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Workshop on Mathematical Models in Biology

Montag, 20.01.2014

Workshop on Mathematical Models in Biology


University of Graz, Jan 29th, 2014
Room SR 38.21, Harrachgasse 23 (Zentrum für Weiterbildung), 2nd floor

11:15-11:30 Welcome


11:30-12:30 Vincenzo Lombardi


Laboratory of Physiology, Department of Biology, University of Florence, Italy
The working stroke of the myosin II motor in muscle is not tightly coupled to release of orthophosphate from its active site


12:30-13:30 Christian Schmeiser


Institute of Mathematics, University of Vienna, Austria
Simulation and imaging of actin driven pathogen propulsion in cells


13:30-14:30 Coffee break


14:30-15:30 Elfriede Friedmann


Department of Applied Mathematics, University Heidelberg, Germany
About the role of diffusion in cellular signaling analyzed via PDE/ODE systems


15:30-16:00 Angelika Manhart


Institute of Mathematics, University of Vienna, Austria
Model and Simulation of Actin-dependent Cell Movement


16:00-16:30 Klemens Fellner


Institute of Mathematics and Scientific Computing, University of Graz, Austria
On mixed volume/surface reaction-diffusion systems


Organizers:


Contact:


Klemens Fellner, Gudrun Schappacher-Tilp
gudrun.schappacher-tilp@uni-graz.at


Abstracts


The working stroke of the myosin II motor in muscle is not tightly coupled to release of orthophosphate from its active site


Marco Caremani, Luca Melli, Mario Dolfi, Marco Linari and Vincenzo Lombardi
Laboratory of Physiology, Department of Biology, University of Florence, Italy


Skeletal muscle shortens faster against a lower load. This force–velocity relationship is the fundamental determinant of muscle performance in vivo and is due to ATP-driven working strokes of myosin II motors, during their cyclic interactions with the actin filament in each half-sarcomere. Crystallographic studies suggest that the working stroke is associated with the release of phosphate (Pi) and consists of 70° tilting of the light-chain domain that connects the catalytic domain of the myosin motor to the myosin tail and filament. However, the coupling of the working stroke with Pi release is still an unsolved question. Using nanometer–microsecond mechanics on skinned muscle fibres, we impose stepwise drops in force on an otherwise isometric contraction and record the isotonic velocity transient, to measure the mechanical manifestation of the working stroke of myosin motors and the rate of its regeneration in relation to the half-sarcomere load and [Pi].We show that the rate constant of the working stroke is unaffected by [Pi], while the subsequent transition to steady velocity shortening is accelerated. We propose a new chemo-mechanical model that reproduces the transient and steady state responses by assuming that: (i) the release of Pi from the catalytic site of a myosin motor can occur at any stage of the working stroke, and (ii) a myosin motor, in an intermediate state of the working stroke, can slip to the next actin monomer during filament sliding. This model explains the efficient action of muscle molecular motors working as an ensemble in the half-sarcomere.
Supported by Ministero dell’Istruzione dell’Università e della Ricerca (MIUR, PRIN 2011), Ente Cassa di Risparmio di Firenze and Telethon (GGP12282, 2012), Italy.


Simulation and imaging of actin driven pathogen propulsion in cells


Christian Schmeisser
Institute of Mathematics, University of Vienna, Austria


Pathogens need to be motile inside cells to reach their objectives. Some of them hijack a part of the cytoskeleton to build a propulsion system in the form of actin 'comet tails'. In an interdisciplinary cooperation with the Small group (IMBA), electron tomography and mathematical modelling of them intracellular activity of baculovirus have been combined to uncover some of the details of this mechanism.
About the role of diffusion in cellular signaling analyzed via PDE/ODE systems
Elfriede Friedmann
Department of Applied Mathematics, University Heidelberg, Heidelberg, Germany
The relevance of diffusion for the long-time dynamics of signaling pathways is still a matter of debate. We aim at analyzing and quantifying diffusive effects in intra- and inter-cellular signaling.
Therefore, we use an extended definition of diffusion which contains in addition to the classical one also complex chemical and biological processes. Our data-based models result in a system of mixed differential equations coupled through (non-) linear Robin boundary conditions for which no standard methods exist for their analytical or numerical treatment. We develop methods for the theoretical
analysis and numerical simulation of such systems to show properties of the solution which are important for reliable numerical simulations and interpretation of their results. The numerical methods utilize a Galerkin space discretization by finite elements, an iterative operator splitting or fully coupled multilevel algorithm as solver and an adaptive time scheme. The simulation outcome allows us to analyze different biological aspects. Considering firstly the smallest unit of life, a single cell, we will analyze on specific data-based models the influence of cell shape and diffusivity on the regulatory response to the activated pathway, the size of concentration gradients and their effect to gene expression. On a larger scale, in cell systems, we are interested in the long-range diffusion of molecules, in the spatial distribution and range of influence of concentrations, the number of activated cells and the concentration amounts.


Model and Simulation of Actin-dependent Cell Movement


Angelika Manhart
Institute of Mathematics, University of Vienna, Austria


Several types of cells use a sheet-like structure called lamellipodium for movement. The main structural components, actin filaments, are connected via cross-linking proteins. Adhesions allow for a connection with the substrate and the contraction agent myosin helps pulling the cell body forward. Excluded volume effects and charges on the filaments also lead to forces between the filaments. Additionally the cell has to regulate its filament number locally by nucleation (via branching) of new filaments and degradation (via capping and severing) of existing ones.
A continuous model of this structure including the forces created by these molecular players will be presented with an emphasis on the new modelling additions (nucleation and degradation of filaments). This non-linear model is approximated using the finite element method. The simulation can reproduce stationary and moving steady states, describe the transition between the two, mimic chemotaxis and simulate turning cells.


On mixed volume/surface reaction-diffusion systems


Bao Q. Tang, Stefan Rosenberger, Evangeos Latos, Klemens Fellner
Institute of Mathematics and Scientific Computing, University of Graz, Austria


We consider various mathematical models derived from the process of localization of so-called fate-determinant proteins during asymmetric stem cell division. These models feature diffusion in a volume (e.g. the cytoplasm) and on the surface of this volume (e.g. the cell-cortex) together with nonlinear reaction connecting cytoplasm and cortex.

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