Both groups of input fibers of cerebellum (mossy, climbing) start 2 pathways: 1) project directly to the deep nuclei 2) project to cerebellar cortex, which then (after some processing) sends projection back to deep nuclei through Purkinje cells.
What is the purpose of such an architecture?
And closely related question: is the input information to DCN (the first pathway) and to cerebellar cortex (the second pathway) the same?
Short answers:
1) The true purpose of this architecture is not known (yet).
2) Yes, it is the same information, since the signal comes from the same axon (for climbing fibers see e.g. De Zeeuw et al., 1997).
Comment on the first answer:
Of course, though, there are many theories about the function of the cerebellar circuits, including these collaterals of the mossy and the climbing fibers. I would refer to the articles on wikipedia and scholarpedia as entry points.
To give you an extremely simplified scenario where such an architecture could be useful:
Let's say the mossy fibers contain the motor plan, coming from the cerebral cortex and the climbing fibers contain the true state of the limbs coming from the peripheral sensors (formulated like this, these statements are certainly not true). Now the direct signals to the deep cerebellar nuclei (DCN) could be used to quickly compute a rough "movement error" (i.e. planned trajectory vs. real trajectory) that already initiates a quick, rough movement correction. The signals to the cerebellar cortex would be used to compute an exact "movement error" which is also integrated at the DCN "a bit later" (i.e. some synaptic transmissions later) to further refine the movement correction.
Again, this is certainly not what is going on in the cerebellum but might give you some intuition of why such a circuitry could exist.
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