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.