Unravelling glioblastoma heterogeneity by means of single-cell RNA sequencing.

Glioblastoma (GBM) is the most invasive and deadliest brain cancer in adults. Its inherent heterogeneity has been designated as the main cause of treatment failure. Thus, a deeper understanding of the diversity that shapes GBM pathobiology is of utmost importance. Single-cell RNA sequencing (scRNA-seq) technologies have begun to uncover the hidden composition of complex tumor ecosystems. Herein, a semi-systematic search of reference literature databases provided all existing publications using scRNA-seq for the investigation of human GBM. We compared and discussed findings from these works to build a more robust and unified knowledge base. All aspects ranging from inter-patient heterogeneity to intra-tumoral organization, cancer stem cell diversity, clonal mosaicism, and the tumor microenvironment (TME) are comprehensively covered in this report. Tumor composition not only differs across patients but also involves a great extent of heterogeneity within itself. Spatial and cellular heterogeneity can reveal tumor evolution dynamics. In addition, the discovery of distinct cell phenotypes might lead to the development of targeted treatment approaches. In conclusion, scRNA-seq expands our knowledge of GBM heterogeneity and helps to unravel putative therapeutic targets.post-print4967 K

A unified hyperbolic formulation for viscous fluids and elastoplastic solids

We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics, and solid dynamics. The fundamental difference from the classical continuum models, such as the Navier-Stokes for example, is that the finite length scale of the continuum particles is not ignored but kept in the model in order to semi-explicitly describe the essence of any flows, that is the process of continuum particles rearrangements. To allow the continuum particle rearrangements, we admit the deformability of particle which is described by the distortion field. The ability of media to flow is characterized by the strain dissipation time which is a characteristic time necessary for a continuum particle to rearrange with one of its neighboring particles. It is shown that the continuum particle length scale is intimately connected with the dissipation time. The governing equations are represented by a system of first order hyperbolic PDEs with source terms modeling the dissipation due to particle rearrangements. Numerical examples justifying the reliability of the proposed approach are demonstrated.Comment: 6 figure

A unified framework for Schelling's model of segregation

Schelling's model of segregation is one of the first and most influential models in the field of social simulation. There are many variations of the model which have been proposed and simulated over the last forty years, though the present state of the literature on the subject is somewhat fragmented and lacking comprehensive analytical treatments. In this article a unified mathematical framework for Schelling's model and its many variants is developed. This methodology is useful in two regards: firstly, it provides a tool with which to understand the differences observed between models; secondly, phenomena which appear in several model variations may be understood in more depth through analytic studies of simpler versions.Comment: 21 pages, 3 figure

A Dynamical Theory of Electron Transfer: Crossover from Weak to Strong Electronic Coupling

We present a real-time path integral theory for the rate of electron transfer reactions. Using graph theoretic techniques, the dynamics is expressed in a formally exact way as a set of integral equations. With a simple approximation for the self-energy, the rate can then be computed analytically to all orders in the electronic coupling matrix element. We present results for the crossover region between weak (nonadiabatic) and strong (adiabatic) electronic coupling and show that this theory provides a rigorous justification for the salient features of the rate expected within conventional electron transfer theory. Nonetheless, we find distinct characteristics of quantum behavior even in the strongly adiabatic limit where classical rate theory is conventionally thought to be applicable. To our knowledge, this theory is the first systematic dynamical treatment of the full crossover region.Comment: 11 pages, LaTeX, 8 Postscript figures to be published in J. Chem. Phy