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Medical researchers have found a way to grow new skin from stem cells created fr

ID: 84654 • Letter: M

Question

Medical researchers have found a way to grow new skin from stem cells created from a patient's own skin. If a patient has been burned and needs a skin transplant for 50 cm2 of skin, using your general knowledge of the average size of a mammalian cell, estimate the number of cells that would need to be grown to cover the transplant area. Assuming that a stem cell (and all its descendants) can be made to divide once a day, how long would it take to grow enough for the patient if we start with (a) one stem cell? (b) 100 stem cells? 104 stem cells?

Be sure to clearly state your assumptions and how you came to the numbers you estimated, since grading on this problem will be mostly based on your reasoning, not on your answer.

Explanation / Answer

The average human skin cell is about 30 micrometres in diameter.

1 micrometre = 0.0001 cm

Therfore, 30 micrometre = 0.003 cm

Size of one cell = 0.003 cm

To make an area of 50 cm2, we require, (50/0.003) cells

= 16667 cells

a) The multiplication of cells is given by the formula,

2number of generations x initial cell count

Here, the final cell count needed is 16667

2x x 1 = 16667

2x = 16667

log 2x = log 16667

x log 2 = log 16667

x = log 16667 / log 2

= 4.22 / 0.301

= 14

Here, the generation time is one day

We need 14 days to make 50cm2 from one stem cell

b) For 100 stem cells,

2number of generations x initial cell count

Here, the final cell count needed is 16667

2x x 100 = 16667

2x = 166.67

log 2x = log 166.67

x log 2 = log 166.67

x = log 166.67 / log 2

= 2.221 / 0.301

= 7.4

So, with 100 stem cells, we need 7 days and 9 hours to make 50 cm2 area

c) For 104 stem cells

2number of generations x initial cell count

Here, the final cell count needed is 16667

2x x 104 = 16667

2x = 160.25

log 2x = log 160.25

x log 2 = log 160.25

x = log 160.25 / log 2

= 2.204 / 0.301

= 7.3

So, with 104 stem cells, we need 7 days and 7 hours to make 50 cm2 area