Reaction-diffusion kinetics on lattice at the microscopic scale

Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME), can simulate for extended spatial and temporal scales but cannot directly account for the microscopic effects in the cell such as volume exclusion and diffusion-influenced reactions. Nonetheless, schemes based on the high-resolution microscopic lattice method (MLM) can directly simulate these effects by representing each finite-sized molecule explicitly as a random walker on fine lattice voxels. The theory and consistency of MLM in simulating diffusion-influenced reactions have not been clarified in detail. Here, we examine MLM in solving diffusion-influenced reactions in 3D space by employing the Spatiocyte simulation scheme. Applying the random walk theory, we construct the general theoretical framework underlying the method and obtain analytical expressions for the total rebinding probability and the effective reaction rate. By matching Collins-Kimball and lattice-based rate constants, we obtained the exact expressions to determine the reaction acceptance probability and voxel size. We found that the size of voxel should be about 2% larger than the molecule. MLM is validated by numerical simulations, showing good agreement with the off-lattice particle-based method, eGFRD. MLM run time is more than an order of magnitude faster than eGFRD when diffusing macromolecules with typical concentrations in the cell. MLM also showed good agreements with eGFRD and mean-field models in case studies of two basic motifs of intracellular signaling, the protein production-degradation process and the dual phosphorylation cycle. Moreover, when a reaction compartment is populated with volume-excluding obstacles, MLM captures the non-classical reaction kinetics caused by anomalous diffusion of reacting molecules

Towards first-principles understanding of the metal-insulator transition in fluid alkali metals

By treating the electron-ion interaction as perturbation in the first-principles Hamiltonian, we have calculated the density response functions of a fluid alkali metal to find an interesting charge instability due to anomalous electronic density fluctuations occurring at some finite wave vector {\bi Q} in a dilute fluid phase above the liquid-gas critical point. Since |{\bi Q}| is smaller than the diameter of the Fermi surface, this instability necessarily impedes the electric conduction, implying its close relevance to the metal-insulator transition in fluid alkali metals.Comment: 11 pages, 5 figure

Combination of gastric atrophy, reflux symptoms and histological subtype indicates two distinct aetiologies of gatric cardia cancer.

<b>INTRODUCTION</b> Atrophic gastritis is a risk factor for non-cardia gastric cancer, and gastro-oesophageal reflux disease (GORD) for oesophageal adenocarcinoma. The role of atrophic gastritis and GORD in the aetiology of adenocarcinoma of the cardia remains unclear. We have investigated the association between adenocarcinoma of the different regions of the upper gastrointestinal tract and atrophic gastritis and GORD symptoms. <b>METHODS</b> 138 patients with upper GI adenocarcinoma and age and sex matched controls were studied. Serum pepsinogen I/II was used as a marker of atrophic gastritis and categorised to five quintiles. History of GORD symptoms, smoking and H.pylori infection was incorporated in logistic regression analysis. Lauren classification of gastric cancer was used to subtype gastric and oesophageal adenocarcinoma. <b>RESULTS</b> Non-cardia cancer was associated with atrophic gastritis but not with GORD symptoms; 55% of these cancers were intestinal subtype. Oesophageal adenocarcinoma was associated with GORD symptoms, but not with atrophic gastritis; 84% were intestinal subtype. Cardia cancer was positively associated with both severe gastric atrophy [OR, 95% CI: 3.92 (1.77 – 8.67)] and with frequent GORD symptoms [OR, 95% CI: 10.08 (2.29 – 44.36)] though the latter was only apparent in the nonatrophic subgroup and in the intestinal subtype. The association of cardia cancer with atrophy was stronger for the diffuse versus intestinal subtype and this was the converse of the association observed with non-cardia cancer. <b>CONCLUSION</b> These findings indicate two distinct aetiologies of cardia cancer, one arising from severe atrophic gastritis and being of intestinal or diffuse subtype similar to non-cardia cancer, and one related to GORD and intestinal in subtype, similar to oesophageal adenocarcinoma. Gastric atrophy, GORD symptoms and histological subtype may distinguish between gastric versus oesophageal origin of cardia cancer

Calcospherites in Rabbit Incisor Predentin

Calcospherites from the lower incisor dentin of rabbits were investigated by scanning and transmission electron microscopy (TEM), energy dispersive spectroscopy (EDS) and electron diffraction analyses. In the labial predentin, globular calcospherites of 8-31 μm were present at the root apex, decreasing in size toward the incisal region. The calcospherites at the intermediate region were of mulberry- as well as of spindle-shape of 1.5-4 μm diameter. The incisal pulp horn contained micro-calcospherites of 0.3-0.6 μmin diameter. In the lingual predentin, small granular calcospherites of 1. 8-3 μm were present at the root apex, increasing in size toward the intermediate region. Ultrathin sections of globular calcospherites showed bundles of collagen fibrils at the root apex of the labial predentin. The diameters of individual bundles ranged from 1.2-3.4 μm. The width of the fibrils in the bundles was approximately 120-170 nm. Bundles of collagen fibrils were not found in the lingual predentin. Crystals of calcospherites were identified as apatite by electron diffraction. Those at the intermediate region showed preferred orientation of the c-axis. TEM-EDS analyses indicated that Ca and P were the major elements, with small amounts of Mg. The Mg/Ca molar ratios decreased from the root apex to the incisal pulp horn. Ca peak intensities increased from the root apex to the incisal region

Reflection and Refraction of Bose-condensate Excitations

We investigate the transmission and reflection of Bose-condensate excitations in the low energy limit across a potential barrier separating two condensates with different densities. The Bogoliubov excitation in the low energy limit has the incident angle where the perfect transmission occurs. This condition corresponds to the Brewster's law for the electromagnetic wave. The total internal reflection of the Bogoliubov excitation is found to occur at a large incident angle in the low energy limit. The anomalous tunneling named by Kagan et al. [Yu. Kagan et al., Phys. Rev. Lett., 90, 130402 (2003)] can be understood in terms of the impedance matching. In the case of the normal incidence, comparison with the results in Tomonaga-Luttinger liquids is made.Comment: 23 pages, 5 figure

Continuous deformations of the Grover walk preserving localization

The three-state Grover walk on a line exhibits the localization effect characterized by a non-vanishing probability of the particle to stay at the origin. We present two continuous deformations of the Grover walk which preserve its localization nature. The resulting quantum walks differ in the rate at which they spread through the lattice. The velocities of the left and right-traveling probability peaks are given by the maximum of the group velocity. We find the explicit form of peak velocities in dependence on the coin parameter. Our results show that localization of the quantum walk is not a singular property of an isolated coin operator but can be found for entire families of coins

Absence of Anomalous Tunneling of Bogoliubov Excitations for Arbitrary Potential Barrier under the Critical Condensate Current

We derive the exact solution of low energy limit of Bogoliubov equations for excitations of Bose-Einstein condensate in the presence of arbitrary potential barrier and maximum current of condensate. Using this solution, we give the explicit expression for the transmission coefficient against the potential barrier, which shows partial transmission in the low energy limit. The wavefunctions of excitations in the low energy limit do not coincide with that of the condensate. The absence of the perfect transmission in the critical current state originates from local enhancement of density fluctuations around the potential barrier.Comment: 4 pages, 1 figur