TABLE 1.

Candidate slope and intercept functions with free parameters c, f, g, h, k, m, p, q, and s, chosen to assess the linear energy transfer (LET) dependence of the slope and intercept of the linear correlation between proton and x‐ray radiosensitivity. The functions were chosen to either increase (intercept) or decrease (slope) with increasing LET, but with additional functions chosen to allow for non‐monotonic behavior

Slope		Intercept
Function	Behavior	Function	Behavior
$c·e^{-f·\mathrm{LET}}$	Slope decreases exponentially with LET, asymptotically approaching zero.	m	Intercept has the same constant value for all LET values.
$c·e^{-f·\mathrm{LET}}+g$	Slope decreases exponentially with LET and asymptotes to a non‐zero value.	$p·LET$	Intercept increases linearly with LET.
$c·e^{-f·LET-h·LE{T}^2}+g$	Slope follows a Gaussian dependence on LET, allowing non‐monotonic behavior but decreasing exponentially for high LET values.	$m+p·LET$	Intercept increases linearly with LET with a constant offset.
$(c+h·LET)·e^{-f·LET}+g$	Slope depends on the product of an increasing linear and decreasing exponential dependence on LET, allowing for non‐monotonic behavior that ultimately decreases exponentially for high LET values.	$m+p·LET+q·LE{T}^2$	Intercept increases quadratically with LET, allowing for non‐monotonic behavior.
$c·ln(LET-h)·e^{-f·LET}+g$	Slope depends on the product of an increasing logarithmic and decreasing exponential dependence on LET, allowing for non‐monotonic behavior that ultimately decreases exponentially for high LET values.	$q·e^{s·\mathrm{LET}}$	Intercept increases exponentially with LET.
$\frac{c}{\mathrm{\Gamma }(f·LET+h+1)}+g$	Slope decreases via an inverse gamma dependence on LET—this is motivated by the Poisson‐like distribution described below, but with fewer free parameters.	$q·e^{s·\mathrm{LET}}+m$	Intercept increases exponentially with LET, beginning at a small positive value.
$\frac{c{k}^{f·(LET-h)}·e^{-k}}{\mathrm{\Gamma }(f·(LET-h)+1)}+g$	Slope follows a Poisson‐like (functionally similar, but continuous) LET dependence, allowing for non‐monotonic LET dependence while being parameterized by a function of particular relevance to radiation biology.	$q·{\mathrm{e}}^{-s·LET}+p·LET+m$	Intercept initially decreases exponentially with LET before increasing linearly at higher LET values, allowing for non‐monotonic behavior.