(Assume the mass of human body is 70kg) 3. A typical bacterial cell (that is, E.

Question

(Assume the mass of human body is 70kg)

3. A typical bacterial cell (that is, E. coli ) has a surface area of 6 m2 and a volume of 1 m3 (10 points) (a) Express this volume in femtoliters (1 points). Estimate of the mass of such a bacterium (2 points). (b) Roughly 2-3 kg of bacteria are harbored in your large intestine. Make an estimate of the total number of bacteria inhabiting your intestine (2 points). Estimate the total number roughly 10 m in diameter and has a spherical shape with the sane density as that of water and that that thirty percent of the human mass corresponds to cells (2 points). (c) Compare the two figures in the total number of bacteria and human cells (1 point) Please explain why you have this result (2 points).

Explanation / Answer

A) The surface area 6µm2 and volume 1µm3 .

which are both close enough to verify that A 6µm2 and V 1µm3 .

To find this in femtoliters (fm) recall 1000L = m3 and femto = 1015,

which means V = 1µm3 = 1µm3 ( m /106µm)3 ( 1000L /1m3 ) (1015fL / 1L) = 1fL

-Cells have the same density () as water: c w 1g/cm3 .

So then the mass of a single cell is approximately Mc = V c V w = 1µm3 (1g / cm3)

=[(106 )3 m3 /(102) 3 m3 ] 1g

= 1018 / 106 g

= 1012g = 1pg.

Ans B)

Let MIL = 2 3kg. we know to pick 3kg. So the number of bacteria cells in your large intestine is

NLI = MLI / Mc 3kg /1012g/cell = 3 × 1015cells

Now to estimate the number of cells in human body. First off, human cells are much larger than E.coli. Let’s say in general they are spherical with radius R and mass MH. They aren’t going to be a millimeter big (or even 0.1mm) and they are bigger than E. coli; therefore,

1µm <R < 100µm
R 10µm
MH V = w 4/3R3 = 4 wR3
= 1g/1cm3 (1cm3/106m3) × 4 × (105)3 m3 = 4 × 109g

3 × 109g

(remember only powers of 10 and 3 allowed when estimating). To know the number of human cells we need to know what weigh. so then

M = 70kg, which means that the number of human cells is approximately

NH M / MH = 74 g / 3 × 109g = 7 / 3x 1013

2.33 × 1013

AnsC)

So then we estimate that there are two orders of magnitude more bacterium in large intestine than human cells in human body

NLI / NH = 3 × 1015 / 2.33 × 1013 = 128.75

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