We report scanning tunneling microscopy observations, which imply that all atoms in a Cu(001) surface move frequently, even at room temperature. Using a low density of embedded indium "tracer" atoms, we visualize the diffusive motion of surface atoms. Surprisingly, the indium atoms seem to make concerted, long jumps. Responsible for this motion is an ultralow density of surface vacancies, diffusing rapidly within the surface. This interpretation is supported by a detailed analysis of the displacement distribution of the indium atoms, which reveals a shape characteristic for the vacancy mediated diffusion mechanism that we propose.

Many bacteria are propelled by flagellar motors that stochastically switch between the clockwise and counterclockwise rotation direction. Although the switching dynamics is one of their most important characteristics, the mechanisms that control it are poorly understood. We present a statistical-mechanical model of the bacterial flagellar motor. At its heart is the assumption that the rotor protein complex, which is connected to the flagellum, can exist in two conformational states and that switching between these states depends on the interactions with the stator proteins, which drive the rotor. This couples switching to rotation, making the switch sensitive to torque and speed. Another key element is that after a switch, it takes time for the load to build up, due to conformational transitions of the flagellum. This slow relaxation dynamics of the filament leads, in combination with the load dependence of the switching frequency, to a characteristic switching time, as recently observed. Hence, our model predicts that the switching dynamics is not only controlled by the chemotaxis-signaling network, but also by mechanical feedback of the flagellum.

We have used the indium/copper surface alloy to study the dynamics of surface vacancies on the Cu(0 0 1) surface. Individual indium atoms that are embedded within the first layer of the crystal, are used as probes to detect the rapid diffusion of surface vacancies. STM measurements show that these indium atoms make multi-lattice-spacing jumps separated by long time intervals. Temperature dependent waiting time distributions show that the creation and diffusion of thermal vacancies form an Arrhenius type process with individual long jumps being caused by one vacancy only. The length of the long jumps is shown to depend on the specific location of the indium atom and is directly related to the lifetime of vacancies at these sites on the surface. This observation is used to expose the role of step edges as emitting and absorbing boundaries for vacancies.

We develop a version of the vacancy mediated tracer diffusion model, which follows the properties of the physical system of In atoms diffusing within the top layer of Cu(001) terraces. This model differs from the classical tracer diffusion problem in that (i) the lattice is finite, (ii) the boundary is a trap for the vacancy, and (iii) the diffusion rate of the vacancy is different, in our case strongly enhanced, in the neighborhood of the tracer atom. A simple continuum solution is formulated for this problem, which together with the numerical solution of the discrete model compares well with our experimental results.

Push–pull networks are ubiquitous in signal transduction pathways in both prokaryotic and eukaryotic cells. They allow cells to strongly amplify signals via the mechanism of zero-order ultrasensitivity. In a push–pull network, two antagonistic enzymes control the activity of a protein by covalent modification. These enzymes are often uniformly distributed in the cytoplasm. They can, however, also be colocalized in space; for instance, near the pole of the cell. Moreover, it is increasingly recognized that these enzymes can also be spatially separated, leading to gradients of the active form of the messenger protein. Here, we investigate the consequences of the spatial distributions of the enzymes for the amplification properties of push–pull networks. Our calculations reveal that enzyme localization by itself can have a dramatic effect on the gain. The gain is maximized when the two enzymes are either uniformly distributed or colocalized in one region in the cell. Depending on the diffusion constants, however, the sharpness of the response can be strongly reduced when the enzymes are spatially separated. We discuss how our predictions could be tested experimentally.