While manufactured objects tend to be built by putting together different parts of fixed size, like lego bricks, living systems are constructed by cell growth and division. In fact, all the cells in a multicellular animal, like a human or fly, are derived in this way from a single fertilised egg cell. How then do organisms generate the cell type diversity required to build complex organs and tissues? This is achieved in part from cell divisions that are asymmetric - as single cells divide to generate siblings that take up different fates as the result of asymmetries in their inheritance or in their environment. While the asymmetric segregation of molecules that help to determine differences in sibling cell fate have been studied in detail, many of these divisions are also characterised by reproducible differences in sibling cell size and shape. How and why this is the case is not understood. To shed light on this, here we aim to study the regulation and function of the differences in cell mass, volume and surface area that arise from asymmetries in the division process. Although the importance of the size and shape of an animal cell for its behavior and function has been recognised for at least 100 years, since D'Arcy Thompson, little work has been done to quantify the variation in sibling cell size and shape, to define the mechanisms that underlie division errors, nor their contribution to cell behavior and function. Nevertheless, the fact that reproducible differences in sibling cell size and shape are frequently associated with asymmetric stem cell divisions, suggests that they are likely to be important. This is probably more significant in the context of organ development, where cells with different fates must work together as a functional unit. A good example of this is the developing fly bristle, where four cells generated via a series of asymmetric divisions form a complex three dimensional structure that functions in mechanosensation. Here, taking advantage of recent advances in imaging, we aim to use two complementary model systems, mammalian cells in culture and cells of the fly bristle lineage to determine: i) sources of error that affect the distribution of cell mass and volume at division during both symmetric and asymmetric divisions, ii) the points at which errors in division symmetry are corrected in both cases (differences between cells mustn't be eliminated during asymmetric divisions), and iii) the functions of asymmetries in the size and shape of sibling cells in the context of organogenesis. Moreover, in the case of the bristle, where cells must wrap around one another in order to form a functional organ, we will explore the extent to which differences in the volume and apical surface area of individual cells generated by asymmetries in division are corrected or amplified. Overall, we expect our analysis to have an important impact on our understanding of conserved elements of the division process that determine its accuracy, and to shed light on the function of size and shape differences between sibling cells in the context of organogenesis. We also expect this work to have implications for our understanding of stem cell divisions in humans, many of which are thought to be asymmetric, and for cancer research since cancer cells frequently exhibit a profound loss of cell size homeostasis.

In this proposal I describe my plan to attack several important open problems facing our understanding of multi-component, non-equilibrium fluid membranes. In a biological context these often interact with the cytoskeleton of a living cell. I will study how membrane microphase separation is induced by applied forces, such as might arise from coupling to the active cytoskeleton. This model is desperately needed to understand recent data, e.g. for large variations in the local membrane diffusion constant.I also plan to study the regulation and transient adaptation of the membrane tension and pressure of a living cell. I will construct an appropriate non-equilibrium model for the creation of transient bonds between the membrane and the cytoskeleton and use this to establish a self-consistent theory for the steady state, and time variation, of these quantities. Forces generated by molecular motors anchored to the cytoskeleton act on these bonds. The lifetime of the bonds depends on the membrane compliance, which in turn depends on it tension and pressure in a way that can be computed self-consistently. The transient response of the cell following rapid changes in volume or membrane area, can be probed by modern micropipette or tether-pulling experiments. We thereby hope to construct a theory for the active mechanical properties of the cell membrane.I will also work to rigorously test the long standing but untested Saffman-Delbruck theory for membrane diffusion. I will analyse experimental data from Prof Bassereau's group at the Institut Curie. These ongoing experiments have been motivated by our recent theoretical analysis of flows on cylindrical membrane tubes in which we suggest that the controlled variation of tube radius in this geometry may provide the most discriminatory test of the Saffman-Delbruck theory yet proposedI will also study the assembly and dynamics of the FtsZ contractile ring. This protein, a bacterial analogue of tubulin, assembles into fibers that form a ring around dividing bacterial cells. This process involves molecular force generation, fibre self assembly, depolymerisation and membrane-mediated forces, all of which are fields in which I have significant expertise. Very recently model in vitro experiments have studied the role of FtsZ in generating membrane deformation. We plan to repeat similar experiments in membrane vesicles but with the addition of additional vital molecular components, such as FtsA, which plays an important role in associating the FtsZ ring with the membrane. A testable physical model for the action of these dividing rings in generating controlled membrane deformation would be most useful in a field which is of the very highest contemporary interest. There is the hope that this may also have pharmaceutical relevance, e.g. in new antibacterial treatments that target the cell division apparatus.There is an additional element to this proposal which is not included here for reasons of confidentiality.

Understanding how metastatic cancer cells move will enable the search for therapies targeting secondary tumour forming cells. Recent experiments suggest that the cell nucleus, which is disrupted and generally much softer in cancerous cells compared to healthy cells, plays an important role in cell migration. Specifically the nucleus is thought to be involved in setting or maintaining the direction of cell motion. Connections between the nucleus and the cytoskeleton (the main structural body of the cell) appear to be essential for migration in soft 3D tissue-like environments. Finally whether or not the nucleus gets stuck determines whether a cell successfully squeezes through constrictions. This project will develop theoretical models whose predictions, once tested, will determine the physical roles of the nucleus in cell migration. From a physics perspective the cell cytoskeleton can be described as a soft gel-like material that is "active" or "out of equilibrium" meaning it is consuming biochemical energy. This type of material has been successfully described by the recently developed theory of "active gels", which has already proved useful in modelling cell movement. Usually in such models the nucleus of the cell is ignored and the cell is treated as a single material, however this project specifically addresses the role of the nucleus. Understanding the mechanical roles of a passive elastic object embedded in an active fluid is a challenging problem within the emerging field of the physics of active (out of equilibrium) matter. Elucidating the physical roles of the nucleus in cell migration will make an important contribution to the grand challenge of understanding the physics of life.

United Kingdom

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.