Modeling Regulation of Zinc Uptake via ZIP Transporters in Yeast and Plant Roots

In yeast (Saccharomyces cerevisiae) and plant roots (Arabidopsis thaliana) zinc enters the cells via influx transporters of the ZIP family. Since zinc is both essential for cell function and toxic at high concentrations, tight regulation is essential for cell viability. We provide new insight into the underlying mechanisms, starting from a general model based on ordinary differential equations and adapting it to the specific cases of yeast and plant root cells. In yeast, zinc is transported by the transporters ZRT1 and ZRT2, which are both regulated by the zinc-responsive transcription factor ZAP1. Using biological data, parameters were estimated and analyzed, confirming the different affinities of ZRT1 and ZRT2 reported in the literature. Furthermore, our model suggests that the positive feedback in ZAP1 production has a stabilizing function at high influx rates. In plant roots, various ZIP transporters are involved in zinc uptake. Their regulation is largely unknown, but bZIP transcription factors are thought to be involved. We set up three putative models: activator only, activator with dimerization and activator/inhibitor. These were fitted to measurements and analyzed. Simulations show that the activator/inhibitor model outperforms the other two in providing robust and stable homeostasis at reasonable parameter ranges.Comment: 23 pages including 2 tables and 7 figure

Homogenization approach to water transport in plant tissues with periodic microstructures

Water flow in plant tissues takes place in two different physical domains separated by semipermeable membranes: cell insides and cell walls. The assembly of all cell insides and cell walls are termed symplast and apoplast, respectively. Water transport is pressure driven in both, where osmosis plays an essential role in membrane crossing. In this paper, a microscopic model of water flow and transport of an osmotically active solute in a plant tissue is considered. The model is posed on the scale of a single cell and the tissue is assumed to be composed of periodically distributed cells. The flow in the symplast can be regarded as a viscous Stokes flow, while Darcy's law applies in the porous apoplast. Transmission conditions at the interface (semipermeable membrane) are obtained by balancing the mass fluxes through the interface and by describing the protein mediated transport as a surface reaction. Applying homogenization techniques, macroscopic equations for water and solute transport in a plant tissue are derived. The macroscopic problem is given by a Darcy law with a force term proportional to the difference in concentrations of the osmotically active solute in the symplast and apoplast; i.e. the flow is also driven by the local concentration difference and its direction can be different than the one prescribed by the pressure gradient.Comment: 31 page

Transport phenomena in plant-internal processes: growth and carbon dioxide transport

Aim of the here presented work was the quantitative modeling of plant-internal processes. Growth of cells and tissues was one of the central themes, although the lateral transport of carbon dioxide (CO2 ) was also treated. These processes depend strongly on fluxes of water, hormones and/or CO2 . Thus, suitable transport equations were sought for to describe these processes. Using the Lockhart-Equations, which are well known in biology to describe the growth of a whole cell, local formulations of energy and mass conservation were obtained. These formulations can be used to determine local growth patterns in cells. This was shown through a numerical example of a spherical cell. Finally, the conservation equations found, were shown to be consistent with the empirical Lockhart-Equations. Plant organs, such as roots and hypocotyls, have spatial and temporal growth patterns. For example, the spatial distributions of growth in primary roots is given by a bell-shaped distribution along the organ axis. This particular one dimensional growth pattern was modeled here through the transport of two hypothetical phytohormones and using the Lockhart-Equations as the underlying growth equations. Because the hypothetical hormones were chosen to have auxin and cytokinin (two of the most important plant hormones) properties, the model stays in a plant physiological context. Not only one dimensional growth patterns are found in roots and hypocotyls. These tend to have organ curvature and torsion, as becomes clear particularly in tropisms (e.g. gravitropism, hydrotropisms and phototropism). Although these processes are known for a long time in biology, no suitable measures to characterize the production of curvature and torsion have been defined. Using a curvature and torsion conservation equation, a measure for their production was found here. These measures were then exemplified in a simple model of the root gravitropic reaction, and applied in the characterization of the gravitropic reaction of Arabidopsis thaliana (L.) Heynh. wild-type and pin3 mutant roots. The gravitropic reaction is believed to be regulated by the hormone auxin. pin3 mutants are deficient in the PIN3 protein, which is essential in the transport of auxin in the root tip. Through comparison of the reaction of wild-type and pin3 roots, it was shown here that the gravitropic reaction is not solely regulated by auxin, so that other regulation mechanisms need to exist. Finally, transport equations were found, which describe the transport and assimilation of CO2 in leaves. Using gas-exchange and chlorophyll fluorescence measurements, the homogenized lateral diffusion coeffcient of leaves was determined. Moreover, the strategy behind the existence of lateral diffusion in leaves was discussed (plants differ in the porosity of their leaves). Throughout the work presented here, it became clear how fructiferous the application of transport equations in biology is. The importance of a quantitative description in biology became also clear. Everyday new questions arise in biology. An answer to these may only be found using an interdisciplinary approach

Global Hopf bifurcation in the ZIP regulatory system

Regulation of zinc uptake in roots of Arabidopsis thaliana has recently been modeled by a system of ordinary differential equations based on the uptake of zinc, expression of a transporter protein and the interaction between an activator and inhibitor. For certain parameter choices the steady state of this model becomes unstable upon variation in the external zinc concentration. Numerical results show periodic orbits emerging between two critical values of the external zinc concentration. Here we show the existence of a global Hopf bifurcation with a continuous family of stable periodic orbits between two Hopf bifurcation points. The stability of the orbits in a neighborhood of the bifurcation points is analyzed by deriving the normal form, while the stability of the orbits in the global continuation is shown by calculation of the Floquet multipliers. From a biological point of view, stable periodic orbits lead to potentially toxic zinc peaks in plant cells. Buffering is believed to be an efficient way to deal with strong transient variations in zinc supply. We extend the model by a buffer reaction and analyze the stability of the steady state in dependence of the properties of this reaction. We find that a large enough equilibrium constant of the buffering reaction stabilizes the steady state and prevents the development of oscillations. Hence, our results suggest that buffering has a key role in the dynamics of zinc homeostasis in plant cells.Comment: 22 pages, 5 figures, uses svjour3.cl

Yeast: Role of ZRT1 and ZRT2 and ZAP1 feedback.

<p>A, contributions of ZRT1 or ZRT2 to the total zinc influx for varying external zinc concentration. B, ZAP1 activity for varying values of ZRT independent influx . The stable solution is marked with a solid line, the unstable solution is dotted.</p

Yeast simulations.

<p>Comparison between measurements and simulated steady states of ZAP1, internal zinc, ZRT1 and ZRT2 for varying external zinc concentration. Measurements: ZRT1 and ZRT2 from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0037193#pone.0037193-Bird1" target="_blank">[21]</a>, ZAP1 and zinc from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0037193#pone.0037193-Zhao2" target="_blank">[15]</a>.</p