42-101 Intro to BHE (Przybycien)

Spring 2005

PROBLEM SET No. 3

Posted:

Wed, 1/26/05

updated Wed, 2/2/05 hold problems #3 and #4 to next problem set

Due:

Fri, 2/4/05 in class

 Problems for grading:

1.

Basic Biochemistry.  Women’s One-A-Day Vitamins from our friends at the Consumer Care division of Bayer Corporation contain the following components (in order of decreasing amount): calcium carbonate, starch, ferrous fumarate, ascorbic acid, gelatin, vitamin E acetate, modified cellulose gum, niacinamide, dextrin, zinc oxide, titanium dioxide, calcium pantothenate, pyridoxine hydrochloride, vitamin A acetate, riboflavin, thiamine mononitrate, beta carotene, tartrazine, FD&C Yellow #6, folic acid, vitamin D, vitamin B12.

For each component above, 1. identify whether it is a carbohydrate (or derivative), amino acid (or derivative), nucleotide (or derivative), fatty acid (or derivative), inorganic species or some “other” type of compound and 2. state why it is included in each tablet.  [Hint: the Merck Index in the reference section of the Engineering & Science library and at Mellon Institute library would be very helpful as would a “compound” search on the GenomeNet site {http://www.genome.jp/}]

2.

Metabolic Stoichiometry.  An aerobic bacterium is used to clean up an oil spill.  The bacterium can be represented with the cellular formula CH1.66N0.14O0.50P0.0057, the oil serves as the carbon source (average composition of this particular oil is C24.7H43.2N0.31O0.27) and an oleophilic, slow-release solid fertilizer (Grace Sierra Chemicals “Customblen” a blend of ammonium nitrate and ammonium phosphate giving an NPK ratio of 28-8-0) is used as the nitrogen and phosphorous source.  Finally, the cells can convert 42% of the substrate carbon to biomass carbon on a weight basis.  For this system:

a.   Determine a stoichiometric formula, HwNxOyPz, for the fertilizer.  [Hint: the NPK ratio gives mass percent of each element present in the fertilizer.  Scale the formula so that x=1.]

b.  Write the biochemical reaction expression for bacterial growth on the oil/fertilizer mixture using variables (a, b, c etc.) as stoichiometric coefficients.  [Hint: the phosphorous by-product of aerobic growth is inorganic phosphate.]

c.  Calculate the stoichiometric coefficients that balance the biochemical reaction.

d. Calculate the respiratory quotient, RQ (mol CO2/mol O2) and yield coefficients Yx/s (g dry biomass/g substrate) and Yx/N-source (g dry biomass/g N-source).

3.

Mass Balancing.  An utterly delightful and intriguing continuation of problem number 2….  An oil tanker runs aground off the shore at Bayonne, NJ and spills 100,000 gallons of oil into the surface of the ocean; the density of the oil is 0.89 kg/L, causing it to float on the surface of the ocean to form an oil slick.  Armed with the genetically engineered bacterium from above, you spring into action.  From a helicopter hovering over the gooey mess, you sprinkle a mixture of 1000 kg of dried bacteria and just the right amount of oleophilic fertilizer onto the spill.  Wave action provides good aeration of the bacteria-laden oil slick.

Set this scenario up as a mass balance problem with three inputs, bacteria, fertilizer and oxygen, and one output, bioreaction products.  What is the system in this case? Determine total amount, in kg, and composition, in mass fraction, of each stream.  Can the problem be solved as stated?  Are any assumptions necessary?  Don’t forget to “think” about your solution.  [Hint: the 28-8-0 fertilizer consists of (100-{28+8+0})wt% inert material.]

4.

Kinetics. 

a.  Estimate how long will it take, in hours, for the bacteria to consume all of the oil and urea from problem 4 if the specific growth rate of the bacteria is 1.35 hr-1.  You may assume that the oil and urea are plentiful right up until the time they are completely consumed; this is a rough approximation of actual behavior as we know that as substrate levels become low, growth will slow, but hey, we’re just trying to get an estimate here for cryin’ out loud.

b.  The growth rate of a species of bacteria is measured in twelve separate experiments.  The average ± 1 standard deviation of the specific growth rate is estimated at 1.37±0.24 hr-1.  How many minutes would be required for a sample of this bacteria to increase in numbers by a factor of ten?  Report your answer as a mean ± 1 estimated standard deviation.  If you started with (1.00 ± 0.15)´106 cells/mL, what concentration of many cells would you have after 3 hrs of unimpeded growth?  Report as mean ± 1 estimated standard deviation.

 Updated on 2/2/05 by TMP