Exercise 11. Batch Growth of Escherichia coli

Objectives 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: 1. 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.

2. What is the average doubling time of E.coli? What factors contribute

to changes in this value? 3. 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 ?-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

[pic] where ? 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)

[pic] The time required for the cell numbers or dry weight to double, the

doubling time td, is related to the specific growth rate by [pic] 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: [pic] When ? and ? 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 [pic] 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:

[pic] 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 ? (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:

[pic] which for a batch system becomes

[pic] where X=Xo at t=0. This result is known as the logistic equation. The

maximum cell concentration attained at large times is 1/?, and the initial

rate of growth is approximately exponential, as ? 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[1] 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 ....

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