I hope to simulate the concentration variation process of a DNAzyme reaction.
The principle of the Michaelis-Menten model seems inappropriate. I wonder if
there is an model for this kind of reaction.
Could you please light my way?
Thank you.
From my very brief reading on the subject, it seems that DNAzymes are single-turnover catalysts because they are strongly product-inhibited, so it would not be appropriate to use steady-state kinetic analysis. It might be suitable to employ single-turnover kinetic analysis. These papers may have relevant information:
http://pubs.acs.org/doi/full/10.1021/bi051792i
http://www.sciencedirect.com/science/article/pii/0020711X77901094
These slides discuss the details of single-turnover kinetics, starting on slide 30.
http://www.msg.ucsf.edu/BI204/Lectures/Q1/Miller/Miller_EnzymesAloneWk5.pdf
The short answer is 'yes', but with several caveats. Catalytic DNAs (whatever the reaction they catalyze) may be expected to obey Michaelis-Menten kinetics, to a first approximation. I happened to study a RNA-cleaving DNAzyme, and indeed it would behave as a MM catalyst under the appropriate conditions:http://nar.oxfordjournals.org/content/32/3/916.long.
However, as Adam pointed out, when DNAzymes recognize their substrates by base-pairing, and when such pairing is extensive, product inhibition may be severe, to a point where reactions become effectively single-turnover. Furthermore DNAzymes (much like protein enzymes) may show allosteric effects, which give rise to non-MM curves. Sometimes, apparent allosteric effects may also be observed (for an example, see Fig. 3B in the following paper:
http://www.jbc.org/content/282/49/35510.long
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