FociCounter: a freely available PC programme for quantitative and qualitative analysis of gamma-H2AX foci.

Gamma-H2AX foci are sensitive and specific indicator for the induction of DNA double-strand breaks (DSBs) and an immunocytochemical assay with antibodies recognizing gamma-H2AX has become the gold standard for the detection of this type of DNA lesion. Quantification of gamma-H2AX foci can be achieved by various methods such as Western blotting, flow cytometry, visual analysis and computational analysis with a fluorescence microscope. The best sensitivity is achieved by computer analysis. Since no freeware programme for the analysis of gamma-H2AX foci exists for a PC platform, the aim of our study was to develop a simple and user-friendly public-domain software. The algorithm applied in our programme allows determination of the number of foci in a single cell, a focus intensity per cell, as well as a cell intensity. Its graphical user interface is based on a GTK+ library and the whole application can be run under a variety of operating systems, including MS Windows and Linux. The programme called FociCounter is publicly available at http://focicounter.sourceforge.net. Application of the programme was tested by analysing gamma-H2AX foci in CHO and MO59K cells irradiated in vitro with X-rays and validated by comparing the results obtained with the outcome of automated image analysis and flow cytometry.

Finite-size anisotropy in statistically uniform porous media.

Anisotropy of the permeability tensor in statistically uniform porous media of sizes used in typical computer simulations is studied. Although such systems are assumed to be isotropic by default, we show that de facto their anisotropic permeability can give rise to significant changes in transport parameters such as permeability and tortuosity. The main parameter controlling the anisotropy is a/L , being the ratio of the obstacle to system size. Distribution of the angle alpha between the external force and the volumetric fluid stream is found to be approximately normal, and the standard deviation of alpha is found to decay with the system size as (a/L);{d/2} , where d is the space dimensionality. These properties can be used to estimate both anisotropy-related statistical errors in large-scale simulations and the size of the representative elementary volume. For porous media types studied here, the anisotropy effect becomes negligible only if a/L < or = 0.01 . This constraint was apparently violated in many previous computer simulations that need now to be recalculated.

Critical p=1/2 in percolation on semi-infinite strips.

We study site percolation on lattices confined to a semi-infinite strip. For triangular and square lattices we find that the probability that a cluster touches the three sides of such a system at the percolation threshold has a continuous limit of 1/2 and argue that this limit is universal for planar systems. This value is also expected to hold for finite systems for any self-matching lattice. We attribute this result to the asymptotic symmetry of the separation lines between alternating spanning clusters of occupied and unoccupied sites formed on the original and matching lattice, respectively.

Tortuosity-porosity relation in porous media flow.

We study numerically the tortuosity-porosity relation in a microscopic model of a porous medium arranged as a collection of freely overlapping squares. It is demonstrated that the finite-size, slow relaxation and discretization errors, which were ignored in previous studies, may cause significant underestimation of tortuosity. The simple tortuosity calculation method proposed here eliminates the need for using complicated, weighted averages. The numerical results presented here are in good agreement with an empirical relation between tortuosity (T) and porosity (varphi) given by T-1 proportional, variantlnvarphi , that was found by others experimentally in granule packings and sediments. This relation can be also written as T-1 proportional, variantRSvarphi with R and S denoting the hydraulic radius of granules and the specific surface area, respectively. Applicability of these relations appears to be restricted to porous systems of randomly distributed obstacles of equal shape and size.

Jammed systems of oriented needles always percolate on square lattices.

Random sequential adsorption (RSA) is a standard method of modeling adsorption of large molecules at the liquid-solid interface. Several studies have recently conjectured that in the RSA of rectangular needles, or k-mers, on a square lattice, percolation is impossible if the needles are sufficiently long (k of order of several thousand). We refute these claims and present rigorous proof that in any jammed configuration of nonoverlapping, fixed-length, horizontal, or vertical needles on a square lattice, all clusters are percolating clusters.

Reaction-diffusion fronts in systems with concentration-dependent diffusivities.

We examine properties of a reaction front that forms in irreversible reaction-diffusion systems with concentration-dependent diffusivities. We study two different models of such systems and find that in the limit of a vanishingly small diffusivity of the reaction product, the reaction front dynamics enters a separate universality class, with the front width asymptotically tending to a constant value, and the reaction rate at the reaction front center diminishing with time t as t(-1/2). This behavior can be also observed in systems with nonvanishing (but small) diffusivity of the reaction product at intermediate times.

Power-exponential velocity distributions in disordered porous media.

Velocity distribution functions link the micro- and macro-level theories of fluid flow through porous media. Here we study them for the fluid absolute velocity and its longitudinal and lateral components relative to the macroscopic flow direction in a model of a random porous medium. We claim that all distributions follow the power-exponential law controlled by an exponent γ and a shift parameter u_{0} and examine how these parameters depend on the porosity. We find that γ has a universal value 1/2 at the percolation threshold and grows with the porosity, but never exceeds 2.

A cross-platform public domain PC image-analysis program for the comet assay.

The single-cell gel electrophoresis, also known as the comet assay, has gained wide-spread popularity as a simple and reliable method to measure genotoxic and cytotoxic effects of physical and chemical agents as well as kinetics of DNA repair. Cells are generally stained with fluorescent dyes. The analysis of comets--damaged cells which form a typical comet-shaped pattern--is greatly facilitated by the use of a computer image-analysis program. Although several image-analysis programs are available commercially, they are expensive and their source codes are not provided. For Macintosh computers a cost-free public domain macro is available on the Internet. No ready for use, cost-free program exists for the PC platform. We have, therefore, developed such a public domain program under the GNU license for PC computers. The program is called CASP and can be run on a variety of hardware and software platforms. Its practical merit was tested on human lymphocytes exposed to gamma-rays and found to yield reproducible results. The binaries for Windows 95 and Linux, together with the source code can be obtained from: http://www.casp.of.pl.

Maximal force exerted by a molecular motor.

We consider a particle diffusing in a one-dimensional periodic lattice with arbitrary transition rates between nearest-neighbor sites. We show rigorously that the ratio of the drift velocity V to the diffusion coefficient D has the upper bound 2N/d, where N is the number of nodes in an elementary cell and d denotes its length. Applying this result to a model of a molecular motor introduced by Fisher and Kolomeisky [Proc. Natl. Acad. Sci. USA 96, 6597 (1999)] we show that the so called Einstein force, which sets the lower bound for the force exerted by a molecular motor, is bounded from above by 2k(B)TN/d irrespective of the actual values of the jump rates between internal states of the motor.

Asymptotic expansion for reversible A+B<-->C reaction-diffusion process.

We study long-time properties of reversible reaction-diffusion systems of type A+B<-->C by means of the perturbation expansion in powers of 1/t (inverse of time). For the case of equal diffusion coefficients we present exact formulas for the asymptotic forms of reactant concentrations and a complete, recursive expression for an arbitrary term of the expansions. Taking an appropriate limit we show that by studying reversible reactions one can obtain "singular" solutions typical of irreversible reactions.

Anisotropy of flow in stochastically generated porous media.

Models of porous media are often applied to relatively small systems, which leads not only to system-size-dependent results, but also to phenomena that would be absent in larger systems. Here we investigate one such finite-size effect: anisotropy of the permeability tensor. We show that a nonzero angle between the external body force and macroscopic flux vector exists in three-dimensional periodic models of sizes commonly used in computer simulations and propose a criterion, based on the ratio of the system size to the grain size, for this phenomenon to be relevant or negligible. The finite-size anisotropy of the porous matrix induces a pressure gradient perpendicular to the axis of a porous duct and we analyze how this effect scales with the system and grain sizes. We also analyze how the size of the representative elementary volume (REV) for anisotropy compares with the REV for permeability.

Hydraulic tortuosity in arbitrary porous media flow.

Tortuosity (T) is a parameter describing an average elongation of fluid streamlines in a porous medium as compared to free flow. In this paper several methods of calculating this quantity from lengths of individual streamlines are compared and their weak and strong features are discussed. An alternative method is proposed, which enables one to calculate T directly from the fluid velocity field, without the need of determining streamlines, which greatly simplifies determination of tortuosity in complex geometries, including those found in experiments or three-dimensional computer models. Based on numerical results obtained with this method, (a) a relation between the hydraulic tortuosity of an isotropic fibrous medium and the porosity is proposed, (b) a relation between the divergence rate of T with the system size at percolation porosity and the scaling of the most probable traveling length at bond percolation is found, and (c) a range of porosities for which the shape factor is constant is identified.