why do processivity experiments require a molar excess of template to Pol to obtain accurate measurements?
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Polymerase has a certain binding affinity for the primed templates: if there were equal concentrations of template and polymerase, a certain proportion of templates and polymerase would be bound to each other and a different proportion of templates and polymerase molecules would be unbound in solution. Moreover, because in this special case the number of templates and polymerase molecules are equal, the proportion of bound polymerase molecules Pp equals the proportion of bound template molecules Pt and the same can be said for the proportions of unbound molecules.
Consider the cases when polymerase is present in vast excess of template and when template is present in vast excess of polymerase. Whichever molecule is present in excess is competing for binding with the molecule present in limiting concentration. A much lower proportion of the excess molecule will be bound while a much higher proportion of the limiting molecule (almost all) will be bound.
Now think about what you need to accurately quantify the production in each round of the productivity experiment. You need to know how many bound complexes exist in each round; moreover, the math is much, much nicer if that number stays the same.
If you started with more polymerase then template, the first few rounds would be easy: the number of new templates per round would be roughly equal to the number of template molecules in the solution. But what would happen as the number of templates approached the number of polymerase molecules? You'd be okay for the first few cycles, then you'd be cooked.
Instead, you want to start with the special case where polymerase is present in much lower quantity. That way, the number of bound complexes (and hence new templates) in each rounds can not only be assumed roughly constant but also roughly equal to the number of polymerase molecules in the reaction mix, which is really easy to measure at the start of the experiment.
That turned out longer than I intended, but does it make sense?