1,557 research outputs found
Targeting ATM pathway for therapeutic intervention in cancer
The Ataxia Telangiectasia Mutated gene encodes the ATM protein, a key element in the DNA damage response (DDR) signalling pathway responsible for maintaining genomic integrity within the cell. The ATM protein belongs to a family of large protein kinases containing the phosphatidylinositol-3 catalytic domain, including ATM, ATR and PI3K. ATM provides the crucial link between DNA damage, cell cycle progression and cell death by first sensing double stranded DNA breaks and subsequently phosphorylating and activating other downstream proteins functioning in DNA damage repair, cell cycle arrest and apoptotic pathways,. Mammalian cells are constantly challenged by genotoxic agents from a variety of sources and therefore require a robust sensing and repair mechanism to maintain DNA integrity or activate alternative cell fate pathways. This review covers the role of ATM in DDR signalling and describes the interaction of the ATM kinase with other proteins in order to fulfil its various functions. Special emphasis is given to how the growing knowledge of the DDR can help identify drug targets for cancer therapy, thus providing a rationale for exploiting the ATM pathway in anticancer drug development. Moreover, we discuss how a network modelling approach can be used to identify and characterise ATM inhibitors and predict their therapeutic potential
Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. II. Anisotropy in particle shape
We extend the results from the first part of this series of two papers by
examining hyperuniformity in heterogeneous media composed of impenetrable
anisotropic inclusions. Specifically, we consider maximally random jammed
packings of hard ellipses and superdisks and show that these systems both
possess vanishing infinite-wavelength local-volume-fraction fluctuations and
quasi-long-range pair correlations. Our results suggest a strong generalization
of a conjecture by Torquato and Stillinger [Phys. Rev. E. 68, 041113 (2003)],
namely that all strictly jammed saturated packings of hard particles, including
those with size- and shape-distributions, are hyperuniform with signature
quasi-long-range correlations. We show that our arguments concerning the
constrained distribution of the void space in MRJ packings directly extend to
hard ellipse and superdisk packings, thereby providing a direct structural
explanation for the appearance of hyperuniformity and quasi-long-range
correlations in these systems. Additionally, we examine general heterogeneous
media with anisotropic inclusions and show for the first time that one can
decorate a periodic point pattern to obtain a hard-particle system that is not
hyperuniform with respect to local-volume-fraction fluctuations. This apparent
discrepancy can also be rationalized by appealing to the irregular distribution
of the void space arising from the anisotropic shapes of the particles. Our
work suggests the intriguing possibility that the MRJ states of hard particles
share certain universal features independent of the local properties of the
packings, including the packing fraction and average contact number per
particle.Comment: 29 pages, 9 figure
Betti number signatures of homogeneous Poisson point processes
The Betti numbers are fundamental topological quantities that describe the
k-dimensional connectivity of an object: B_0 is the number of connected
components and B_k effectively counts the number of k-dimensional holes.
Although they are appealing natural descriptors of shape, the higher-order
Betti numbers are more difficult to compute than other measures and so have not
previously been studied per se in the context of stochastic geometry or
statistical physics.
As a mathematically tractable model, we consider the expected Betti numbers
per unit volume of Poisson-centred spheres with radius alpha. We present
results from simulations and derive analytic expressions for the low intensity,
small radius limits of Betti numbers in one, two, and three dimensions. The
algorithms and analysis depend on alpha-shapes, a construction from
computational geometry that deserves to be more widely known in the physics
community.Comment: Submitted to PRE. 11 pages, 10 figure
Mark correlations: relating physical properties to spatial distributions
Mark correlations provide a systematic approach to look at objects both
distributed in space and bearing intrinsic information, for instance on
physical properties. The interplay of the objects' properties (marks) with the
spatial clustering is of vivid interest for many applications; are, e.g.,
galaxies with high luminosities more strongly clustered than dim ones? Do
neighbored pores in a sandstone have similar sizes? How does the shape of
impact craters on a planet depend on the geological surface properties? In this
article, we give an introduction into the appropriate mathematical framework to
deal with such questions, i.e. the theory of marked point processes. After
having clarified the notion of segregation effects, we define universal test
quantities applicable to realizations of a marked point processes. We show
their power using concrete data sets in analyzing the luminosity-dependence of
the galaxy clustering, the alignment of dark matter halos in gravitational
-body simulations, the morphology- and diameter-dependence of the Martian
crater distribution and the size correlations of pores in sandstone. In order
to understand our data in more detail, we discuss the Boolean depletion model,
the random field model and the Cox random field model. The first model
describes depletion effects in the distribution of Martian craters and pores in
sandstone, whereas the last one accounts at least qualitatively for the
observed luminosity-dependence of the galaxy clustering.Comment: 35 pages, 12 figures. to be published in Lecture Notes of Physics,
second Wuppertal conference "Spatial statistics and statistical physics
Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres
Hyperuniform many-particle distributions possess a local number variance that
grows more slowly than the volume of an observation window, implying that the
local density is effectively homogeneous beyond a few characteristic length
scales. Previous work on maximally random strictly jammed sphere packings in
three dimensions has shown that these systems are hyperuniform and possess
unusual quasi-long-range pair correlations, resulting in anomalous logarithmic
growth in the number variance. However, recent work on maximally random jammed
sphere packings with a size distribution has suggested that such
quasi-long-range correlations and hyperuniformity are not universal among
jammed hard-particle systems. In this paper we show that such systems are
indeed hyperuniform with signature quasi-long-range correlations by
characterizing the more general local-volume-fraction fluctuations. We argue
that the regularity of the void space induced by the constraints of saturation
and strict jamming overcomes the local inhomogeneity of the disk centers to
induce hyperuniformity in the medium with a linear small-wavenumber nonanalytic
behavior in the spectral density, resulting in quasi-long-range spatial
correlations. A numerical and analytical analysis of the pore-size distribution
for a binary MRJ system in addition to a local characterization of the
n-particle loops governing the void space surrounding the inclusions is
presented in support of our argument. This paper is the first part of a series
of two papers considering the relationships among hyperuniformity, jamming, and
regularity of the void space in hard-particle packings.Comment: 40 pages, 15 figure
Modeling Heterogeneous Materials via Two-Point Correlation Functions: I. Basic Principles
Heterogeneous materials abound in nature and man-made situations. Examples
include porous media, biological materials, and composite materials. Diverse
and interesting properties exhibited by these materials result from their
complex microstructures, which also make it difficult to model the materials.
In this first part of a series of two papers, we collect the known necessary
conditions on the standard two-point correlation function S2(r) and formulate a
new conjecture. In particular, we argue that given a complete two-point
correlation function space, S2(r) of any statistically homogeneous material can
be expressed through a map on a selected set of bases of the function space. We
provide new examples of realizable two-point correlation functions and suggest
a set of analytical basis functions. Moreover, we devise an efficient and
isotropy- preserving construction algorithm, namely, the Lattice-Point
algorithm to generate realizations of materials from their two- point
correlation functions based on the Yeong-Torquato technique. Subsequent
analysis can be performed on the generated images to obtain desired macroscopic
properties. These developments are integrated here into a general scheme that
enables one to model and categorize heterogeneous materials via two-point
correlation functions.Comment: 37 pages, 26 figure
Stochastic reconstruction of sandstones
A simulated annealing algorithm is employed to generate a stochastic model
for a Berea and a Fontainebleau sandstone with prescribed two-point probability
function, lineal path function, and ``pore size'' distribution function,
respectively. We find that the temperature decrease of the annealing has to be
rather quick to yield isotropic and percolating configurations. A comparison of
simple morphological quantities indicates good agreement between the
reconstructions and the original sandstones. Also, the mean survival time of a
random walker in the pore space is reproduced with good accuracy. However, a
more detailed investigation by means of local porosity theory shows that there
may be significant differences of the geometrical connectivity between the
reconstructed and the experimental samples.Comment: 12 pages, 5 figure
Billiards in a general domain with random reflections
We study stochastic billiards on general tables: a particle moves according
to its constant velocity inside some domain until it hits the boundary and bounces randomly inside according to some
reflection law. We assume that the boundary of the domain is locally Lipschitz
and almost everywhere continuously differentiable. The angle of the outgoing
velocity with the inner normal vector has a specified, absolutely continuous
density. We construct the discrete time and the continuous time processes
recording the sequence of hitting points on the boundary and the pair
location/velocity. We mainly focus on the case of bounded domains. Then, we
prove exponential ergodicity of these two Markov processes, we study their
invariant distribution and their normal (Gaussian) fluctuations. Of particular
interest is the case of the cosine reflection law: the stationary distributions
for the two processes are uniform in this case, the discrete time chain is
reversible though the continuous time process is quasi-reversible. Also in this
case, we give a natural construction of a chord "picked at random" in
, and we study the angle of intersection of the process with a
-dimensional manifold contained in .Comment: 50 pages, 10 figures; To appear in: Archive for Rational Mechanics
and Analysis; corrected Theorem 2.8 (induced chords in nonconvex subdomains
Luminosity- and morphology-dependent clustering of galaxies
How does the clustering of galaxies depend on their inner properties like
morphological type and luminosity? We address this question in the mathematical
framework of marked point processes and clarify the notion of luminosity and
morphological segregation. A number of test quantities such as conditional
mark-weighted two-point correlation functions are introduced. These descriptors
allow for a scale-dependent analysis of luminosity and morphology segregation.
Moreover, they break the degeneracy between an inhomogeneous fractal point set
and actual present luminosity segregation. Using the Southern Sky Redshift
Survey~2 (da Costa et al. 1998, SSRS2) we find both luminosity and
morphological segregation at a high level of significance, confirming claims by
previous works using these data (Benoist et al. 1996, Willmer et al. 1998).
Specifically, the average luminosity and the fluctuations in the luminosity of
pairs of galaxies are enhanced out to separations of 15Mpc/h. On scales smaller
than 3Mpc/h the luminosities on galaxy pairs show a tight correlation. A
comparison with the random-field model indicates that galaxy luminosities
depend on the spatial distribution and galaxy-galaxy interactions. Early-type
galaxies are also more strongly correlated, indicating morphological
segregation. The galaxies in the PSCz catalog (Saunders et al. 2000) do not
show significant luminosity segregation. This again illustrates that mainly
early-type galaxies contribute to luminosity segregation. However, based on
several independent investigations we show that the observed luminosity
segregation can not be explained by the morphology-density relation alone.Comment: aastex, emulateapj5, 20 pages, 13 figures, several clarifying
comments added, ApJ accepte
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