Geom Cell Design of Cell Geometry Jlius Parulek

Geom. Cell 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 /24

Overview n n n Introduction to Geom. Cell Previous work on geometrical modeling of muscle cells Representation of mitochondrial shape Geom. Cell Implementation Conclusions and future work 2

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

Muscle Cell Organelles (Courtesy of Dr. Novotová) 4

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

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

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

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

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

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

Extended Interpolation n Spatial warp metamorphosis utilized in sarcoplasmic reticulum (SR) modeling n n 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 11

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

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

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

Method Overview n Transformation (MS) maps the 2 D template along the curve using so-called reference frames (RF) fe n Rotation of RF around C’(t) 15

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

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

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

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

Geom. Cell Implementation n Computationally intensive tasks n n n 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 n n retrieval of cell models using metadata (morphological and stereological data, images, MDL spec. , …) eased with a GUI portal 20

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

Thank You for Your Attention Homepage: www. sccg. sk/~parulek Cell modeling project: www. sccg. sk/~parulek/cell Grid implementation: http: //cvs. ui. sav. sk/twiki/bin/view/EGEE/ /Geom. Cell. In. EGEE-Muscle. Cell. Modeling. On. The. Grid Visualization of a volumetric format of a cell model 24