Many biological processes have to occur at specific locations on the cell membrane. These locations are often specified by the localised activity of small GTPase proteins. Some processes require the formation of a single cluster of active GTPase, also called unipolar polarisation (here “polarisation”), whereas others need multiple coexisting clusters. Moreover, sometimes the pattern of GTPase clusters is dynamically regulated after its formation. This raises the question how the same interacting protein components can produce such a rich variety of naturally occurring patterns. Most currently used models for GTPase-based patterning inherently yield polarisation. Such models may at best yield transient coexistence of at most a few clusters, and hence fail to explain several important biological phenomena. These existing models are all based on mass conservation of total GTPase and some form of direct or indirect positive feedback. Here, we show that either of two biologically plausible modifications can yield stable coexistence: including explicit GTPase turnover, i.e., breaking mass conservation, or negative feedback by activation of an inhibitor like a GAP. Since we start from two different polarising models our findings seem independent of the precise self-activation mechanism. By studying the net GTPase flows among clusters, we provide insight into how these mechanisms operate. Our coexistence models also allow for dynamical regulation of the final pattern, which we illustrate with examples of pollen tube growth and the branching of fungal hyphae. Together, these results provide a better understanding of how cells can tune a single system to generate a wide variety of biologically relevant patterns.
Various environmental signals integrate into a network of floral regulatory genes leading to the final decision on when to flower. Although a wealth of qualitative knowledge is available on how flowering time genes regulate each other, only a few studies incorporated this knowledge into predictive models. Such models are invaluable as they enable to investigate how various types of inputs are combined to give a quantitative readout. To investigate the effect of gene expression disturbances on flowering time, we developed a dynamic model for the regulation of flowering time in Arabidopsis thaliana. Model parameters were estimated based on expression time-courses for relevant genes, and a consistent set of flowering times for plants of various genetic backgrounds. Validation was performed by predicting changes in expression level in mutant backgrounds and comparing these predictions with independent expression data, and by comparison of predicted and experimental flowering times for several double mutants. Remarkably, the model predicts that a disturbance in a particular gene has not necessarily the largest impact on directly connected genes. For example, the model predicts that SUPPRESSOR OF OVEREXPRESSION OF CONSTANS (SOC1) mutation has a larger impact on APETALA1 (AP1), which is not directly regulated by SOC1, compared to its effect on LEAFY (LFY) which is under direct control of SOC1. This was confirmed by expression data. Another model prediction involves the importance of cooperativity in the regulation of APETALA1 (AP1) by LFY, a prediction supported by experimental evidence. Concluding, our model for flowering time gene regulation enables to address how different quantitative inputs are combined into one quantitative output, flowering time.
A dynamic model of leaf CO assimilation was developed as an extension of the canonical steady-state model, by adding the effects of energy-dependent non-photochemical quenching (qE), chloroplast movement, photoinhibition, regulation of enzyme activity in the Calvin cycle, metabolite concentrations, and dynamic CO diffusion. The model was calibrated and tested successfully using published measurements of gas exchange and chlorophyll fluorescence on Arabidopsis thaliana ecotype Col-0 and several photosynthetic mutants and transformants affecting the regulation of Rubisco activity (rca-2 and rwt43), non-photochemical quenching (npq4-1 and npq1-2), and sucrose synthesis (spsa1). The potential improvements on CO assimilation under fluctuating irradiance that can be achieved by removing the kinetic limitations on the regulation of enzyme activities, electron transport, and stomatal conductance were calculated in silico for different scenarios. The model predicted that the rates of activation of enzymes in the Calvin cycle and stomatal opening were the most limiting (up to 17% improvement) and that effects varied with the frequency of fluctuations. On the other hand, relaxation of qE and chloroplast movement had a strong effect on average low-irradiance CO assimilation (up to 10% improvement). Strong synergies among processes were found, such that removing all kinetic limitations simultaneously resulted in improvements of up to 32%.
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