with two separate diatoms according to Figure 1.24. When several diatoms drift with hydrophobic apices on the water surface, patterns are formed in which the ends preferably stick together. This results in locally star-shaped and polygonal structures. Not all diatoms have a pronounced hydrophobic apex. It is enough to stay on the water surface, but the attractive interaction is barely recognizable in the movement. There are systematic differences in the strength of the hydrophobicity in diatoms from different localities that affect the patterns. A low interaction leads to loose arrangements (Figure 1.22), a strong interaction to patterns where the apices are close together (Figure 1.26). It will probably not be possible to give an analytical representation of the attractive force. A simplified modeling consists in the replacement of the diatom by two rotationally symmetric hydrophobic particles, which are connected by a rod having the length of the diatom. For the experimental determination of the attractive interaction one can examine the motion of diatoms, which move toward each other, or the movement of a hydrophobic particle like spores of Lycopodium in the vicinity of a diatom. Under the plausible assumption that the inertia force can be neglected in the equation of motion, and Stokes’ law holds, the velocity is proportional to the force. In Figure 1.27 the speed of a diatom, which is proportional to the force, is plotted versus the distance between two approaching diatoms. It was determined from a video recorded at 30 fps. This is not sufficient to measure the high speeds shortly before the collision. The fluctuations in velocity at longer distances are probably due to the different drift velocities of the diatoms. This image is primarily intended to illustrate the method.
Figure 1.25 Sketch of two adjacent Nitzschia sigmoidea on the water surface seen from the horizontal direction.
Figure 1.26 Very regular structure of a diatom cluster on the water surface (dark field).
A remarkable aspect is the dynamics of movement. Different forms of movement occur, which indicate different mechanisms. Single floating diatoms are able to move slowly in the direction of the apical axis. This is similar to the movement on substrate, but hardly any longer distances are covered. Adhering lumps of EPS are typically not visible. Since no axenic cultures are used, bacteria can usually be seen on the water surface in phase contrast, making water movement observable. One recognizes changing currents of the water along the raphes, which run opposite to the movement of the diatoms. Apparently, the activity of the raphes can couple to a liquid medium. I do not want to exclude the possibility that the bacteria have an influence on the movement by mechanically coupling to the raphes, but in view of their small size and their lack of mutual contact, I consider their influence to be small. Theories of motility that require adhesion to a solid substrate cannot adequately explain this phenomenon. The movement of diatoms in hanging drops at the interface to air was interpreted by Nultsch in 1957 on the basis of the since disproved cytoplasmic streaming theory. Wavelike movements of microfibrils, as suggested by Bertrand [1.4] in 2008 (translation in Chapter 12 of this book), could cause the observed water transport along the raphe. They strengthen this hypothesis. I could not observe this form of movement with certainty in clusters of several connected diatoms, possibly because they contribute little to movement compared to the other forces acting there.
Figure 1.27 Relative speed of two diatoms plotted versus their distance.
It is obvious in Nitzschia sigmoidea cultures with high population density that the diatoms secrete EPS. These excretions can accumulate and lead to the formation of flakes of living diatoms. Sometimes it can be noticed that more or less large lumps of EPS adhere to individual diatoms on the water surface. When two diatoms come into contact through the mediation of an EPS lump, the transport of this lump along the raphes of both diatoms leads to a fast and remarkable movement. As there is no adhesion to a solid substrate, the two diatoms “dance” around each other. This movement pattern often occurs without the EPS lumps being recognizable.
Diatoms that have come together in structures such as those shown in Figure 1.22 and Figure 1.26 show a peculiar dynamic. The attractive interaction of the hydrophobic apices is of great importance here. If only this attractive interaction existed, a pattern would be formed on the water surface, whereby the movement would come to rest as soon as a local minimum of energy is reached. However, the activity along the raphe and in the area of the apical pore field leads to continuous changes of the pattern. According to the simple model of two hydrophobic particles in the distance of the apices one expects structures with few unbound ends. For example, when there are three diatoms in a cluster, energetically favorable configurations in which all ends have bonds to other diatoms should prevail (Figure 1.28). A chain of three diatoms should close to a triangle because of the attractive interaction of the free ends. But the diatoms are not passive floating objects, but show active movement. They release energy and thus temporarily produce patterns with higher energy. There are elementary processes which are observable locally in the entire structure pattern. The end of one or more parallel diatoms can be moved by another diatom along its raphe (Figure 1.29). At the beginning of this movement, an existing connection at an apex of the moved diatom can be broken. Energy is released locally from the diatom into the structure. Angular changes at connected apices (Figure 1.29b) are very frequent. Diatoms that adhere with the apex on a substrate are capable of performing tilting movements. Probably it is the same mechanism as observed on the water surface. It is by no means certain that all motion sequences can be explained thereby, because the simultaneously occurring changes in this many-body system are very complex. One striking feature is the separation of connections at the apex without subsequent transport along a raphe. It could be due to opposing forces within the cluster. The static attractive force of the apices, the active movement along the raphe, the active change of the angle between two connected diatoms and possibly other mechanisms can generate a very large number of patterns and sequences in a system of several diatoms (Figure 1.30). These processes are fundamentally different from those on a solid substrate.
In nature, the currents in the water are also likely to whirl up diatoms that do not have a high adhesion to the ground. They may occasionally reach the water surface. The ability to stay there for a longer period of time could lead to dispersal by drifting, i.e., hydrochory.
Figure 1.28 Energetically favorable patterns of three diatoms on the water surface: all diatoms parallel (a) and diatoms form a triangle
