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Posted: July 26th, 2022

Examination and clarification of bioluminescence in marine creatures

In order to isolate bioluminescent bacteria from marine samples, one must have a better understanding of the phenomena of bioluminescence. Bioluminescence is a type of luminescence. The light that usually occurs at low temperatures is called luminesence [1]. Chemiluminescence, fluorescence is all the other types of luminescence and should not be confused with bioluminescence.

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As the result of a given reaction, emission of heat and light takes place, this phenomenon is referred to as chemiluminescence or in other words, chemiluminescence refers to the emission of light in an exergonic reaction. For example, if two reactants namely A and B react, it results in the formation of product, with an excited intermediate C and generation of light.

[A] + [B] → [C] → [Products] + light

This is how a chemical reaction takes place [1].

When a substance that has absorbed light or any other radiation of different wavelength in the electromagnetic spectrum, an emission of light takes place by that substance, this is referred to as fluorescence. In most cases, emitted light has a longer wavelength, and therefore lower energy, than the absorbed radiation which has a higher energy [1].

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In simple language, bioluminescence is the emission of light from living organisms. One can also describe bioluminescence as chemiluminescence in living organisms.

Further clarifications regarding the types of luminescence can be carried out with the help of an experiment that involves the use of glow or light sticks. A solution of luminol in DMSO, sodium hydroxide pellets, an aqueous solution of fluorescent dye and test tubes. Luminol is a versatile chemical that exhibits chemiluminescence, with a striking blue glow, when mixed with an appropriate oxidizing agent [1] [2].

Glow sticks are used to demonstrate the effect of temperature on the rates of chemical

reactions. The glow sticks contain two chemicals that are mixed when the glass tube on the

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inside is broken. This initiates a chemical reaction that gives off light. Higher the reaction

temperature, faster is the reaction, and more intense the chemiluminescence. Reaction rates

increase about two times for every 10°C rise in temperature [2].

The luminol experiment demonstrates chemiluminescence and fluorescence. Luminol is

oxidized (with molecular oxygen) in the presence of sodium hydroxide pellets. On shaking the test tube (containing luminol and sodium hydroxide pellets), oxygen is introduced into the solution. Hence chemiluminescence stops when the test tube is set aside [2].

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When a fluorescent dye is added to the solution, the dye absorbs the light emitted by the luminol and re-emits light at a longer wavelength, changing the color, thus explaining the phenomena of fluorescence [2].

Bioluminescence is the emission of light observed in living organisms. Apart from bioluminescence, there are two other kinds of light emission that may take place from a living organism. These include:

(I)Photosynthetic delayed light emission:. It is a weak red light which is emitted by all green plants and algae. This intensity is so low that one cannot see it, though it can be measured [3].

(II)Ultraweak light emission: this occurs in all organisms. It is due to various processes, mostly (but not always) involving molecular oxygen. It is regarded as a by-effect of metabolic activity, but doesn’t have a biological function. It cannot be seen [3].

2. Bioluminescence

This is the best known biological luminescence phenomena, mostly because it can be observed using one’s eyes only. The bioluminescence occurs among a variety of organisms ranging from bacteria, dinoflagellates, protozoa, sponges, mollusks, echinoderms, insects and fish. The majority of bioluminescent species live in the sea, although there are also many terrestrial bioluminescent insects, especially the beetles. It has been estimated that 60-80% of the fishes in the deep sea are bioluminescent [3].

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(i) jellyfish

(ii) lightfish

(iii) fungi

(iv) beetle

Fig 2.1: The above pictures show bioluminescence in variety of organisms.

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The bioluminescent bacteria mainly falls under three genera namely – Photobacterium, Vibrio, and Photorhabdus. Species within the genus Photobacterium and Vibrio generally exist in marine environment whereas the terrestrial species belong to the genus Photorhabdus. Species within the Photobacterium genus are generally light organ symbionts of marine animals, whereas the Vibrio species exist as free-living forms as well as symbionts in the sea [4].The luminescence of these microorganisms should not be confused with the host organisms. Many fish and molluscs species which have been regarded as bioluminescent organisms have been shown to glow by the light of symbiotic bacteria [3]. The bacteria forms a symbiotic relationship with the host organism as it is provided with a nutrient rich environment for its growth and the host organism has the benefit of camouflage and protection from its predator. Some of the bioluminescent bacteria are obligate symbionts that fulfill their nutritional requirements only from the host, hence they cannot be grown in the laboratory as they cannot be separated from the host organism [4]. Apart from sharing a symbiotic relationship with the host organisms, some of the bioluminescent bacteria are also parasitic in nature, for example, the species in the genus Photobacterium and Vibrio infect the male crustaceans whereas the species in Photorhabdus genus infect terrestrial insects such as caterpillars with nematodes acting as an intermediate host for the bacteria. Majority of the bioluminescent bacteria present on the surface of the marine organisms act as non-specific parasites. The bacterium that resides in the guts of some marine organisms such as crustaceans produces chitinase (an enzyme) that facilitates the decomposition of chitin which is present in their exoskeleton.

The different species of bioluminescent bacteria differ from each other in a number of properties including the optimal growing conditions i.e. the nutritional requirements and optimal growth temperature, and the reaction kinetics of the enzyme luciferase involved in light generation.

However, the morphology of all bioluminescent bacteria is the same i.e. they are rod-shaped, gram-negative microorganisms with flagella facilitating motion. Bioluminescent bacteria are also capable of growth when the supply of molecular oxygen is limited; therefore they are also examples of facultative anaerobes. Despite the physiological diversity among different species of bioluminescent bacteria, all these microorganisms utilize highly homologous biochemical machineries to produce light. The onset and the energy output of this light-producing molecular machinery are tightly regulated under a central signaling pathway [4].

2.1 Bioluminescence by squids:

Light-emission by most of the marine organisms belongs in the blue and green light spectrum.This is due to two reasons, firstly because the blue-green light (wavelength around 470 nm) transmits farthest in water, and secondly because most of the organisms are sensitive only to blue light, lacking pigments for the visualization of longer or shorter wavelengths[1].

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Squid changes the color of the light emitted i.e. either blue or green light depending on its surrounding temperature. In case of squids, it produces green light when swimming in warm water and blue light in cold water [5]. During the day, the squid resides in the deep waters rather than on surface waters. The sunlight that falls on the deep waters has been filtered with only blue light remaining. The squid matches this color by turning on its blue photophores (photophores are light producing tissues). During the night, the squid is present on the shallow water. The moonlight at shallow depths has not been filtered to a greater extent, as a result both blue and green light remains. The squid matches this color by turning on both of its green and blue photophores [5].

Fig 2.1.1: The picture shows squid’s bioluminescence [5]

2.2 Advantages of Bioluminescence:

There are four main advantages attributed to bioluminescence: Camouflage, attraction, repulsion, and communication.

Camouflage

Some squids by using the phenomena of bioluminescence defend themselves against predators by producing light (a soft glow) on their ventral surface to match the light coming from above and making their presence indetectable to the potential predators(just as a darker dorsal surface makes aquatic organisms difficult to detect from above. Some can also change the color of their luminescence to match moonlight or sunlight. This is referred to as counterillumination [1].

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Attraction

Bioluminescence is also used as to attract prey by several deep sea fish, such as the anglerfish. A dangling appendage or a light-emitting rod that extends from the head of the fish that carries the bioluminescent bacteria attracts small animals to the front of its mouth.

Fig 2.2.1: Anglerfish lures its prey by using bioluminescence [4].

The cookie cutter shark also uses bioluminescence for luring its prey. A small patch on its underbelly remains dark and tends to appear as a small fish to large predatory fish like tuna. When these fish such as tuna try to consume the small fish, they themselves become prey for the the shark. Dinoflagellates have an interesting twist on this mechanism. When a predator of plankton is sensed through motion in the water, the dinoflagellate luminesces. This in turn attracts even larger predators, which then consume the would-be predator of the dinoflagellate. The attraction of mates in fireflies during the mating season is another proposed mechanism of bioluminescent action. This is done by periodic flashing in their abdomens to attract the potential mates [1].

Repulsion

Certain small crustaceans also use bioluminescent chemical mixtures. A cloud of luminescence is emitted, which confuses and then repels a potential predator while the crustacean escapes to safety. This is also shown in some squids [1].

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Communication

Bioluminescence also plays a direct role in communication between bacteria. It promotes the symbiotic induction of bacteria into host species, and sometimes also plays a role in colony aggregation [1].

2.3 Biochemistry of the Bioluminescence Reaction

As mentioned earlier, bioluminescence is defined as emission of light by living organisms arising from exothermic or exergonic chemical reactions. It is due to the substrate-enzyme complex of luciferin-luciferase within the cytoplasm of the cell. Luciferin refers to any light-emitting compound whereas luciferase is an enzyme. The luciferin-luciferase complex differs among species.

In 1887, a scientist named Raphaël Dubois isolated light producing chemicals from the

piddock, which is a clam that stays in the burrow. He discovered that on placing the

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clam in cold water, light was seen in the water, that glowed for several minutes, indicating

that a light producing chemical was extracted from the clam’s tissues. He also observed that

if he made a hot-water extract from another clam and added this to the original cold-water

extract, he could reactivate the light reaction. Dubois called his hot-water extract luciferin and

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the cold-water extract luciferase. The reaction produces a molecule that is in an electronically excited state. After the molecule gives off energy, it goes back to the ground state and a photon of light is released [2].

Bacterial luciferase is the main enzyme that is used in the phenomena of bioluminescence. Apart from the involvement of luciferase, there are certain other enzymes that supply and regenerate the substrates of luciferase. In bacteria the expression of the genes related to bioluminescence are encoded by an operon called the lux operon. The lux operon is a 9 kilobase fragment that controls bioluminescence through the catalyzation of the enzyme luciferase. The lux operon has a known gene sequence of luxCDAB(F)E, where lux A and lux B code for the components of luciferase, and the lux CDE codes for a fatty acid reductase complex that makes the fatty acids necessary for the luciferase mechanism. Lux C codes for the enzyme acyl-reductase, lux D codes for acyl-transferase, and lux E makes the proteins needed for the enzyme acyl-protein synthetase. Apart from these genes, there are two more genes namely luxR and luxI that play an important role in the regulation of the operon [1]. Other genes including luxF, luxG, and luxH, whose functions are neither clearly defined nor apparently necessary for bioluminescence are also found in some lux operons [4].

Fig 2.3.1The arrangement of luxCDABE operon [4]

Luciferase is a heterodimer consisting of two different polypeptide chains- alpha and beta (molecular mass 40 kDa and 37 kDa, respectively, and encoded by the luxA andluxB genes, respectively). The active site is located within the alpha-beta subunit. Absence of beta subunit leads to light emission of a weaker intensity. Studies have shown that the crystal structure of V. harveyi luciferase interacts and forms complex binding patterns between several side chains and backbone amides of the alpha and beta subunits. Studies also reveal that the function of the beta subunit is to act as a supporting scaffold by assisting in the conformational change of the subunit during the catalysis [4].

Fig 2.3.2: Bacterial luciferase structure [4].

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Fig 2.3.3: The rectangular box highlights the inter-subunit interactions’ (ionic attractions, hydrogen bonds, hydrophobic interactions) that play an important role in the assembly of bacterial luciferase enzyme [4].

Bacterial luciferase uses reduced flavin mononucleotide (FMNH2), molecular oxygen, and long chain fatty aldehyde as substrates. During the reaction, the oxidation of FMNH2 and aldehyde concomitant takes place along with the reduction of molecular oxygen and emission of energy, which is released as blue/green light ( MAX~ 490 nm). The energy level of the photon that was produced when the excited electron on the flavin chromophore returns to the ground state is indicated by the characteristic color. Studies have shown that point mutations at the flavin chromophore’s binding site brings about a change in the color emission spectrum of bacterial bioluminescence, indicating that the distinctive emission color depends not only on the chromophore, but also on the electronic nature of the chromophore-binding microenvironment in luciferase.

Aside from bacterial luciferase, some luminescent bacteria also carry fluorescent proteins to; distinguish themselves from other strains by modulating the emission color [4].

For continuous light emission, constant supply of the substrates should be maintained by the enzymes coded by the Lux operon.

In addition to bacterial bioluminescence, all the other biological luminescence systems (such as fireflies, coelenterates and dinoflagellates) also utilize molecular oxygen as the oxidizing agent in their luminescence biochemistry, and the processes involved in the reduction of the molecular oxygen serves as an energy sink, draining the reducing power of the substrates. High energy unstable intermediates are formed that dissipate the potential energy of the excited chromophore in the form of light. In this regard, molecular oxygen can be considered to serve as a key to unleash the energy deposited in FMNH2 and fatty aldehyde for bacterial bioluminescence [4]. 

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Fig 2.3.4: The pathway [4]

For example, in case of fireflies luciferin reacts with oxygen, with luciferase acting as an enzyme aided by cofactors such as calcium ions, thus emitting light.

2.4 Quorum sensing:

The definition of quorum sensing states that it is a type of decision making process used by decentralized groups to coordinate behavior [1]. From the biological aspect, there are many species of bacteria such as Vibrio fischeri, Escherichia coli, Salmonella enterica, Pseudomonas aeroginosa that use quorum sensing to coordinate their gene expression according to the local density of their population. It was first discovered in Vibrio fischeri [1].

Since Vibrio fischeri uses quorum sensing, it constantly produces signaling molecules called as autoinducers. These bacteria have a receptor that recognizes these signaling molecules. When the autoinducers bind to these receptors, it results in the transcription of certain genes, including those for inducer synthesis. There are less chances of the bacterium recognizing its own signaling molecules, hence for the activation of gene transcription, the cell must also encounter signaling molecules from the local environment. Autoinducers and inducers are interchangeably used. If there is less number of same types of bacteria present in the local environment, then the concentration of the inducer decreases to zero thus inactivating the gene transcription. But if the population of the bacteria increases, the concentration of the autoinducers increases, thereby resulting in the activation of gene transcription, thus causing bioluminescence. Therfore, quorum sensing plays a very important role in the regulation of luxCDAB(F)E expression in bioluminescent bacteria [1] [4] .

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Fig 2.4.1: Chemical structure of the autoinducers of bioluminescent bacteria [4]

The autoinducer is a metabolic product that diffuses easily across the cellular membrane [4].

Fig 2.4.2: The fig. shows the role played by an autoinducer in the mechanism of quorum sensing [4].

Marine bioluminescent bacteria that is not present as a symbiont (free living bacteria) does not emit light. This is because for the emission of light, accumulation of autoinducers is necessary and this is possible only in a nutrient rich environment which is provided to the symbiotic bacteria [4].

2.5 Applications of bioluminescence:

One of the major applications of bioluminescence is the development of biosensors. A biosensor is a device that detects, records, and transmits information regarding a physiological change or the presence of various chemical or biological materials in the environment. Some bacteria have been designed that gives off a detectable signal when in presence of a pollutant (e.g. – toluene) that it likes to consume [6].

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In terms of using the phenomena of bioluminescence, efforts are being made to engineer agricultural plants that show luminescence when need watering [1].

As the primary function of bacterial luciferase is to catalyze the emission of light, this feature together with generation of the aldehyde substrate by fatty acid reductase can be successfully produced in other bacteria, by the transfer of the luxCDABE genes, which convert nonluminescent bacteria into light emitters [4].

Fig 2.5.1: The insertion of the foreign luxCDABE structural genes into the organism such as E. coli confers the organism the ability to emit light [4].

The ability of the non-luminescent bacteria to emit light by means of recombinant DNA technology has provided researchers an easy alternative to measure and detect the growth and living conditions of bacteria. The phenomena of bacterial bioluminescence are used in the detection of pathogenic bacteria in human food sources. By culturing a food sample in the presence of a recombinant bacteriophage (vector) carrying the luxCDABE insert, one can readily determine the contamination by bacteria in the food source. In addition, the light emitting property of the luxCDABE genes has been employed as a reporter of gene expression for studying regulatory controls involved in affecting the efficiency of RNA polymerase in initiation and transcription at different promoters. Then the luxCDABE genes are under the control of an environmentally regulated promoter (e.g., promoters whose efficiency is highly sensitive to the level of mercury, arsenic, or other pollutants), the structural lux genes can function as a biosensor, whose expression will monitor the presence of toxic waste in the environment. In the pharmaceutical industry, genetically modified bacteria carrying the lux genes have been utilized to evaluate the efficiency of antibiotics in fighting against bacterial infections in mammals; with animals such as mice, pigs, and monkeys serving as potential human models. In this screening procedure, the lesser the intensity of luminescence in the infected organs/tissues, the more efficient the antibiotics against bacterial infection; therefore, bacterial bioluminescence serves as an indicator of bacterial growth allowing the proper dosages of antibiotics to be determined and effective treatment to be established [4]. 

3. Laboratory Experiment

3.1 Sample Collection:

After the literature study, it was decided that squid will serve as a sample for this experiment as it is readily available in the U.A.E. fish market. A fresh catch was taken as a sample for this experiment. Since some of these microbes i.e. bioluminescent bacteria are also found in seawater, seawater sample from Sharjah was also collected for this experiment.

3.2 Methodology for the isolation of bioluminescent bacteria from squid:

Materials Required:

Squid

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Luminescent Broth (Appendix 1)

Luminescent Agar (BOSS Medium) (pH=7.3) (Appendix 2)

Procedure:

1. The squid is placed in a beaker and just enough 3.0% NaCl solution is added such that approximately 10-20% of the sample is above the level of the liquid as shown in fig 3.2.1. The NaCl solution preserves the squid by preventing any other microbial growth other than that of bioluminescent bacteria, as required.

Fig 3.2.1: Squid placed in a beaker containing NaCl solution.

2. The flask is then kept for incubation in a cool dark room (18-22°C) and is observed at intervals up to 24 hours. The room is darkened totally such that the flask can be observed for luminous areas on the sample. Sometimes the squid secretes ink that might hinder the view of luminous areas on the squid. In order to prevent this, the NaCl solution is changed when required.

3. Four petriplates of Luminescent Agar (formula above) are streaked from four different luminous areas on the squid. Forceps and craft knife are required and it is used one at a time in the burner for its sterilization. The knife and forceps are then cooled for a while. Squid is held with the forceps and its skin is gently scraped of that shows luminescence with the tip of the knife. The scraped off skin is transferred on to a sterile inoculating loop for streaking on the plates.

4. The plates are then kept for incubation in the cool room (18-22°C) for 24 hours. (No more than 48 hours.)

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5. After observing luminous isolated colonies, these isolated colonies are individually streaked on to a new plate of Luminescent Agar and incubated as above.

Fig 3.2.2: Streaked petriplates

6. One or more of the more brilliant colonies is then chosen and streaked onto a slant of Luminescent Agar. The agar slants are incubated overnight or until luminescent growth is seen and then refrigerated.

7. From the agar slants, flasks of Luminescent Broth are inoculated. The flasks are then placed in the shaking incubator for 10-15 hrs at 18-22°C.

[8]

The flasks that show bioluminesence is then used for studying the growth curves and characterization of the bioluminescent bacteria.

Result and Inference:

No luminous colonies were observed from the squid on the first attempt, even though the squid did show luminous areas on its body surface. The failure can be attributed to the fact that streaking was not carried out on the same day it showed luminescence.

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However, on the second attempt, out of the four petriplates that were streaked with the skin of the squid, only one petriplate showed six luminous colonies.

Fig 3.1.3: The above pictures are a reference as to how colonies appear when placed in light (left picture) and dark (right picture) [10].

The colonies that appeared during the course of my experiment (only six in number) were not so densely populated as observed in the pictures above.

These six colonies were then streaked on six different petriplates containing Luminescent Agar. The picture below shows bioluminescence in the streaked petriplates.

Fig 3.2.4: The picture below shows bioluminescence in the streaked petriplates.

The agar slants were also prepared from the petriplates.

The six flasks containing Luminescent Broth were then inoculated with culture from the agar slants. The flasks were then kept in the shaking incubator for 18-24 hrs. at room temperature.

Out of the six flasks containing Luminescent Broth, only three flasks showed microbial growth. The bacterial cultures were then used for growth curves.

3.3 Methodology for the isolation of bioluminescent bacteria from seawater sample:

Materials Required:

Seawater sample was collected from Sharjah.

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Seawater Complete Agar (Appendix 3)

Procedure:

1. Seawater sample is collected in a clean container

2. Two plates of SWC agar medium were then prepared.

3. The two plates were then pipetted with 0.1 ml and 0.2 ml of seawater sample respectively.

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4. The samples were thoroughly spread over the surfaces of the plates with a L-shaped glass rod.

5. The plates are then inverted after the samples have absorbed into the agar (about 5 minutes) and then kept for incubation at room temperature.

6. The plates were then examined after 18-36 hours.

[7]

Result and Inference:

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The plates did not show any luminous growth. This maybe because the sample that was collected was not from deep water as bioluminescent bacteria tends to be present in deep waters. Since no growth was observed, further steps involving the preparation and inoculation of agar slants and luminescent broth could not be carried out.

3.4 Bacterial Growth curve of the isolates:

Out of the six flasks that contained Luminescent Broth, only three flasks showed microbial growth. The three flasks that showed microbial growth were then again inoculated into three flasks containing luminescent broth. Their O.D. (optical density) values were measured after every 30 minutes (for 5 hrs) at 530 nm using UV-visible spectrophotometer. The initial O.D. value should be set at 0.05 so that there is sufficient bacterial culture in the broth. The values then helped us in determining the bacterial growth curves.

Fig 3.4.1: UV-visible spectrophotometer [11]

Procedure:

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1. The machine along with the monitor screen is turned on using the switch.

2. The necessary adjustments are then made in the program.

3. For auto zeroing the sample, the blank (broth in which are bacteria is growing) is placed in the cuvette. The cuvette is then placed in the holder.

4. The O.D. values of all the three samples are measured after every 30 minutes for 5 hrs.

5. The optical density vs. time graph is then plotted for all the three samples.

Observation Table:

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Table 3.4.1: Sample 1

Time (in hrs.)

O.D. values

0

0.08

0.5

0.09

1

0.12

1.5

0.16

2

0.21

2.5

0.28

3

0.38

3.5

0.5

4

0.71

4.5

0.99

5

1.14

5.5

1.41

Table 3.4.2: Sample 2

Time (in hrs.)

O.D. values

0

0.05

0.5

0.06

1

0.08

1.5

0.12

2

0.16

2.5

0.21

3

0.25

3.5

0.38

4

0.44

4.5

0.48

Table 3.4.3: Sample 3

Time (in hrs.)

O.D.values

0

0.13

0.5

0.15

1

0.18

1.5

0.23

2

0.3

2.5

0.38

3

0.53

3.5

0.71

4

1.04

4.5

1.16

5

1.37

Result and Inference:

Graph 3.4.1: Bacterial growth curve of sample 1

Graph 3.4.2: Bacterial growth curve of sample 2

Graph 3.4.3: Bacterial growth curve of sample 3

The bacterial growth curves of all the three samples suggest that the cultures are still in their exponential phase. The 0.D .values should be measured for a much longer duration so that the stationary and the death phases can also be observed. The broth was kept overnight in the shaking incubator at 18-22°C. Next morning, only one of the samples showed bioluminescence indicating that the bacterial culture has grown to that level when the lux genes are switched on.

Fig 3.4.2: The picture is a reference as to how a flask containing Luminescent Broth shows luminescent growth [6]. The bioluminescence that was observed during my experiment was of low intensity.

3.5 Luminescence (light emission intensity) curve studies on the isolates:

For the growth curve studies, agar slants were used to streak on to the petriplates, for the isolation of bioluminescent bacteria. The same set of agar slants were used to revive the culture. The revived culture was then streaked on to the luminescent agar petriplates to study the luminescence curve. However, contamination was observed in the petriplates, even though luminescent colonies were formed. Majority of the colonies that were formed were circular in shape and opaque with a dense material in the centre. Some of the colonies were circular and translucent. These colonies were then again used for sub-culturing. Contamination was again observed in the petriplates. This might be attributed to some error in the methodology of streaking the petriplates. Finally, after five attempts, successful isolation of bioluminescent bacteria took place. These bacteria were then inoculated in the flasks containing luminescent broth. After an over night incubation, these flasks showed bioluminescence. These samples were then taken for measuring their light emission studies with the help of an autoanalyser. The luminescence is measured after every one hour. It is measured in terms of counts per second (cps). Meanwhile, the samples are kept in the shaking incubator.

Fig 3.5.1: Perkin-Elmer Auto-analyzer [12]

Procedure:

1. The machine along with the monitor screen is turned on using the switch.

2. The luminescence mode is then chosen.

3. The wells in the microtitre plate containing the sample are then chosen in the protocol editor.

4. The program is then started.

5. The luminescence of all the three samples is measured after every 1hour.

5. The optical density, luminescence vs. time graph is then plotted for all the three samples.

Observation Table:

Table 3.5.1: Bacterial Sample 1

Time (hrs.)

Cell Density(O.D.)

Light emission

Intensity (cpu)

0

0.0785

0.5

0.0926

1

0.1189

1.5

0.155

2

0.2139

2.5

0.2826

3

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