Science and Cooking: Problem Set 9
Due on Canvas by 11 PM on Saturday, November 15th
Please type or write your answers within this document or on a separate sheet of paper.
Then save your work as either a Microsoft word document (.doc or .docx) or as a PDF
file (.pdf) and upload to Canvas. If you write your answers by hand, you may scan your
work and paste the images into either of these file types, but submissions that are NOT
either of these file types will not upload properly. Your work must be organized and
legible – if your TF can’t understand what you wrote, they won’t give you credit.
Show your work for derivations and calculations. YOU WILL NOT RECEIVE FULL
CREDIT WITHOUT SHOWING YOUR WORK. Be sure to calculate all results fully
(don’t leave numbers in fraction form, or in terms of pi, etc) and to provide answers in
the requested units, if applicable.
Equations of the Week
𝑁(𝑡) = 𝑁0 𝑒 𝑘𝑡 where 𝑘 =
Concept
N(t)
N0
k
t
τ
ln 2
Description
Number of cells at time t
Number of cells at time 0
Growth or death rate of cells
Time elapsed
Doubling time
𝜏
Units
Microbes
Microbes
s-1
s
s
Problem 1: Cornflake Chocolate Chip Marshmallow cookies. (27 points)
This week, Christina Tosi showed us how she makes her cornflake chocolate chip
marshmallow cookies, a delicious throwback to childhood chock-full of science. Here is the
recipe (from http://milkbarstore.com/main/press/recipes-and-how-tos/ ):
225 g (16 tbs) butter, at room temperature
250 g (1 1/4 cups) granulated sugar
150 g (2⁄3 cup tightly packed) light brown sugar
1 egg
2 g (1/2 tsp) vanilla extract
240 g (1 1/2 cups) flour
2 g (1/2 tsp) baking powder
1.5 g (1/2 tsp) baking soda
5 g (1 1/2 teaspoons) kosher salt
3/4 recipe (3 cups) cornflake crunch
125 g (2⁄3 cup) mini chocolate chips
65 g (1 1/4 cups) mini marshmallows
1. combine the butter and sugars in the bowl of a stand mixer fitted with the paddle
attachment and cream together on medium-high for 2 to 3 minutes. scrape down the sides
of the bowl, add the egg and vanilla, and beat for 7 to 8 minutes.
2. reduce the mixer speed to low and add the flour, baking powder, baking soda, and salt.
mix just until the dough comes together, no longer than 1 minute. (do not walk away from
the machine during this step, or you will risk over mixing the dough.) scrape down the sides
of the bowl with a spatula.
3. still on low speed, paddle in the cornflake crunch and mini chocolate chips just until
they’re incorporated, no more than 30 to 45 seconds. paddle in the mini marshmallows just
until incorporated.
4. using a 2 3/4 oz ice cream scoop (or a 1/3 cup measure), portion out the dough onto a
parchment-lined sheet pan. pat the tops of the cookie dough domes flat. wrap the sheet pan
tightly in plastic wrap and refrigerate for at least 1 hour, or up to 1 week. do not bake your
cookies from room temperature—they will not hold their shape.
5. heat the oven to 375°f.
6. arrange the chilled dough a minimum of 4 inches apart on parchment- or silpat-lined
sheet pans. bake for 18 minutes. the cookies will puff, crackle, and spread. at the 18-minute
mark, the cookies should be browned on the edges and just beginning to brown toward the
center. leave them in the oven for an additional minute or so if they aren’t and they still
seem pale and doughy on the surface.
7. cool the cookies completely on the sheet pans before transferring to a plate or to an
airtight container for storage. at room temperature, the cookies will keep fresh for 5 days; in
the freezer, they will keep for 1 month.
a. The “cornflake crunch” component of this recipe is a simple ingredient prepared by
toasting a mix of cornflakes, milk powder, sugar, and butter. What is the name of the
reaction that gives these cornflakes their delicious flavor? (1 points)
Maillard reactions
b. How much water is there in this recipe? Assume the volume of an egg is 34mL and
that it is almost entirely water and that butter is roughly 15% water (by weight). The
density of butter is 0.911g/cm 3 (2 points)
1 egg = 34mL
225g butter/0.911g/cm 3 = 247ml∙0.15 = 37ml
34 + 37 = 71mL
c. Why do you have to beat your mixture in part 1 for 7-8 minutes whereas you can
only beat your mixture in part 2 for up to 1 minute? (3 points)
It is important for small air bubbles to form and become trapped in the egg and
butter. In addition, it is important that the sugar becomes incorporated into the
emulsion. You should mix the dry ingredients for a short time so you don’t create too
much gluten and get a bready cookie
d. Will all of the sugar in this recipe dissolve in the dough? How about the baking soda?
Assume that you can dissolve 9 grams of baking soda for every 100mL of water.
Also assume that baking powder is about ⅓ baking soda, by weight. (5 points)
Solubility of sugar = 2g/ml
250+150g sugar = 400g sugar
400g/71mL = 5.6g/ml so no
Solubility of baking soda = 0.09g/ml
2g baking powder/3 = 0.67g + 1.5g = 2.17g
2.17g/71mL = 0.03g/ml so yes!
e. When fresh from the oven, these cookies appear significantly puffed. Which
ingredient(s) are most likely involved in trapping air inside the cookies? (2 points)
Proteins from the eggs and the gluten in the flour
f.
How many moles of carbon dioxide can potentially be formed by this recipe?
Assume that all baking soda in the recipe is consumed during baking. (3 points)
NaHCO3 + acid = CO2 + H2O + Na salt
1 mol baking soda = 1 mol CO2
2.17g/84g/mol = 0.026mol baking soda produces 0.026mol CO2
g. How many liters of carbon dioxide does your answer to (f) make? Is this more or less
than the total amount of “puffing” you see after removing the cookies from the oven?
Why or why not? (5 points)
1 mol of gas at standard temp and pressure = 22.4L
0.026mol∙22.4L/mol = 0.58L
This is likely much more than the puffing you see in the cookie because not all the
air is trapped inside the cookie by the proteins and a lot escapes as you bake it.
h. The dough is refrigerated before baking, which will mean that it sits for some time
after mixing. Using the chart below and your answer to (b), about how much carbon
dioxide, in moles, can be dissolved in the water for the dough assuming your
refrigerator is at 4 degrees Celsius? How does this compare to your answer in (f)? (3
points)
Can dissolve about 3kg/kg
3g gas/kg water∙1kg/1000mL = 0.003g/mL
0.003g/mL/44g/mol = 6.8∙10-5 mol/mL
What we have = .026mol/71mL = 0.00037mol/mL
The gas we produce will not all be able to dissolve
i.
There are two major sources of acid in this recipe. What are they? What would
happen if they were left out? (3 points)
Tartaric acid in the baking powder and brown sugar. If you left them out, you would
get very flat cookies because you wouldn’t produce any carbon dioxide to puff them
up.
Also, it’s possible that the cookies would get a lot browner because there would be a
lot of baking soda around to help along the Maillard reaction
Problem 2: Enzymes in Cooking (28 points)
Enzymes are protein machines that are responsible for thousands of different kinds of
reactions that help sustain life in every living organism! Please watch this introductory video
with Chef Wylie Dufresne and Chef Ted Russin on the transglutaminase enzyme and
answer
the
following
questions
about
enzymes.
http://cm.dce.harvard.edu/cs50player/youtube.html?title=&youtube_id=DPmUrgGwssc&srt_
url=srts/DPmUrgGwssc.srt
a. Transglutaminase is an enzyme that chefs use to bind proteins together. Which two
amino acids does transglutaminase like to create a bond between? (2 points)
Glutamine and lysine
b. If you just put these two amino acids close to each other without an enzyme, would
they create a bond with each other? Why or why not? What does the enzyme
change to allow this reaction to take place. (5 points)
They would not create a bond. The activation energy for that reaction is too high for
them to spontaneously bind to eachother. The enzyme lowers this activation energy
speeding up the reaction
c. There are five factors that are important for the action of enzymes that chefs can
manipulate to control an enzyme’s action. What are they? (5 points)
Temperature, pH, time, agitation, physical proximity
Transglutaminase is often affectionately referred to as “meat glue” because it is most often
used to stick two pieces of meat together, but Chef Wylie Dufresne and Chef Ted Russin
demonstrate that it can also be used to completely change the shape of a food. Please
watch
the
shrimp noodle
video
and answer
the following
questions.
http://cm.dce.harvard.edu/cs50player/youtube.html?title=&youtube_id=9uQxwYedjkc&srt_ur
l=srts/9uQxwYedjkc.srt
d. They work very hard to get the enzyme into solution at the beginning of the video.
Why is this important? (2 points)
Enzymes must be surrounded by their optimal environment in order to function
correctly. Without being surrounded by water, they will not function correctly.
e. After you add the enzyme, it is important to work quickly because if you wait too
long, the shrimp mixture will “start to set” and end up stuck in whatever shape it was
set in. What do the chefs mean by this? What role does the enzyme play in the
“setting” process? (3 points)
They mean that it is beginning to harden. As soon as the enzyme comes in to
contact with its substrates, it will begin to act. In this case, the enzyme begins gluing
the proteins together, hardening the mix and preventing it from being easy to work
with
f.
Why do they extrude the noodles into a 50 degree water bath? Does the
temperature of the water bath matter here? What do you think would happen if the
water bath had been ice cold? What about if it had been boiling? (4 points)
Transglutaminase works best around this temperature. So, the rate at which it
performs the reaction speeds up quite a bit, quickly hardening the shrimp noodles. If
the water was ice cold, the enzyme would react so slowly, it would essentially not
work at all. If it had been boiling, the enzyme would have denatured and not work at
all
This is a really cool enzymatic reaction, but there are a lot of different kinds of enzymatic
reactions that are absolutely essential for certain types of food. For the following problems,
fill in the blank with one of the following words (words may be used once, more than once,
or not at all). Answers can be found in the lecture. (7 points)
polyphenols, enzymatic browning, bromelain, protease(s), glycosylase(s), alliicin,
gelatin, pectin, ascorbic acid, alliinase, papain, lachrymatory factor synthase, baking
soda
h. Enzymatic browning is a process where a class of enzymes called oxidases change
compounds called _polyphenols__ in to brown compounds. Heat and _ascorbic
acid_ can inactivate the enzymes responsible for this.
j. Proteases are a class of enzymes that are very common in cooking. These enzymes
have the ability to break down proteins into smaller peptides and amino acids. Two
enzymes of this class, _papain_ and _bromelain_ come from papaya and pineapple
respectively. These enzymes can not be mixed with _gelatin_ because it will break
down the protein into its amino acids preventing it from gelling.
l.
_allinase__ is an enzyme found in vegetables in the Allium family like garlic. When it
comes in to contact with the sulfur-containing garlic compound, Alliin, it converts it in
to Alliicin which is the compound that causes the classical intense garlic smell. A
similar reaction occurs in onions. _lachrymatory factor synthase__ is an enzyme that
creates the compound that makes us cry when cutting in to them.
Problem 3: American Coolship Ale and Fermentation (30 points)
Note: The lecture on fermentation will be on Thurs, November 7. To get a head start on this
question, you can read chapter 10 of the course companion and/or watch the videos on the
science of fermentation under week 11 of the course schedule online.
American Coolship Ales are a type of sour beer that is made by spontaneous fermentation.
Traditionally, this type of beer is made by exposing the wort (boiled mix of sugars extracted
from boiled grains) to the open air. During this time, wild yeast and bacteria falls into the
wort to ferment it as it is aged in oak casks for up to three years. Right before bottling, a fruit
slurry is added.
a. What is the balanced chemical reaction for the fermentation of sugar. (3 points)
C6H12O6 -> 2C2H5OH + 2CO2
Scientists like to use spontaneously fermented foods to study the way microbial populations
change over time. Figure B below shows the number of bacteria and yeast per mL, and
figure C shows the pH and concentration of sugar in the beer.
squares = yeast cells
diamonds = bacterial cells
triangles = pH
circles = °Plato (1 °Plato = 1% sugar by weight)
Bokulich et al. 2012. “Brewhouse-resident microbiota are responsible for multi-stage fermentation of American Coolship
Ale.” PLoS One 7(4): e35507.
b. For the first 10 weeks, the number of cells was measured every two weeks. What is
the doubling time of yeast if the maximum concentration the yeast reaches is
2x10^6cells/ml at week 6? (3 points)
6 weeks = 42 days
N(t) =N0ekt
k = ln(N(t)/N0)/t = ln(2∙106cells/ml/1∙104cells/ml)/(42 days) = 0.126 days
k = ln2/τ
τ = k/ln2 = 0.126 days/ln2 = 0.18 days = 4.4 hrs = 262 min = 15724s
c. Once the yeast cells reach a certain concentration, they rapidly die off. What is their
death rate from the maximum concentration at week 6 to week 10? Why is this
happening? (4 points)
4 weeks = 28 days
k = ln(N(t)/N0)/t = ln(1∙104cells/ml/2∙106cells/ml)/(28 days) = -0.19 day-1 = -.0079 hrs-1
This could be happening for two reasons (accept either one). On graph C, we can
see that most of the sugars are gone from the beer at this point which means that
1. At this point, all the sugars have been used by the bacteria for energy, and when
there is nothing left for them to eat, they die.
2. It is also possible at this point that the alcohol concentration has gotten so high
that the cells can no longer survive.
d. What is the change in sugar concentration from the beginning to the end of the
fermentation? (2 points)
At beginning 12%. At end 1%
12 – 1 = 11%
e. For a 355mL bottle, how many moles of sugar has been fermented into ethanol?
Assume all of the sugar is glucose (MW = 180g/mol) (3 points)
In 355mL, 11% by mass has been fermented.
Assume 1g/mL density before fermentation
355g∙0.11 = 39.05g sugar
39.05g/180g/mol = 0.217mol
f.
How many moles of ethanol is produced? (MW = 46g/mol) (3 points)
For each mole of sugar, 2 moles of ethanol is produced
0.217mol sugar∙2 = 0.434mol ethanol
g. What is the concentration of ethanol in the final beer? Answer in percent by volume
or ABV (density of ethanol = 0.79g/ml) (3 points)
0.434mol ∙ 46g/mol = 19.96g
19.96g/0.79g/mL = 25.26mL
25.26mL/355mL = 7.1%
h. On average, these types of beers have an alcohol content between 4-8% by volume.
Does your answer confirm this? What are some reasons why it might not? (3 points)
Yes it does!
It is on the high end though, likely because we assumed it was all glucose and that
all of it was fermented. Some of this sugar was probably actually metabolized by the
bacteria.
i.
The majority of the bacteria that grow in the beer belong to the same class of
bacteria that is used to make yogurt. This class of bacteria can take sugars and
convert them in to acids. If you tried to make this beer without the bacteria, do you
think it would taste differently? If yes, how? (3 points)
This type of bacteria make acids and acids have a sour taste. Without the bacteria,
this beer it would taste differently. It would not be sour at all and would just be a
regular fruity beer.
j.
At the arrow, fruit is added to the beer before bottling, and the concentration of yeast
increases dramatically! Form a well-reasoned hypothesis on why the yeast grows
after fruit is added, but not the bacteria. (3 points)
It’s likely that the yeast are better at metabolizing the sugars in to fruit than the
bacteria are, so they grow faster and don’t give the bacteria a chance to get going.
It’s also possible that at this alcohol content, the bacteria in the beer are barely
surviving, but can not grow anymore.
k. Based on your answer above, if during the bottling process, the beer was
contaminated with a small amount of bad bacteria like Salmonella, do you think the
beer would be safe to drink? Why? (2 points)
Because we can see that the bacteria are having a hard time growing in this
condition, it is also likely that the Salmonella will have a hard time growing.
Therefore, if only a few bacteria got in, it would probably be fine to drink.
Problem 4: Weekly Progress Report 1 (15 points)
See comments on online quiz