Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Coupling biochemical models to physics of transport in leaf physiology
Ansgar Bohmann, Andrés Chavarría-Krauser

Last modified: 2014-06-09


Photosynthesis is the core process of plant life and indirectly of virtually any form of life on earth. For all land plants contact with the atmosphere is both essential and detrimental at the same time since it means a trade-off between carbon gain and water loss. Hence material fluxes and biochemistry has to be tightly controlled to fit a particular ecological niche. Most existing models on plant leaf physiology focus in great detail on biochemistry and control of photosynthesis or on stomatal behavior. These models are either steady state models (e.g. the classical Farquhar-von-Caemmerer-Berry model) in form of algebraic equations or dynamical models in the form of ordinary differential equations. This means they are strictly local although spatial effects are known to play an important role.

In particular, phenomena like stomatal patchiness, lateral diffusion, and inverse stomatal behavior are well documented. There have been hypotheses about a putative purpose of such patchy behavior as sign of an emergent and problem solving behavior, but consensus on its mechanical origin is still lacking. Furthermore, environmental parameters (especially irradiance) are usually not uniform over the entire leaf but introduce lateral gradients in relevant physical variables within a leaf and in turn causing material and energy fluxes.

Also the inverse behavior of stomata following abrupt changes in environment parameters is attributed to lateral mechanical and water flow effects in the leaf epidermis. Most computational models however neglect these spatial effects within each leaf.

We introduce building blocks for models that take into account transport processes (diffusion and advection) in the interstitial air space, evaporation, apoplastic water flow and solute diffusion, and tissue mechanics coupled to photosynthesis and stomatal behavior. Water flow is governed by water potential gradients or differences between compartments. Diffusion in the interstitial air space is modeled as multicomponent Maxwell-Stefan diffusion and as Fickian diffusion for solutes in water.

A single model combining all aspects mentioned above would turn out as a system of coupled ordinary and partial differential equations, both numerically and analytically hard to treat. An even bigger problem is the number of parameters which are not directly accessible for measurement. Finally, it is not easy to gain deeper biological insight and understanding from such a complex model. Hence we reduce our considerations to the coupling of only a few of these building blocks and make use of well know physical material properties and other parameters from literature. Therefore we discuss to what extent timescales for different processes can be separated. Depending on the time horizon of interest, models can be reduced.

Finally we also show numerical results for typical interactions of biochemistry and physics of transport. For numerical computations a simple discretization scheme was chosen.

To summarize, we introduce a framework of relevant physical and biochemical processes, compare timescales and scales of spatial interaction and show first results on the interaction of lateral diffusion, advection, and mechanics with photosynthesis and stomatal control in plant leaves.