Abstract—The paper addresses quantitative analysis of three-dimensional (3D) porous media (natural hydrocarbon reservoirs) based on topological invariants—the Minkowski functionals (MF) and presents the solutions of several applied problems obtained using integral geometry methods. The analysis of binarization of a 3D image of sandstone as a dynamic process is demonstrated and the stability of the Minkowski functionals to the choice of the binarization threshold is proved. The approach to solving the classification problem for samples of hydrocarbon reservoirs and finding the analog samples is proposed. Synthetic model samples of porous media and samples of real geological objects are studied.

The technique of numerical analysis of three-dimensional tomographic images of the pore space of soil objects has been used in this paper. It applies methods of integral geometry, topology and morphological analysis. To characterize quantitatively the transformation of the pore space structure, tomographic images of four undisturbed soils were analyzed, i.e., heavy loamy agro-gray soil (Retic Phaeozem), agromineral (Sapric Rheic Mineralic Histosols), and hypnum (brown moss Sapric Rheic Histosols) peat soils in dry and wet conditions. For samples of the subplow horizon in agro-gray soil, a decrease in both Betty numbers was observed on wetting, where the zero number ( b 0 ) stands for the amount of topologically simple closed pores, and the first number ( b 1 ) indicates a decrease in pore connectivity, which varies in a narrower range of pore sizes as compared to b 0 . When a sample of agromineral peat soil is moistened, the Euler–Poincaré characteristic is negative ​in the pore range of 0.1–0.16 mm, which points to the predominating complicated branched structure of the pore space and high pore connectivity. When hypnum moss is saturated, a lot of tunnel pores get narrower (“collapse”), and the connectivity decreases due to the structural specifics of long-stemmed plant residues. The number of pores and connections between them in peat soils is an order of magnitude higher than those in the subplow horizon A of the agro-gray soil. The provided quantitative changes in the considered parameters of tomographic images of the soil pore space confirm the possibility of applying them for estimating the transformation of the pore space in soils.

The mathematical model of group of neurons and astrocytes in the ischemic stroke is discussed. The model includes the description of synaptic signal transmission between the neurons, calcium signaling in astrocytes, ionic currents between the cells and extracellular space and the diffusion through extracellular space. The new modeling approach, based on the creation of appropriate graph, is developed to describe the structure of the system. Using the model, we have analyze the influence of inhibitory synapses on system functioning. We also have shown how the use of medications supporting the activity of inhibitory synapses affects the system behavior in ischemic stroke.

A multiparticle computer model of plastocyanin-cytochrome f complex formation in the thylakoid lumen has been designed, which takes into account the electrostatic interactions of proteins and membrane. The Poisson-Boltzmann formalism was used to determine the electrostatic potentials of the electron carrier proteins and the thylakoid membrane at different ionic strengths. The membrane electrostatic field was shown to influence plastocyanin diffusion and interaction with cytochrome f. The rate constants for plastocyanin-cytochrome f complex formation were calculated as a function of ionic strength and membrane surface charge.

Plastocyanin diffusion in the thylakoid lumen and its binding to cytochrome f (a subunit of the membrane b 6 f complex) were studied with a direct multiparticle simulation model that could also take account of their electrostatic interaction. Experimental data were used to estimate the model parameters for plastocyanin-cytochrome f complexing in solution. The model was then employed to assess the dependence of the association rate constant on the dimensions of the lumen. Highest rates were obtained at a lumen span of 8–10 nm; narrowing of the lumen below 7 nm resulted in drastic deceleration of complexing. This corresponded to the experimentally observed effect of hyperosmotic stress on the interaction between plastocyanin and cytochrome f in thylakoids.

It is important to understand the coordinated performance of cells in tissue. One possible mechanism in this coordination involves intracellular Ca2+ signaling. The topology of intercellular connections in tissue should also play an important role in this process. It is most relevant for plane tissues, in which the interaction between cells is due to gap junctions (epithelium, blood vessels). We demonstrate the importance of the topology of intercellular connectivity by investigating the properties of a model of Ca2+ signaling for a small number of connected cells.

A novel approach based on the approximation of tissue structure by the Voronoi diagram has been elaborated to study cell-to-cell signaling in a tissue mediated by gap junctions. This methodology was applied for the analysis of Ca2+ signaling in the airway epithelium, where adjacent cells were taken to be coupled by gap junctions whose permeability depended on Ca2+ concentration in their cytoplasm. The number of junctional channels connecting a given pair of cells was postulated to be directly proportional to the length of the boundary between them. In a certain range of parameters, a modeled cell generate intracellular Ca2+ oscillations upon the stimulation with the purinergic agonist ATP, and the Ca2+ signal propagated through the tissue due to a Ca2+ rise in adjacent connected cells. The influence of variable sensitivity of cells to ATP on Ca2+ signaling in the tissue was also examined. The model also showed that a mechanical disturbance of a single airway epithelial cell resulted in a prolonged increase in Ca2+ concentration in its cytoplasm, which entailed the spreading of a Ca2+ wave along the tissue.

The diffusion of the protein plastocyanine and complex formation between plastocyanine and cytochrome f (a subunit of a cytochrome b6/f complex) in the chloroplast thylakoid lumen has been studied. A 3D computer simulation model of diffusion and binding of plastocyanine and cytochrome f has been constructed, which considers their electrostatic interaction. Based on the experimental data, the parameters of the model for complex formation between plastocyanine and cytochrome f in solution have been estimated. The dependence of the rate of plastocyanine-cytochrome f reaction on the size of the luminal space has been studied. It was shown that the contraction of the luminal space leads to a decrease in the reaction rate, which is in agreement with the experimental data on the inhibition of the reaction under hyperosmotic stress.

The stochastic nature of an energy and charge deposition process is examined using a model based on discrete loss approximation (DLA). Deposited energy deviations computed using the continuous slowing down approximation (CSDA) and DLA are compared. It is shown that CSDA underestimates fluctuations in deposited energy.

Submitted for the MAR07 Meeting of The American Physical Society Modeling of the SWNT-DNA complexes in the water solution ALEXEY A. TSUKANOV, EUGENE A. GRACHEV, Moscow State University, SLAVA V. ROTKIN, Physics Department and Center for Advanced Materials and Nanotechnology, Lehigh University — It is known that the single-wall nanotubes (SWNTs) may form a hybrid with a single-stranded DNA having a regular helical structure of the DNA wrap around the SWNT cylinder. Such DNA wrapping creates a periodic potential at the NT surface, which results in developing a specific modulation of the NT bands. Numerical self-consistent modeling of these effects requires knowledge of the polarization of the environment. We have shown that the result is very sensitive to what extent the exterior water (and ions in the solution) are polarized to screen the potential of the DNA. Both the NT screening and the response of the environment are important to include self-consistently to obtain quantitative results. We present the Monte-Carlo simulation of the interaction of a NT, a DNA and a solvent and provide heuristic physics interpretation of the results. We show that the NT screening is different from what one expects for a metal or insulator material due to non-local Coulomb correlations. An effective dielectric screening of the water exterior is extracted from the simulations. Alexey A. Tsukanov Moscow State University Date submitted: 20 Nov 2006 Electronic form version 1.4

Buffer performance of mitochondria in intracellular calcium signaling is studied in relation to the amount of cytosolic calcium-binding proteins and calcium ion fluxes across the plasma membrane of the cell.

Further developing the method for direct multiparticle modeling of electron transport in the thylakoid membrane, here we examine the influence of the shape of the reaction volume on the kinetics of the interaction of the mobile carrier with the membrane complex. Applied to cyclic electron transport around photosystem I, with account of the distribution of complexes in the membrane and restricted diffusion of the reactants, the model demonstrates that the biphasic character of the dark reduction of P700+ is quite naturally explained by the spatial heterogeneity of the system.

Problems of simulation of deposited during beam irradiation charge and energy (dose) simulation. Results obtained using Monte-Carlo method in discrete and continuous looses. Analytical approximations for depth-dose and charge-dose for Si, An, Ag, Cu, GaN obtained.