Self-Diffusion of a Polymer Chain in a Melt

Self-diffusion of a polymer chain in a melt is studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. Polymer chains, each of which consists of $N$ segments, are located on an $L \times L \times L$ simple cubic lattice under periodic boundary conditions, where each segment occupies $2 \times 2 \times 2$ unit cells. The results for $N=32, 48, 64, 96, 128, 192, 256, 384$ and 512 at the volume fraction $\phi \simeq 0.5$ are reported, where $L = 128$ for $N \leq 256$ and L=192 for $N \geq 384$. The $N$-dependence of the self-diffusion constant $D$ is examined. Here, $D$ is estimated from the mean square displacements of the center of mass of a single polymer chain at the times larger than the longest relaxation time. From the data for $N = 256$, 384 and 512, the apparent exponent $x_{\rm d}$, which describes the apparent power law dependence of $D$ on $N$ as $D \propto N^{- x_{\rm d}}$, is estimated as $x_{\rm d} \simeq 2.4$. The ratio $D \tau /$ seems to be a constant for $N = 192, 256, 384$ and 512, where $\tau$ and $$ denote the longest relaxation time and the mean square end-to-end distance, respectively.Comment: 4 pages, 3 figures, submitted to J. Phys. Soc. Jp

Models for synthetic biology

Synthetic biological engineering is emerging from biology as a distinct discipline based on quantification. The technologies propelling synthetic biology are not new, nor is the concept of designing novel biological molecules. What is new is the emphasis on system behavior

Determining the Orientation of Protegrin-1 in DLPC Bilayers Using an Implicit Solvent-Membrane Model

Continuum models that describe the effects of solvent and biological membrane molecules on the structure and behavior of antimicrobial peptides, holds a promise to improve our understanding of the mechanisms of antimicrobial action of these peptides. In such methods, a lipid bilayer model membrane is implicitly represented by multiple layers of relatively low dielectric constant embedded in a high dielectric aqueous solvent, while an antimicrobial peptide is accounted for by a dielectric cavity with fixed partial charge at the center of each one of its atoms. In the present work, we investigate the ability of continuum approaches to predict the most probable orientation of the β-hairpin antimicrobial peptide Protegrin-1 (PG-1) in DLPC lipid bilayers by calculating the difference in the transfer free energy from an aqueous environment to a membrane-water environment for multiple orientations. The transfer free energy is computed as a sum of two terms; polar/electrostatic and non-polar. They both include energetic and entropic contributions to the free energy. We numerically solve the Poisson-Boltzmann equation to calculate the electrostatic contribution to the transfer free energy, while the non-polar contribution to the free energy is approximated using a linear solvent accessible surface area relationships. The most probable orientation of PG-1 is that with the lowest relative transfer free energy. Our simulation results indicate that PG-1 assumes an oblique orientation in DLPC lipid bilayers. The predicted most favorable orientation was with a tilt angle of 19°, which is in qualitative agreement with the experimentally observed orientations derived from solid-state NMR data

Optimization in computational systems biology

Optimization aims to make a system or design as effective or functional as possible. Mathematical optimization methods are widely used in engineering, economics and science. This commentary is focused on applications of mathematical optimization in computational systems biology. Examples are given where optimization methods are used for topics ranging from model building and optimal experimental design to metabolic engineering and synthetic biology. Finally, several perspectives for future research are outlined