Appendix 1—table 2. Mathematical empirical normalized relationships between the motoneuron (MN) properties ${\displaystyle D_{soma},R,C,\tau ,I_{th},}$${\displaystyle AHP}$, and ${\displaystyle ACV}$.

Each column provides the relationships between one and the six other MN properties. All constants and properties are normalized up to a theoretical 100% maximum value. To scale the normalized relationships ${\displaystyle A=k\cdot B^c}$ for a specific mammalian species, the normalized intercept $k$ must be scaled with a pair of values for properties $A$ and $B$ obtained from the same motoneuron in that species.

	${\displaystyle D_{soma}}$	${\displaystyle R}$	${\displaystyle C}$	${\displaystyle \tau }$	${\displaystyle I_{th}}$	${\displaystyle AHP}$	${\displaystyle ACV}$
${\displaystyle D_{soma}}$		${\displaystyle R=\frac{9.6\cdot {10}^5}{D_{soma}^{2.4}}}$	${\displaystyle C=1.2\cdot D_{soma}}$	${\displaystyle \tau =\frac{2.6\cdot {10}^4}{D_{soma}^{1.5}}}$	${\displaystyle I_{th}=9.0\cdot {10}^{-4}\cdot D_{soma}^{2.5}}$	${\displaystyle AHP=\frac{2.5\cdot {10}^4}{D_{soma}^{1.5}}}$	${\displaystyle ACV=4.0\cdot D_{soma}^{0.7}}$
${\displaystyle R}$	${\displaystyle D_{soma}=\frac{2.9\cdot {10}^2}{R^{0.4}}}$		${\displaystyle C=\frac{2.7\cdot {10}^2}{R^{0.4}}}$	${\displaystyle \tau =5.8\cdot R^{0.6}}$	${\displaystyle I_{th}=\frac{1.5\cdot {10}^3}{R}}$	${\displaystyle AHP=4.7\cdot R^{0.6}}$	${\displaystyle ACV=\frac{2.0\cdot {10}^2}{R^{0.3}}}$
${\displaystyle C}$	${\displaystyle D_{soma}=8.6\cdot {10}^{-1}\cdot C}$	${\displaystyle R=\frac{1.4\cdot {10}^6}{C^{2.5}}}$		${\displaystyle \tau =\frac{3.3\cdot {10}^4}{C^{1.5}}}$	${\displaystyle I_{th}=6.2\cdot {10}^{-4}\cdot C^{2.6}}$	${\displaystyle AHP=\frac{3.1\cdot {10}^4}{C^{1.6}}}$	${\displaystyle ACV=3.6\cdot C^{0.7}}$
${\displaystyle \tau }$	${\displaystyle D_{soma}=\frac{9.5\cdot {10}^2}{{\tau }^{0.7}}}$	${\displaystyle R=5.6\cdot {10}^{-2}\cdot {\tau }^{1.6}}$	${\displaystyle C=\frac{8.5\cdot {10}^2}{{\tau }^{0.7}}}$		${\displaystyle I_{th}=\frac{2.9\cdot {10}^4}{{\tau }^{1.7}}}$	${\displaystyle AHP=7.8\cdot {10}^{-1}\cdot \tau }$	${\displaystyle ACV=\frac{4.6\cdot {10}^2}{{\tau }^{0.5}}}$
${\displaystyle I_{th}}$	${\displaystyle D_{soma}=1.6\cdot {10}^1\cdot I_{th}^{0.4}}$	${\displaystyle R=\frac{1.1\cdot {10}^3}{I_{th}}}$	${\displaystyle C=1.7\cdot {10}^1\cdot I_{th}^{0.4}}$	${\displaystyle \tau =\frac{4.2\cdot {10}^2}{I_{th}^{0.6}}}$		${\displaystyle AHP=\frac{3.7\cdot {10}^2}{I_{th}^{0.6}}}$	${\displaystyle ACV=2.7\cdot {10}^1\cdot I_{th}^{0.3}}$
${\displaystyle AHP}$	${\displaystyle D_{soma}=\frac{8.1\cdot {10}^2}{AH{P}^{0.7}}}$	${\displaystyle R=8.4\cdot {10}^{-2}\cdot AH{P}^{1.6}}$	${\displaystyle C=\frac{7.3\ast {10}^2}{AH{P}^{0.6}}}$	${\displaystyle \tau =1.3\cdot AHP}$	${\displaystyle I_{th}=\frac{1.9\ast {10}^4}{AH{P}^{1.7}}}$		${\displaystyle ACV=\frac{4.1\cdot {10}^2}{AH{P}^{0.5}}}$
${\displaystyle ACV}$	${\displaystyle D_{soma}=1.4\cdot {10}^{-1}\cdot AC{V}^{1.4}}$	${\displaystyle R=\frac{1.2\cdot {10}^8}{AC{V}^{3.5}}}$	${\displaystyle C=1.7\cdot {10}^{-1}\cdot AC{V}^{1.4}}$	${\displaystyle \tau =\frac{5.0\cdot {10}^5}{AC{V}^{2.1}}}$	${\displaystyle I_{th}=5.9\cdot {10}^{-6}\cdot AC{V}^{3.6}}$	${\displaystyle AHP=\frac{5.0\cdot {10}^5}{AC{V}^{2.2}}}$