Fluctuations and freezing of biofilm-air interfaces

Abstract

The study of interfacial roughening is common in physics, from epitaxial growth in the lab to pio-neering mathematical descriptions of universality in models of growth processes. These studies led to the identification of a series of general principles. Typically, stochastic growth produces an interface that becomes rougher as the deposit grows larger; this roughening can only be counteracted by mechanisms that act on the top of deposit, such as surface tension or surface diffusion. However, even when relaxation mechanisms are present, interfaces that continue to grow stochastically continue to change; new peaks and troughs emerge and disappear as stochastic growth produces a constantly changing, dynamic interface. These universal phenomena have been observed for bacterial colonies in a variety of contexts. However, previous studies have not characterized the interfacial phenomena at the top surface of a colony, i.e., the colony-air interface, when activity is only present at the bottom surface, i.e., the colony-solid interface, where nutrients are available, over long times. As traditional interfacial roughening models primarily focus on activity occurring at the top surface it is unclear what phenomena to expect over long times. Here, we use white light interferometry to study the roughening of bacterial biofilms, from many different species. We find that these colonies are remarkably smooth, suggesting that a mechanism of interfacial relaxation is at play. However, colonies remain remarkably smooth even after growing large. We discover that topographic fluctuations "freeze" in place, despite the fact that growth continues for hundreds of microns more. With simple simulations, we show that this emergent freezing is due to the dampening of fluctuations from cell growth by the cells between the growing zone and the surface. We find that the displacement field caused by a single perturbation decays exponentially, with a decay length of{delta} L. In line with that observation we also show that the topography ceases to change when perturbations are a distance{delta} L away from the surface. Thus, over-damped systems in which activity occurs at the bottom surface represent a distinct class of interfacial growth phenomena, capable of producing frozen topographies and remarkably smooth surfaces from spatially and temporally stochastic growth.