Coupling kinetic models and advection-diffusion equations to model vascular transport in plants, applied to sucrose accumulation in sugarcane

[摘要] ENGLISH ABSTRACT: The sugarcane stalk, besides being the main structural component of the plant, is also the majorstorage organ for carbohydrates. Sucrose forms the bulk of stored carbohydrates. Previousstudies have modelled the sucrose accumulation pathway in the internodal storage parenchymaof sugarcane using kinetic models cast as systems of ordinary differential equations. Typically,results were analysed with methods such as metabolic control analysis. The present study extendsthose original models within an advection-diffusion-reaction framework, requiring the useof partial differential equations to model sucrose metabolism coupled to phloem translocation.Let N be a stoichiometric matrix, v a vector of reaction rates, s a vector of species concentrationsand r the gradient operator. Consider a coupled network of chemical reactions wherethe species may be advected with velocities, U, or diffuse with coefficients, D, or both. Wepropose the use of the dynamic system, s + r (Us) + r (Drs) = Nv; for a kinetic model where species can exist in different compartments and can be transportedover long distances in a fluid medium, or involved in chemical reactions, or both. Darcy'slaw is used to model fluid flow and allows a simplified, phenomenological approach to beapplied to translocation in the phloem. Similarly, generic reversible Hill equations are used tomodel biochemical reaction rates. These are also phenomenological equations, where all theparameters have operationally defined interpretations.Numerical solutions to this formulation are demonstrated with time-courses of two toymodels. The first model uses a simple 'linear pathway definition to study the impact ofthe system geometry on the solutions. Although this is an elementary model, it is able todemonstrate the up-regulation of photosynthesis in response to a change in sink demand. Thesecond model elaborates on the reaction pathway while keeping the same geometry definition asthe first. This pathway is designed to be an abstracted model of sucrose metabolism. Finally,a realistic model of sucrose translocation, metabolism and accumulation is presented, spanningeight internodes and four compartments. Most of the parameters and species concentrationsused as initial values were obtained from experimental measurements.To analyse the models, a method of sensitivity analysis called the Fourier Amplitude SensitivityTest (FAST) is employed. FAST calculates the contribution of the possible variation ina parameter to the total variation in the output from the model, i.e. the species concentrationsand reaction rates.The model predicted that the most important factors affecting sucrose accumulation are thesynthesis and breakdown of sucrose in futile cycles and the rate of cross-membrane transportof sucrose. The models also showed that sucrose moves down a concentration gradient fromthe leaves to the symplast, where it is transported against a concentration gradient into thevacuole. There was a net gain in carbohydrate accumulation in the realistic model, despite anincrease in futile cycling with internode maturity.The model presented provides a very comprehensive description of sucrose accumulationand is a rigorous, quantitative framework for future modelling and experimental design.

[发布机构] Stellenbosch University