The Growth of Some Bacterial Populations Can Be Described by ,matlab
The Growth of Bacterial Populations (page iii) (This chapter has four pages) © Kenneth Todar, PhD The Bacterial Growth Bend In the laboratory, under favorable atmospheric condition, a growing bacterial population doubles at regular intervals. Growth is by geometric progression: 1, ii, 4, eight, etc. or 20, twoone, 2two, ii3.........2n (where n = the number of generations). This is called exponential growth. In reality, exponential growth is only function of the bacterial life cycle, and non representative of the normal pattern of growth of bacteria in Nature. When a fresh medium is inoculated with a given number of cells, and the population growth is monitored over a period of fourth dimension, plotting the data will yield a typical bacterial growth curve (Figure three below). Four characteristic phases of the growth cycle are recognized. 1. Lag Stage. Immediately subsequently inoculation of the cells into fresh medium, the population remains temporarily unchanged. Although there is no apparent cell partition occurring, the cells may be growing in book or mass, synthesizing enzymes, proteins, RNA, etc., and increasing in metabolic activeness. The length of the lag stage is apparently dependent on a broad variety of factors including the size of the inoculum; time necessary to recover from physical harm or shock in the transfer; fourth dimension required for synthesis of essential coenzymes or division factors; and time required for synthesis of new (inducible) enzymes that are necessary to metabolize the substrates present in the medium. 2. Exponential (log) Stage. The exponential phase of growth is a pattern of counterbalanced growth wherein all the cells are dividing regularly by binary fission, and are growing by geometric progression. The cells split up at a constant charge per unit depending upon the limerick of the growth medium and the weather condition of incubation. The rate of exponential growth of a bacterial civilization is expressed equally generation fourth dimension, also the doubling time of the bacterial population. Generation time (Yard) is defined as the time (t) per generation (n = number of generations). Hence, G=t/due north is the equation from which calculations of generation time (below) derive. three. Stationary Phase. Exponential growth cannot be connected forever in a batch culture (e.m. a closed system such equally a exam tube or flask). Population growth is limited by 1 of three factors: 1. exhaustion of available nutrients; two. accumulation of inhibitory metabolites or stop products; 3. exhaustion of infinite, in this instance called a lack of "biological space". During the stationary stage, if feasible cells are beingness counted, it cannot be determined whether some cells are dying and an equal number of cells are dividing, or the population of cells has but stopped growing and dividing. The stationary phase, like the lag phase, is not necessarily a period of quiescence. Bacteria that produce secondary metabolites, such as antibiotics, do then during the stationary stage of the growth cycle (Secondary metabolites are defined equally metabolites produced after the active stage of growth). It is during the stationary phase that spore-forming leaner take to induce or unmask the activity of dozens of genes that may be involved in sporulation process. 4. Death Phase. If incubation continues after the population reaches stationary phase, a death phase follows, in which the viable jail cell population declines. (Note, if counting by turbidimetric measurements or microscopic counts, the death stage cannot be observed.). During the expiry phase, the number of viable cells decreases geometrically (exponentially), substantially the reverse of growth during the log phase. Growth Rate and Generation Fourth dimension Equally mentioned to a higher place, bacterial growth rates during the phase of exponential growth, nether standard nutritional conditions (culture medium, temperature, pH, etc.), define the bacterium'south generation fourth dimension. Generation times for bacteria vary from about 12 minutes to 24 hours or more than. The generation fourth dimension for East. coli in the laboratory is 15-20 minutes, but in the intestinal tract, the coliform's generation time is estimated to be 12-24 hours. For most known leaner that tin be cultured, generation times range from nearly 15 minutes to ane 60 minutes. Symbionts such every bit Rhizobium tend to accept longer generation times. Many lithotrophs, such equally the nitrifying bacteria, too have long generation times. Some bacteria that are pathogens, such as Mycobacterium tuberculosis and Treponema pallidum, have specially long generation times, and this is thought to be an reward in their virulence. Generation times for a few bacteria are are shown in Table 2. Tabular array 2. Generation times for some mutual bacteria under optimal conditions of growth. 
Figure 3. The typical bacterial growth curve. When leaner are grown in a closed system (also called a batch culture), like a examination tube, the population of cells almost ever exhibits these growth dynamics: cells initially adapt to the new medium (lag phase) until they can starting time dividing regularly past the process of binary fission (exponential phase). When their growth becomes limited, the cells stop dividing (stationary stage), until somewhen they show loss of viability (death stage). Note the parameters of the x and y axes. Growth is expressed as alter in the number feasible cells vs time. Generation times are calculated during the exponential phase of growth. Fourth dimension measurements are in hours for bacteria with short generation times.
Bacterium Medium Generation Time (minutes) Escherichia coli Glucose-salts 17 Bacillus megaterium Sucrose-salts 25 Streptococcus lactis Milk 26 Streptococcus lactis Lactose broth 48 Staphylococcus aureus Heart infusion goop 27-30 Lactobacillus acidophilus Milk 66-87 Rhizobium japonicum Mannitol-salts-yeast excerpt 344-461 Mycobacterium tuberculosis Synthetic 792-932 Treponema pallidum Rabbit testes 1980
Calculation of Generation Time
When growing exponentially by binary fission, the increase in a bacterial population is by geometric progression. If we outset with 1 cell, when it divides, there are 2 cells in the first generation, four cells in the second generation, 8 cells in the third generation, and and then on. The generation time is the time interval required for the cells (or population) to divide.
G (generation time) = (time, in minutes or hours)/n(number of generations)
G = t/n
t = time interval in hours or minutes
B = number of bacteria at the beginning of a time interval
b = number of bacteria at the terminate of the time interval
n = number of generations (number of times the cell population doubles during the fourth dimension interval)
b = B x 2north (This equation is an expression of growth by binary fission)
Solve for due north:
logb = logB + nlog2
due north = logb - logB
log2
due north = logb - logB
.301
n = iii.three logb/B
K = t/n
Solve for Thou
G = t
3.iii log b/B
Example: What is the generation time of a bacterial population that increases from x,000 cells to 10,000,000 cells in four hours of growth?
One thousand = t_____
iii.three log b/B
K = 240 minutes
three.3 log 107/104
G = 240 minutes
iii.three x 3
G = 24 minutes
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