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Could someone help me understand this equation please? I found it in a paper which said that it was DNA replication, but why?

$\ce{dNTP + dNMP_{n} -> dNMP_{n +1} + PPi}$

I found that dNTP means deoxy nucleotide triphosphate and dNTP means deoxy nucleotide monophosphate. Deoxy nucleotide monophosphate is a monomer in DNA, but dNTP isn't.

I also would like to know if there is an equation like this in other processes in the central dogma (such as transcription and translation)?

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    $\begingroup$ NTP stands for nucleoside triphosphate. A subtle difference. With nucleotides, the phosphate is implied. $\endgroup$ – canadianer Jun 29 '15 at 5:49
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The notation you are referring to is a way to express the elongation of a nucleotide strand (Fig. 1).

dNTP + dNMP(n) → dNMP(n+1) + PPi 

means

Existing strand + deoxynucleotidetriphosphate → elongated-strand + pyrophospate.

elongation

Fig. 1. Elongation of DNA. Source: Concepts in Genetics.


This reaction holds for DNA replication as well as transcription.

Translation is all about protein synthesis from amino acid precursors. Each subsequent amino acid is coupled to the growing peptide by a peptide bond between the carboxyl of the growing peptide and the amino group of the new amino acid. A water molecule is eliminated during the reaction (Fig. 2).

peptide synthesis
Fig. 2. Peptide bond formation. Source: An Introduction to Molecular Biology

Hence translation can be written analogously to replication as:

amino acid + peptide(n) → peptide(n+1) 

However, also in this polymerization reaction energy is needed and amino acids are activated while they are bound to the messenger RNA (mRNA) through the action of ATP. Moreover, during translation the ribosome (i.e., the protein synthesizing machinery) uses another source of energy to move across the RNA template, namely GTP. Hence, the net reaction can be written as:

amino acid + peptide(n) + ATP + GTP → peptide(n+1) + AMP + GDP + PPi + Pi 

Note that this notation in itself is not a dogma as other ways are in use to denote DNA and RNA synthesis. According to Merriam-Webster a dogma is:

A belief or set of beliefs that is accepted by the members of a group without being questioned or doubted.

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    $\begingroup$ It's incorrect to say that amino acids are not activated. tRNA charging is the activation step of protein synthesis and creates an ester bond with high and negative free energy of hydrolysis (whose cleavage subsequently drives peptide bond formation). tRNA charging requires ATP. A net equation for peptide synthesis could be written as amino acid + peptide_n + ATP -> peptide_(n+1) + AMP + 2Pi. This equation (like that discussed in the question) is over simplified, but gets the point across. $\endgroup$ – canadianer Jun 29 '15 at 5:25
  • $\begingroup$ @canadianer - Great point, will include shortly $\endgroup$ – AliceD Jun 29 '15 at 5:36
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    $\begingroup$ Additional point to what @canadianer said. Each elongation step requires a molecule of GTP per codon. So the reaction for translation elongation should be: amino-acid + Peptide(n) + ATP + GTP → Peptide(n+1) + AMP + GDP + PPi + Pi $\endgroup$ – WYSIWYG Jun 29 '15 at 8:25
  • $\begingroup$ @WYSIWYG - I edited the answer. Thanks. I must say that both mRNA activation and the ribosome movement are both indirectly related to the translation reaction. The direct substrates are mRNA and the growing peptide. ATP and GTP are indirectly involved. So I reverted to my old answer and added your comment alongside Canadianer's in a separate section for clarity's sake. Thanks for your suggestions and the edits! $\endgroup$ – AliceD Jun 29 '15 at 10:43
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DNA is a polymer of dNMPs (dAMP, dTMP, dCMP, and dGMP). That's why you could describe DNA by dNMPn (n base length). When another dNTP is added to DNA (dNMPn), one pyrophosphate (PPi) is released. It is obvious that the length of the DNA results in n+1 bases.

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