Syntaphilin Ubiquitination Regulates Mitochondrial Dynamics and Tumor Cell Movements.

Syntaphilin (SNPH) inhibits the movement of mitochondria in tumor cells, preventing their accumulation at the cortical cytoskeleton and limiting the bioenergetics of cell motility and invasion. Although this may suppress metastasis, the regulation of the SNPH pathway is not well understood. Using a global proteomics screen, we show that SNPH associates with multiple regulators of ubiquitin-dependent responses and is ubiquitinated by the E3 ligase CHIP (or STUB1) on Lys111 and Lys153 in the microtubule-binding domain. SNPH ubiquitination did not result in protein degradation, but instead anchored SNPH on tubulin to inhibit mitochondrial motility and cycles of organelle fusion and fission, that is dynamics. Expression of ubiquitination-defective SNPH mutant Lys111!Arg or Lys153!Arg increased the speed and distance traveled by mitochondria, repositioned mitochondria to the cortical cytoskeleton, and supported heightened tumor chemotaxis, invasion, and metastasis in vivo. Interference with SNPH ubiquitination activated mitochondrial dynamics, resulting in increased recruitment of the fission regulator dynamin-related protein-1 (Drp1) to mitochondria and Drp1-dependent tumor cell motility. These data uncover nondegradative ubiquitination of SNPH as a key regulator of mitochondrial trafficking and tumor cell motility and invasion. In this way, SNPH may function as a unique, ubiquitination-regulated suppressor of metastasis

A level-set method for the evolution of cells and tissue during curvature-controlled growth

Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or cell behavioural in nature. The control of geometry on tissue growth has been evidenced in many in-vivo and in-vitro experiments, including bone remodelling, wound healing, and tissue engineering scaffolds. In this paper, we propose a generalisation of a mathematical model that captures the mechanistic influence of curvature on the joint evolution of cell density and tissue shape during tissue growth. This generalisation allows us to simulate abrupt topological changes such as tissue fragmentation and tissue fusion, as well as three dimensional cases, through a level-set-based method. The level-set method developed introduces another Eulerian field than the level-set function. This additional field represents the surface density of tissue synthesising cells, anticipated at future locations of the interface. Numerical tests performed with this level-set-based method show that numerical conservation of cells is a good indicator of simulation accuracy, particularly when cusps develop in the tissue's interface. We apply this new model to several situations of curvature-controlled tissue evolutions that include fragmentation and fusion.Comment: 15 pages, 10 figures, 3 supplementary figure

Travelling wave analysis of a mathematical model of glioblastoma growth

In this paper we analyse a previously proposed cell-based model of glioblastoma (brain tumour) growth, which is based on the assumption that the cancer cells switch phenotypes between a proliferative and motile state (Gerlee and Nelander, PLoS Comp. Bio., 8(6) 2012). The dynamics of this model can be described by a system of partial differential equations, which exhibits travelling wave solutions whose wave speed depends crucially on the rates of phenotypic switching. We show that under certain conditions on the model parameters, a closed form expression of the wave speed can be obtained, and using singular perturbation methods we also derive an approximate expression of the wave front shape. These new analytical results agree with simulations of the cell-based model, and importantly show that the inverse relationship between wave front steepness and speed observed for the Fisher equation no longer holds when phenotypic switching is considered.Comment: Corrected error in the equation for the Jacobia

A robust method for calculating interface curvature and normal vectors using an extracted local level set

The level-set method is a popular interface tracking method in two-phase flow simulations. An often-cited reason for using it is that the method naturally handles topological changes in the interface, e.g. merging drops, due to the implicit formulation. It is also said that the interface curvature and normal vectors are easily calculated. This last point is not, however, the case in the moments during a topological change, as several authors have already pointed out. Various methods have been employed to circumvent the problem. In this paper, we present a new such method which retains the implicit level-set representation of the surface and handles general interface configurations. It is demonstrated that the method extends easily to 3D. The method is validated on static interface configurations, and then applied to two-phase flow simulations where the method outperforms the standard method and the results agree well with experiments.Comment: 31 pages, 18 figure

Nanopipettes as Monitoring Probes for the Single Living Cell: State of the Art and Future Directions in Molecular Biology.

Examining the behavior of a single cell within its natural environment is valuable for understanding both the biological processes that control the function of cells and how injury or disease lead to pathological change of their function. Single-cell analysis can reveal information regarding the causes of genetic changes, and it can contribute to studies on the molecular basis of cell transformation and proliferation. By contrast, whole tissue biopsies can only yield information on a statistical average of several processes occurring in a population of different cells. Electrowetting within a nanopipette provides a nanobiopsy platform for the extraction of cellular material from single living cells. Additionally, functionalized nanopipette sensing probes can differentiate analytes based on their size, shape or charge density, making the technology uniquely suited to sensing changes in single-cell dynamics. In this review, we highlight the potential of nanopipette technology as a non-destructive analytical tool to monitor single living cells, with particular attention to integration into applications in molecular biology

Numerical Methods for Two-Dimensional Stem Cell Tissue Growth.

Growth of developing and regenerative biological tissues of different cell types is usually driven by stem cells and their local environment. Here, we present a computational framework for continuum tissue growth models consisting of stem cells, cell lineages, and diffusive molecules that regulate proliferation and differentiation through feedback. To deal with the moving boundaries of the models in both open geometries and closed geometries (through polar coordinates) in two dimensions, we transform the dynamic domains and governing equations to fixed domains, followed by solving for the transformation functions to track the interface explicitly. Clustering grid points in local regions for better efficiency and accuracy can be achieved by appropriate choices of the transformation. The equations resulting from the incompressibility of the tissue is approximated by high-order finite difference schemes and is solved using the multigrid algorithms. The numerical tests demonstrate an overall spatiotemporal second-order accuracy of the methods and their capability in capturing large deformations of the tissue boundaries. The methods are applied to two biological systems: stratified epithelia for studying the effects of two different types of stem cell niches and the scaling of a morphogen gradient with the size of the Drosophila imaginal wing disc during growth. Direct simulations of both systems suggest that that the computational framework is robust and accurate, and it can incorporate various biological processes critical to stem cell dynamics and tissue growth

A mathematical model of tumour & blood pHe regulation: The HCO-3/CO2 buffering system

Malignant tumours are characterised by a low, acidic extracellular pH (pHe) which facilitates invasion and metastasis. Previous research has proposed the potential benefits of manipulating systemic pHe, and recent experiments have highlighted the potential for buffer therapy to raise tumour pHe, prevent metastases, and prolong survival in laboratory mice. To examine the physiological regulation of tumour buffering and investigate how perturbations of the buffering system (via metabolic/respiratory disorders or changes in parameters) can alter tumour and blood pHe, we develop a simple compartmentalised ordinary differential equation model of pHe regulation by the View the MathML source buffering system. An approximate analytical solution is constructed and used to carry out a sensitivity analysis, where we identify key parameters that regulate tumour pHe in both humans and mice. From this analysis, we suggest promising alternative and combination therapies, and identify specific patient groups which may show an enhanced response to buffer therapy. In addition, numerical simulations are performed, validating the model against well-known metabolic/respiratory disorders and predicting how these disorders could change tumour pHe

Conceptual design of a nonscaling fixed field alternating gradient accelerator for protons and carbon ions for charged particle therapy

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.The conceptual design for a nonscaling fixed field alternating gradient accelerator suitable for charged particle therapy (the use of protons and other light ions to treat some forms of cancer) is described.EPSR