Mathematical relationships between spinal motoneuron properties

Figures

Figure 1

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Figure 3

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Figure 3—source data 1

All the cat datasets presented in Figure 3.

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Figure 4

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Figure 7

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Figure 7—source data 1

Datasets used in the rat plot.

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Figure 7—source data 2

Datasets used in the mouse plots.

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Appendix 1—figure 1

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Appendix 1—figure 2

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Appendix 1—figure 3

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Appendix 1—figure 4

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Tables

Table 1

	Properties	Notation	Unit
MN properties	Size: Neuron surface area Soma diameter	$S_{MN}$ $S_{neuron}$ $D_{soma}$	${\displaystyle \left[{\mathrm{m}}^2\right]}$ ${\displaystyle \left[\mathrm{m}\right]}$
	Resistance	$R$	$\left[\mathrm{\Omega }\right]$
	Specific resistance per unit area	$R_m$	${\displaystyle \left[\mathrm{\Omega }\cdot {\mathrm{m}}^2\right]}$
	Capacitance	$C$	${\displaystyle \left[\mathrm{F}\right]}$
	Specific capacitance per unit area	$C_m$	${\displaystyle \left[\mathrm{F}\cdot {\mathrm{m}}^{-2}\right]}$
	Time constant	$\tau$	${\displaystyle \left[\mathrm{s}\right]}$
	Rheobase (current recruitment threshold)	$I_{th}$	${\displaystyle \left[\mathrm{A}\right]}$
	Voltage threshold	$∆V_{th}$	${\displaystyle \left[\mathrm{V}\right]}$
	Afterhyperpolarization duration	$AHP$	${\displaystyle \left[\mathrm{s}\right]}$
	Axonal conduction velocity	$ACV$	${\displaystyle \left[\mathrm{m}\cdot {\mathrm{s}}^{-1}\right]}$
mU properties	Size:	${\displaystyle S_{mU}}$
	Total fibre cross-sectional area	${\displaystyle CS{A}^{tot}}$	${\displaystyle [{\mathrm{m}}^2]}$
	Mean fibre cross-sectional area	${\displaystyle CS{A}^{mean}}$	${\displaystyle [{\mathrm{m}}^2]}$
	Innervation ratio	${\displaystyle IR}$	${\displaystyle []}$
	Tetanic force	${\displaystyle F^{tet}}$	${\displaystyle [\mathrm{N}]}$
	Twitch force	$F^{tw}$	${\displaystyle [\mathrm{N}]}$

Table 2

MN size (SMN)	mU size (SmU)
${\displaystyle S_{neuron}}$	${\displaystyle F^{tet}}$
${\displaystyle D_{soma}}$	${\displaystyle IR}$
	${\displaystyle CS{A}^{mean}}$
	${\displaystyle CS{A}^{tot}}$

Table 3

MN property	${\displaystyle \mathit{A}={\mathit{k}}_{\mathit{a}}\cdot {\mathit{B}}^{\mathit{a}}}$(normalized global datasets)						${\displaystyle \mathit{A}={\mathit{k}}_{\mathit{c}}\cdot {\mathit{S}}_{\mathit{M}\mathit{N}}^{\mathit{c}}}$(final MN-size dependent datasets)
${\displaystyle \mathit{A}}$	Relationship	$k_a$	${\displaystyle a}$	${\displaystyle r^2}$	p-value	Reference studies	${\displaystyle k_c}$	${\displaystyle c}$	${\displaystyle r^2}$	p-value	${\displaystyle N}$ points
${\displaystyle \mathit{A}\mathit{C}\mathit{V}}$	$ACV=k_a\bullet S_{MN}^a$	4.0 (2.5; 6.4)	0.7 (0.6; 0.8)	0.58	< 10-5	Cullheim, 1978; Kernell and Zwaagstra, 1981; Burke et al., 1982	4.0 (2.5; 6.4)	0.7 (0.6; 0.8)	0.58	< 10-5	109
${\displaystyle \mathit{A}\mathit{H}\mathit{P}}$	$AHP=k_a\bullet S_{MN}^a$	6.1 · 103 (1.2 · 103; 3.2 · 104)	−1.2 (−1.6; −0.8)	0.34	< 10-5	Zwaagstra and Kernell, 1980	2.5 · 104 (1.2 · 104; 5.0 · 104)	−1.5 (−1.7; −1.3)	0.41	< 10-5	492
	$AHP=k_a\bullet {ACV}^a$	1.5 · 104 (7.4 · 103; 2.9 · 104)	−1.4 (−1.5; −1.2)	0.41	< 10-5	Eccles et al., 1958a; Zwaagstra and Kernell, 1980; Gustafsson and Pinter, 1984b; Foehring et al., 1987
${\displaystyle \mathit{R}}$	$R=k_a\bullet S_{MN}^a$	1.5 · 105 (2.7 · 104; 7.9 · 105)	−2.1 (−2.5; −1.7)	0.61	< 10-5	Kernell and Zwaagstra, 1981; Burke et al., 1982	9.6 · 105 (4.1 · 105; 2.3 · 106)	−2.4 (−2.6; −2.2)	0.37	< 10-5	745
	$R=k_a\bullet AC{V}^a$	6.3 · 105 (1.9 · 105; 2.1 · 106)	−2.3 (−2.6; −2.0)	0.38	< 10-5	Kernell, 1966; Burke, 1968; Barrett and Crill, 1974; Kernell and Zwaagstra, 1981; Fleshman et al., 1981; Gustafsson and Pinter, 1984b; Sasaki, 1991
	$R=k_a\bullet AH{P}^a$	6.2 · 10−1 (4.1 · 10−1; 9.2 · 10−1)	1.1 (0.9; 1.2)	0.65	< 10-5	Gustafsson, 1979; Gustafsson and Pinter, 1984b; Foehring et al., 1987; Pinter and Vanden Noven, 1989; Sasaki, 1991
${\displaystyle {\mathit{I}}_{\mathit{t}\mathit{h}}}$	$I_{th}=k_a\bullet R^a$	1.1 · 103 (0.8 · 103; 1.3 · 103)	−1.0 (−1.1; −0.9)	0.37	< 10-5	Kernell, 1966; Fleshman et al., 1981; Gustafsson and Pinter, 1984a; Zengel et al., 1985; Munson et al., 1986; Foehring et al., 1987; Krawitz et al., 2001	9.0 · 10−4 (4.7 · 10−4; 1.7 · 10−3)	2.5 (2.4; 2.7)	0.37	< 10-5	722
	$I_{th}=k_a\bullet AC{V}^a$	3.2 · 10−6 (1.3 · 10−7; 8.2 · 10−5)	3.7 (3.0; 4.4)	0.37	< 10-5	Kernell and Monster, 1981; Gustafsson and Pinter, 1984a
	$I_{th}=k_a\bullet AH{P}^a$	2.5 · 104 (1.3 · 104; 4.8· 104)	−1.7 (−1.9; −1.6)	0.60	< 10-5	Gustafsson and Pinter, 1984a
${\displaystyle \mathit{C}}$	$C=k_a\bullet R^a$	2.4 · 102 (2.0 · 102; 3.9 · 102)	−0.4 (−0.4; −0.3)	0.57	< 10-5	Gustafsson and Pinter, 1984b	1.2 (0.7; 2.0)	1.0 (0.9; 1.2)	0.28	< 10-5	444
	$C=k_a\bullet I_{th}^a$	2.9 · 101 (2.4 · 101; 3.5 · 101)	0.3 (0.2; 0.3)	0.51	< 10-5	Gustafsson and Pinter, 1984a
	$C=k_a\bullet AH{P}^a$	2.8 · 102 (1.8 · 102; 4.4 · 102)	−0.4 (−0.5; −0.3)	0.24	< 10-5	Gustafsson and Pinter, 1984b
	$C=k_a\bullet AC{V}^a$	2.5 (0.7; 8.4)	0.8 (0.5; 1.0)	0.17	< 10-5	Gustafsson and Pinter, 1984b
$\mathit{\tau }$	$\tau =k_a\bullet R^a$	8.7 (7.2; 10.6)	0.5 (0.4; 0.6)	0.52	< 10-5	Burke and ten Bruggencate, 1971; Barrett and Crill, 1974; Gustafsson, 1979; Gustafsson and Pinter, 1984b; Zengel et al., 1985; Pinter and Vanden Noven, 1989; Sasaki, 1991	2.6 · 104 (1.5 · 104; 4.5 · 104)	−1.5 (−1.6; −1.4)	0.46	< 10-5	649
	$\tau =k_a\bullet AH{P}^a$	2.2 (1.3; 3.5)	0.8 (0.7; 1.0)	0.63	< 10-5	Gustafsson and Pinter, 1984b
	$\tau =k_a\bullet I_{th}^a$	2.3 · 102 (1.9 · 102; 2.7 · 102)	−0.4 (−0.5; −0.3)	0.72	< 10-5	Gustafsson and Pinter, 1984a
	$\tau =k_a\bullet AC{V}^a$	1.2 · 104 (2.2 · 103; 6.6 · 104)	−1.3 (−1.7; −0.9)	0.30	< 10-5	Gustafsson and Pinter, 1984b

Table 4

	${\displaystyle S_{neuron}\left[{\mathrm{m}}^2\right]}$	${\displaystyle D_{soma}\left[\mathrm{m}\right]}$	${\displaystyle R\left[\mathrm{\Omega }\right]}$	${\displaystyle R_m\left[\mathrm{\Omega }\cdot {\mathrm{m}}^2\right]}$	${\displaystyle C\left[\mathrm{F}\right]}$	${\displaystyle \tau \left[\mathrm{s}\right]}$	${\displaystyle I_{th}\left[\mathrm{A}\right]}$	${\displaystyle AHP\left[\mathrm{s}\right]}$	${\displaystyle ACV\left[\mathrm{m}\cdot {\mathrm{s}}^{-1}\right]}$
${\displaystyle S_{neuron}\left[{\mathrm{m}}^2\right]}$		${\displaystyle D_{soma}=1.8\cdot {10}^2\cdot S_{neuron}}$	${\displaystyle R=\frac{1.7\cdot {10}^{-10}}{S_{neuron}^{2.43}}}$	${\displaystyle R_m=\frac{1.0\cdot {10}^{-10}}{S_{neuron}^{1.43}}}$	${\displaystyle C=1.3\cdot {10}^{-2}\cdot S_{neuron}}$	${\displaystyle \tau =\frac{1.0\cdot {10}^{-12}}{S_{neuron}^{1.48}}}$	${\displaystyle I_{th}=3.8\cdot {10}^8\cdot S_{neuron}^{2.52}}$	${\displaystyle AHP=\frac{1.0\cdot {10}^{-11}}{S_{neuron}^{1.51}}}$	${\displaystyle ACV=3.0\cdot {10}^6\cdot S_{neuron}^{0.69}}$
${\displaystyle D_{soma}\left[\mathrm{m}\right]}$	${\displaystyle S_{neuron}=5.5\cdot {10}^{-3}\cdot D_{soma}}$		${\displaystyle R=\frac{5.1\cdot {10}^{-5}}{D_{soma}^{2.43}}}$	${\displaystyle R_m=\frac{1.7\cdot {10}^{-7}}{D_{soma}^{1.43}}}$	${\displaystyle C=7.9\cdot {10}^{-5}\cdot D_{soma}}$	${\displaystyle \tau =\frac{2.3\cdot {10}^{-9}}{D_{soma}^{1.48}}}$	${\displaystyle I_{th}=7.8\cdot {10}^2\cdot D_{soma}^{2.52}}$	${\displaystyle AHP=\frac{2.7\cdot {10}^{-8}}{D_{soma}^{1.51}}}$	${\displaystyle ACV=8.1\cdot {10}^4\cdot D_{soma}^{0.69}}$
${\displaystyle {\displaystyle R\left[\mathrm{\Omega }\right]}}$	${\displaystyle S_{neuron}=\frac{9.5\cdot {10}^{-5}}{R^{0.41}}}$	${\displaystyle D_{soma}=\frac{1.7\cdot {10}^{-2}}{R^{0.41}}}$		${\displaystyle R_m=5.7\cdot {10}^{-5}\cdot R^{0.59}}$	${\displaystyle C=\frac{1.5\cdot {10}^{-6}}{R^{0.40}}}$	${\displaystyle \tau =9.6\cdot {10}^{-7}\cdot R^{0.61}}$	${\displaystyle I_{th}=\frac{2.7\cdot {10}^{-2}}{R^{1.04}}}$	${\displaystyle AHP=1.3\cdot {10}^{-5}\cdot R^{0.62}}$	${\displaystyle ACV=\frac{4.9\cdot {10}^3}{R^{0.29}}}$
${\displaystyle {\displaystyle R_m\left[\mathrm{\Omega }\cdot {\mathrm{m}}^2\right]}}$	${\displaystyle S_{neuron}=\frac{1.5\cdot {10}^{-7}}{R_m^{0.70}}}$	${\displaystyle D_{soma}=\frac{2.6\cdot {10}^{-5}}{R_m^{0.70}}}$	${\displaystyle R=6.8\cdot {10}^6\cdot R_m^{1.70}}$		${\displaystyle C=\frac{1.8\cdot {10}^{-9}}{R_m^{0.69}}}$	${\displaystyle \tau =1.4\cdot {10}^{-2}\cdot R_m^{1.04}}$	${\displaystyle I_{th}=\frac{2.2\cdot {10}^{-9}}{R_m^{1.76}}}$	${\displaystyle AHP=2.2\cdot {10}^{-1}\cdot R_m^{1.06}}$	${\displaystyle ACV=\frac{5.4\cdot {10}^1}{R_m^{0.48}}}$
${\displaystyle {\displaystyle C\left[\mathrm{F}\right]}}$	${\displaystyle S_{neuron}=1.2\cdot {10}^2\cdot C}$	${\displaystyle D_{soma}=2.1\cdot {10}^4\cdot C}$	${\displaystyle R=\frac{1.5\cdot {10}^{-15}}{C^{2.48}}}$	${\displaystyle R_m=\frac{1.7\cdot {10}^{-13}}{C^{1.46}}}$		${\displaystyle \tau =\frac{8.6\cdot {10}^{-16}}{C^{1.51}}}$	${\displaystyle I_{th}=6.5\cdot {10}^{13}\cdot C^{2.57}}$	${\displaystyle AHP=\frac{7.7\cdot {10}^{-15}}{C^{1.54}}}$	${\displaystyle ACV=8.2\cdot {10}^7\cdot C^{0.71}}$
${\displaystyle \tau \left[\mathrm{s}\right]}$	${\displaystyle S_{neuron}=\frac{8.4\cdot {10}^{-9}}{{\tau }^{0.67}}}$	${\displaystyle D_{soma}=\frac{1.5\cdot {10}^{-6}}{{\tau }^{0.67}}}$	${\displaystyle R=7.1\cdot {10}^9\cdot {\tau }^{1.64}}$	${\displaystyle R_m=3.6\cdot {10}^1\cdot {\tau }^{0.96}}$	${\displaystyle C=\frac{1.6\cdot {10}^{-10}}{{\tau }^{0.66}}}$		${\displaystyle I_{th}=\frac{1.6\cdot {10}^{-12}}{{\tau }^{1.70}}}$	${\displaystyle AHP=1.7\cdot {10}^1\cdot {\tau }^{1.02}}$	${\displaystyle ACV=\frac{7.5}{{\tau }^{0.47}}}$
${\displaystyle {\displaystyle I_{th}\left[\mathrm{A}\right]}}$	${\displaystyle S_{neuron}=4.0\cdot {10}^{-4}\cdot I_{th}^{0.40}}$	${\displaystyle D_{soma}=7.1\cdot {10}^{-2}\cdot I_{th}^{0.40}}$	${\displaystyle R=\frac{3.1\cdot {10}^{-2}}{I_{th}^{0.96}}}$	${\displaystyle R_m=\frac{7.4\cdot {10}^{-6}}{I_{th}^{0.57}}}$	${\displaystyle C=5.9\cdot {10}^{-6}\cdot I_{th}^{0.39}}$	${\displaystyle \tau =\frac{1.2\cdot {10}^{-7}}{I_{th}^{0.59}}}$		${\displaystyle AHP=\frac{1.5\cdot {10}^{-6}}{I_{th}^{0.60}}}$	${\displaystyle ACV=1.3\cdot {10}^4\cdot I_{th}^{0.27}}$
${\displaystyle {\displaystyle AHP\left[\mathrm{s}\right]}}$	${\displaystyle S_{neuron}=\frac{5.5\cdot {10}^{-8}}{AH{P}^{0.66}}}$	${\displaystyle D_{soma}=\frac{9.8\cdot {10}^{-6}}{AH{P}^{0.66}}}$	${\displaystyle R=7.5\cdot {10}^7\cdot AH{P}^{1.61}}$	${\displaystyle R_m=2.5\cdot AH{P}^{0.95}}$	${\displaystyle C=\frac{9.7\cdot {10}^{-10}}{AH{P}^{0.65}}}$	${\displaystyle \tau =6.2\cdot {10}^{-2}\cdot AH{P}^{0.98}}$	${\displaystyle I_{th}=\frac{1.8\cdot {10}^{-10}}{AH{P}^{1.67}}}$		${\displaystyle ACV=\frac{2.7\cdot {10}^1}{AH{P}^{0.46}}}$
${\displaystyle {\displaystyle ACV\left[\mathrm{m}\cdot {\mathrm{s}}^{-1}\right]}}$	${\displaystyle S_{neuron}=4.6\cdot {10}^{-10}\cdot AC{V}^{1.44}}$	${\displaystyle D_{soma}=8.3\cdot {10}^{-8}\cdot AC{V}^{1.44}}$	${\displaystyle R=\frac{8.3\cdot {10}^{12}}{AC{V}^{3.50}}}$	${\displaystyle R_m=\frac{2.3\cdot {10}^3}{AC{V}^{2.06}}}$	${\displaystyle C=9.0\cdot {10}^{-12}\cdot AC{V}^{1.41}}$	${\displaystyle \tau =\frac{7.4\cdot {10}^1}{AC{V}^{2.14}}}$	${\displaystyle I_{th}=1.1\cdot {10}^{-15}\cdot AC{V}^{3.64}}$	${\displaystyle AHP=\frac{1.4\cdot {10}^3}{AC{V}^{2.18}}}$

Table 5

Species	$\mathit{A}=\mathit{k}\bullet {\mathit{B}}^{\mathit{c}}$(fitted relationships)					(final relationships)
	Relationship	$c$	$r^2$	p-value	Reference studies	c
Rat	${\displaystyle IR=k\cdot AC{V}^c}$	3.4	0.45	6.10-3	Kanda and Hashizume, 1992	2.4
Cat	${\displaystyle F^{tw}=k\cdot AC{V}^c}$	9.4	0.43	<10-5	Knott et al., 1971	6.6
	${\displaystyle F^{tet}=k\cdot AC{V}^c}$	7.2	0.37	<10-5	Mcphedran et al., 1965; Wuerker et al., 1965; Appelberg and Emonet-Dénand, 1967; Proske and Waite, 1974; Bagust, 1974; Jami and Petit, 1975; Stephens and Stuart, 1975; Burke et al., 1982; Emonet-Dénand et al., 1988	5.0
	$F^{tet}=k\bullet R^c$	-1.3	0.27	6.10-5	Dum and Kennedy, 1980	3.2
	$F^{tet}=k\bullet S_{MN}^c$	2.0	0.21	2.10-2	Burke et al., 1982	2.0
Mouse	$F^{tw}=k\bullet R^c$	-2.1	0.42	<10-5	Manuel and Heckman, 2011; Martínez-Silva et al., 2018	5.1
	$F^{tw}=k\bullet I_{th}^c$	1.3	0.64	2.10-4	Manuel and Heckman, 2011	3.3
	$F^{tet}=k\bullet I_{th}^c$	1.0	0.80	6.10-2	Manuel and Heckman, 2011	2.5
Mean ± sd						3.8 ± 1.5

Table 5—source data 1

Numerical data used to derive the relationships presented in Table 5.

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Appendix 1—table 1

	Studies	Linear	Power	Exponential
${\displaystyle \left\{ACV;S_{MN}\right\}}$	Cullheim, 1978	0.42	0.45	0.43
	Kernell and Zwaagstra, 1981	0.62	0.63	0.6
	Burke et al., 1982	0.23	0.26	0.24
${\displaystyle \left\{AHP;S_{MN}\right\}}$	Zwaagstra and Kernell, 1980	0.33	0.37	0.35
${\displaystyle \left\{AHP;ACV\right\}}$	Eccles et al., 1958b	0.53	0.54	0.54
	Zwaagstra and Kernell, 1980	0.42	0.44	0.42
	Gustafsson and Pinter, 1984a	0.71	0.68	0.7
	Foehring et al., 1987	0.15	0.14	0.14
${\displaystyle \left\{R;S_{MN}\right\}}$	Kernell and Zwaagstra, 1981	0.68	0.71	0.7
	Burke et al., 1982	0.41	0.5	0.46
${\displaystyle \left\{R;ACV\right\}}$	Kernell, 1966	0.70	0.65	0.64
	Burke, 1968	0.28	0.31	0.31
	Kernell and Zwaagstra, 1981	0.68	0.71	0.71
	Fleshman et al., 1981	0.3	0.21	0.2
	Gustafsson and Pinter, 1984a	0.45	0.44	0.42
	Sasaki, 1991	0.68	0.68	0.66
${\displaystyle \left\{R;AHP\right\}}$	Gustafsson, 1979	0.43	0.41	0.42
	Gustafsson and Pinter, 1984a	0.71	0.68	0.67
	Foehring et al., 1987	0.33	0.32	0.33
	Pinter and Vanden Noven, 1989	0.66	0.53	0.59
	Sasaki, 1991	0.57	0.49	0.52
${\displaystyle \left\{I_{th};R\right\}}$	Kernell, 1966	0.52	0.52	0.68
	Fleshman et al., 1981	0.28	0.34	0.38
	Gustafsson and Pinter, 1984b	0.63	0.83	0.83
	Zengel et al., 1985	0.49	0.6	0.62
	Munson et al., 1986	0.34	0.42	0.47
	Foehring et al., 1987	0.34	0.47	0.47
	Krawitz et al., 2001	0.32	0.49	0.44
${\displaystyle \left\{I_{th};ACV\right\}}$	Kernell and Zwaagstra, 1981	0.23	0.24	0.24
	Gustafsson and Pinter, 1984b	0.4	0.52	0.5
${\displaystyle \left\{I_{th};AHP\right\}}$	Gustafsson and Pinter, 1984b	0.55	0.72	0.69
${\displaystyle \left\{C;R\right\}}$	Gustafsson and Pinter, 1984a	0.55	0.57	0.57
${\displaystyle \left\{C;I_{th}\right\}}$	Gustafsson and Pinter, 1984a	0.23	0.34	0.24
${\displaystyle \left\{C;AHP\right\}}$	Gustafsson and Pinter, 1984a	0.25	0.26	0.26
${\displaystyle \left\{C;ACV\right\}}$	Gustafsson and Pinter, 1984a	0.17	0.22	0.19
${\displaystyle \left\{\tau ;R\right\}}$	Burke and ten Bruggencate, 1971	0.04	0.07	0.03
	Gustafsson, 1979	0.6	0.63	0.61
	Gustafsson and Pinter, 1984a	0.63	0.69	0.59
	Zengel et al., 1985	0.39	0.33	0.36
	Pinter and Vanden Noven, 1989	0.65	0.69	0.62
	Sasaki, 1991	0.68	0.72	0.64
${\displaystyle \left\{\tau ;I_{th}\right\}}$	Gustafsson and Pinter, 1984b	0.63	0.59	0.57
${\displaystyle \left\{\tau ;ACV\right\}}$	Gustafsson and Pinter, 1984a	0.69	0.76	0.76
${\displaystyle \left\{\tau ;AHP\right\}}$	Gustafsson and Pinter, 1984a	0.34	0.32	0.31

Appendix 1—table 2

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

Appendix 1—table 3

	Property	Unit	Absolute{min;max}	Average{min; max}	${\displaystyle q_S^E}$	Reference studies	Theoretical range
Cat	${\displaystyle D_{soma}}$	[µm]	${\displaystyle \left\{25.0;90.0\right\}}$	${\displaystyle \left\{36.7;75.5\right\}}$	2.2	Kernell, 1966; Cullheim, 1978; Zwaagstra and Kernell, 1980; Kernell and Zwaagstra, 1981; Ulfhake and Kellerth, 1981; Zwaagstra and Kernell, 1981; Burke et al., 1982; Donselaar et al., 1986; Destombes et al., 1992	[33; 79]
	${\displaystyle S_{neuron}}$	[mm2]	${\displaystyle \left\{0.08;0.64\right\}}$	${\displaystyle \{0.17;0.45\}}$	2.7	Barrett and Crill, 1974; Ulfhake and Kellerth, 1981; Burke et al., 1982; Ulfhake and Kellerth, 1984; Ulfhake and Cullheim, 1988; Moschovakis et al., 1991	[0.18; 0.44]
Rat	${\displaystyle D_{soma}}$	[µm]	${\displaystyle \left\{17.5;66.0\right\}}$	${\displaystyle \{23.9;55.7\}}$	2.4	Swett et al., 1986; Vult von Steyern et al., 1999; Copray and Kernell, 2000; Ishihara et al., 2001; Deardorff et al., 2013; Mierzejewska-Krzyżowska et al., 2014
Mouse	${\displaystyle D_{soma}}$	[µm]	${\displaystyle \left\{14.0;35.0\right\}}$	${\displaystyle \{14.0;35.0\}}$	2.5	Vult von Steyern et al., 1999
	${\displaystyle S_{neuron}}$	[mm2]	${\displaystyle \left\{0.01;0.08\right\}}$	${\displaystyle \{0.01;0.06\}}$	4.4	Amendola and Durand, 2008; Brandenburg et al., 2020

Appendix 1—table 4

MN property	Unit	Absolute exp {min;max}	Average exp {min; max}	${\displaystyle q_A^E}$	Reference studies	${\displaystyle q_A^T}$	${\displaystyle \frac{q_A^E}{q_A^T}}$	Theoretical range
$\mathit{R}$	[MΩ]	${\displaystyle \{0.2;8.1\}}$	${\displaystyle \{0.4;4.0\}}$	10.9	Kernell, 1966; Burke, 1968; Burke and ten Bruggencate, 1971; Barrett and Crill, 1974; Gustafsson, 1979; Kernell and Zwaagstra, 1981; Fleshman et al., 1981; Burke et al., 1982; Ulfhake and Kellerth, 1984; Gustafsson and Pinter, 1984a; Zengel et al., 1985; Foehring et al., 1986; Munson et al., 1986; Foehring et al., 1987; Sasaki, 1991; Krawitz et al., 2001	8.4	1.3	${\displaystyle \left[0.5;4.0\right]}$
$\mathit{C}$	[nF]	${\displaystyle \{2.2;8.5\}}$	${\displaystyle \{2.2;8.5\}}$	3.9	Gustafsson and Pinter, 1984a; Gustafsson and Pinter, 1985	2.3	1.6	${\displaystyle \left[3.2;7.5\right]}$
$\mathit{\tau }$	[ms]	${\displaystyle \left\{2.0;14.2\right\}}$	${\displaystyle \left\{2.9;10.2\right\}}$	3.5	Burke and ten Bruggencate, 1971; Barrett and Crill, 1974; Gustafsson, 1979; Ulfhake and Kellerth, 1984; Gustafsson and Pinter, 1984a; Gustafsson and Pinter, 1985; Sasaki, 1991	3.7	0.9	${\displaystyle \left[2.8;10.3\right]}$
${\displaystyle {\mathit{I}}_{\mathit{t}\mathit{h}}}$	[nA]	${\displaystyle \left\{1.7;52.7\right\}}$	${\displaystyle \left\{2.3;36.6\right\}}$	16.3	Fleshman et al., 1981; Kernell and Monster, 1981; Ulfhake and Kellerth, 1984; Gustafsson and Pinter, 1984b; Zengel et al., 1985; Foehring et al., 1986; Munson et al., 1986; Foehring et al., 1987; Krawitz et al., 2001	9.1	1.8	${\displaystyle \left[3.9;35.0\right]}$
${\displaystyle \mathit{A}\mathit{H}\mathit{P}}$	[ms]	${\displaystyle \left\{10.6;266.6\right\}}$	${\displaystyle \left\{44.2;158.7\right\}}$	4.1	Eccles et al., 1957; Gustafsson, 1979; Dum and Kennedy, 1980; Zwaagstra and Kernell, 1980; Ulfhake and Kellerth, 1984; Gustafsson and Pinter, 1984a; Zengel et al., 1985; Foehring et al., 1987; Sasaki, 1991	3.8	1.1	${\displaystyle \left[42.6;160.2\right]}$
${\displaystyle \mathit{A}\mathit{C}\mathit{V}}$	[m·s-1]	${\displaystyle \left\{51.1;127.2\right\}}$	${\displaystyle \left\{65.3;114.8\right\}}$	1.8	Eccles et al., 1957; Mcphedran et al., 1965; Kernell, 1966; Appelberg and Emonet-Dénand, 1967; Burke, 1968; Barrett and Crill, 1974; Proske and Waite, 1974; Bagust, 1974; Stephens and Stuart, 1975; Cullheim, 1978; Dum and Kennedy, 1980; Zwaagstra and Kernell, 1980; Kernell and Zwaagstra, 1981; Fleshman et al., 1981; Glenn and Dement, 1981; Burke et al., 1982; Gustafsson and Pinter, 1984a; Zengel et al., 1985; Foehring et al., 1986; Foehring et al., 1987	2.3	0.8	${\displaystyle \left[63.5;116.6\right]}$

Appendix 1—table 5

Animal	Dataset	Reference studies	$\mathit{n}\mathit{M}\mathit{E}\mathit{}\left(\mathit{\%}\right)$	$\mathit{n}\mathit{R}\mathit{M}\mathit{S}\mathit{E}\mathit{}\left(\mathit{\%}\right)$	${\mathit{r}}_{\mathit{p}\mathit{r}\mathit{e}\mathit{d}}^2$	${\mathit{r}}_{\mathit{e}\mathit{x}\mathit{p}}^2$
Rat	$\left\{I_{th};R\right\}$	Gardiner, 1993; Bakels and Kernell, 1993; Lee and Heckman, 1998; Button et al., 2008; Turkin et al., 2010; Krutki et al., 2015	352	16	0.53	0.54
Mouse	$\left\{I_{th};R\right\}$	Delestrée et al., 2014; Martínez-Silva et al., 2018; Huh et al., 2021	385	16	0.46	0.46
	$\left\{\tau ;R\right\}$	Manuel et al., 2009	1219	168	0.35	0.40
	$\left\{C;R\right\}$	Manuel et al., 2009	1915	98	0.38	0.38

Author response table 1

For one {A; B} global dataset	Training set	Test set
Permutation 1	p1, p2, p3, p4	p5
Permutation 2	p2, p3, p4, p5	p1
Permutation 3	p1, p3, p4, p5	p2
Permutation 4	p1, p2, p4, p5	p3
Permutation 5	p1, p2, p3, p5	p4

Author response table 2

Datasets	Previous validation	New validation
	nME	nRMSE	R2	nME	nRMSE	R2
AHP = ka ∙ SMNa	70	14	0,40	67	12	0,46
AHP = ka ∙ ACVa	158	20	0,43	147	19	0,43
R = ka ∙ SMNa	255	20	0,56	312	31	0,51
R = ka ∙ ACVa	246	23	0,43	205	18	0,46
R = ka ∙ AHPa	153	21	0,63	143	21	0,66
Ith = ka ∙ Ra	410	19	0,37	300	19	0,36
Ith = ka ∙ ACVa	171	26	0,34	155	20	0,42
Ith = ka ∙ AHPa	84	15	0,59	78	17	0,61
C = ka ∙ Ra	61	12	0,58	55	13	0,57
C = ka ∙ ITaℎ	47	17	0,53	52	19	0,49
C = ka ∙ AHPa	75	16	0,26	62	16	0,22
C = ka ∙ ACVa	82	21	0,16	74	21	0,20
τ = ka ∙ Ra	86	13	0,54	73	13	0,51
τ = ka ∙ AHPa	88	14	0,62	77	13	0,64
τ = ka ∙ ITaℎ	83	15	0,68	65	13	0,74
τ = ka ∙ ACVa	81	17	0,38	84	16	0,44

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