MODELLING DIFFUSION · Mathematical models for diffusion controlled systems: diffusion on cell membrane, cluster formation and maintenance

Mathematical models for diffusion controlled systems: diffusion on cell membrane, cluster formation and maintenance

The Mathematical models for diffusion controlled systems: diffusion on cell membrane, cluster formation and maintenance project was composed by two different parts. The first one was called: 'On the minimal requirement for the generation of neuronal asymmetry: a mathematical / physics approach', and the second one was entitled: 'On lateral diffusion of membrane proteins: software development'. Both of them were carried out successfully and their main results were published in open access journals to increase their positive impacts in the community. Results, conclusions and potential impacts of the first part of the project Neurons are amongst the cell types with the most prominent asymmetry. The correct establishment of polarised domains in neurons enables their directional migration and polarised axon-dendrite formation and is thus one of the most critical steps in brain development. Neuronal polarisation starts with the selection of the site from which the first neurite will grow before morphological changes are evident. It has been shown that the second neurite forms opposite to the first, not randomly. This has important consequences for the neuronal development, since like that initial polarity axis determines the axis of migration and defines axonal and dendritic domains. However, it is not clear whether the formation of the second neurite also requires 'external' triggering mechanisms or is the consequence of a 'passive' mechanism, derived from the first one. To test this hypothesis, we proposed a mathematical model that was based in those proposed by Altschuler et al. (Nature 2008) and Turing (Philos. T. R. Soc. B 1952). Our model assumes an activator-inhibitor dynamics and diffusion-driven instabilities. Extensive analyses on the equilibrium points and phase and bifurcation diagrams were done, allowing us to study spontaneous symmetry breaking. As a very novel idea, we also included the effect of membrane growing and studied how polarity domains are affected by it. To experimentally validate predictions of our model we compared results of our simulations with intensity distributions of Sec8. Sec8 is a exocyst subunit localised in multiple endocytic compartments. Its intensity is a measure of endocytic and exocytic traffic which is correlated with protein accumulation on the plasma membrane due to dynamic maintenance. Our approach suggests that localised membrane growth enhances polarity and it predicts the second bud localisation. The comparison between our results and Sec8 distribution was really successful. This work has already been published in PLoS ONE (Menchón SA, Gärtner A, Román P, Dotti CG, 2011 Neuronal (Bi)Polarity as a Self-Organised Process Enhanced by Growing Membrane. PLoS ONE 6(9): e24190. doi:10.1371/journal.pone.0024190). We chose to publish our work in PLoS ONE because it is an Open Access Journal with a wide audience and electronic circulation, which increases the positive impact in the scientific community. Results, conclusions and potential impacts of the second part of the project Single-particle tracking is a powerful tool for tracking individual particles with high precision. It provides useful information that allows the study of diffusion properties as well as the dynamics of movement. Changes in particle movement behaviour such as transitions between Brownian motion and temporary confinement can reveal interesting biophysical interactions. Many informatic tools are now available, which make it possible to analyse some biological processes. However, these applications require a thorough knowledge of programming, which makes their use difficult for biologists. The aim of our work was to provide a user-friendly, accessible and open-source tool for the analysis of data from two-dimensional single-particle tracking experiments. We developed a tool called APM_GUI (analysing particle movement), which is a MatLab-implemented application with a graphical user interface (GUI) and is based on Simson and Saxton's models (Biophys J. 1995 and 1993). This user-friendly application detects confined movement considering non-random confinement when a particle remains in a region longer than a Brownian diffusant would remain. In addition, APM_GUI can be used by individuals without programming skills and exports the results, which allows users to analyse this information using software that they are familiar with. The application has been tested observing the movement of AMPA receptors and studying how their diffusion coefficients change in different regions of the synapses. The experiments were done using young neurons, (14 DIV) and they showed that the lateral diffusion of AMPA receptors increases upon activation with exogenous glutamate. This work has already been accepted in BMC Biophysics (Menchón SA, Martín, MG, Dotti CG, 2012 APM GUI: analysing particle movement on the cell membrane and determining confinement. BMC Biophysics 2012, 5(4) doi:10.1186/2046-1682-5-4, provisional pdf is available). This journal is also an Open Access Journal. The application has been distributed under the terms of the GNU General Public Licence, as published by the Free Software Foundation, version 3 and it is available as an additional file at the Journal web page as well as in the project home page: http://www.bits.vib.be/ under BioInfo at VIB - developed at VIB. This application has also been used to compare diffusion regimes of AMPA receptors between young and old neurons, showing that the lateral diffusion of AMPA receptors does not increase upon activation with exogenous glutamate in hippocampal neurons with decreased cholesterol levels, (paper in prepation Martín, MG, Ahmed T, Menchón SA, Munck S, Balschun D and Dotti CG, Impaired LTD in the aged resulting from constitutive cholesterol loss).

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