You aim to make an antidote to a toxin, which is present in the bloodstream at 5 nM concentration. You engineer a small protein to bind the toxin with 2.5 nM affinity.

a. What concentration of antidote protein must be initially present in the bloodstream to bind 90% of the toxin at equilibrium?

b. After the system has equilibrated, unbound antidote protein is removed from the bloodstream, while toxin-protein complex remains. Within 12 minutes, 15% of the toxin-protein complex has dissociated. Neglecting any rebinding of dissociated protein (because it is efficiently diluted and removed in the bloodstream), what is the association rate constant for the toxin-protein interaction? Is the association rate constant relatively fast, slow, or normal?

The numerical answer is 27nm for part a and 9.0x10^-4 for part b but I don't know how to get there.