The mechanism that caffeine increases activity by is via antagonizing adenosine A2 A receptors (the standard mechanism of caffeine). Adenosine normally suppresses the effects of dopamine on locomotion (via working in opposition on neuronal excitation  ) in the striatum where A2 A and dopaminergic neurons co-exist, and preventing this suppression with an antagonist increases the effects of dopamine on D2, of which include spontaneous activity and (in rats) rotational behaviour when unilateral lesions are induced in the striatum.   Non-caffeine adenosine antagonists also share this effect on locomotion, further implicating A2A antagonism and dopamine as the cause rather than a separate, unseen effect of caffeine.  As for why A2 A is mentioned more frequently than A1 in this section, it is since A2 A receptors appear to co-exist with dopamine receptors in many parts of the brain (nuclear accumbens, striatum, tuberculum olfactorium) whereas although A1 are heterogeneously expressed in the brain, there is no pattern with dopamine receptors.  Interactions with motor control appear to be highly relevant to the striatum, where A2 A predominates.
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In almost all cases, the point of a program is to have effects other then mapping things going in to things coming out. The idea of controlling the side-effect is that you can organize code in a way that is easier to understand and reason about. If you put all the side effect together, in a place that is very explicit and central, it's easy to know where to look and trust that this is all that's happening, no more. If you have the input be very explicit too, it helps test the behavior for different input, and it's easier to use, since you don't need to change the input in a lot of different places, some which might not be obvious, just to get what you want.