BIOSYST-MeBioS

Model-based approach Purpose Improve understanding Optimization Control Macroscale approach (Ho et al., 2006) Geometry: intact fruit Gas transport coupled with respiration kinetics

BIOSYST-MeBioS Gas transport properties of macroscale Assumption Homogeneous material Measurement Biological variability D CO2 > D O2 Anisotropic diffusivity Apparant values D eff

BIOSYST-MeBioS Microscopic overview of tissue Parenchyma tissue structure Grouped cells Random distribution of cells and pores Cell wall Plasma membranes Transport phenomena Geometry required Two phases Gas Liquid Cell membrane Passive transport Active transport Intra-cellular enzymatic reactions Plant Cell wall (Albert et al., 1994)

BIOSYST-MeBioS Objective To verify the applicability of a microscale modelling approach to the gas transport at tissue level in a multiscale framework To quantify the pathways of gas transport in relation to the microstructure of fruit tissue

BIOSYST-MeBioSwww.biw.kuleuven.be Microscale modelling of gas diffusion in fruit tissue Q. Tri Ho, Hibru K. Mebatsion, Fernando Mendoza, Bert E. Verlinden, Pieter Verboven, Stefan Vandewalle and Bart M. Nicolaï IUFoST 13TH WORLD CONGRESS OF FOOD SCIENCE & TECHNOLOGY Food is Life, September 2006 Nantes France

BIOSYST-MeBioS Geometry model Light microscopy images ( Mebatsion et al, 2006) Parenchyma tissues of ‘Conference’ pear Resolution 1pixel~0.735µm Digitization of image Geometry model generation ( Mebatsion et al, 2006) Ellipse tessellation algorithm

BIOSYST-MeBioS Ellipse tesselation Cell Cell wall Intercellular space TEM image of Conference pear Cells

BIOSYST-MeBioS Concept of gas transport Air filled intercellular space O 2,l CO 2,l ADP +P i ATP synthase ATP Work Mitochondrion Cytosol ATP HCO 3 - CO 2,g O 2,g Liquid Pore Gas exchange of fruit At the interface Intra-cell

BIOSYST-MeBioS Model of O 2 transport in tissue Assumption Cell wall was assumed gas phase with effective diffusivity D O2,w Passive gas transport through cell membrane Henry’s law at the inter-phase Model equation (Fick’s second law of diffusion) Pore Cell wall Cell

BIOSYST-MeBioS O 2 model equation in liquid phase O 2 consumption at intra-cell Michaelis-Menten reaction C O2,l can be rewritten in equilibrium gas phase C O2,g

BIOSYST-MeBioS Model of O 2 transport in tissue Model equations Pore Cell wall Cell Flux through cell membrane

BIOSYST-MeBioS Physical parameters LiteratureModel Diffusivity: Pore Cell Cell wall D O2,gas =1.6×10 -5 m 2 /s (1) D O2,l =2.01×10 -9 m 2 /s (1) D O2,W = ? D O2,gas =1.6 ×10 -9 m 2 /s D O2,l =2.01 ×10 -9 m 2 /s D O2,W = 5×10 -9 m 2 /s Cell wall thickness0.76 µm MembraneL =6-10 nm (2) D O2,membrane =2.91×10 -9 m 2 /s (3) Permeability h O2 =3.63 ×10 -2 m/s Henry’s constantH O2 = (mol/m 3 Pa) (1) H O2 = (mol/m 3 Pa) Source : 1 : Lide (1999) 2 : Gunning and Steer (1996) 3 : Uchida et al. (1992)

BIOSYST-MeBioS Numerical solution Meshing elements Solution Finite element method Femlab 3.1 (Comsol AB, Stockholm)

BIOSYST-MeBioS Estimation of D tissue, eff Steady state Boundary condition Side 1: C 1 ; Side 2: C 2 C2C2 C1C1 L tissue Isolated boundary

BIOSYST-MeBioS Simulation result

BIOSYST-MeBioS Sensitivity analysis Relative sensitivity of parameter: ∆P was taken 10% of value P Relative change of D O2, tissue corresponded to a relative change of model parameter ParameterValueJ Do2,P D g (m 2 /s)1.6× ×10 -4 D l (m 2 /s)2.01× ×10 -1 D w (m 2 /s)5× ×10 -1 h_coeff (m/s)3.63× ×10 -5 H O2 (mol/m 3 kPa )1.37× ×10 -1 Thickness of cell wall (µm ) ×10 -1

BIOSYST-MeBioS Estimated O 2 diffusivity of pear tissue D O2, tissue (m 2 /s) Micro scale Ellipse Tesselation 3.2× Measurement (Macro scale) (2.56  0.48)  (Ho et al., 2005) (4.3  1.7)  (Schotsmans et al., 2003) D O2,cell wall =5×10 -9 m 2 /s Cell wall thickness= 0.73 µm (TEM, Mebatsion 2006, unpublished data)

BIOSYST-MeBioS Upscaling to macroscale 20 kPa O 2, 0 kPa CO 2, 5°C

BIOSYST-MeBioS Micro structure and storage disorders Concentration profile along a line through the tissue at y=1×10 -4 m inside cells in pores

BIOSYST-MeBioS 3D X-ray microtomography

BIOSYST-MeBioS Conclusions A model was presented to study gas transport at the microscale O 2 mainly transports in the gas phase of intercellular space and cell wall networks Macroscopic diffusivity was estimated using microscale simulations Important consequences for respiration– related disorders

BIOSYST-MeBioS Thank you