I agree with what others have said about this paper. One, that regulation of proteins and pathways in the cell is very complex, and two, that this paper just talks about the conformational states of the complex MDMX protein - how it can fold in different shapes that then either inhibit or activate (remove inhibition) p53.
An attempt at a simple? re-telling:
MDMX is another molecule (like MDM2) that inhibits p53 activity.
Normally, MDMX inhibits p53 when the p53-similar part of MDMX binds to the p53 binding pocket (the part of MDMX that binds to p53 and inhibits it), actually causing a change in the shape of MDMX to better enable it to bind to and inhibit p53.
MDMX inhibition of p53 is turned off (i.e. p53 is activated) when DNA damage causes CK1a to disrupt MDMX from sticking to itself (the p53 mimic portion no longer binds to the p53 binding pocket), thus hiding the p53 binding pocket so it no longer interacts with p53. So, when DNA is damaged, MDMX changes from its normal shape, inhibits p53 less, p53 is activated, and the DNA damage is dealt with.
I suppose this would be another way to activate p53 besides kevetrin MOA and besides the MDM2 inhibitors (which make p53 more stable and slow to be broken down). If one can mimic CK1a or otherwise alter MDMX so it no longer inhibits p53, this is an additional route of p53 activation. The authors also claim this paper validates their protein fragment release (PFR) method of studying how different portions of a large protein interact with the other portions.