GENETIC ENGINEERING - EXAMPLE 27.4 : According to Hardy-Weinberg Equation, p x p + 2 x p x q + q x q = 1 where p = dominant allele frequency and q = recessive allele frequency. Let p + q = 1. Fraction of population has 2 copies of the p gene = p x p. Fraction of population has 2 copies of the q gene = q x q. Fraction of population has a copy of p gene and a copy of q gene = 2 x p x q. In a small town, the allele frequency is q = 0.2 for a recessive gene, the delta-32 mutation, that gives human protection from HIV infection. (a) Find the allele frequency of a dominant gene, p. (b) What percent of the population has at least a copy of the gene that cause the population either immune to HIV or less susceptible to the disease?

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MICROBIOLOGICAL ENGINEERING - QUESTION 28.1 : In the calculation of the growth of bacteria, colony forming unit (CFU) in serial dilution is used. In a laboratory, viable count assay is used to estimate CFU. Formula applied is CFU / mL = (number of colonies x dilution) / (amount plated, in unit mL). Acceptable plate count is either between 20 and 200 or between 30 and 300 according to 2 different references. A wastewater sample of 200 ml is added to and mixed with 1.8 L of sterile water. Another 200 ml of the mixture is added to and mixed with 1.8 L of sterile water. (a) Calculate the dilution of first mixture and the dilution of the second mixture. (b) 100 microlitres of wastewater samples from the first mixture and the second mixture are placed separately on 2 different alga plates. The first plate has 250 colonies and the second plate has 23 colonies. Calculate the average CFU / mL.

MICROBIOLOGICAL ENGINEERING - QUESTION 28.2 : A hemocytometer is a device that is used for counting cells. In an engineering experiment, 100 microlitres of cell suspension is diluted with 50 microlitres of Trypan blue dye. Only death cells appear blue in color when stained with the dye. There are 57 cells detected in a hemocytometer, where 5.3 % of them appear blue when the chamber of the meter is placed under a microscope. Each square of a chamber can contain 0.0001 mL of liquid. (a) Calculate the number of viable cells. (b) The cells occupied 5 squares. Calculate the average number of viable cells / square. (c) Calculate the dilution factor of the cell suspension by using the formula : Dilution = final volume / initial volume. (d) Calculate the concentration of viable cells / mL by using the formula : Concentration = (Average number of viable cells / square) x dilution x (square / volume).

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MICROBIOLOGICAL ENGINEERING - QUESTION 28.3 : In the calculation of the growth of bacteria, absorbance, A in spectrophotometry is used. According to Beer-Lambert Law, A = e x l x c where A is the absorbance of the solution (no unit), l is the distance of light travels through the solution (in cm), e is the molar absorptivity or the molar extinction coefficient [ in L / (mol.cm) ]. For a particular solute and fixed path length : As / Ao = Cs / Co where Ao is the observed signal for a known concentration Co, and As is the observed signal for a sample concentration Cs. (a) For a cell concentration of 560 cells / mL, a spectrophotometre gives an absorbance reading of 1.0. A mixture of concentration 3600000 cells / mL can be diluted in several operations, with each operation having a dilution of 1:20. How many dilutions should be made so that the concentration of this mixture can be calculated within a range of A = 0.0 to 1.0. (b) In another experiment, a sample tube of 1 cm in width is used. Let A = 0.06 and e = 0.0012 ml / (cell.cm). Find the cell concentration of the sample.

BIOCHEMICAL ENGINEERING INSTRUMENTATION - EXAMPLE 29.1 : In the application of Theory of Spectrometry in spectrophotometer, let n = N x C x V, V = A x t, e = a x N where n = number of molecules, N = Avogadro's number, V = volume of cuvette, A = area of cuvette, t = thickness of cuvette, C = concentration of fluid in the cuvette, e = extinction coefficient, a = effective area of molecule. (a) By using calculus in dI = -I x a x N x C x dt, prove that ln (I / Io) = -a x N x C x t, where dI is the small difference in I and dt is the small difference in t. I = intensity of light. Io = initial intensity of light. (b) Show by calculations that ln (Io / I) = e x C x t based on the answer in the previous question (a). (c) Find the equation of log (Io / I) as a function of e, C and t based on the answer in the previous question (b).

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Question 110 - When an algebraic product is defined on the space, the Lie bracket is the commutator [x,y] = xy - yx according to Lie algebra in mathematics. If [p,x] f(x) = px f(x) - xp f(x), p = -ih d / dx, find the value of [p,x] in term of i and h.

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BIOCHEMICAL ENGINEERING INSTRUMENTATION - EXAMPLE 29.2 : (a) In order to determine the slurry volume (L) in chromatography, arrange the formula using the following parameters : slurry concentration (%), slurry volume (L), settled chromatography medium volume (L), 100. (b) In order to determine the chromatography medium volume (L) in gel filtration chromatography, arrange the formula using the following parameters : sample volume to be processed (L), chromatography medium volume (L), sample volume in percent of total column volume (%), 100.

BIOCHEMICAL ENGINEERING INSTRUMENTATION - EXAMPLE 29.3 : In thin layer chromatography (TLC), let retention factor Rf = (distance traveled by solute) / (distance traveled by solvent). Silica gel is used as stationary phase which is more polar than the hexane solvent as mobile phase. If the Rf values of 3 solutes A, B and C are 1.5, 0.75 and 1 respectively, compare the polarities of A, B and C with reasons.

BIOCHEMICAL ENGINEERING INSTRUMENTATION - EXAMPLE 29.4 : The resolution of separation, Rs for chromatography is given by the formula Rs = (difference in retention time) / (average width at the base). In a chromatogram, 3 peaks a, b and c are found. Average widths W at the bases of the solutes are : Wa = 20 s, Wb = 40 s, Wc = 30 s. Resolutions of separation, Rs for solutes b and c in comparison to a are 2 and 4 respectively. The differences in retention times T for b and c in comparison to a are (Tb - Ta) and (Tc - Ta), Ta = Tc - Tb : (a) Form 2 equations involving Rs as a function of Wa, Wb, Wc, Ta, Tb and Tc. (b) Find the values of Ta, Tb and Tc.