Single-cell analysis of the physiology of mechanosensation in bacteria

Escherichia coli is one of the best studied living organisms and a model system for many biophysical investigations. Despite countless discoveries of the details of its physiology, we still lack a holistic understanding of how these bacteria react to changes in their environment. One of the most important examples is their response to osmotic shock. One of the mechanistic elements protecting cell integrity upon exposure to sudden changes of osmolarity is the presence of mechanosensitive channels in the cell membrane. These channels are believed to act as tension release valves protecting the inner membrane from rupturing. This thesis presents an experimental study of various aspects of mechanosensation in bacteria. We examine cell survival after osmotic shock and how the number of MscL (Mechanosensitive channel of Large conductance) channels expressed in a cell influences its physiology. We developed an assay that allows real-time monitoring of the rate of the osmotic challenge and direct observation of cell morphology during and after the exposure to osmolarity change. The work described in this thesis introduces tools that can be used to quantitatively determine at the single-cell level the number of expressed proteins (in this case MscL channels) as a function of, e.g., growth conditions. The improvement in our quantitative description of mechanosensation in bacteria allows us to address many, so far unsolved, problems, like the minimal number of channels needed for survival, and can begin to paint a clearer picture of why there are so many distinct types of mechanosensitive channels.

Yang-Mills theory in six-dimensional superspace

The superspace approach provides a manifestly supersymmetric formulation of supersymmetric theories. For N= 1 supersymmetry one can use either constrained or unconstrained superfields for such a formulation. Only the unconstrained formulation is suitable for quantum calculations. Until now, all interacting N>1 theories have been written using constrained superfields. No solutions of the nonlinear constraint equations were known.

In this work, we first review the superspace approach and its relation to conventional component methods. The difference between constrained and unconstrained formulations is explained, and the origin of the nonlinear constraints in supersymmetric gauge theories is discussed. It is then shown that these nonlinear constraint equations can be solved by transforming them into linear equations. The method is shown to work for N=1 Yang-Mills theory in four dimensions.

N=2 Yang-Mills theory is formulated in constrained form in six-dimensional superspace, which can be dimensionally reduced to four-dimensional N=2 extended superspace. We construct a superfield calculus for six-dimensional superspace, and show that known matter multiplets can be described very simply. Our method for solving constraints is then applied to the constrained N=2 Yang-Mills theory, and we obtain an explicit solution in terms of an unconstrained superfield. The solution of the constraints can easily be expanded in powers of the unconstrained superfield, and a similar expansion of the action is also given. A background-field expansion is provided for any gauge theory in which the constraints can be solved by our methods. Some implications of this for superspace gauge theories are briefly discussed.