Table 1. Analytic conclusions in equation form for the different DP, NC, CA, and unified mechanisms models described in our work.

Predicted expressions for active RAF at baseline (no drug), active RAF, total RAF dimers, and analytic conditions for PA to occur are shown in the rows for each of the mechanism associated models. The columns show models corresponding to the PA mechanisms of drug-modulated conformational autoinhibition (CA model), drug-induced dimerization potentiation mechanism (DP model), negative cooperativity toward second drug binding (NC model), and a model that combines all these mechanisms (unified model). The lower part of the table is a key that presents the abbreviated expressions, which allow presentation into similar functional forms for corresponding model results.

Model type	Conformational autoinhibition (CA)	Dimer potentiation (DP)	Negative cooperativity (NC)	Unified model
Core model assumptions	Monomeric RAF autoinhibits Non-autoinhibited RAF can dimerize and bind drug RAF dimers signal downstream	RAF can dimerize and bind drug Drug binding reduces dissociation constant of RAF dimers. RAF dimers signal downstream	RAF can dimerize and bind drug Singly bound RAF dimers resist drug binding at second site RAF dimers signal downstream	CA model assumptions DP model assumptions NC model assumptions
Baseline active RAF (relative to total)	${\displaystyle \frac{{\left(-1+\sqrt{\left(1+E3\right)}\right)}^2}{E3}}$	${\displaystyle \frac{{\left(-1+\sqrt{\left(1+8RA{F}_{rel}\right)}\right)}^2}{8RA{F}_{rel}}}$	${\displaystyle \frac{{\left(-1+\sqrt{\left(1+8RA{F}_{rel}\right)}\right)}^2}{8RA{F}_{rel}}}$	${\displaystyle \frac{{\left(-1+\sqrt{\left(1+E3\right)}\right)}^2}{E3}}$
Active RAF (relative to total)	${\displaystyle \frac{{\left(E1-\sqrt{E{1}^2+E2c}\right)}^2}{E2c\left(1+d_{rel}\right)}}$	${\displaystyle \frac{{\left(E1\mathrm{d}-\sqrt{E1{\mathrm{d}}^2+E2\mathrm{d}}\right)}^{2}f\left(E1\mathrm{d}+\left(-1+f\right)f\right)}{E2\mathrm{d}\left(E1{\mathrm{d}}^2+\left(-1+f\right)f^2\right)}}$	${\displaystyle \frac{E1n{\left(E1n-\sqrt{E1n^2+E2n}\right)}^2{g}^2}{E2n\left(g+2g{d}_{rel}+d_{rel}^2\right)}}$	${\displaystyle \frac{{\left(E1-\sqrt{E{1}^2+E2u}\right)}^{2}g\left(f+d_{rel}\right)}{E2u\left(fg+2g{d}_{rel}+d_{rel}^2\right)}}$
Total RAF dimers (relative to active RAF)	${\displaystyle \frac{1}{2}\left(1+d_{rel}\right)}$	${\displaystyle \frac{f+d_{rel}\left(2+d_{rel}\right)}{2\left(f+d_{rel}\right)}}$	${\displaystyle \frac{\mathrm{g}}{2g\left(1+d_{rel}\right)}+d_{rel}}$	${\displaystyle \frac{f\mathrm{g}+d_{rel}\left(2\mathrm{g}+d_{rel}\right)}{2\mathrm{g}\left(f+d_{rel}\right)}}$
RAF PA conditions	${\displaystyle RA{F}_{rel}<}$${\displaystyle \frac{1}{8}\left(1+3K_A\right)\times \left(K_A-1\right)}$ (** necessary and sufficient)	${\displaystyle d_{rel}<1-2f}$ ${\displaystyle 8\times \mathrm{R}\mathrm{A}\mathrm{F}\mathrm{r}\mathrm{e}\mathrm{l}<(3-8\mathrm{f}+4\mathrm{f}2)}$ ${\displaystyle f<1/2}$ (* sufficient)	No PA possible	${\displaystyle g\ge 1}$ ${\displaystyle 2f\ge 1+K_A}$ ${\displaystyle 8\times RA{F}_{rel}<}$${\displaystyle 4f^2-8f\left(1+K_A\right)+3{\left(1+K_A\right)}^2}$ (*sufficient)
Key	${\displaystyle E1d=\left(drel+1\right)f}$		${\displaystyle E1=\left(d_{rel}+1+K_A\right)}$
	${\displaystyle E2d=8f\times RA{F}_{rel}\left(f+2d_{rel}+d_{rel}^2\right)}$		${\displaystyle E2c=8RA{F}_{rel}\left(1+2d_{rel}+d_{rel}^2\right)}$
	${\displaystyle E1n=\left(d_{rel}+1\right)}$		${\displaystyle E3=\left(8RA{F}_{rel}\right)/{\left(1+K_A\right)}^2}$
	${\displaystyle E2n=8RA{F}_{rel}\left(g+2g{d}_{rel}+d_{rel}^2\right)}$		${\displaystyle E2u=8RA{F}_{rel}\left(fg+2g{d}_{rel}+d_{rel}^2\right)/\left(fg\right)}$
	*Sufficient: conditions that allow PA		**Necessary and sufficient: The only conditions that allow PA.