Different types of cells, i.e. from different tissues, typically look quite different from each other. Even when cultured on two-dimensional surfaces like glass slides or tissue culture polystyrene under identical conditions, cells adopt different shapes. These shapes are in general functions of the cytoskeletal properties of those cells, itself a subset of what we can call the “state” of the cell. Experimental evidence over several decades has indicated that for some cell types, imposed changes in shape lead to changes in cellular differentiation and other properties. Conversely there is increasing evidence that some changes in cell state can lead to stereotypical changes in cell shape. We have developed a large number of morphological parameters to quantify cell shape and cytoskeletal morphology. Using these parameters to quantify morphologies of different cell lines, as well as cells in different experimental conditions, we show that quantifiers of cell shape and cytoskeletal texture can be used to discriminate between different cell states. A neural network is able to correctly classify different cell states with high accuracy. Using projections of the data to lower-dimensional shape space, we find that we can distinguish between similar and dissimilar changes in shape. We use this method to identify similarities in shape changes between breast cancer and osteosarcoma cell lines accompanying the acquisition of invasive characteristics. Our data indicates that cellular morphology is a powerful and sensitive window into the physiological state of the cell, and underline the need to develop mechanistic models that relate cell state to cell shape.

The green sea turtle Chelonia midas travels for thousands of miles from the coast of Brazil to a small island in the Atlantic Ocean, Ascension Island. There the turtles lay their eggs into the warm sand on the beach. It is a classic scientific challenge to understand the navigational skills of the turtles and several orienteering mechanisms are discussed, such as geomagnetic information, chemotaxis, Atlantic flow patterns etc. In this talk I will present a mathematical model for the homing of sea turtles and discuss how it can be used to identify the navigational mechanisms of sea turtles. (joint work with K.J. Painter).

Swimming bacteria with helical flagella are self-propelled micro-swimmers in nature, and the swimming strategies of such bacteria vary depending on the number and the position of flagella on the cell body. In this talk, I will introduce two microorganisms, multi-flagellated E. coli and single-flagellated Vibrio A. The Kirchhoff rod theory is used to model the elastic helical flagella and the rod-shaped cell body is represented by a hollow ellipsoid that can translate and rotate as a neutrally buoyant rigid body interacting with a surrounding fluid. The hydrodynamic interaction between the fluid and the bacteria is described by the regularized version of Stokes flow. I will focus on how bacteria can swim and reorient swimming course for survival and how Mathematics can help to understand the swimming mechanism of such bacteria.

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