A batch system is one in which all nutrients are present at the beginning and are not resupplied—there is no inflow or outflow, except perhaps for aeration. The flask of medium above in which E. coli was growing is a good example. In nature, a fresh deposit of cow manure on soil or the death of a fish in a pond would represent "batches" of nutrients made available at one time.
As the E. coli example demonstrated, exponential growth cannot continue for very long in a batch system. Depletion of substrates and/or buildup of inhibitory products will soon lead to decreasing specific growth rates. Thus, much of the time, microorganisms are likely to be growing at rates that are far below their m value. Equation (11.3) can still be used to describe this curve, but since m 6= constant, it can no longer be integrated to give equations (11.1) and (11.4).
Figure 11.22 shows a typical growth curve for a newly inoculated batch laboratory culture. For convenience, it can be broken up into the five phases shown and is discussed below. A similar response would be expected for other batch cultures.
Lag Phase The transfer of a small inoculum of "seed" cells into a fresh batch of medium generally involves new conditions for the organisms, such as different organic substrates, form of nitrogen, pH, oxygen tension, and/or salt concentration. It will frequently take some time, referred to as a lag, for the cells to become adapted to this new environment before they start growing exponentially. This may involve production of enzymes to metabolize new organic substrates or utilize nutrients in another form, or simply replacement of cell constituents that had been depleted previously. Depending on how big a change is required and how rapidly the organism can respond, the lag period may vary from seconds to many hours.
Some scientists differentiate between a lag period, during which there is no growth (m = 0), and the lag phase, which lasts until exponential growth begins. For a short time between these two points, the culture may appear to be growing at a rate that is linear in a plot of X vs. t. This sometimes is referred to as an arithmetic growth phase. However, it should be noted that increases in biomass during exponential growth start off very slowly, and unless very precise and sensitive measurements are made, this may mimic a lag or arithmetic growth period.
Exponential Growth Phase If an appropriate medium has been provided, once the organisms adapt to their new environment they will grow exponentially (m = c, where c is a constant greater than 0). Plenty of substrate and nutrients are available, and no harmful products of metabolism have yet accumulated. Thus, m will approach the maximum specific growth rate m for the organism in that particular environment (in Section 11.7.6 we discuss some factors that affect p.). However, this phase can last for only a relatively short period of time before the ideal conditions deteriorate.
Declining Rate of Growth Phase An old adage states that ''all good things must come to an end,'' and this certainly applies to unrestricted growth within a batch reactor. Eventually, one or more factors (usually, substrate depletion, but perhaps product buildup, pH shift, nutrient deficiency, and/or something else) trigger an inevitable decline in cell growth rate. Biomass still increases, but at a continually decreasing rate (m > 0, but decreasing).
Most often this decrease in m is the result of substrate depletion. This is commonly modeled by Monod kinetics, in which m = m
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