Population Balances
Although population balances date back to the days of Boltzmann, this is an area in which chemical engineering leadership has been notable since the 1960s.71,72,55 The contribution of chemical engineers has been especially creative since the coinage of the term “internal” coordinates by Hulburt and Katz71 for variables other than spatial location of an entity which opened the flood gates to a plethora of applications. Numerous reviews provide perspectives of population balances.73,74,75,76. An application of consequence to biology is the formulation of signal transduction problems in a population setting. The signaling variables become internal coordinates of the cell and the stochastic process characterizing the dynamics of intracellular reactions translating into the convective and diffusive transport of cells in the abstract space of internal coordinates. This transport can also occur in conjunction with spatial transport if the cells were in motion through physical space.77,78 The transfer of drug resistance between bacterial species, which has been of major concern in combating bacterial infection, is a significant area of application.79,80 This transfer occurs by exchange of resistance bearing plasmid DNA from the “donor” cell to the “recipient” following signaling reactions in the donor as shown in Figure 1. A single cell stochastic model, oblivious to the presence of other cells in the neighborhood, would show a steady state population distribution in which individual cells exhibit stochastic dynamics, whereas the more relevant population balance model would paint a different picture of the same scenario as shown in Figure 2.