How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 570

Maintenance coefficient (m S ) is an important parameter in fermentation process and has
great influence on the biomass and product yield. The primary method for the determination
of maintenance coefficient is obtained from the linear relation E qn (11.28) . To get an accurate
result of m s , the rates should be precisely measured in a wide range. However, the true
substrate consumption rate for maintenance process may be a function of the specific growth
rate when both cell maintenance requirements and endogenous metabolic needs are consid-
ered. A linear relation between the total or true maintenance coefficient and the cell growth
rate has been proposed by Ma et al. (H.W. Ma, X.M. Zhao, X.F. Guo. 2002. “Calculation of
empirical and true maintenance coefficients by flux balance analysis”, Chinese J. Chem.
Eng., 10 (1): 89 e 92)

m true

S ¼ am G þ b (11.30)
where m true is the true maintenance coefficient (J. Nielsen, J. Villadsen, G. Lid ´ n. 2003 Bio-
reaction Engineering Principles, Plenum Press: New York). However m true is difficult to be

determined experimentally. We normally drop the superscript true.
Despite its empirical nature, the maintenance coefficient approach, Eqn (11.28) gives
a good description of the specific substrate uptake rate for many cellular systems especially
at high growth rates. However, the simple linear rate equation does not in a biologically satis-
factory way explain what the extra substrate consumed for maintenance is in processes. Not
only m S is a constant, but YF X/S varies apparently with the specific growth rate as well.
During the stationary phase where little external substrate is available, endogenous metab-
olism of biomass components (no substrate consumption) is used for maintenance energy.
Cellular maintenance represents energy expenditures to repair damaged cellular compo-
nents, to transfer some nutrients and products in and out of cells, for motility, and to adjust
the osmolarity of the cells' interior volume.
Utilization of energy, and consequently substrate, in all the processes involved with cell
maintenance is likely to be a function of the specific growth rate. When the specific growth
rate is high, there is a high turnover of macromolecules (eg. mRNA), and with increasing
activity level in the cell, it is for example necessary to pump more protons out of the cell.
Furthermore, with a higher flux through the cellular pathways, there is a higher loss of
energy due to the hydrolysis of high-energy phosphates such as ATP. This is biologically
reasonable since when the cells grow under limited conditions (a low specific growth
rate), they will try to use the substrate as efficiently as possible, and the maintenance
processes are therefore curtailed. The energy expenditure in maintenance processes is there-
fore likely to be an increasing function of the specific growth rate. Thus, part of the Gibbs free
energy spent in these maintenance processes may be included in the overall yield factor YF X/S ,
and only the part of free energy that is spent not directly proportional to the specific growth
rate are included in the maintenance coefficient.
Bauchop and Elsden (T. Bauchop, S.R. Esden. 1960 “The growth of microorganisms in rela-
tion to their energy supply”, J. Gen. Microb. 23 :35 e 43) introduced the concept of ATP require-
ments for biomass synthesis via the yield factor YF ATP/X and proposed a balance equation
that is analogous to Eqn (11.28) :

r ATP ¼ YF ATP =X m G þ m ATP (11.31)