Intrinsic ripples in graphene

The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations. The discovery of graphene, the first truly 2D crystal and the recent experimental observation of ripples in freely hanging graphene makes these issues especially important. Beside the academic interest, understanding the mechanisms of stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest for its unusual Dirac spectrum and electronic properties. Here we address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 \AA which is compatible with experimental findings (50-100 \AA) but not with the current understanding of stability of flexible membranes. This unexpected result seems to be due to the multiplicity of chemical bonding in carbon.Comment: 14 pages, 6 figure

Breast cancer prognostic classification in the molecular era: the role of histological grade

Breast cancer is a heterogeneous disease with varied morphological appearances, molecular features, behavior, and response to therapy. Current routine clinical management of breast cancer relies on the availability of robust clinical and pathological prognostic and predictive factors to support clinical and patient decision making in which potentially suitable treatment options are increasingly available. One of the best-established prognostic factors in breast cancer is histological grade, which represents the morphological assessment of tumor biological characteristics and has been shown to be able to generate important information related to the clinical behavior of breast cancers. Genome-wide microarray-based expression profiling studies have unraveled several characteristics of breast cancer biology and have provided further evidence that the biological features captured by histological grade are important in determining tumor behavior. Also, expression profiling studies have generated clinically useful data that have significantly improved our understanding of the biology of breast cancer, and these studies are undergoing evaluation as improved prognostic and predictive tools in clinical practice. Clinical acceptance of these molecular assays will require them to be more than expensive surrogates of established traditional factors such as histological grade. It is essential that they provide additional prognostic or predictive information above and beyond that offered by current parameters. Here, we present an analysis of the validity of histological grade as a prognostic factor and a consensus view on the significance of histological grade and its role in breast cancer classification and staging systems in this era of emerging clinical use of molecular classifiers. © 2010 BioMed Central Lt

Equilibrium, affinity, dissociation constants, IC5O: Facts and fantasies

International audienceThe interaction between ligands and receptors is often described in terms of 50% inhibitory concentrations (IC50). However, IC50 values do not accurately reflect the dissociation constants (Kd), and the domain of application and precision of proposed approximations for Kd estimation are unclear. The effect of affinity and of experimental conditions on the differences between IC50 and Kd has been assessed from exact mass action law calculations and from computer simulations. Competitions between [111In]DTPA‐indium and a few metal‐DTPA complexes for binding to a specific antibody are discussed as a practical example. Exact calculations of competition assays have been implemented in Microsoft Excel and performed for a variety of concentrations of receptor, tracer, and competitor. The results are identical to those of software packages. IC50 is found larger than Kd by less than 20% only when tracer concentration is small compared with Kd and to the receptor concentration and when this receptor concentration is small compared with Kd. Otherwise, Kd and IC50 may be very different and approximations proposed in the literature to obtain Kd values from graphically derived IC50 are not acceptable as soon as the concentrations of tracer or of receptor approach Kd. Under most experimental conditions, IC50 values do not reflect Kd values. Using available software packages to determine and report Kd values would allow for more meaningful comparisons of results obtained under different experimental conditions