Consider a human cell, which is 15jxm in diameter. Assume the average length of

Question

Consider a human cell, which is 15jxm in diameter. Assume the average length of a human protein is 350 amino acids. Using simple lengths of chemical bonds as your starting point, provide an estimate of how many proteins could fit in a cell if you totally packed a human cell with proteins. b) Scientists have empirically found that you get ~0.2g of protein per mL of cell volume. Using this figure, calculate how many proteins are in each human cell. c) From your calculations from a) and b), how far can an average protein travel before hitting another protein in the cell? How many proteins would fit in that distance?

Explanation / Answer

Q 3

b)Step 1 : To find volume of a human cell

Human cell diameter , d = 15 m

Radius of human cell , r = 15/2 = 7.5 m

Volume of a human cell , V = 4r3

                                                     3

                                                  = 4 x 22 x (7.5 m) 3

                                                      3 x 7

                                                   = 1767.8 m3

Step 2: To find number of proteins per cell volume

Given : Proteins mass per volume , Cp = 0.2 g/mL

              Average length of a human protein, Laa = 350 aminoacids(aa)/protein

              Average mass of an amino acid, maa = 110 Dalton(Da)/ amino acid

                Number of proteins per cell volume, N / V = Cp / (Laa x maa)

                                                                                        =           (0.2 g/mL)                   

                                                                                              (350 aa/protein) x (110 Da/aa)

Now, 1 Dalton = 1/ Avogadro’s Number, NA = 1 / (6.022 x 1023 Da/g)

So, Number of proteins per cell volume, N / V = Cp / (Laa x maa)

                                                                                        =           (0.2 g/mL)   x (6.022 x 1023 Da/g )                

                                                                                              (350 aa/protein) x (110 Da/aa)

                                                                                      = 3 x 1018 proteins/ mL

We know that 1 mL = 1012 m3

So. Number of proteins per cell volume = 3 x 1018 proteins

                                                                                  1012   m3

                                                                                = 3 x 106 proteins/ m3

Step 3: To find Number of proteins in each human cell

Volume of each human cell, V = 1767.8 m3

Number of proteins per cell volume, N/V = 3 x 106 proteins/ m3

So,

No. of proteins in each human cell, N = No. of proteins per cell volume x Volume of each human cell

N = (3 x 106 proteins/ m3 ) x (1767.8 m3)

    = 530 x 107 proteins / human cell

So, each human cell has 530 x 107 proteins.

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