MODELLING DIFFUSION

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

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 Obiettivo del progetto (Objective)

'Assembly of transient and stable signaling platforms in the plasma membrane of cells has been implicated in functions as varied as death and survival, polarity, differentiation, migration, cell-cell communication, virus entry, exocytosis, endocytosis. Naturally, the assembly of signaling microdomains requires the use of most complex molecular mechanisms capable of transducing intrinsic or extrinsic information into the actual making of the domain. Consensus exist that the lateral diffusion and heterogeneity of membrane proteins is absolutely necessary. However, more and more data indicate that the clustering of specific proteins to form a signaling platform involves as well the free lateral diffusion of stable assemblies of sphingoipids and cholesterol (rafts). Despite their fundamental relevance for cell function, the basic events responsible for the formation and dynamics of membrane microdomains is not well understood. Mathematical models are very useful tools for describing diffusion processes in an inhomogeneous medium with some anomalies as well as self-organized systems. Hence, it is my plan to use mathematical models to study the formation of protein-lipid clusters and how normal diffusion on an inhomogeneous membrane can be modified. The formation of protein clusters is a necessary condition for cell polarity and it could be related with the generation of pattern. I will propose a Turing-mechanism model to know if it is possible to generate stable spatial inhomogeneity on the cell surface. In order to formulate the equations it will be needed to make some assumptions about the biological system. Made assumptions will be refused or accepted according to the comparative analysis between theoretical results and experimental data. My background in physics make me feel suitable for undertaking the task of modelling these features. The validation experiments will be performed in the laboratory of Prof. Carlos Dotti where I have chosen to carry out this project.'

Introduzione (Teaser)

Cells are surrounded by a phospholipid bilayer, a membrane in which proteins, lipids and other molecules are embedded. Mathematical models of diffusion mechanisms within the membrane are providing insight into signalling in health and disease.

Descrizione progetto (Article)

Formation of transient and stable signalling platforms or groups of molecules likely plays a role in establishment of cell polarity, the asymmetric spatial organisation of various cellular entities. Polarity is essential to the functioning of many if not all cell types and, thus, signalling platforms directly and indirectly affect numerous cellular functions.

Despite the important roles of these assemblies in the plasma membranes of cells, the fundamental mechanisms of their formation and dynamics are still poorly understood. EU-funded scientists working on the project MODELLING DIFFUSION developed mathematical models of the diffusion of protein-lipid clusters in inhomogeneous membranes.

Researchers first developed a mathematical model to simulate the early stages of development of neuronal polarity. The stereotypical cell has the signal-sending axon extending from one side of the cell body and the signal-receiving dendritic tree on the opposite side. Axon-dendrite formation is one of the most critical steps in brain development. Extensive analyses of equilibrium points and bifurcations facilitated the study of spontaneous symmetry breaking, with results leading to a publication in a peer-reviewed scientific journal (PloS ONE).

The team then went on to develop a stochastic version of the deterministic model. In the latter case, it is shown that formation of a single pole of molecular asymmetry is very robust to noise; furthermore, the region of self-organisation became bigger and neuronal polarization could occur even with reduced feedback strength. This work was also published in a peer-reviewed scientific journal (Eur. Phys. J. B).

Researchers also study the diffusion of one of the most important excitatory neurotransmitter (glutamate) receptors. Scientists studied diffusion differences between young and old neurons during activation with glutamate. This work has been published in a peer-reviewed scientific journal (EMBO Molecular Medicine). In order to analyse the data from Single Particle Tracking, a software application for MatLab was developed (APM_GUI) and it is distributed under the terms of the GNU General Public License. The algorithm has been published in a peer-reviewed scientific journal (BMC Biophysics).

Finally, the team has begun studies of changes in the membrane diffusion of an important target of phosphorylation, a major signalling pathway. They are looking for a potential correlation between changes in diffusion patterns with ageing and the decline of cognitive and motor performance.

Mathematical descriptions of cellular polarity developed within MODELLING DIFFUSION are providing insight into diffusion mechanisms in cellular membranes. With a focus on the role of cluster formation and maintenance, the team is shedding light on development, normal function, ageing and disease.