Exercise 11. Batch Growth of Escherichia coli - Berkeley
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Exercise 11. Batch Growth of Escherichia coli
Knowledge of the growth characteristics of an organism is an essential part of biotechnology in order to design bioreactors, achieve reproducible transformation efficiencies and for obtaining reproducible plasmid and recombinant protein yields. The rate of growth of an organism determines the batch fermentation time and the maximum dilution rate that can be employed in continuous fermentation. In this experiment we will examine the kinetics of growth of the bacterium Escherichia coli.
Prelab Questions for Exercise 11:
Sketch a growth curve for batch growth of E.coli with x-axis as growth time and y-axis as the log(# of cells). Label the phases of growth.
What is the average doubling time of E.coli? What factors contribute to changes in this value?
What factors cause the cells to die during the cell death exponential phase?
Phases of the Batch Growth-Cycle
When microbial cells are inoculated into a batch reactor containing fresh culture medium and their increase in concentration is monitored, several distinct phases of growth can be observed. There is an initial lag phase, which is of variable duration. This is then followed by the exponential growth phase, where cell number (and dry weight) increases exponentially. This is also referred to as the logarithmic phase, the name arising from the common method of plotting the logarithm of cell number against time. Following this is a short phase of declining growth, and then the stationary phase. Here the cell numbers are highest. Finally the cell numbers decline during the death phase.
The lag phase results from several factors. When cells are placed in fresh medium, intracellular levels of cofactors (e.g., vitamins), amino acids and ions (e.g., Mg2+, Ca2+ etc.) may be transported across the cell membrane and thus their concentration may decrease appreciably. If intermediates in metabolic pathways are required for enzyme activity, this dilution may reduce the rate at which various pathways operate. Cells must then metabolize the available carbon sources to replenish the intracellular pools prior to initiating cell division. Similarly, if the inoculum is grown in a medium containing a different carbon source from that of the new medium, new enzymes may need to be induced to catabolize the new substrate and this will also contribute to a lag. The point in the growth cycle from which the inoculum was derived is also important. Cells taken from the exponential phase and used as an inoculum generally show a shorter lag phase than those taken from later phases. These exponentially-derived inocula will have adequate concentrations of intermediates and will not suffer from the dilution effect. If an inoculum is placed in a rich medium, one containing amino acids and other complex carbon and nitrogen sources, a shorter lag phase results as the intermediates of metabolism are already provided.
When cells are placed in a medium which contains several carbon sources, several lag phases may result. This is known as diauxic growth. Cells preferentially use one carbon source prior to consuming the second, due to catabolite repression of the enzymes required to metabolize the second carbon source. For example, when E. coli is placed in a medium containing both glucose and lactose, glucose is consumed first and a lag phase follows as cells synthesize the enzyme bð-galactosidase, which is required for lactose utilization. During growth on glucose, the formation of this enzyme is under catabolite repression by cyclic AMP, and thus indirectly by glucose. Its concentration in the cell is thus very low. The cells consume glucose (with no additional metabolic energy expenditure) prior to lactose, which requires the synthesis of this enzyme.
Cell division occurs in the exponential phase. The rate of increase of cell number (N) is proportional to the number of cells. Cells increase in a geometric progression 20, 21, 22,..2m after m divisions. For example, if the initial cell number was No, the number after m generations is 2mNo.
Instead of cell number, it is often more convenient to use dry cell weight per volume X as a measure of cell concentration. During the exponential phase in a batch reactor we can write
where mð is the specific growth rate of the cells. The above equation can be integrated from the end of the lag phase (X = Xo, t = tlag) to any point in the exponential phase (X,t)
The time required for the cell numbers or dry weight to double, the doubling time td, is related to the specific growth rate by
Occasionally it is found that the doubling times for cell number and cell dry weight may differ, as a result of a non-constant cell mass per cell during the exponential phase. Therefore, we define the cell number specific growth rate (hr-1) separately from the specific growth rate (hr-1) as follows:
When nð and mð are equal, growth is referred to as balanced. In balanced growth, there is an adequate supply of all non-limiting nutrients, so that the composition of the cell is constant even though the concentrations of all other nutrients may be decreasing. On the other hand, when growth is unbalanced, variations in cell composition (e.g., protein content) may occur. Although the cell number growth rate may be constant, the cell mass growth rate will vary.
At low nutrient concentrations, it is found that the specific growth rate depends on the nutrient concentration. At high concentrations, the specific growth rate reaches a maximum value, set by the intrinsic kinetics of intracellular reactions, which are related to DNA transcription and translation. The end of the exponential phase arises when some essential nutrient, for example the carbon or nitrogen source, is depleted or when some toxic metabolite accumulates to a sufficient level. Even if very high concentrations of nutrients are employed, the accumulation of toxic metabolites (e.g., acetic acid in the case of E. coli growing on glucose) will limit the concentration of cells that can be attained in the exponential phase in a batch reactor. This limitation can be overcome by retaining cells by filtration, while supplying a continuous flow of nutrients and removing products.
Following the exponential growth phase, the rate of exponential growth decreases (declining growth phase) and is followed by the stationary phase. The duration of the stationary phase may vary with cell type, previous growth conditions etc. Some cells may lyse, releasing nutrients that can be consumed by other cells, and thus maintain the cell population. Following this is the death phase. During the death phase, it is thought that cell lysis occurs and the population decreases. Intracellular metabolites are scavenged by different enzyme systems within the cell and toxic metabolites may accumulate. The rate of decline is also exponential, and is represented during the death phase as
We shall now turn our attention to models which relate the specific growth rate to substrate concentrations and other external variables. The simplest of these do not consider the various phases of the growth cycle, but predict only the rate of growth in the exponential phase. We shall then consider more complex models.
Unstructured Growth Models
The simplest relationships describing exponential growth are unstructured models. These models view the cell as a single species in solution and attempt to describe the kinetics of cell growth based on cell and nutrient concentration profiles. The models that were first developed for cell growth did not account for the dependency of the exponential growth rate on nutrient concentration; they were devised to have a maximum achievable population built into the constitutive expressions employed. Such models find applicability today when the growth-limiting substrate cannot be identified. The simplest model is that of Malthus:
where rX is the volumetric rate of increase in dry cell weight (which we shall abbreviate as DCW) (e.g., gm DCW/liter-hr) and mð (hr-1) is constant. This model predicts unlimited growth with time ("Mathusian" growth). To provide a means to limit growth, Verlhulst (1844) and later Pearl and Reed (1920) proposed the addition of an inhibition term which was cell concentration dependent:
which for a batch system becomes
where X=Xo at t=0. This result is known as the logistic equation. The maximum cell concentration attained at large times is 1/bð, and the initial rate of growth is approximately exponential, as bð is usually considerably less than unity.
The Monod Model
One of the simplest models which includes the effect of nutrient concentration is the model developed by Jacques Monod based on observations of the growth of E. coli at various glucose concentrations. It is assumed that only one substrate (the growth-limiting substrate, S) is important in determining the rate of cell proliferation. The form of the Monod equation is similar to that of Michaelis-Menten enzyme kinetics; in fact if substrate transport to the cell is limited by the activity of a permease, cell growth might well be expected to follow the Michaelis-Menten form given below:
Thus for batch growth at constant volume:
where mðmax is the maximum specific growth rate of the cells, and KS is the value of the limiting nutrient concentration which results in a growth rate of half the maximum value. This equation has two limiting forms. At high substrate concentrations, S >> KS, and the equation reduces to a zeroth order dependence on substrate concentration. At low substrate concentrations, S