An integrative view on vacuolar pH homeostasis in Arabidopsis thaliana: Combining mathematical modeling and experimentation.

The acidification of plant vacuoles is of great importance for various physiological processes, as a multitude of secondary active transporters utilize the proton gradient established across the vacuolar membrane. Vacuolar-type H+ -translocating ATPases and a pyrophosphatase are thought to enable vacuoles to accumulate protons against their electrochemical potential. However, recent studies pointed to the ATPase located at the trans-Golgi network/early endosome (TGN/EE) to contribute to vacuolar acidification in a manner not understood as of now. Here, we combined experimental data and computational modeling to test different hypotheses for vacuolar acidification mechanisms. For this, we analyzed different models with respect to their ability to describe existing experimental data. To better differentiate between alternative acidification mechanisms, new experimental data have been generated. By fitting the models to the experimental data, we were able to prioritize the hypothesis in which vesicular trafficking of Ca2+ /H+ -antiporters from the TGN/EE to the vacuolar membrane and the activity of ATP-dependent Ca2+ -pumps at the tonoplast might explain the residual acidification observed in Arabidopsis mutants defective in vacuolar proton pump activity. The presented modeling approach provides an integrative perspective on vacuolar pH regulation in Arabidopsis and holds potential to guide further experimental work.

Impact of explicit area scaling on kinetic models involving multiple compartments.

BACKGROUND: Computational modelling of cell biological processes is a frequently used technique to analyse the underlying mechanisms and to generally understand the behaviour of these processes in the context of a pathway, network or even the whole cell. The most common technique in this context is the usage of ordinary differential equations that describe the kinetics of the relevant processes in mechanistic detail. Here, it is usually assumed that the content of the cell is well-stirred and thus homogeneous - which is of course an over-simplification, but often worked in the past. However, many processes happen at membranes and thus not in 3D, but in 2D. The scaling of the rates of these processes poses a special problem, if volumes of compartments are changed. They will typically scale with an area, but not with the volume of the involved compartment. However, commonly, this is neglected when setting up models and/or volume scaling also sometimes automatically happens when using modelling software in the field. RESULTS: Here, we investigate generic as well as specific, realistic cases to find out, how strong the impact of the wrong scaling is for the outcome of simulations. We show that the importance of correct area scaling depends on the architecture of the reaction site and its changes upon volume alterations and it is hard to foresee, if it has a significant impact or not just by looking at the original model set-up. Moreover, scaled rates might exhibit more or less control over the behaviour of the system and therefore, accordingly, incorrect scaling will have more or less influence. CONCLUSIONS: Working with multi-compartment reactions requires a careful consideration of the correct scaling of the rates when changing the volumes of the involved compartments. The error following incorrect scaling - often done by scaling with the volume of the respective compartments can lead to significant aberrations of model behaviour.

Computational systems biology of cellular processes in Arabidopsis thaliana: an overview.

Systems biology strives for gaining an understanding of biological phenomena by studying the interactions of different parts of a system and integrating the knowledge obtained into the current view of the underlying processes. This is achieved by a tight combination of quantitative experimentation and computational modeling. While there is already a large quantity of systems biology studies describing human, animal and especially microbial cell biological systems, plant biology has been lagging behind for many years. However, in the case of the model plant Arabidopsis thaliana, the steadily increasing amount of information on the levels of its genome, proteome and on a variety of its metabolic and signalling pathways is progressively enabling more researchers to construct models for cellular processes for the plant, which in turn encourages more experimental data to be generated, showing also for plant sciences how fruitful systems biology research can be. In this review, we provide an overview over some of these recent studies which use different systems biological approaches to get a better understanding of the cell biology of A. thaliana. The approaches used in these are genome-scale metabolic modeling, as well as kinetic modeling of metabolic and signalling pathways. Furthermore, we selected several cases to exemplify how the modeling approaches have led to significant advances or new perspectives in the field.

Robustness of frequency vs. amplitude coding of calcium oscillations during changing temperatures.

Intracellular calcium oscillations have been widely studied. It is assumed that information is conveyed in the frequency, amplitude and shape of these oscillations. In particular, calcium signalling in mammalian liver cells has repeatedly been reported to display frequency coding so that an increasing amount of stimulus is translated into an increasing frequency of the oscillations. However, recently, we have shown that calcium oscillations in fish liver cells rather exhibit amplitude coding with increasing stimuli being translated into increasing amplitudes. Practical consequences of this difference are unknown so far. Here we investigated advantages and disadvantages of frequency vs. amplitude coding, in particular in environments with substantially changing temperatures (e.g. 10-20 degrees). For this purpose, we use computational modelling and a new approach to generate a calcium model exactly displaying a specific frequency and/or amplitude. We conclude that despite the advantages in flexibility that frequencies might offer for the transmission of information in the cell, amplitude coding is obviously more robust with respect to changes in environmental temperatures. This potentially explains the observed differences between two classes of organisms, one operating at constant temperatures whereas the other is not.