. 2016 Apr 20;12(4):e1004874. doi: 10.1371/journal.pcbi.1004874

Table 2. HPOL model parameters, values and sensitivity ranking (sens.).

Parameter	Value	Units	Function	Source	Sens.
Pituitary
k_s,mFSH	0.05895	(pg/μg RNA)/hr	Rate of mFSH synthesis	[45]²^,⁶	67
α_mFSH,GnRH	2.0917	unitless	Stimulatory factor on mFSH synthesis due to GnRH	[46]²^,⁶	44
k_d,mFSH	0.2446	hr^-1	Rate of mFSH degradation	Eq (7) and optimized around mFSH data.⁶	48
k_s,mLH	0.0512	(pg/μg RNA)/hr	Rate of mLH synthesis	Assumed to be within ±25% of k_s,mFSH.⁶	45
α_mLH,GnRH	0.01	unitless	Stimulatory factor on mLH synthesis due to GnRH	[47]	23
α_mLH,E2	4.15	ml/ng	Stimulatory factor on mLH synthesis due to E2	[45]²^,⁶	56
k_d,mLH	0.1046	hr^-1	Rate of mLH degradation	Used E2 data from [41].⁴^,⁶	66
k_s,LH	1.004	(pg/μg RNA)^-1 ng/mg pituitary/hr	Rate of LH synthesis	Used E2 data from [41] and DHP and mLH from our experiment.⁴^,⁶	58
k_d,LH	0.06	hr^-1	Rate of LH degradation	Used E2 data from [41] and DHP and mLH from our experiment.⁴^,⁶	46
k_r,LH	66700	hr^-1	Rate of LH release from the pituitary into the blood	Used E2 data from [41] and DHP and mLH from our experiment.⁴^,⁶	9
T_E2,LH	23	ng/ml	Threshold value for E2 levels that allow LH release from the pituitary into the plasma	[48]²^,⁶	39
n_E2	9	unitless	Determines the range of E2 levels that allow for LH release from the pituitary into the plasma	Used E2 data from [41] and DHP and mLH from our experiment.⁴^,⁶	21
N_E2	36.78	ml/mg pituitary	Conversion factor of E2 to the minimum amount of D2r needed to maintain the block on LH release	Used E2 data from [41] and DHP and mLH from our experiment.⁴^,⁶	42
N_DHP	2.8	ml/mg pituitary	Conversion factor of DHP to the minimum amount of D2r needed to maintain the block on LH release	Used E2 data from [41] and DHP and mLH from our experiment.⁴^,⁶	22
w_Pit	15	mg/kg	Pituitary weight	Directly measured	71
Plasma
V_FSH	156	ml/kg	FSH volume of distribution	[49,50]²^, ⁶	20
k_s,FSH	0.0138	(pg/μg RNA)^-1 ng/mg pituitary/hr	Rate of appearance of FSH in the blood	[45]²^,⁶	61
Cl_FSH	1.7372	ml/hr/kg	FSH clearance	[49]²^,⁶	63
V_LH	156	ml/kg	LH volume of distribution	Assumed to be equal to FSH, based on [49,50]	7
Cl_LH	1.7372	ml/hr/kg	LH clearance	Assumed to be equal to FSH	14
V_E2	261	ml/kg	E2 volume of distribution	[51]¹	12
Cl_E2	22	ml/hr/kg	E2 clearance	[51]¹	75
V_DHP	261	ml/kg	DHP volume of distribution	Assumed to be equal to E2	19
Cl_DHP	57	ml/hr/kg	DHP clearance	Assumed from observed data.²^,⁶	33
$V_{V T G_{P}}$	240	ml/kg	Plasma VTG volume of distribution	[52]¹	29
Cl_VTG,trans	42.2	ml/hr/kg	Intercompartmental clearance between central and peripheral	[52]¹	26
Cl_VTG,Seq	170	ml/hr/kg	Clearance of VTG from blood due to uptake by the ovaries	[12]²^,⁶	31
T_Seq,FSH	13.7	ng/ml	Threshold value for FSH effect on VTG uptake by the ovaries	[36]²^,⁶	15
Cl_VTG	29.3	ml/hr/kg	Total body clearance of VTG	[52]¹	32
$V_{V T G_{N}}$	318	ml/kg	Volume of distribution of VTG in peripheral tissues	[52]¹	17
Ovary
k_E2	0.0053	ng/hr/ follicle	Rate of E2 basal production	[53]²^,⁶	38
n_oocyte	2500	follicle/kg	Number of oocyte follicles per kg of fish	[38]²	59
$C l_{E 2, S_{2}}$	0.00057	ml/hr/ follicle	Clearance of E2 from the follicle due to stimulation by FSH in stage 2	Used FSH data from our experiment.⁴^,⁶	16
$C l_{E 2, S_{3}}$	0.00057	ml/hr/ follicle	Clearance of E2 from the follicle due to stimulation by FSH in stage 3	Used FSH data from our experiment.⁴^,⁶	35
$C l_{E 2, S_{4}}$	0.0027	ml/hr/ follicle	Clearance of E2 from the follicle due to stimulation by FSH in stage 4	Used FSH data from our experiment.⁴^,⁶	50
$C l_{E 2, S_{5}}$	0.0561	ml/hr/ follicle	Clearance of E2 from the follicle due to stimulation by FSH in stage 5	Used FSH data from our experiment.⁴^,⁶	49
$C l_{E 2, S_{6}}$	0.0617	ml/hr/ follicle	Clearance of E2 from the follicle due to stimulation by FSH in stage 6	Used FSH data from our experiment.⁴^,⁶	28
$C l_{D H P, S_{2}}$	0.0003	ml/hr/ follicle	Clearance of DHP from the follicle due to stimulation by LH in stage 2	Used LH data from our experiment.⁴^,⁶	11
$C l_{D H P, S_{3}}$	0.0003	ml/hr/ follicle	Clearance of DHP from the follicle due to stimulation by LH in stage 3	Used LH data from our experiment.⁴^,⁶	24
$C l_{D H P, S_{4}}$	0.0003	ml/hr/ follicle	Clearance of DHP from the follicle due to stimulation by LH in stage 4	Used LH data from our experiment.⁴^,⁶	18
$C l_{D H P, S_{5}}$	0.0003	ml/hr/ follicle	Clearance of DHP from the follicle due to stimulation by LH in stage 5	Used LH data from our experiment.⁴^,⁶	27
$C l_{D H P, S_{6}}$	0.3	ml/hr/ follicle	Clearance of DHP from the follicle due to stimulation by LH in stage 6	Used LH data from our experiment.⁴^,⁶	4
$C l_{D H P, S_{F O M}}$	0.79	ml/hr/ follicle	Clearance of DHP from the follicle due to stimulation by LH in FOM	Used LH data from our experiment.⁴^,⁶	3
_{$k_{N V, O_{A v g}}$}	0.00067	mm/hr/kg	Growth rate of individual non-vitellogenic follicles	[53]²^,⁶	55
_{$k_{V, O_{A v g}}$}	2.19e-7	mm/mg	Growth rate per amount of VTG sequestered by an individual follicle	Used VTG data from [45] and FSH data from our experiment.⁴^,⁶	25
_{$α_{O_{V a r}, S_{1}}$}	0.0214	mm²	Maximal variance of follicles in stage 1	[38]²^,⁶	5
$α_{O_{V a r}, S_{2}}$	0.0433	mm²	Maximal variance of follicles in stage 2	[38] ²^,⁶	6
$α_{O_{V a r}, S_{3}}$	0.0748	mm²	Maximal variance of follicles in stage 3	[38] ²^,⁶	40
$α_{O_{V a r}, S_{4}}$	0.0907	mm²	Maximal variance of follicles in stage 4	[38] ²^,⁶	57
$α_{O_{V a r}, S_{5}}$	0.0338	mm²	Maximal variance of follicles in stage 5	[38] ²^,⁶	36
$α_{O_{V a r}, S_{6}}$	0.014	mm²	Maximal variance of follicles in stage 6	[38] ²^,⁶	2
$α_{O_{V a r}, S_{F O M}}$	0.0067	mm²	Maximal variance of the follicles in FOM	[38] ²^,⁶	8
s₁	0.2	mm	Follicle diameter dividing stages 1 and 2 (follicles are able to produce E2)	[5]¹	13
s₂	0.6	mm	Follicle diameter dividing stages 2 and 3 (follicles are able to take up VTG)	[37]¹	68
s₃	1.17	mm	Follicle diameter dividing stages 3 and 4 (follicles enter the mid-vitellogenic stage)	Used the data from our experiment and [41].⁶	69
s₄	1.69	mm	Follicle diameter dividing stages 4 and 5 (follicles enter the late vitellogenic stages)	Used the data from our experiment and [41].⁶	74
s₅	3.4	mm	Follicle diameter dividing stages 5 and 6 (follicles are able to produce substantially more DHP)	Used the data from our experiment and [41].⁶	62
s₆	5.3	mm	Follicle diameter dividing stages 6 and FOM (follicles are no longer able to sequester VTG)	Based on [5]: (s₆-s₂)/O_M = 0.84, where O_M is the maximum average oocyte diameter from [41]	10
FOM_final	0.98	unitless	Proportion of follicles in FOM needed before ovulation	Assumed⁶	30
DHP_final	120	ng/ml	Concentration of DHP needed before ovulation can occur	Assumed based on DHP levels from present experiment.⁶	1
Liver
w_L	15	g/kg	Liver weight	[12]³	41
k_s,mR	30	pg/ug RNA/hr	Rate of mR synthesis	[12]³	78
α_mR,ER	0.0667	g liver/ fmol	Maximal stimulatory fold-increase in mR synthesis due to ER complex	[12]³	65
k_d,mR	0.5	hr^-1	Rate of mR degradation	[12]³	73
k_s,R	0.0113	(pg/ug RNA)^-1 fmol/g liver/hr	Rate of R synthesis	[12]³	76
k_d,R	0.466	hr^-1	Rate of R degradation	[12]³	52
k_on,ER	0.826	(ng/ml)^-1 hr^-1	Association rate constant for ER	[12]³	60
k_off,ER	0.347	hr^-1	Dissociation rate constant for ER	[12]³	64
k_d,ER	0.0766	hr^-1	Rate of ER complex degradation	[12]³	77
k_s,mVTG	6.93E-05	pg/ug RNA/hr	Rate of mVTG synthesis	[12]³	70
α_mVTG,ER	5.456e6	g liver/ fmol	Stimulatory factor on VTG synthesis due to ER complex	[12]³	72
k_d,mVTG	0.00462	hr^-1	Rate of mVTG degradation	[12]³	54
k_s,VTG	9.02E-06	mg/g liver/hr	Rate of VTG synthesis	[12]²^,⁶	53
N_mVTG	1000	pg/ug RNA	Scaling factor for mVTG concentration	[12]³	47
γ	2.48	unitless	Amplification factor on the translation of VTG	[12]³	79
k_r,VTG	7.87	hr^-1	Rate of VTG release from the liver into the plasma	[12]³	43
Transit Compartments
D_FSH,E2	875	hr	Delay of E2 synthesis due to FSH	Used FSH data from our experiment and E2 data from [41].⁵^,⁶	51
D_E2,mLH	240	hr	Delay of mLH synthesis due to E2	Used E2 data from [41] and mLH data from our experiment.⁵^,⁶	37
D_LH,DHP	72	hr	Delay of DHP synthesis due to LH	Used LH data and DHP data from our experiment.⁵^,⁶	34

¹ Parameter value was obtained directly from source.

² Guided initial estimates of the parameter value.

³ Parameter value was obtained from prior modeling efforts.

⁴ Specified data was used to create an input curve and an initial estimate was obtained through optimization methods solving a minimum number of differential equations.

⁵ Initial estimate was obtained by calculating time delays in the relative extrema from specified data.

⁶ Final parameter value was refined through optimization methods using experimental data from [41] and our experiment. See the Methods Section for details.