by mikejf, Sept. 12, 2017, 9 p.m., 0 comments

I'm going to try to upload my class notes from Caltech "bioscience bootcamp" since I don't have time to work on this site otherwise. It will help me remember and I hope they will be interesting to readers.
Yesterday, I was fortunate enough to receive a lecture by Rob Phillips where we went over methods of [Street Fighting Mathematics](https://ocw.mit.edu/courses/mathematics/18-098-street-fighting-mathematics-january-iap-2008/readings/sf_math.pdf) (by Sanjoy Mahan), methods of solving problems by estimating and converting units. Most of the results are order-of-magnitude estimates, but it's still amazing how accurate the answers are.
A couple questions we answered with guesstimation were:
**What is the power output from the sun on earth in watts per square meter?**
![Power spectrum of sun][1]
The power output of the sun is in the figure above. The dimension of the y-axis is \\(W/(m^2nm)\\). By integrating the "sunlight at sea level" (red) curve, we can get the power output of the sun in Watts per square meter.
As street fighters we don't have to integrate any complicated equation to get the answer, we can simply approximate the area under the curve as a triangle so
$$ A = \frac{1}{2}bh \approx \frac{1}{2}(2000 \ nm) (1 \ W/(m^2 * nm))= 1000\ W/m^2.$$
**What is the wattage of the human body?**
Well we eat around 2500 kCals per day, according to nutrition labels. 1 calorie can be converted to about 4.184 Joules.
$$2.5 * 10^6 \mbox{ calorie} * 4.184 \mbox{ J/calorie} \approx 10^7$$
There are \\(60*60*24 \approx 10^5\\) seconds per day, therefore the wattage of a human is approximately
$$ \frac{10^7 \mbox{ Joules}}{10^5 \mbox{ seconds}} \approx 100 \mbox{ Watts}, $$
or 2 lightbulbs!
**What is the wattage of a house?**
Another way to guestimate a quantity is to produce a lower bound, an upper bound, and take the geometric mean. For a house, I would assume that it takes the power of at least 10 lightbulbs to power it, but I'm not so sure about 100 lightbulbs. I know that it probably takes less than 1000 lightbulbs to power one home, so I can take the geometric mean of 10 and 1000 lightbulbs,
$$ \sqrt{10*1000} = \sqrt{10,000}, $$
to get that a house is powered by something on the order of 100 lightbulbs, or about \\(10^4\\) watts.
This answer combined with "sun power output" answer are why some houses are able to be powered by \\(\approx\\) 10 square meters of solar panels (of course the problem is not just power generation, but storage and power conversion efficiency as well).
**How many proteins are produced per second by an E-coli bacteria?**
Some facts we were given to start this were that a ribosome can process about 10 amino acids per second and a protein is on average 300 amino acids. Therefore the problem was as simple as deducing the number of ribosomes in an E-coli cell, then converting units.
For this we had an image of an E-coli cell, with ribosomes colored in. We could see completely through the cell. From this image I could deduce that there were about 10 ribosomes per \\(250 \ nm^2\\). An E-coli cell has a cross-sectional size on the order of 1 \\(\mu m^2\\). Plugging in the numbers results in:
$$ \left ( \frac{10 \mbox{ ribosome}}{250 \mbox{ nm}^2} \right )\left ( 10^6 \mbox{ nm}^2\right )\left ( \frac{10 \mbox{ amino acids}}{s \cdot \mbox{ribosome}}\right ) \left ( \frac{1 \mbox{ protein}}{300 \mbox{ amino acids}}\right )$$
$$ \approx 10^3 \mbox{proteins/s}$$
This estimate turns out to be pretty accurate.
**Question for the reader: We now know that a human runs on about 100W of power. Assuming that the amount of energy released per ATP molecule is \\(10^{-19}\\) J and the molar mass of ATP is 500 g/mol, what mass of ATP must the human body produce every day?**
[1]: https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Solar_spectrum_en.svg/220px-Solar_spectrum_en.svg.png