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What's the least number of tRNA molecules needed to form a polypeptide chain that contain 50 amino acids of 15 types?

I know that each type of amino acid has at least one unique type of tRNA that recognizes it and transport it, so according to my understanding the 15 types of amino acids need at least 15 tRNA molecules of different types unless there was a reason that prevents one tRNA molecule from transporting two identical amino acids (two alanine) to the same polypeptide chain

•In other words: Can one tRNA molecule carry two identical amino acids (ex: two alanine) to the same polypeptide chain that's being synthesized or not?

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    $\begingroup$ No, there is no way the same species of tRNA can carry two different amino acids no matter how similar they are. Each tRNA carries only one particular species of amino acid and there is no way it can just "switch to" any other one. $\endgroup$ – Yordan Yordanov Mar 30 '17 at 12:39
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    $\begingroup$ I have to check this out but aren't the amino acids modified after they become inserted into the growing chain, not before. I will make a quick search online now. Here is one paper I managed to find with a very "quick" online search-ncbi.nlm.nih.gov/pmc/articles/PMC3130931 . As far as I can see all modifications are done after translation, not before. But there might be exceptions yet. I guess I would have to go deeper for this question. $\endgroup$ – Yordan Yordanov Mar 30 '17 at 12:58
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    $\begingroup$ Please clarify what you mean by "of the same type". $\endgroup$ – David Mar 30 '17 at 13:03
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    $\begingroup$ @David amino acid having the same code ex: two amino acid molecules with (GCG) code. $\endgroup$ – Jasmin Badawy Mar 30 '17 at 13:09
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    $\begingroup$ Jasmin, each codon (not code) specifies only one amino acid (in a given organism and subcellular compartment). GCG is the codon for alanine. If you think a codon can specify more than one amino acid (except in the special cases of selenocysteine) then you should study an elementary text on the genetic code. $\endgroup$ – David Mar 30 '17 at 14:45
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In the basic model of protein synthesis the events involving tRNA and amino acids are as follows (see any standard text, e.g. Lodish et al. section 4.4):

  1. An amino acid is attached to the appropriate tRNA (the one with the anticodon that recognizes a codon for that amino acid) by one of twenty specific amino acyltRNA synthase enzymes in a reaction requiring ATP. This is called charging or aminoacylation of tRNA.

  2. The tRNA corresponding to the mRNA codon is brought to the ribosome by an elongation factor (EF1) and the peptidyl transferase activity of the large ribosomal subunit catalyses the formation of a peptide bond between the growing polypeptide chain* and the amino acid of the tRNA, releasing deacylated tRNA.

I am unclear why you are concerned with this problem, but if there were two alanine codons in the mRNA, in theory after a particular discrete tRNA molecule had inserted the first alanine it could be recharged by the aminoacyl tRNA synthetase and then be used to insert the second alanine. However the concentration of tRNA molecules in the cell needed to support protein synthesis is such that the actual probability of this same discrete molecule being used, rather than another tRNA carrying alanine, is remote.

*A real-life complication is that a polypeptide chain has to be initiated by an initiator methionine-tRNA that is distinct from the methionine-tRNA that inserts internal methionines (see Lewin et al. section 4.5).

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