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4.7(10 ) bacteria in one day assuming a generation time of 20 minutes. Using the dimension of a bacterium of 2 pm diameter by 12 pm length, the volume of one bacterium is equal to 3.77(10_17) cubic meter. Thus, assuming that the density of the bacteria is the same as that of water, one bacterial cell will reproduce to (1000)(3.77) (10_17)(5)(1021) _ 188,500,000 kg in 24 hours! This mass is, of course, impossible to be obtained from one bacterium in a day. What this means, though, is, that in a real-world situation, the bacterium does not divide unrestricted, but is influenced by other environmental factors such as crowding and exhaustion of the food supply.

2.3.2 Test for the Coliform Group

The coliform group of microorganisms is defined as all aerobic and anaerobic, Gramnegative, nonspore-forming, rod-shaped bacteria that ferment lactose with gas and acid formation within 48 hours at 35°C. The group belongs to the genera Escherichia,

Aerobacter, Klebsiella, and Paracolobacterium and mostly inhabits the intestinal tract of humans, although they could also be found in the outside environment. Although also found outside the intestinal tract, this group of organisms is used as an indicator for the presence of pathogens in waters. Surface waters can be used for drinking purposes after treatment, so effluents from sewage treatment plant discharges are limited for the acceptable concentrations of these organisms, thus the necessity for testing.

The test for the coliform group may be qualitative or quantitative. As the name implies, the qualitative test simply attempts to identify the presence or absence of the coliform group. The quantitative test, on the other hand, quantifies the presence of the organisms. In all the tests, whether qualitative or quantitative, all media, utensils, and the like must be sterilized. This is to preclude unwanted organisms that can affect the results of the analysis.

Qualitative tests. Three steps are used in the qualitative test: presumptive, confirmed, and completed tests. These tests rely on the property of the coliform group to produce a gas during fermentation of lactose. An inverted small vial is put at the bottom of fermentation tubes. The vial, being inverted, traps the gas inside it forming bubbles indicating a positive gas production.

A serial dilution is prepared such as 10-, 1-, 0.1-, and 0.01-mL portions of the sample. Each of these portions is inoculated into a set of five replicate tubes. For example, for the 10-mL portion, each of five fermentation tubes is inoculated with 10-mL portions of the sample. For the 1-mL portion, each of five fermentation tubes is also inoculated with 1-mL portions of the sample and so on with the rest of the serial dilutions. In this example, because four serial dilutions (10, 1, 0.1, and 0.01) are used, four sets of five tubes each are used, making a total of 20 fermentation tubes.

In the presumptive test, a portion of the sample is inoculated into a number of test tubes containing lactose broths (or lauryl tryptose broth, also containing lactose) and other ingredients necessary for growth. The tubes are then incubated at 35 ± 0.5°C. Liberation of gases within 24 to 48 ± 3 hours indicates a positive presumptive test. Organisms other than coliforms can also liberate gases at this fermentation temperature, so a positive presumptive test simply signifies the possible presence of the coliform group.

A further test is done to confirm the presumptive test result; this is called the confirmed test. The theory behind this test uses the property of the coliforms to ferment lactose even in the presence of a green dye. Noncoliform organisms cannot ferment lactose in the presence of this dye. The growth medium is called brilliant green lactose bile broth. A wire loop from the positive presumptive test is inoculated into fermentation tubes containing the broth. As in the presumptive test, the tubes are incubated at 35 ± 0.5°C. Liberation of gases within 24 to 48 ± 3 hours indicates a positive confirmed test.

The coliform group of organisms does not come from only the intestinal tract of man but also from the outside surroundings. There are situations, as in pollution surveys of a water supply with a raw water source, that the fecal variety needs to be differentiated from the nonfecal ones. For this and similar situations, the procedure is modified by raising the incubation temperature to 44.5 ± 0.2°C. The broth used is the EC medium which still contains lactose. The high incubation temperature precludes the nonfecal forms from metabolizing the EC medium. Positive test results are, again, heralded by the evolution of fermentation gases not within 48 ± 3 hours but within 24 ± 2 hours.

Normally, qualitative tests are conducted only up to the confirmed test. There may be situations, however, where one would want to actually see the organism in order to identify it. Both the presumptive and the confirmed tests are based on circumstantial evidence only—not on actually seeing the organisms. If desired, the completed test is performed.

In the completed test, a wire loop from the positive confirmed test fermentation tube is streaked across either an Endo or MacConkey agar in prepared petri dishes or plates. The dishes are then incubated at 35 ± 0.5°C for 24 ± 2 hours. At the end of this period, the dishes are examined for growth. Typical colonies are growths that exhibit a green sheen; atypical colonies are light-colored and without the green sheen. The typical colonies confirm the presence of the coliform group while the atypical colonies neither confirm nor deny their presence. (From this, Endo agar method can also be used as an alternative to the brilliant green bile broth method.)

The typical or atypical colony from the Endo plate is inoculated into an agar slant in a test tube and to a fermentation tube containing lactose. If no gas evolves within 24 to 48 ± 3 hours after incubating at 35 ± 0.5°C, the completed test is negative. If gases had evolved from the tubes, the growth from the agar slant is smeared into a microscopic slide and the Gram-stain technique performed. If spores or Gram-positive rods are present, the completed test is negative. If Gram-negative rods are present, the completed test is positive.

Quantitative tests. In some situations, actual enumeration of the number of organisms present may be necessary. This is the case, for example, for limitations imposed on a discharge permit. Generally, two methods are used to enumerate coliforms: the membrane-filter technique and the multiple-tube technique.

The membrane-filter technique consists of filtering under vacuum a volume of water through a membrane filter having pore openings of 0.45 fim, placing the filter in a Petri dish and incubating, and counting the colonies that developed after incubation. The 0.45-um opening retains the bacteria on the filter. The volume of sample to be filtered depends on the anticipated bacterial density. Sample volumes that yield plate counts of 20 to 80 colonies on the Petri dish is considered most valid. The standard volume filtered in potable water analysis is 100 mL. If the anticipated concentration is high requiring a smaller volume of sample (such as 20 mL), the sample must be diluted to disperse the bacteria uniformly. The dispersion will ensure a good spread of the colonies on the plate for easier counting.

The M-Endo medium is used for the coliform group and the M-FC medium for the fecal coliforms. The culture medium is prepared by putting an absorbent pad on a petri dish and pipetting enough of the M-Endo medium or M-FC into the pad. After filtration, the membrane is removed by forceps and placed directly on the pad. The culture is then incubated at 35 ± 0.5°C in the case of the coliform group and at 44.5 ± 0.2°C in the case of the fecal coliforms. At the end of the incubation period of 24 ± 2 hours, the number of colonies that developed are counted and reported as number of organisms per 100 mL.

The other method of enumerating coliforms is through the use of the multiple-tube technique. This method is statistical in nature and the result is reported as the most probable number (MPN) of organisms. Hence, the other name of this method is the MPN technique. This technique is an extension of the qualitative techniques of presumptive, confirmed, and completed tests. In other words, MPN results can be a presumptive, confirmed, and completed MPNs. The number of tubes liberating gases is counted from each of the set of five tubes. This information is then used to compute the most probable number of organisms in the sample per 100 mL.

2.3.3 The Poisson Distribution

To use the MPN method, a probability distribution called the Poisson distribution is used. From any good book on probability, the probability (also called probability function) that a random variable X following the Poisson distribution will have a value y is where X is the mathematical expectation. Mathematical expectation is the average value obtained if the random variable X is measured exceedingly many times. Random variable is a function dependent on chance and whose values are real numbers. A certain probability is attached to the function; this contrasts with an ordinary variable in which the probability of its occurrence is not a concern, although it will always have a corresponding probability.

In order to gain an insight into the Poisson distribution, let us derive Equation (2.27). Assume conducting an experiment of sampling microorganisms from a population to obtain a sample consisting of n microorganisms. (A population is the total set of all possible measurements in a particular problem. A sample is a subset of the population that contains measurements obtained by an experiment.) Let y be the corresponding number of bacteria in the sample. The proportion of bacteria is therefore y/n. This is not, however, the true proportion of bacteria in the entire population. The true proportion is given by the limit limitn^Ny/n. In equation form, where in the limit y is replaced by the expected number of bacteria, X, and N is the total number of microorganisms in the population. (As will be learned later, X eventually determines the most probable number of bacteria.) Because X/N is the true proportion, it represents the probability that a bacterium can be picked from the sample or from the population. A single picking or observation of a bacterium in the sample is also called a trial. In this context, note that the sample can be thought of as comprising of several observations (picking) or trial.

If the probability of picking a bacterium is X/N, then the probability of not picking a bacterium is 1 _ X/N. It was assumed that there are y bacteria in a given

limity =

sample. Because these y bacteria are occurring at the same time, their simultaneous appearances are an intersection. From the intersection probability of events, the probability of obtaining these y bacteria is (X/N )(X/N )(X/N )...(X/N) = (UN )y. The occurrence of these bacteria, however, happens at the same time as the occurrence of the "not bacteria." If the number of bacteria in the sample is y, the number of not bacteria is n - y which, from the intersection probability of events, has a probability of occurrence of (1 - X/N)(1 - X/N)...(1 - UN) = (1 - X/N)n-y. Now, the simultaneous appearances of the bacteria and the not bacteria also has intersection probability, and this is given by the product of the probabilities as (X/N )y(1 - X/N )n-y.

There are several ways to obtain the y bacteria in the sample. The number of ways is given by the number of combinations of the n microorganisms taken y at a time, (n). We will not derive the formula for the number of combinations here since this concept is discussed in college algebra. The formula is

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