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Receptor competition for ligand: Stochastic modelling and cellular fate

Final Report Summary - VEGFR (Receptor competition for ligand: Stochastic modelling and cellular fate)

This inter-disciplinary project aimed at developing new stochastic mathematical models of the vascular endothelial growth factor receptor (VEGFR) and its binding to vascular endothelial growth factor (VEGF or ligand), as well as receptor dimerisation, internalisation, signalling, trafficking, degradation, and subsequent regulation of endothelial cell fate. These models were meant to be tuned and tested using experimental data obtained from the literature or generated within experiments to be designed and conducted during the execution of this project. We hypothesized that the insights derived from the analysis, simulation, validation and comparison of the stochastic models would advance our current understanding of the biology of the VEGFR receptor as one of the fundamental molecular mechanisms underlying blood vessel development (angiogenesis), and vascular repair.
The detailed literature review conducted during the first months of the project, in particular the work of Popel and colleagues, made evident that a very complete collection of mathematical models have already been proposed and published, for describing vascular endothelial growth factor receptor dimerisation, internalisation, signalling, trafficking, degradation, and subsequent regulation of endothelial cell fate due to binding to VEGF. Each of those models has an architecture containing the following information: The biochemical species considered, their interaction relationships (i.e. the so-called “wiring diagram” of the model), and the cellular compartments they can occupy.
Biological evidence and knowledge is what primarily determines the model’s architecture. While most of these models have been conceived as deterministic models, their architecture is equally valid if the model is regarded as a stochastic description of reality.
Consequently, in a first step the fellow decided to implement stochastic versions of already published models to explore what conclusions could be derived from such models, in particular, what differences would arise in comparison to the corresponding deterministic versions. To this end, the fellow used COPASI (Hoops, Sahle et al. 2006), a very well established computational platform for mathematical modelling and computer simulation of biochemical networks. A few stochastic simulations of the COPASI-implementation of one of the models published by Popel and colleagues revealed that the computer simulation of a stochastic version of a model capable of describing receptor dimerisation, internalisation, signalling, trafficking, degradation, and subsequent regulation of endothelial cell fate due to ligand binding is far beyond standard computing power. While the simulation of the deterministic version is computationally tractable, the stochastic version would take a prohibitive amount of time, when using standard algorithms implemented in COPASI.
This insight implies that stochastic models that are sufficiently complex to describe the biochemical and cellular processes involved, besides not being analytically tractable, resist a computational analysis based on computer simulation using standard algorithms.
This result called for adjustments in the methodological approach for this project. We reflected that a possible recourse to circumvent this issue would be the development of smarter numerical schemes and algorithms. However, the fellow decided to carry out the project in a different manner.
In order to be compliant with the goal of generating new biological insights into the molecular mechanisms underlying blood vessel development, vascular repair, and angiogenesis, and into the role played by the VEGF-receptor, the fellow devised and implemented a new experimental strategy. The idea was to establish an experimental platform based on live cell imaging using fluorescent microscopy to study, in living cells, the dynamics of cell signalling upon stimulation of the VEFG-receptor with VEGF. To this end, he utilized state-of-the-art intracellular fluorescent markers recently developed by a researcher group in Japan (Aoki and Matsuda 2009) and successfully applied by other researchers (Albeck, Mills et al. 2013) in order to unveil the dynamics of cell signalling upon stimulation with growth factors. In contrast to measuring the average response of an entire population of cells, as it was originally proposed in Annex I of the Grant Agreement, this method allowed for the assessment of individual living cells at a higher time resolution.
A significant amount of time was required to optimize this technique within the infrastructural framework of the laboratory and the imaging facility at University of Leeds.
We managed to measure the response of individual cells to a “step function” increase in the extracellular concentration of VEGF. The sudden injection of a VEGF solution into the imaging chamber containing the cells simulated the very fast increase of VEGF concentration. In the attached figure, a typical time course of the step response is depicted.
This technique turned out to be sensitive enough to detect pathway activations resulting from the stress induced on the cells simply by opening the lid of the imaging chamber containing them. This finding further underlined the need for a cell chamber capable of keeping the cells in a constant environment during imaging, while, at the same time, allowing for the experimental conditions to be deliberately changed in a dynamic fashion. A microfluidics device provides such a solution. After establishing a scientific collaboration with the Molecular and Nanoscale Physics Group at the physics department of University of Leeds, we designed, manufactured, and tested a series of microfluidics chambers. We managed to culture, grow, transfect, and image cells inside the various microfluidics chambers. The experience gathered during these steps led to better designs, including the incorporation and proper positioning of valves.
In summary, we have developed and tested a live cell imaging and microfluidics based experimental platform in order to study, in living cells, the dynamics of cell signalling upon stimulation of the VEFG-receptor with VEGF.
This highly sensitive platform can be used not only to deepen our understanding of the molecular mechanisms of angiogenesis, but to also to study the biochemical changes induced by cancer drugs that target angiogenesis in order to impair tumour vascularization. While initially linked to high expectations, the performance of this class of drugs in the treatment of human cancer has been disappointingly poor. We hypothesize that the current lack of knowledge of the intracellular signaling dynamics that precede the macroscopic events of cell proliferation and cell migration needed for angiogenesis may explain the current failure of anti-angiogenic strategies. Indeed, as recently shown by Albeck et al., the macroscopic outcomes (e.g. cell proliferation) of exposing epithelial cells to extracellular growth factor input signals appear to be frequency modulated, i.e. the rate at which pulses of pathway activity emerge within the cell, rather than the amplitude of these pulses, regulates and controls further cellular processes. This counterintuitive finding, if found to be also valid in the context of VEGF stimulation of vascular endothelial cells, might force researchers to revise the conventional view of dose-response relationship that underlies traditional anti-angiogenic cancer treatment approaches.
The experimental platform we have set up is now ready to take up this challenge.

Albeck, John G., Gordon B. Mills and Joan S. Brugge (2013). "Frequency-Modulated Pulses of ERK Activity Transmit Quantitative Proliferation Signals." Molecular Cell 49(2): 249-261.
Aoki, K. and M. Matsuda (2009). "Visualization of small GTPase activity with fluorescence resonance energy transfer-based biosensors." Nat. Protocols 4(11): 1623-1631.
Hoops, S., S. Sahle, R. Gauges, C. Lee, J. Pahle, N. Simus, M. Singhal, L. Xu, P. Mendes and U. Kummer (2006). "COPASI—a COmplex PAthway SImulator." Bioinformatics 22(24): 3067-3074.

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