposed nonpolar solvation model.

Using decentralized medical education to address the workforce needs of a rural state: a partnership between Maine Medical Center and Tufts University school of medicine.

CONTEXT: In February 2008, a new partnership between Maine Medical Center and Tufts University School of Medicine was formed to create a model medical school program. ISSUE: Major forces for change included: the increasing physician workforce needs of Maine, the need to increase access for medical education for Maine students, the opportunity for educational innovation, the societal imperative to increase the number of primary care physicians, and the desire for clinical and research collaborations. LESSONS LEARNED: The authors describe the process for exploring this partnership, and establishing a separate track and campus for 36 students per year. The key components of the 4 year curriculum, which includes clinical training based in Maine, are described, and 13 lessons learned to date are outlined. The authors hope these lessons provide guidance to other academic medical centers and medical schools wishing to address rural physician workforce challenges, through regional models of medical education, and similar partnerships.

Simulation studies of self-organization of microtubules and molecular motors.

We perform Monte Carlo type simulation studies of self-organization of microtubules interacting with molecular motors. We model microtubules as stiff polar rods of equal length exhibiting anisotropic diffusion in the plane. The molecular motors are implicitly introduced by specifying certain probabilistic collision rules resulting in realignment of the rods. This approximation of the complicated microtubule-motor interaction by a simple instant collision allows us to bypass the "computational bottlenecks" associated with the details of the diffusion and the dynamics of motors and the reorientation of microtubules. Consequently, we are able to perform simulations of large ensembles of microtubules and motors on a very large time scale. This simple model reproduces all important phenomenology observed in in vitro experiments: Formation of vortices for low motor density and raylike asters and bundles for higher motor density.

Developmental model of static allometry in holometabolous insects.

The regulation of static allometry is a fundamental developmental process, yet little is understood of the mechanisms that ensure organs scale correctly across a range of body sizes. Recent studies have revealed the physiological and genetic mechanisms that control nutritional variation in the final body and organ size in holometabolous insects. The implications these mechanisms have for the regulation of static allometry is, however, unknown. Here, we formulate a mathematical description of the nutritional control of body and organ size in Drosophila melanogaster and use it to explore how the developmental regulators of size influence static allometry. The model suggests that the slope of nutritional static allometries, the 'allometric coefficient', is controlled by the relative sensitivity of an organ's growth rate to changes in nutrition, and the relative duration of development when nutrition affects an organ's final size. The model also predicts that, in order to maintain correct scaling, sensitivity to changes in nutrition varies among organs, and within organs through time. We present experimental data that support these predictions. By revealing how specific physiological and genetic regulators of size influence allometry, the model serves to identify developmental processes upon which evolution may act to alter scaling relationships.