Random sequential adsorption of lattice animals on a three-dimensional cubic lattice.

The properties of the random sequential adsorption of objects of various shapes on simple three-dimensional (3D) cubic lattice are studied numerically by means of Monte Carlo simulations. Depositing objects are "lattice animals," made of a certain number of nearest-neighbor sites on a lattice. The aim of this work is to investigate the impact of the geometrical properties of the shapes on the jamming density θ_{J} and on the temporal evolution of the coverage fraction θ(t). We analyzed all lattice animals of size n=1, 2, 3, 4, and 5. A significant number of objects of size n⩾6 were also used to confirm our findings. Approach of the coverage θ(t) to the jamming limit θ_{J} is found to be exponential, θ_{J}-θ(t)∼exp(-t/σ), for all lattice animals. It was shown that the relaxation time σ increases with the number of different orientations m that lattice animals can take when placed on a cubic lattice. Orientations of the lattice animal deposited in two randomly chosen places on the lattice are different if one of them cannot be translated into the other. Our simulations performed for large collections of 3D objects confirmed that σ≅m∈{1,3,4,6,8,12,24}. The presented results suggest that there is no correlation between the number of possible orientations m of the object and the corresponding values of the jamming density θ_{J}. It was found that for sufficiently large objects, changing of the shape has considerably more influence on the jamming density than increasing of the object size.

Particle morphology effects in random sequential adsorption.

The properties of the random sequential adsorption of objects of various shapes on a two-dimensional triangular lattice are studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding lattice steps, whereby the size of the objects is gradually increased by wrapping the walks in several different ways. The aim of this work is to investigate the impact of the geometrical properties of the shapes on the jamming density θ_{J} and on the temporal evolution of the coverage fraction θ(t). Our results suggest that the order of symmetry axis of a shape exerts a decisive influence on adsorption kinetics near the jamming limit θ_{J}. The decay of probability for the insertion of a new particle onto a lattice is described in a broad range of the coverage θ by the product between the linear and the stretched exponential function for all examined objects. The corresponding fitting parameters are discussed within the context of the shape descriptors, such as rotational symmetry and the shape factor (parameter of nonsphericity) of the objects. Predictions following from our calculations suggest that the proposed fitting function for the insertion probability is consistent with the exponential approach of the coverage fraction θ(t) to the jamming limit θ_{J}.

Adsorption-desorption processes of polydisperse mixtures on a triangular lattice.

Adsorption-desorption processes of polydisperse mixtures on a triangular lattice are studied by numerical simulations. Mixtures are composed of the shapes of different numbers of segments and rotational symmetries. Numerical simulations are performed to determine the influence of the number of mixture components and the length of the shapes making the mixture on the kinetics of the deposition process. We find that, above the jamming limit, the time evolution of the total coverage of a mixture can be described by the Mittag-Leffler function θ(t)=θ∞-ΔθE[-(t/τ)ß] for all the mixtures we have examined. Our results show that the equilibrium coverage decreases with the number of components making the mixture and also with the desorption probability, via corresponding stretched exponential laws. For the mixtures of equal-sized objects, we propose a simple formula for predicting the value of the steady-state coverage fraction of a mixture from the values of the steady-state coverage fractions of pure component shapes.

Structural characterization of submerged granular packings.

We consider the impact of the effective gravitational acceleration on microstructural properties of granular packings through experimental studies of spherical granular materials saturated within fluids of varying density. We characterize the local organization of spheres in terms of contact connectivity, distribution of the Delaunay free volumes, and the shape factor (parameter of nonsphericity) of the Voronoï polygons. The shape factor gives a clear physical picture of the competition between less and more ordered domains of particles in experimentally obtained packings. As the effective gravity increases, the probability distribution of the shape factor becomes narrower and more localized around the lowest values of the shape factor corresponding to regular hexagon. It is found that curves of the pore distributions are asymmetric with a long tail on the right-hand side, which progressively reduces while the effective gravity gets stronger for lower densities of interstitial fluid. We show that the distribution of local areas (Voronoï cells) broadens with decreasing value of the effective gravity due to the formation of lose structures such as large pores and chainlike structures (arches or bridges). Our results should be particularly helpful in testing the newly developed simulation techniques involving liquid-related forces associated with immersed granular particles.

Optimization of the monolayer growth in adsorption-desorption processes.

Kinetics of the deposition process of dimers in the presence of desorption is studied by Monte Carlo method on a one-dimensional lattice. The aim of this work is to investigate how do various temporal dependencies of the desorption rate hasten or slow down the deposition process. The growth of the coverage θ(t) above the jamming limit to its steady-state value θ(∞) is analyzed when the desorption probability P(des) decreases both stepwise and linearly (continuously) over a certain time domain. We report a numerical evidence that the time needed for a system to reach the given coverage θ can be significantly reduced if P(des) decreases in time. Finally, a self-consistent optimization procedure, when the probability P(des) depends on the current coverage density θ(t), is formulated and tested. The present model reproduces qualitatively the densification kinetics and the memory effects of vibrated granular materials. Our results suggest that the process of vibratory compaction of granular materials can be optimized by using a time dependent intensity of external excitations.

Percolation in random sequential adsorption of extended objects on a triangular lattice.

The percolation aspect of random sequential adsorption of extended objects on a triangular lattice is studied by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding lattice steps on the lattice. Jamming coverage θ{jam}, percolation threshold θ{p}, and their ratio θ{p}/θ{jam} are determined for objects of various shapes and sizes. We find that the percolation threshold θ{p} may decrease or increase with the object size, depending on the local geometry of the objects. We demonstrate that for various objects of the same length, the threshold θ{p} of more compact shapes exceeds the θ{p} of elongated ones. In addition, we study polydisperse mixtures in which the size of line segments making up the mixture gradually increases with the number of components. It is found that the percolation threshold decreases, while the jamming coverage increases, with the number of components in the mixture.

Simulation study of anisotropic random sequential adsorption of extended objects on a triangular lattice.

The properties of the anisotropic random sequential adsorption (RSA) of objects of various shapes on a two-dimensional triangular lattice are studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding lattice steps, whereby the first step determines the orientation of the object. Anisotropy is introduced by positing unequal probabilities for orientation of depositing objects along different directions of the lattice. This probability is equal p or (1-p)/2, depending on whether the randomly chosen orientation is horizontal or not, respectively. Approach of the coverage θ(t) to the jamming limit θ(jam) is found to be exponential θ(jam)-θ(t)is proportional to exp(-t/σ), for all probabilities p. It was shown that the relaxation time σ increases with the degree of anisotropy in the case of elongated and asymmetrical shapes. However, for rounded and symmetrical shapes, values of σ and θ(jam) are not affected by the presence of anisotropy. We finally analyze the properties of the anisotropic RSA of polydisperse mixtures of k-mers. Strong dependencies of the parameter σ and the jamming coverage θ(jam) on the degree of anisotropy are obtained. It is found that anisotropic constraints lead to the increased contribution of the longer k-mers in the total coverage fraction of the mixture.

Relaxation properties in a diffusive model of k-mers with constrained movements on a triangular lattice.

We study the relaxation process in a two-dimensional lattice gas model, based on the concept of geometrical frustration. In this model the particles are k-mers that can both randomly translate and rotate on the planar triangular lattice. In the absence of rotation, the diffusion of hard-core particles in crossed single-file systems is investigated. We monitor, for different densities, several quantities: mean-square displacement, the self-part of the van Hove correlation function, and the self-intermediate scattering function. We observe a considerable slowing of diffusion on a long-time scale when suppressing the rotational motion of k-mers; our system is subdiffusive at intermediate times between the initial transient and the long-time diffusive regime. We show that the self-part of the van Hove correlation function exhibits, as a function of particle displacement, a stretched exponential decay at intermediate times. The self-intermediate scattering function (SISF), displaying slower than exponential relaxation, suggests the existence of heterogeneous dynamics. For each value of density, the SISF is well described by the Kohlrausch-Williams-Watts law; the characteristic timescale τ(q(n)) is found to decrease with the wave vector q(n) according to a simple power law. Furthermore, the slowing of the dynamics with density ρ(0) is consistent with the scaling law 1/τ(q(n);ρ(0))∝(ρ(c)-ρ(0))(Ï°), with the same exponent Ï°=3.34±0.12 for all wave vectors q(n). The density ρ(c) is approximately equal to the closest packing limit, θ(CPL)≲1, for dimers on the two-dimensional triangular lattice. The self-diffusion coefficient D(s) scales with the same power-law exponent and critical density.

Adsorption, desorption, and diffusion of k-mers on a one-dimensional lattice.

Kinetics of the deposition process of k -mers in the presence of desorption or/and diffusional relaxation of particles is studied by Monte Carlo method on a one-dimensional lattice. For reversible deposition of k-mers, we find that after the initial "jamming," a stretched exponential growth of the coverage theta(t) toward the steady-state value theta(eq) occurs, i.e., theta(eq)-theta(t) is proportional to exp[-(t/tau)(beta)]. The characteristic time scale tau is found to decrease with desorption probability P(des) according to a power law, tau is proportional to P(des)(-gamma), with the same exponent gamma=1.22+/-0.04 for all k-mers. For irreversible deposition with diffusional relaxation, the growth of the coverage theta(t) above the jamming limit to the closest packing limit (CPL) theta(CPL) is described by the pattern theta(CPL)-theta(t) is proportional to E(beta)[-(t/tau)(beta)], where E(beta) denotes the Mittag-Leffler function of order beta(0,1) . Similarly to the reversible case, we found that the dependence of the relaxation time tau on the diffusion probability P(dif) is consistent again with a simple power-law, i.e., tau is proportional to P(dif)(-delta). When adsorption, desorption, and diffusion occur simultaneously, coverage always reaches an equilibrium value theta(eq), which depends only on the desorption/adsorption probability ratio. The presence of diffusion only hastens the approach to the equilibrium state, so that the stretched exponential function gives a very accurate description of the deposition kinetics of these processes in the whole range above the jamming limit.

Modelling the role of intrinsic electric fields in microtubules as an additional control mechanism of bi-directional intracellular transport.

Active transport is essential for cellular function, while impaired transport has been linked to diseases such as neuronal degeneration. Much long distance transport in cells uses opposite polarity molecular motors of the kinesin and dynein families to move cargos along microtubules. It is clear that many types of cargo are moved by both sets of motors, and frequently in a reverse direction. The general question of how the direction of transport is regulated is still open. The mechanism of the cell's differential control of diverse cargos within the same cytoplasmic background is still unclear as is the answer to the question how endosomes and mitochondria move to different locations within the same cell. To answer these questions we postulate the existence of a local signaling mechanism used by the cell to specifically control different cargos. In particular, we propose an additional physical mechanism that works through the use of constant and alternating intrinsic (endogenous) electric fields as a means of controlling the speed and direction of microtubule-based transport. A specific model is proposed and analyzed in this paper. The model involves the rotational degrees of freedom of the C-termini of tubulin, their interactions and the coupling between elastic and dielectric degrees of freedom. Viscosity of the solution is also included and the resultant equation of motion is found as a nonlinear elliptic equation with dissipation. A particular analytical solution of this equation is obtained in the form of a kink whose properties are analyzed. It is concluded that this solution can be modulated by the presence of electric fields and hence may correspond to the observed behavior of motor protein transport along microtubules.

Random sequential adsorption of polydisperse mixtures on discrete substrates.

We study random sequential adsorption of polydisperse mixtures of extended objects both on a triangular and on a square lattice. The depositing objects are formed by self-avoiding random walks on two-dimensional lattices. Numerical simulations were performed to determine the influence of the number of mixture components and length of the shapes making the mixture on the kinetics of the deposition process. We find that the late stage deposition kinetics follows an exponential law theta(t) approximately theta_{jam}-Aexp(-tsigma) not only for the whole mixture, but also for the individual components. We discuss in detail how the quantities such as jamming coverage theta_{jam} and the relaxation time sigma depend on the mixture composition. Our results suggest that the order of symmetry axis of the shape may exert a decisive influence on adsorption kinetics of each mixture component.

Reversible random sequential adsorption of mixtures on a triangular lattice.

Reversible random sequential adsorption of binary mixtures of extended objects on a two-dimensional triangular lattice is studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding lattice steps. We concentrate here on the influence of the symmetry properties of the shapes on the kinetics of the adsorption-desorption processes in two-component mixtures. We provide a detailed discussion of the significance of collective events for governing the time coverage behavior of component shapes with different rotational symmetries. We also investigate the role that the mixture composition plays in the deposition process. For the mixtures of equal sized objects, we propose a simple formula for predicting the value of the steady-state coverage fraction of a mixture from the values of the steady-state coverage fractions of pure component shapes.

Simulation study of random sequential adsorption of mixtures on a triangular lattice.

Random sequential adsorption of binary mixtures of extended objects on a two-dimensional triangular lattice is studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding random walks on the lattice. We concentrate here on the influence of the symmetry properties of the shapes on the kinetics of the deposition processes in two-component mixtures. Approach to the jamming limit in the case of mixtures is found to be exponential, of the form: theta(t) approximately theta jam - Deltatheta exp(- t/sigma), and the values of the parameter sigma are determined by the order of symmetry of the less symmetric object in the mixture. Depending on the local geometry of the objects making the mixture, jamming coverage of a mixture can be either greater than both single-component jamming coverages or it can be in between these values. Results of the simulations for various fractional concentrations of the objects in the mixture are also presented.

Rapid screening and sensitive detection of NPM1 (nucleophosmin) exon 12 mutations in acute myeloid leukaemia.

Nucleophosmin mutations of exon 12 (NPM1 mutations) represent the most frequent molecular aberration that can be found in patients with acute myeloid leukaemia (AML) and can be detected in about 35% of AML patients. NPM1 mutations are characterised by four basepair insertions within the region corresponding to the C-terminus of the protein leading to its translocation out of the nucleus. Until now, more than 40 different subsets of mutations have been identified and about 90% of NPM1 mutations are represented by subtype A and B (78% versus 12%, respectively). So far, standard screening of NPM1 mutations using conventional polymerase chain reaction (PCR) followed by capillary electrophoresis is rather time consuming. We established a new method for rapid screening of NPM1 mutations using the fluorescence resonance energy transfer (FRET) principle. Furthermore, based on individual NPM1 mutations type A and B, we designed mutation specific primers to perform a highly sensitive PCR assay that can be applied for the detection of minimal residual disease (MRD). In summary, we demonstrate new methodological approaches for rapid screening of NPM1 mutations as well as for MRD analyses based on the most frequent NPM1 mutations.

ATRA can enhance apoptosis that is induced by Flt3 tyrosine kinase inhibition in Flt3-ITD positive cells.

Among activating Flt3 mutations that have been shown in 25-30% of acute myeloid leukaemia (AML) Flt3-internal tandem duplication (ITD) mutations are predominant. We investigated the influence of all-trans-retinoic acid (ATRA) and granulocyte colony stimulating factor (G-CSF) for their effects on differentiation and apoptosis in human cell lines with different Flt3 variants (THP-1 versus MV4-11 and MOLM13) dependent on the inhibition of Flt3 tyrosine kinase by the bis(lH-2-indolyl)methanone D-65476. While myeloid differentiation was not observed in both Flt3-ITD cell lines (MV4-11 and MOLM13), we demonstrate an enhanced proapoptotic effect of D-65476 in the presence of ATRA that was restricted to the Flt3-ITD expressing cells. The combined treatment with ATRA and D-65476 also led to a pronounced down-regulation of surviv in on mRNA and protein level in Flt3-ITD but not in Flt3 wildtype expressing cells (THP-1). Surprisingly, there was no differential expression of important proteins like Bcl-X(L), Bcl-2 or Bax that might explain enhanced apoptosis. Furthermore, Akt phosphorylation after stimulation with Flt3 ligand dependent on D-65476 was not affected by pretreatment with ATRA. We suggest that regulation of inhibitors of apoptosis might play a crucial role how ATRA can increase the proapoptotic effect of Flt3 inhibitors in myeloid leukemia cells expressing Flt3-ITD. This effect can potentially be exploited for the treatment of Flt3-ITD positive acute myeloid leukemia.

Improved definition of chromosomal breakpoints using high-resolution multicolour banding.

Characterisation of chromosome rearrangements using conventional banding techniques often fails to determine the localisation of breakpoints precisely. In order to improve the definition of chromosomal breakpoints, the high-resolution multicolour banding (MCB) technique was applied to identify human chromosome 5 breakpoints from 40 clinical cases previously assessed by conventional banding techniques. In 30 cases (75%), at least one breakpoint was redefined, indicating that MCB markedly improves chromosomal breakpoint localisation. The MCB pattern is highly reproducible and, in contrast to conventional banding pattern, is consistent in both short and elongated chromosomes. This might be of fundamental interest for the detection of chromosomal abnormalities, especially in tumour cells. Moreover, MCB even allows the detection of abnormalities that remain cryptic in GTG-banding analysis.

Molecular cytogenetic characterization of an acquired minute supernumerary marker chromosome as the sole abnormality in a case clinically diagnosed as atypical Philadelphia-negative chronic myelogenous leukaemia.

A case of chronic myelogenous leukaemia (CML) in a 48-year-old man is reported. To the best of our knowledge, this is the first report of a Philadelphia-negative CML with an acquired small supernumerary marker chromosome (SMC) 11 as the sole abnormality. The derivative chromosome 11 was studied in detail using molecular cytogenetic methods; fluorescence in situ hybridization (FISH) using centromere- and region-specific probes for chromosome 11, microdissection, micro-comparative genomic hybridization (micro-CGH) and the recently developed multicolour banding (MCB) technique. The acquired SMC was determined to be a ring chromosome that can be described as r(11)(:p11.2-->q13.1:q14:).

A new multicolor-FISH approach for the characterization of marker chromosomes: centromere-specific multicolor-FISH (cenM-FISH).

Centromere-specific multi-color FISH (cenM-FISH) is a new multicolor FISH technique that allows the simultaneous characterization of all human centromeres by using labeled centromeric satellite DNA as probes. This approach allows the rapid identification of all human centromeres by their individual pseudo-coloring in one single step and is therefore a powerful tool in molecular cytogenetics. CenM-FISH fills a gap in multicolor karyotyping using WCP probes and distinguishes all centromeric regions apart from the evolutionary highly conserved regions on the chromosomes 13 and 21. The usefulness of the cenM-FISH technique for the characterization of small supernumerary marker chromosomes with no (or nearly no) euchromatin and restricted amounts of available sample material is demonstrated in prenatal, postnatal, and tumor cytogenetic cases. In addition, rarely described markers with the involvement of heterochromatic material inserted into homogeneously staining regions could be identified and characterized by using the cenM-FISH technique.

A long distance-PCR derived FISH probe detects a deletion between p15 and p16 in CML and T-ALL patients.

The tumor suppressor genes p15INK4B and p16INK4A, located in the chromosomal region 9p21, are frequently inactivated by homo- or hemizygous deletions, point mutation or promotor methylation in various types of cancer. No commercial probe is yet available that allows the detection of such deletions by FISH. Long distance (LD)-PCR was successfully used to generate a FISH probe, that covers a sequence stretch of 11.68 kb, located between the tumor suppressor genes p15 and p16. The LD-PCR amplicon was cloned and biotinylated by DOP-PCR (degenerated oligonucleotide primed-PCR) or nick translation. The FISH probe was hybridized on different samples of 16 patients with leukemia (3 T-ALL, 13 CML) and normal controls. Loss of at least one FISH-signal was found in 2/3 (67%) of the T-ALL- and 2/13 (15%) of the CML-cases. The new FISH probe presented here was proven to be advantageous for the detection of deletions in chromosomal region 9p21, especially between p15 and p16.

The human GRAF gene is fused to MLL in a unique t(5;11)(q31;q23) and both alleles are disrupted in three cases of myelodysplastic syndrome/acute myeloid leukemia with a deletion 5q.

We have isolated the human GRAF gene (for GTPase regulator associated with the focal adhesion kinase pp125(FAK)). This gene was fused with MLL in a unique t(5;11)(q31;q23) that occurred in an infant with juvenile myelomonocytic leukemia. GRAF encodes a member of the Rho family of the GTPase-activating protein (GAP) family. On the protein level, it is 90% homologous to the recently described chicken GRAF gene that functions as a GAP of RhoA in vivo and is thus a critical component of the integrin signaling transduction pathway. The particular position of the human GRAF gene at 5q31 and the proposed antiproliferative and tumor suppressor properties of its avian homologue suggest that it also might be pathogenetically relevant for hematologic malignancies with deletions of 5q. To investigate this possibility, we sequenced 4-5 individual cDNA clones from 13 cases in which one allele of GRAF was deleted. We found point mutations within the GAP domain of the second GRAF allele in one patient. In two additional patients we found an insertion of 52 or 74 bp within the GRAF cDNA that generates a reading frame shift followed by a premature stop codon. GRAF maps outside the previously defined commonly deleted 5q31 region. Nevertheless, inactivation of both alleles in at least some cases suggests that deletions and mutations of the GRAF gene may be instrumental in the development and progression of hematopoeitic disorders with a del(5q).