Table 1.

Starting values for model parameters and state variables used in a biologically based computational model for the hypothalamic-pituitary-thyroid (HPT) axis in X. laevis larvae.^a

Parameter	Term	Value	Source
Body growth
Starting body weight (g)	$BW$	0.28	Haselman et al. [21]; extrapolated to $t_0$
Rate of change of BW (1/h)	$R_{\text{BW}}$	0.0027	Haselman et al. [21]; fitted to measured growth data
Plasma and follicular cell iodide
Plasma concentration (pmol/ml)	$C_{\text{I},\text{PL}}$	1,000	This study (SI4)
Starting follicular cell concentration (pmol/ml)	$C_{\text{I},\text{FC}}$	20,000	$20\times C_{\text{I},\text{PL}}$
To calculate plasma concentration of TSH
Starting amount of TSH in plasma (pmol)	$A_{\text{TSH},\text{PL}}$	0.00165	Estimated from Korte et al. [41] and then optimized
Apparent volume of TSH distribution (ml/g)	$V{D}_{\text{TSH}}$	0.0554	McLanahan et al. [40]
Starting maximum rate of TSH secretion (pmol/h)	$V_{\text{MAX},\text{TSH}}$	0.325	Optimized
Rate of change of $V_{\text{MAX},\text{TSH}}$ (1/h)	$R_{V_{\text{MAX},\text{TSH}}}$	0.005	Optimized
$C_{\text{T}3,\text{FF},\text{PL}}$ resulting in half-maximal TSH secretion (pmol/ml)	$K_{\text{M},\text{TSH}}$	1.1×10−6	1/100th starting $C_{\text{T}3,\text{FF},\text{PL}}$
Starting rate of change of $K_{\text{M},\text{TSH}}$ (1/h)	$R_{K_{\text{M},\text{TSH}}}$	2.0×10−8	Optimized
Rate of change of $R_{K_{\text{M},\text{TSH}}}$ (1/h)	$R_{R_{K_{\text{M},\text{TSH}}}}$	1.0×10−9	Optimized
Plasma clearance constant (ml/h/g)	$C{L}_{\text{TSH}}$	0.11	Lemarchand-Beraud and Berthier [42]b
To calculate the aggregated volume of thyrocytes
Starting number of thyrocytes in NF stage 54 larvae	$FC{N}_{\text{TOT}}$	8,000	Haselman et al. [21]; extrapolated to $t_0$
Rate of change of thyrocyte number in controls (1/h)	$R_{\text{FCN},\text{CONT}}$	40	Optimized
Max. rate of change of TSH-mediated thyrocyte prolif. (1/h)	$R_{\text{FCN},\text{MAX}}$	700	Optimized
Average thyrocyte volume (ml)	$FCV$	1.0	This study (SI3)
Hill constant for TSH induction of gland growth (unitless)	$K_{\text{H}}$	0.6	Optimized
Hill coefficient for TSH induction of gland growth (unitless)	$n$	3.5	Optimized
To calculate intracellular iodide (see also terms that describe iodide organification and recycling of MIT and DIT)
Maximum rate of TSH-induced NIS activity (pmol/h/ml)	$V_{\text{MAX},\text{NIS}}^{\text{TSH}}$	2.55×107	Optimized
Affinity constant for TSH induction of NIS (pmol/ml)	$K_{\text{M},\text{NIS}}^{\text{TSH}}$	1.0×10−9	10x starting $C_{\text{TSH},\text{PL}}$
Affinity constant for NIS activity (pmol/ml)	$K_{\text{M},\text{NIS}}$	100,000	$100\text{x}{C}_{\text{I},\text{PL}}$
Inhibition constant for autoregulation of NIS by iodide (pmol/ml)	$K_{\text{I},\text{FC}}$	40,000	2x starting $C_{\text{I},\text{FC}}$
Rate constant for diffusion flux of iodide (ml/h/ml)	$k_{\text{D},\text{I}}$	1.1	Optimized
To calculate the rate of Tg synthesis (resulting in secretion of T4 and recycling of MIT and DIT)
Absolute maximum rate of Tg synthesis (pmol/h/ml)	$V_{\text{MAX},\text{TG},\text{SYN}}$	4400	Optimized
Affinity constant for TSH induction of Tg synthesis (pmol/ml)	$K_{\text{M},\text{TG},\text{SYN}}$	1.0	10x starting $C_{\text{TSH},\text{PL}}$
To describe the organification of iodide by TPO as MIT, DIT, and T4 iodine
Total starting amount of Tg in thyroid follicular lumen (pmol)	$A_{\text{TG},\text{TL}}$	0.4	Estimated from [21] and then optimizedc
Starting amount of organified iodine associated with Tg (pmol)	$A_{\text{I},\text{TG},\text{TL}}$	13.135	37 mol/mol iodinated Tgc
Starting amount of organified iodine associated with MIT (pmol)	$A_{\text{MIT},\text{TL}}$	0.355	1 mol/mol iodinated Tgc
Starting amount of organified iodine associated with DIT (pmol)	$A_{\text{DIT},\text{TL}}$	4.26	12 mol/mol iodinated Tgc
Starting amount of organified iodine associated with T4 (pmol)	$A_{\text{T}4,\text{TL}}$	8.52	24 mol/mol iodinated Tgc
Absolute maximum rate of TSH-induced TPO activity (pmol/h/ml)	$V_{\text{MAX},\text{TPO}}^{\text{TSH}}$	4.0×107	Optimized
Affinity constant for TSH induction of TPO (pmol/ml)	$K_{\text{M},\text{TPO}}^{\text{TSH}}$	1.0	10x starting $C_{\text{TSH},\text{PL}}$
Affinity constant for iodide incorporation into Tg via TPO	$K_{\text{M},\text{TPO}}$	2.0×106	100x starting $C_{\text{I},\text{FC}}$
To calculate the rate of Tg proteolysis
Absolute maximum rate of Tg proteolysis (pmol/h/ml)	$V_{\text{MAX},\text{TG},\text{PROT}}$	10,000	Optimized
Affinity constant for TSH induction of Tg proteolysis (pmol/ml)	$K_{\text{M},\text{TG},\text{PROT}}$	10	100x starting $C_{\text{TSH},\text{PL}}$
To calculate plasma T4 concentration
Starting total amount of T4 in plasma (pmol)	$A_{\text{T}4,\text{TOT},\text{PL}}$	0.0073	Haselman et al. [21]
Apparent volume of T4 distribution (ml/g)	$V{D}_{\text{T}4}$	0.156	McLanahan et al. [40]
Conjugative metabolism constant (ml/h/g)	$C{L}_{\text{T}4,\text{CONJ}}$	4.0	Fit to give $t_{1/2}$ of ∼2 h
Plasma protein dissociation constant (unitless)	$K_{\text{D},\text{T}4}$	0.01	Gives 1.0% free fraction
Maximum rate of T4 deiodination (pmol/h)	$V_{\text{MAX},\text{DIO}2}$	0.887	Optimized
Affinity constant for T4 deiodination (pmol/ml)	$K_{\text{M},\text{DIO2}}$	0.167	100x starting $C_{\text{T}4,\text{FF},\text{PL}}$
To calculate plasma T3 concentration
Starting total amount of T3 in plasma (pmol)	$A_{\text{T}3,\text{TOT},\text{PL}}$	0.00112	Haselman et al. [21]
Apparent volume of T3 distribution (ml/g)	$V{D}_{\text{T}3}$	0.186	McLanahan et al. [40]
Plasma clearance constant (ml/h/g)	$C{L}_{\text{T}3,\text{CON}3}$	28.3	Fit to give $t_{1/2}$ of ∼1 h
Plasma protein dissociation constant (unitless)	$K_{\text{D},\text{T}3}$	0.005	Gives 0.5% free fraction
Maximum rate of T3 deiodination (pmol/h)	$V_{\text{MAX},\text{DIO}3}$	0.58	Optimized
Affinity constant for T3 deiodination (pmol/ml)	$K_{\text{M},\text{DIO3}}$	0.011	100x starting $C_{\text{T}3,\text{FF},\text{PL}}$

^aAbbreviations: TPO — thyroperoxidase; Tg — thyroglobulin; TSH — thyroid stimulating hormone; NIS — sodium-iodide symporter; T4 — thyroxine; T3 — 3,5,3’-triiodothyronine; MIT — monoiodotyrosine; DIT — diiodotyrosine.

^bResults in plasma half-life value given by these authors for¹²⁵I-TSH in rats.

^cStarting values for Tg, MIT, DIT, and T4 were informed by measured amounts of MIT, DIT, and T4 in glands of NF 56 X. laevis tadpoles [21]; see main text for details.