Non-Markovian models of intracellular transport in a heterogeneous environment

Transport of all kinds of components within the cell - from vesicles along the cytoskeleton through to transcription factors along DNA - is fundamental to cell function and health. Neurons are particularly susceptible to small changes in vesicle transport, which underlie motor neuron disease and may also contribute to neuronal degeneration seen in Alzheimer's disease and during ageing. Despite experimental facts that intracellular transport is heterogeneous and non-Markovian with subdiffusive and superdiffusive regimes most mathematical models for vesicles trafficking are Markovian and homogeneous.

The main challenge for our Manchester interdisciplinary team is to obtain new non-Markovian models of heterogeneous intracellular transport supported by experiments. These models will provide a tool set for analysing transport processes in a much more realistic way, opening the way for greatly improved analysis and ultimately understanding of these highly complex cellular behaviours. This will allow other researchers to formulate and test new hypotheses. In the long term, therefore, non-Markovian models have the potential to lead to insight into neurological diseases, ageing and other processes that involve intracellular transport such as bacterial and viral infection. Such knowledge will be important for developing new treatments.

Our project combines three different approaches: mathematical modelling, numerical modelling and experimental validation, which complement each other. This strategy will provide multidisciplinary study of the intracellular transport problem and ensure maximum impact across and within several disciplines. Our project will allow applied mathematicians (PI and RA), cell biologists and biophysicists (Co-Is and Project Partners) to collaborate thus making significant advances in intracellular transport research and support a cross-disciplinary dissemination.

The main impact of our project will be in the international development of cell research. We are going to achieve this by setting up a multidisciplinary team of researchers from the University of Manchester, Curie Institute in Paris, Inria Serpico team in Rennes, LIRIS laboratory in Lyon and the University of California at Merced. Our team will consist of applied mathematicians (PI, RA), experimental cell biologists and computational biophysicists (Co-Is and Project Partners). This project has a potential social impact through enhancing of quality of life and health because it can give important insights into intracellular transport which is of fundamental importance to cell biology. Malfunctions in protein and vesicles trafficking inside living cells are major contributory factors in a number of diseases. Defects of intracellular transport contribute to Huntington's disease and Altzheimer's. A deeper understanding of intracellular transport can lead to more effective treatment strategies of cancers, viral infection and bacterial infections. As our Project Partners stated, our models will be used in the Curie Institute in Paris which is the leading world centre specializing on cell biology and the hospital treatment of cancer.

A major strength of our proposal is that it allows direct testing of our new mathematical models on data sets already obtained by the Co-Is. We envisage further experiments (Co-Is and Project Partners) to validate our non-Markovian models. This strengthens the position of the PI and Co-Is, but also improve the UK's knowledge base in non-Markovian intracellular transport. Our new non-Markovian heterogeneous transport models will likely have a broad range of potential applications in many fields such as agriculture, bioengineering and pharmaceutics in the longer term. For example, the transport of substances in random porous media involves a combination of subdiffusion and superdiffusion. Therefore, the pharmaceutical industry might benefit from our new techniques to improve drug delivery.

Together with our Project Partners from France and USA, we intend to organize a international multidisciplinary workshop on stochastic modelling of intracellular transport and to invite key experts in the field. The purposes of this meeting are: (1) to promote the exchange ideas between UK applied mathematicians and USA and European cell biologists; (2) identify potential areas of further collaboration on important aspects of stochastic intracellular transport; (3) to provide training in non-Markovian transport and fractional partial differential equations for PhD students and biologists. Running the workshop will allow to disseminate our results on new transport models.

We are also committed to engaging with non-specialists about the need for high quality basic science and the specific goals and outcomes of this research project. We will engage school science students by writing an article about vesicle movement and how mathematical modelling is crucial for understanding this process, for publication in the Biological Sciences review, which is sent to secondary schools throughout the country. We will take part in Faculty and University activities that showcase our science to the public and schools, such as Faculty open days, the Schools open day, and National Science week, which happen annually. The aim will be to engage with students by expanding their knowledge through describing exciting new research discoveries.