(This essay was written while touring Switzerland by train, July, 2014)
Travel can be joyous but also can involve a lot of work. The basic premise of travel is movement, whether specifically from one destination to another or instead something more random. In either case it takes time for you to move from that one place to another. Even the exploration of a smallish country therefore can take enormous amounts of time, since each of numerous legs of your journey will take some amount of time to traverse. You can purchase a Swiss Pass, and explore much of Switzerland over days and even weeks. You’ll see a lot, but you certainly will see far from everything. These temporal delays that are manifest as you travel are one of things that makes traveling difficult, but at the same time this relative slowness can be what makes a journey worthwhile. If you flittered from place to place at the speed of light, never pausing, you would touch upon much more, but your experience would be far different. Indeed, there are qualitative differences between your experiences as you fly, drive, take a train, ride a motorcycle, ride a bike, walk, or indeed not move at all.
Spatial structure is a property of environments in which delays in movement exist. If you can instantaneously and randomly be anywhere, then there is no spatial structure. In microbiology, spatial structure is seen especially under circumstances that do not substantially involve turbulent flow. When you shake a broth-filled flask, one of the consequences of that action is to reduce spatial structure. In terms of interactions between predators and prey, of bacteriophages and bacteria, the result is that any one individual may interact with any other individual with equivalent probability. If you replace any collision between phages and bacteria with the special kind of interaction that is sex, then you have random mating. If you replace any collision with the special kind of interaction that is phage infection of bacteria, then you have random infection. Either case is implicitly a consequence of a lack of spatial structure in the environment.
Spatial structure generally is what happens within environments almost no matter what. You can strive to remove spatial structure, such as via the shaking or stirring of broth, but absent such measures, or indeed if volumes are large enough and mixing slow enough, then some spatial structure nonetheless will be retained. A static microcosm – where the mixing of broth is reduced essentially to zero and therefore where movement is dominated by either motility or diffusion – thus can represent a spatially structured environment. More obvious is the spatial structure that occurs when movement is reduced even further, as is the case with the addition to environments of various thickening agents such as agar.
In phage biology the classic laboratory-observed consequence of spatial structure is the formation of phage plaques, which are clearings within otherwise turbid bacterial cultures, ones that have been spread or poured onto agar plates. The formation of a plaque requires three processes: phage population growth, phage-mediated reduction of bacterial densities, and, crucially, limitations in phage as well as bacterial movement. Generally a plaque begins with a single plaque forming unit (PFU) which consists of an infective center and in turn can be either an individual phage virion, a clump of phage virions, a phage-infected bacterium, or a clump of bacteria at least one of which is phage infected. This infective center serves as a point source for the outward but nonetheless slow diffusion of phage virions away from their origin. The movement is outward only because the random process of diffusion tends to result in a broadening of the “cloud” of diffusing particles. Because of limitations on the rate of this movement, however, the cloud remains relatively small: the confluent lysis of an entire plate via the growth of a single plaque generally does not occur.
The phage is you. You can start a family and outfit each member of your family with a Swiss Pass. But unless your explorations of the amazing beauty that is Switzerland occurs over extremely long periods, then your and your family’s potential to see all of Switzerland will be relatively limited. This is less true, however, if your family is very large, so large that at least one family member is present to explore each place that may be explored. In this case complete exploration of a discrete area may be achieved. Your ability to explore broader areas nevertheless will be limited at least in part by how long it takes you or your family to get there.
Abedon, S. T., Bartom, E. (2013). Plaques. Brenner’s Encyclopedia of Genetics. Maloy, S., Hughes, K. (eds). Academic Press, pp. 357-357.
Abedon, S. T., Yin, J. (2009). Bacteriophage Plaques: Theory and Analysis. Methods in Molecular Biology 501:161-174. [PubMed link]
Abedon, S. T., Yin, J. (2008). Impact of Spatial Structure on Phage Population Growth. In: Bacteriophage Ecology, Abedon, S. T. (ed), Cambridge University Press, Cambridge, pp. 94-113.
For videos of my explorations of Switzerland, as well as other aspects of my existence, see youtube.com/channel/UCf0uLeBfCToHT3eAoYFmcNA.