Question

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#2: Gene Translation How many ribosomes are actively synthesizing proteins at any instant in an E. coli cell growing with a doubling time of 45-minutes? Use the following assumptions in your calculations- a. The birth size (size just after mitosis is complete) of E. coli is 1 micron in diameter and 2 microns in length. b. Water content of the cell is 85%. 50% of the dry cell mass is protein / enzymes. Also, the density of cell material is approximately 1 gram per mL. c. Rate of amino acid addition per ribosome is 20 amino acids per second, and the average molecular weight of a free amino acid is 126. modo

Answer 1

Ans mass osome 2 Given that - birth size of & coli - diameter 1 micron or 10 meter (d) Density of cell material - I gength = 2 micron or 2x100 meter (1) water content = 85% of total cell mass Dry mass = 15% of cell Protein content 50% of total day mass of cell Doubling time = 45 minutes or 2700 seconds Rate of amino acid addition - 20 amino acid Average molecular weigth of a free amino acid= 126 g/mol Calculation - Avogadro number -8.023 x 1023 Volume of E. coli cell : 0821 or nxdxdxd - 3.14% 0 * 100% 2x109 159x16"8 meter? = 1.57 x 1015 liter De mass of cell - Volume x density & 1.57 x 1012 me Mass of cell = 1.57 x 10" X 1 = 1.57x1012 gm Dry mass of cell = 1.57X10 + 15% = 2.355x 103 m Protein content = 2.355x1013 / 50% = 1.1775 x1013 gm Since doubling time is 2700 seconds, thus total protein addition will be 1.1775 81013 gm in 2700 seconds from all ribosomes. amino acid Per ribosome protein addition 20 amino acidx doubling & Mewt of - 54000 amino acids O time single Total no. of amino = 204 2700x126 = 54000 amino acid acids added per = 68,04,000/amino acid generation time = 1.1775 x 10" x 6.023x10 23 562863690 amino acids. 126 Total number of ribosomes=56286390 - 10423 C 54000 Ans-Total number of ribosomes About 10423