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A biochemo-mechano coupled, computational model combining membrane transport and pericellular proteolysis in tissue mechanics.

ABSTRACT: We present a computational model for the interaction of surface- and volume-bound scalar transport and reaction processes with a deformable porous medium. The application in mind is pericellular proteolysis, i.e. the dissolution of the solid phase of the extracellular matrix (ECM) as a response to the activation of certain chemical species at the cell membrane and in the vicinity of the cell. A poroelastic medium model represents the extra cellular scaffold and the interstitial fluid flow, while a surface-bound transport model accounts for the diffusion and reaction of membrane-bound chemical species. By further modelling the volume-bound transport, we consider the advection, diffusion and reaction of sequestered chemical species within the extracellular scaffold. The chemo-mechanical coupling is established by introducing a continuum formulation for the interplay of reaction rates and the mechanical state of the ECM. It is based on known experimental insights and theoretical work on the thermodynamics of porous media and degradation kinetics of collagen fibres on the one hand and a damage-like effect of the fibre dissolution on the mechanical integrity of the ECM on the other hand. The resulting system of partial differential equations is solved via the finite-element method. To the best of our knowledge, it is the first computational model including contemporaneously the coupling between (i) advection-diffusion-reaction processes, (ii) interstitial flow and deformation of a porous medium, and (iii) the chemo-mechanical interaction impelled by the dissolution of the ECM. Our numerical examples show good agreement with experimental data. Furthermore, we outline the capability of the methodology to extend existing numerical approaches towards a more comprehensive model for cellular biochemo-mechanics.

SUBMITTER: Vuong AT

PROVIDER: S-EPMC5378245 | biostudies-literature | 2017 Mar

REPOSITORIES: biostudies-literature

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A biochemo-mechano coupled, computational model combining membrane transport and pericellular proteolysis in tissue mechanics.

Vuong A-T AT Rauch A D AD Wall W A WA

Proceedings. Mathematical, physical, and engineering sciences 20170308 2199

We present a computational model for the interaction of surface- and volume-bound scalar transport and reaction processes with a deformable porous medium. The application in mind is pericellular proteolysis, i.e. the dissolution of the solid phase of the extracellular matrix (ECM) as a response to the activation of certain chemical species at the cell membrane and in the vicinity of the cell. A poroelastic medium model represents the extra cellular scaffold and the interstitial fluid flow, while ...[more]

PMID: 28413347

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Project description:Background and Aims:Transport of carbohydrates and water are essential aspects of plant function. The aim of this study was to develop and test the methods for mechanistic modelling of quasi-stationary coupled phloem/xylem transport in the context of functional-structural plant modelling. Methods:The novelty of this approach is in combining analytical and computational methods. The plant structure is modelled at a metamer level with the internodes represented by conduit elements and the lateral organs represented by sources and sinks. Transport equations are solved analytically for each internode and then the solutions are adjusted and 'sewn' together using an iterative computational procedure taking into account concentration-dependent sinks and sources. The model is implemented in L-studio and uses the aspect-oriented modelling approach for phloem/xylem coupling. Key Results:To our knowledge, this is the first transport model that provides continuous distributions of the system variables in a complex developing structure. The model takes into account non-linear dependence of phloem resistance and osmotic potential on the local carbohydrate concentration. The model solutions show excellent agreement with the existing results of other analytical and numerical models. These comparisons confirm the validity of the approximations made in the model. Combining analytical and computational methods made it possible to take into account continuous sink/source distribution within internodes without much increase in the complexity of the computational procedure, because the necessary changes in the model were mostly in the analytical part. The results emphasize sensitivity of phloem flux and lateral xylem flux to the presence of distributed sinks and sources along the transport system. Conclusions:The presented approach provides a new insight into mechanistic modelling of phloem/xylem transport in growing plants. It will be useful for both fine-scale modelling of carbohydrate dynamics and for creating simpler models at a growth unit level.

Dataset Information

A biochemo-mechano coupled, computational model combining membrane transport and pericellular proteolysis in tissue mechanics.

Publications

A biochemo-mechano coupled, computational model combining membrane transport and pericellular proteolysis in tissue mechanics.

Similar Datasets

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