You have two cultures of bacteria for incubation experiments on marine snow degr

Question

You have two cultures of bacteria for incubation experiments on marine snow degradation, but you need to make sure that cell counts are sufficient to see any effect during the experiments. Culture A has a doubling time of 20 minutes and culture B has a doubling time of 45 minutes. At time equals zero culture A has a cell count of 100 cells/ml while culture B has a cell count of 200 cells/ml. Calculate cell counts with the time and prepare graphs of the growth of each culture. For your experiments, you require at least 109 cells/mL in each culture solution. When is each culture ready for the experiments? Hint: Put the equations into Microsoft Excel (or whatever spread sheet program you use) to generate and plot the data. I will be grading the quality/proper construction of your plots, so make sure you have the right variables on the x and y axes and be sure they are labeled properly.

Explanation / Answer

Growth kinetics When bacterial cells are placed in a suitable environment with appropriate nutritional composition they grow and eventually divide. The resulting daughter cells may also grow and divide and this will continue at a rate characteristic of the strain and the culture medium until environmental changes prevent further growth. The resulting growth can be described mathematically as follows: If the number of cells added to the medium is N0, then the number of cells at each successive generation is given by the sequence: etc. or etc. therefore, the number of cells at each generation increases exponentially and if the generation time remains constant then a plot of cell numbers against time would produce an exponential curve. The exponential curve can be converted into a straight line in the following way: From the above, after Z generations, the number of cells Nt is given by the expression (1) where N0 is the number of cells present initially and Nt the number present after exponential growth for Z generation times. Taking logarithms lnNt = z. ln(2) + ln(N0) (2) let T = mean generation time and t = time taken for the population to increase exponentially from N0 to Nt then z = t/T (3) and substituting in (2) gives lnNt = (t/T).ln2 + lnN0 (4) Equation (4) is the equation of a straight line (y=mx+c). Therefore, if we plot a graph of ln cell numbers (ie. lnNt., equivalent to the "y" term) against time (ie. t, equivalent to the "x" term) a straight line is produced with slope ln2/T (equivalent to the "m" term). The value of T can thus be determined from the graph. The slope of the graph should be taken over the linear portion of the graph from a time after the culture enters exponential growth ie. after the lag period, L. The slope of the graph is (lnNt - lnN0)/t and this must equal ln2/T (see equation 4). So we can write (lnNt-lnN0)/t = ln2/T (5) which can be rearranged to give T = t.ln2/(lnNt-lnN0) (6) The mean generation time can be easily determined from the graph and equation (5) and is usually expressed in minutes or hours. For some purposes it can be more convenient to consider the specific growth rates, m, rather than the mean generation time T. Using the relation m = ln2/T (7) equation (4) can be written lnNt = m.t + lnN0 (8) so that the graph ln(Nt) against time is a straight line of slope m. T and m can be interconverted through the relation (7) Thus the specific growth rate is expressed as reciprocal minutes (m-1), hours (h-1) or days (d-1). Alternative derivation by calculus The most straightforward way of recording growth rates is by calculating the specific growth rate (m). The rate of increase of a bacterial population may be described by the expression dN/dt = mN (9) where N is the number of bacteria present and the specific growth rate constant Integration of (9) gives lnNt = m.t + lnN0 (that is 8, as above) where Nt is the number of bacteria present at time t and N0 is the number of bacteria present initially. The graph of lnN against t is therefore a straight line of slope m. The use of m to give a quantitative description of growth rate is appropriate in many cases but for some purpose4s it can be more convenient to consider the mean generation time T. As shown earlier, m and T are simply related to each other so that one can readily be calculated from the other. The relation can be derived as follows Rearrangement of (8) gives ln(Nt/N0) = m.t (10) After one generation time (when t - T), Nt = 2 x N0 by definition and so equation (10) becomes ln2 = m.T (12) The above equations adequately describe the exponential or logarithmic phase of growth in batch culture. However, exponential growth may not always begin immediately after inoculation of cells into fresh medium and is frequently preceded by a period known as the lag phase where the cells adjust to the new medium. The duration of the lag phase may depend on many parameters; the organisms, the medium composition, previous cultivation conditions etc. and the transition from lag phase to exponential phase may not be sharp. The duration of the lag phase (L) may be determined graphically by extrapolation of the logarithmic phase back to lnN0. L may also be calculated from the following expression Exponential growth ends and the population enters the stationary phase when an essential nutrient is depleted (eg. carbon source) or the accumulation of products eventually reaches a toxic concentration (eg. hydroxyl or hydrogen ions). PROCEDURE In the following practical you will compare three methods of measuring the growth of Escherichia coli. MEASUREMENTS Optical density Viable cell count Dry weight During this practical session, you will inoculate a shake flask with a culture of E. coli and shake it in an orbital shaker throughout growth, providing an aerobically grown culture. Samples should be taken at given intervals and processed as described below. Five samples A to E should provide sufficient data. METHODS Aseptically remove 3ml of each culture at given time intervals and transfer to a sterile universal bottle marked with the time of incubation. Determine the viable count of each culture (see Method 1). With the remainder of each culture determine the optical density at 540nm (see Method 2). At the end of the practical place all the tubes into the metal boxes provided and make sure all your plates are properly marked (group number, bench number, dilutions). 1. Viable Counts Using five of the tubes of diluent, make a series of hundred-fold or ten-fold dilutions of culture as indicated in the diagram. Use a fresh pipette for each dilution (and discard the used tips into the yellow sharps bin provided on each bench). Mix well (using the Vortex mixer) before sampling. Dilution 1/100 1/100 1/10 1/10 1/10 Culture 10-2 10-4 10-5 10-6 10-7 Dilution Divide the nutrient agar plate into six sectors and using a 20 ml pipette and starting with the highest dilution (ie. 10-7), plate out duplicate samples of dilutions indicated in the diagram below by carefully placing 20 ml on each sector as indicated in the diagram. You should hold the pipette vertically and high enough above the plate to allow the contents to drop onto the surface of the agar and spread, but close enough to prevent the drops bouncing across the agar surface on impact (the technique will be demonstrated). Leave the spots to dry before moving the plate (with the lids on the plates). Once dry, place the plates (upside down) in the plastic box provided for each bench (appropriately labelled). Repeat using the other cultures. 2. Optical density Transfer the cultures into plastic cuvettes and measure their optical density at 540nm using a spectrophotometer (be careful not to mix up the cultures). Use nutrient broth cuvette (provided) to calibrate. Discard all the contaminated cuvettes into the yellow sharps bin provided.

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