No abstract

Let P( ) = F 2 [ 1 , . . . , ] be the polynomial algebra in variables , of degree one, over the field F 2 of two elements. The mod-2 Steenrod algebra A acts on P( ) according to well known rules. A major problem in algebraic topology is of determining A + P( ), the image of the action of the positively graded part of A. We are interested in the related problem of determining a basis for the quotient vector space Q( ) = P( )/A + P( ). Q( ) has been explicitly calculated for = 1, 2, 3, 4 but problems remain for ≥ 5.Both P( ) = ⨁ ≥0 P ( ) and Q( ) are graded, where P ( ) denotes the set of homogeneous polynomials of degree . In this paper,−1 ∈ P ( −1) is an admissible monomial (i.e., meets a criterion to be in a certain basis for Q( −1)), then, for any pair of integers ( , ), 1 ≤ ≤ , and ≥ 0, the monomial ℎ ( ) = +1 ⋅ ⋅ ⋅ −1 ∈ P +(2 −1) ( ) is admissible. As an application we consider a few cases when = 5.

The sugarcane stalk, besides being the main structural component of the plant, is also the major storage organ for carbohydrates. Previous studies have modelled the sucrose accumulation pathway in the internodal storage parenchyma of sugarcane using kinetic models cast as systems of ordinary differential equations. To address the shortcomings of these models, which did not include subcellular compartmentation or spatial information, the present study extends the original models within an advection-diffusion-reaction framework, requiring the use of partial differential equations to model sucrose metabolism coupled to phloem translocation.We propose a kinetic model of a coupled reaction network where species can be involved in chemical reactions and/or be transported over long distances in a fluid medium by advection or diffusion. Darcy’s law is used to model fluid flow and allows a simplified, phenomenological approach to be applied to translocation in the phloem. Similarly, generic reversible Hill equations are used to model biochemical reaction rates. Numerical solutions to this formulation are demonstrated with time-course analysis of a simplified model of sucrose accumulation. The model shows sucrose accumulation in the vacuoles of stalk parenchyma cells, and is moreover able to demonstrate the up-regulation of photosynthesis in response to a change in sink demand. The model presented is able to capture the spatio-temporal evolution of the system from a set of initial conditions by combining phloem flow, diffusion, transport of metabolites between compartments and biochemical enzyme-catalysed reactions in a rigorous, quantitative framework that can form the basis for future modelling and experimental design.

The accompanying paper (Uys et al., in silico Plants, XXXX) presented a core model of sucrose accumulation within the advection-diffusion-reaction framework, which is able to capture the spatio-temporal evolution of the system from a set of initial conditions. This paper presents a sensitivity analysis of this model. Because this is a non-steady-state model based on partial differential equations, we performed the sensitivity analysis using two approaches from engineering. The Morris method is based on a one-at-a-time design, perturbing parameters individually and calculating the influence on model output in terms of elementary effects. FAST is a global sensitivity analysis method, where all parameters are perturbed simultaneously, oscillating at different frequencies, enabling the calculation of the contribution of each parameter through Fourier analysis. Overall, both methods gave similar results. Perturbations in reactions tended to have a large influence on their own rate, as well as on directly connected metabolites. Sensitivities varied both with the time of the simulation and the position along the sugarcane stalk. Our results suggest that vacuolar sucrose concentrations are most sensitive to vacuolar invertase in the centre of the stalk, but that phloem unloading and vacuolar sucrose uptake also contribute, especially towards the stalk edges. Sucrose in the phloem was most sensitive to phloem loading at the nodes, but most sensitive to phloem unloading in the middle of the internodes. Sink concentrations of sucrose in the symplast were most sensitive to phloem unloading in the middle of the internodes, but at the nodes cytosolic invertase had the greatest effect.

This chapter deals with the subject of systems biology, specifically the kinetic modeling of metabolic pathways, as a tool for better understanding the control and regulation of a cellular system and for developing strategies to manipulate it. The concept of network stoichiometry is introduced as a component of all metabolic models; without any additional information, such models are referred to as structural. When, additionally, kinetic information is available for the pathway enzymes, this enables further analyses, i.e., time-course simulation, steady-state analysis, and metabolic control analysis. Strategies for model parameterization and software for modeling are discussed. The approach is illustrated with three models from the general plant physiology literature, before providing an historical overview of the kinetic modeling of sugarcane physiology. A steady-state sugarcane growth model is introduced where the culm is modeled in segments, each internode separately. This model is extended to a continuous growth model that explicitly includes phloem flow linking the internodes and is simulated within an advection-diffusion-reaction framework. Such models allow control points within the network to be identified and may pinpoint potential targets for biotechnological intervention. Future challenges include the integration of kinetic models on the different levels of the cellular and organizational hierarchy.

The present study reports the effect of high molecular weight bacterial fructan (levan) and glucan (reuteran) on growth and carbohydrate partitioning in transgenic sugarcane plants. These biopolymers are products of bacterial glycosyltransferases, enzymes that catalyze the polymerization of glucose or fructose residues from sucrose. Constructs, targeted to different subcellular compartments (cell wall and cytosol) and driven by the Cauliflower mosaic virus-35S: maize-ubiquitin promoter, were introduced into sugarcane by biolistic transformation. Polysaccharide accumulation severely affected growth of callus suspension cultures. Regeneration of embryonic callus tissue into plants proved problematic for cell wall-targeted lines. When targeted to the cytosol, only plants with relative low levels of biopolymer accumulation survived. In internodal stalk tissue that accumulate reuteran (max 0.03 mg/g FW), sucrose content (ca 60 mg/g FW) was not affected, while starch content (<0.4 mg/g FW) was increased up to four times. Total carbohydrate content was not significantly altered. On the other hand, starch and sucrose levels were significantly reduced in plants accumulating levan (max 0.01 mg/g FW). Heterologous expression resulted in a reduction in total carbohydrate assimilation rather than a simple diversion by competition for substrate.

A solution to manage cumbersome data sets associated with large modelling projects is described. A kinetic model of sucrose accumulation in sugarcane is used to predict changes in sucrose metabolism with sugarcane internode maturity. This results in large amounts of output data to be analysed. Growth is simulated by reassigning maximal activity values, specific to each internode of the sugarcane plant, to parameter attributes of a model object. From a programming perspective, only one model definition file is required for the simulation software used; however, the amount of input data increases with each extra interrnode that is modelled, and likewise the amount of output data that is generated also increases. To store, manipulate and analyse these data, the modelling was performed from within a spreadsheet. This was made possible by the scripting language Python and the modelling software PySCeS through an embedded Python interpreter available in the Gnumeric spreadsheet program.