GeomCell Design of Cell Geometry Július Parulek 1,2, Miloš Šrámek 2,3 and Ivan Zahradník 1 (1) Institute of Molecular Physiology and Genetics, Slovak Academy of Sciences, Slovakia (2) Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia (3) Austrian Academy of Sciences, Austria

2/24 Overview Introduction to GeomCell Previous work on geometrical modeling of muscle cells Representation of mitochondrial shape GeomCell Implementation Conclusions and future work

3/24 GeomCell - Intro An environment for virtual cell modeling based on a precise geometric background possibilities of modern computer graphics and computer hardware to represent a virtual micro- world of cells first building blocks for representation of a static cell geometry models of skeletal muscle tissues idealized models rather than exact reconstruction

4/24 Muscle Cell Organelles (Courtesy of Dr. Novotová)

5/24 Muscle Cell Organelles Laongitudinal axis Transversal axis (Courtesy of Dr. Novotová)

6/24 Input Data - EM images (Courtesy of Dr. Novotová) Volume and surface density (stereology) Sizes (morphometry) Sizes (morphometry) Shape (morphology) Shape (morphology)

7/24 Cell Model Organelles Desired subset of cell organelles: 1) Myofibrils 2) Sarcolemma 3) Sarcoplasmic reticulum 4) Mitochondria 5) T-tubules

8/24 XISL Implicit Objects XISL – Implicit modeling environment XML based modeling language C++ library, tools (conversion, rendering,...) f(x) > 0 f(x) < 0 f(x) = 0

9/24 Cross-sectional Graphs Produce carrier skeletons for all virtual organelles Directly used in modeling of myofibrils Thin and long cylindrical objects cross-sectional graphs (c- graph) in a system of parallel planes

10/24 Cross-sectional Graphs (cont.) Real EM images c-graph 2D implicit shapes Quadratic interpolation of the 2D shapes Minimal distance specification

11/24 Extended Interpolation Spatial warp metamorphosis utilized in sarcoplasmic reticulum (SR) modeling two compartments: terminal cisterns of the SR (A) and Longitudinal SR (B) skeleton: a set of seed (C) points distributed in a system of cross-sectional planes A B C

12/24 Mitochondrial Shape Elliptically shaped and prolonged organelles of irregular smooth forms and variable sizes implicit sweep objects

13/24 Components of Sweep Objects A 2D sweep primitive (template) and a 3D sweep trajectory 2D template 3D trajectory Sweep object

14/24 Template defined as 2D implicit ellipsoid with variable dimensions Trajectory as quadratic B-spline Sweep Components for Mitchondria

15/24 Method Overview Transformation (M S ) maps the 2D template along the curve using so-called reference frames (RF) Rotation of RF around C’(t) fefe

16/24 Method Overview (cont.) Estimate all curve points NP(x) (parameters s i ), for which x lies in the template planes Resultant function

17/24 Problem of Parameter Estimation Analytical solution (a, param t) of a general curve trajectory is rarely possible for instance: cubic spline (C(t) is degree 3) - the polynomial (a) is degree 5 Solution in using quadratic curves analytical solution (a)

18/24 End Caps Union with two implicit semi-ellipsoids at both ends

19/24 Model Generation Fully automatic, guided by Model Description Language (MDL) basic cell dimensions c-graph distribution organelle’s geometric parameters specified in a probabilistic sense Quantification, visualization, …

20/24 GeomCell Implementation Computationally intensive tasks generation of large number of models evaluation of volume and surface areas of organelles model visualization High throughput computing required Utilization of a grid environment retrieval of cell models using metadata (morphological and stereological data, images, MDL spec.,…) eased with a GUI portal

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23/24 Conclusions and Future Work System for cell model generation, quantification, visualization and conversion implemented in Grid environment - GeomCell Organelle’s behavior add physical layer to all objects growth, deformations, cell contraction, … Pathological cells

24/24 Thank You for Your Attention Homepage: Cell modeling project: Grid implementation: /GeomCellInEGEE-MuscleCellModelingOnTheGrid Visualization of a volumetric format of a cell model