One E coli cell has a volume of 1 mu m3 and consists of abou

One E. coli cell has a volume of 1 mu m^3, and consists of about 30% proteins by weight. An amino acid weighs on average 100 Daltons. Assuming that amino acids have the same density as water, how many amino acids axe there in an E. coli cell? (b) If an average protein consists of 300 amino acids, how many proteins are there in a cell? (c) One bacterial generation takes 30 minutes, and there are 10000 Ribosomes in a cell. What is average rate of translation in the cell (codons per second per ribosome)? (d) There are about 2000-3000 RNA polymerase in an E. coli If one assumes that transcription and translation occur at the same rates, how many proteins axe produced per mRNA on average?

Solution

(a) It is assumed that amino acids have same density as water.

Density of water = 1g/cm³

= 10^-12 g/ µm³

=   10^-12 g­­­/ µm³                                (Converting to Daltons)

6.022* 10¹¹ dalton/ µm³

            The weight of proteins is 30% of the total weight of E.coli cell.

                30% of the total weight= 1/3* 6.022* 10¹¹

                                                              = 2* 10¹¹ daltons

If an amino acid weighs 100 daltons then total amino acids in an E.coli cell can be calculated as:

                100 daltons in 1 (AA) amino acid,

2* 10¹¹ daltons in 2* 10¹¹ /100

=2* 10⁹    AAs                                                                                                             

                    

(b) No. of proteins in a cell =   No. of AAs / AAs per protein                                                                                                                               

= 2* 10⁹ / 300

= 2/3 * 10⁷

= 0.67 * 10⁷

(c) During translation, the total distance covered by ribosomes in units of codon is same as the total number of AAs (amino acids). Thus,

Rate of translation =        Number of AAs                               

                                  Number of ribosomes and time

                              = 2* 10⁹/10000* 30* 60 sec

                               = 100/ sec or velocity

(d) According to the statement, it is assumed that transcription and translation occur at the same rate. It implies that DNA and RNA have same length i.e. no introns. Thus the number of mRNAs made depends upon velocity, cell generation time and number of RNAPs (RNA polymerases)i.e

No. of mRNA per cell= Velocity*time*no. of RNAPs

      = 100* 30*60* 3000

      = 54* 10⁷

                No. of proteins per mRNA =    No. of AAs

      No. of mRNA codons

    = 2* 10⁹

       54* 10⁷

   = 3.7