/// <summary>
/// Takes observed (or estimated) final leaf numbers for genotype with (V) and without (N) vernalisation in long (L)
/// and short (S) photoperiods and works through calculation scheme and assigns values for vrn expresson parameters
/// </summary>
/// <param name="FLNset">Set of Final leaf number observations (or estimations) for genotype</param>
/// <param name="EnvData">Controlled environment conditions used when observing FLN set</param>
/// <returns>CultivarRateParams</returns>
public CultivarRateParams CalcCultivarParams(
FinalLeafNumberSet FLNset, FLNParameterEnvironment EnvData)
{
//////////////////////////////////////////////////////////////////////////////////////
// Get some parameters organized and set up structure for results
//////////////////////////////////////////////////////////////////////////////////////
// Initialise structure to hold vern rate coefficients
CultivarRateParams Params = new CultivarRateParams();
// Get some other parameters from phenology
double maxLAR = phenology.FindChild <IFunction>("MaxLAR").Value();
double minLAR = phenology.FindChild <IFunction>("MinLAR").Value();
double PTQhf = phenology.FindChild <IFunction>("PTQhf").Value();
LARPTQmodel LARmodel = phenology.FindChild <LARPTQmodel>("LARPTQmodel");
//Calculate base phyllochron
Params.BasePhyllochron = 1 / LARmodel.CalculateLAR(1.0, maxLAR, minLAR, PTQhf);
//////////////////////////////////////////////////////////////////////////////////////
// Calculate phase durations (in Base Phyllochrons)
//////////////////////////////////////////////////////////////////////////////////////
// Base phyllochron duration of Emergence (EmergBP)
double EmergBP = EnvData.TtEmerge / Params.BasePhyllochron;
//Haun stage duration of vernalisation treatment period
double VrnTreatTtDurat = EnvData.VrnTreatTemp * EnvData.VrnTreatDuration;
double VernTreatBP = VrnTreatTtDurat / Params.BasePhyllochron;
// The soonest a wheat plant may exhibit vern saturation
double MinVSBP = ConvertHStoBP(1.1);
// Minimum Haun stage duration from vernalisation saturation to terminal spikelet under long day conditions (MinHSVsTs)
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
// Assume maximum of 3, Data from Lincoln CE (CRWT153) showed varieties that harve a high TSHS hit VS ~3HS prior to TS
double MinBPVsTs = Math.Min(ConvertHStoBP(3.0), (ConvertHStoBP(FLNset.LV) - MinVSBP) / 2.0);
// The HS duratin from Vern sat to final leaf under long Pp vernalised treatment
double VSBP_FL_LV = ConvertHStoBP(FLNset.LV) - MinVSBP - MinBPVsTs;
// The Intercept of the assumed relationship between FLN and TSHS for genotype (IntFLNvsTSHS)
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Params.IntFLNvsTSHS = Math.Min(2.85, VSBP_FL_LV / 1.1);
// Calculate Terminal spikelet duration (TSHS) for each treatment from FLNData
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
double TSBP_LV = ConvertHStoBP(camp.calcTSHS(FLNset.LV, Params.IntFLNvsTSHS));
double TSBP_LN = ConvertHStoBP(camp.calcTSHS(FLNset.LN, Params.IntFLNvsTSHS));
double TSBP_SV = ConvertHStoBP(camp.calcTSHS(FLNset.SV, Params.IntFLNvsTSHS));
double TSBP_SN = ConvertHStoBP(camp.calcTSHS(FLNset.SN, Params.IntFLNvsTSHS));
// Photoperiod sensitivity (PPS) is the difference between TSBP at 8 and 16 h pp under full vernalisation.
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
double PPS = Math.Max(0, TSBP_SV - TSBP_LV);
// Vernalisation Saturation duration (VSBP) for each environment from TSBP and photoperiod response
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
// Terminal spikelet duration less the minimum duration from VS to TS under long day treatment
double VSBP_LV = Math.Max(MinVSBP, TSBP_LV - MinBPVsTs);
double VSBP_LN = Math.Max(MinVSBP, TSBP_LN - MinBPVsTs);
// Terminal spikelet duration less the minimum duration from VS to TS and the photoperiod extension of VS to TS under short day treatment
double VSBP_SV = Math.Max(MinVSBP, TSBP_SV - (MinBPVsTs + PPS));
double VSBP_SN = Math.Max(MinVSBP, TSBP_SN - (MinBPVsTs + PPS));
////////////////////////////////////////////////////////////////////////
// Calculate Photoperiod sensitivities
////////////////////////////////////////////////////////////////////////
// Maximum delta for Upregulation of Vrn3 (MaxDVrn3)
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
// Occurs under long Pp conditions, Assuming Vrn3 increases from 0 - VernSatThreshold between VS to TS and this takes
// MinBPVsTs under long Pp conditions.
Params.MaxDVrn3 = camp.VrnSatThreshold / MinBPVsTs;
// Base delta for upredulation of Vrn3 (BaseDVrn3)
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
// Occurs under short Pp conditions, Assuming Vrn3 increases from 0 - VernSatThreshold from VS to TS
// and this take MinBPVSTs plus the additional BP from short Pp delay.
Params.BaseDVrn3 = camp.VrnSatThreshold / (MinBPVsTs + PPS);
//// Under long day conditions Vrn3 expresses at its maximum rate and plant moves quickley from VS to TS.
//// Genotypic variation in MaxDVrn3 will contribute to differences in earlyness per se
//// Under shord day condition Vrn3 expressssion may be slower, taking longer to get from VS to TS
//// Photoperiod sensitiviey of a genotype is determined by differences in BaseVrn3 and MaxVrn3.
//// if the two values are the same the genotype will not show photoperiod sensitivity
//// the greater the difference the more resonse the genotype will show to photoperiod
//////////////////////////////////////////////////////////////////
// Calculate Base development rate
//////////////////////////////////////////////////////////////////
// Base delta for upregulation of Vrn1 (BaseDVrn1)
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
// The rate of expression is calculated as the amount of expression divided by the duration
// Under short Pp treatment Vrn2 is absent so the amount of Vrn1 expression required for VS to occur is given by VernalisationThreshold
// Under non vernalising conditions Vrn1 expression will happen at the base rate.
// VrnX expression is absent in short days so baseVrn1 is the only contributor to the timing of VS
// BaseVrn1 expression starts when the seed is imbibed so the duration of expression is emergence plus VS
Params.BaseDVrn1 = camp.VrnSatThreshold / (VSBP_SN + EmergBP);
// Genotypic variation in BaseDVrn1 contributes to intrinsic earlyness.
// A genotype with high BaseDVrn1 will reach VS quickly regardless of vernalisation exposure
// A genotype with low BaseDVrn1 will reach VS slowly if not vernalised but the duration of VS may be decreased
// by exposure to vernalising temperatures depending on cold vernalisation sensitivity
//////////////////////////////////////////////////////////////////////////////////////////
// Cold Vernalisation Sensitivity Calculations
//////////////////////////////////////////////////////////////////////////////////////////
// Calcualtions of vernalisation sensitivity use data from short Pp treatments because Vrn2 and Vrnx are absent
// in these conditions and measured vernalistion response will be the result of Vrn1 expression alone.
// Vernalisation Sensitivity (VS) measured simply as the difference between SV and SN treatuemnts
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
double VS = VSBP_SN - VSBP_SV;
// To determine the effects of vernalisation treatment on Vrn1 expression we need to seperate these from baseVrn1 expression
// BaseVrn1 expression at VSBP ('BaseVrn1AtVSBP_SV')
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
double BaseVrn1AtVSBP_SV = (VSBP_SV + EmergBP) * Params.BaseDVrn1;
// Any accelleration in VS due to cold exposure under short Photoperiod will be due to methatalated Vrn1 expression
// The amount of Vrn1 required for VS is given by the Vernalisation Threshold so the amount of methalated Vrn expression
// at VS must be this threshold less the amount of vrn1 contributed by base Vrn1 expression over this duration
// Methalated Cold Vrn1 expression under short Pp vernalisiation treatment (MethColdVern1AtTrans_SV)
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
double MethColdVern1AtTrans_SV = Math.Max(0.0, camp.VrnSatThreshold - BaseVrn1AtVSBP_SV);
// Cold Vrn 1 expression must first be upregulated to a methalation threshold and any further expression beyond this
// threshold is methalated into a persistant vernalisation response. Thus the total expression of cold Vrn1 due to
// the vernalisation treatment applied is givin by MethColdVern1AtTrans_SV plus the Methalation Threshold
// Cold Vern1 expression at VSBP under short Pp vernalised conditions (ColdVrn1AtVSBP_SV)
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
double ColdVrn1AtVSBP_SV = camp.MethalationThreshold + MethColdVern1AtTrans_SV;
// The Base Phyllochron duration over which vernalisation temperatures will have an effect is the minimum of the cold
// treatment duration (VernTreatBP) and the BP when vernalisation occurs as cold exposure after this is irrelevent
// Effective BP duration of cold treatment (EffectiveColdBP)
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
double EffectiveColdBP = Math.Min(VSBP_SV + EmergBP, VernTreatBP);
// Then we calculate the rate as the amount divided by the duration
// Rate of cold Vrn1 expression at the vernalisation treatment temperture ('DVrn1AtVrnTreatTemp')
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
double DVrn1AtVrnTreatTemp = ColdVrn1AtVSBP_SV / EffectiveColdBP;
// This rate is dependent on the temperature of the duration treatment and can be extrapolated to the maximum rate (at 0oC)
// using the exponential funciton proposed by Brown etal 2013 Annals of Botany.
// dVrn1 = MaxdVrn1 * np.exp(k*VrnTreatTemp) as DVrn1 At VrnTreatTemp' is known
// MaxDVrn1 is set to vero for genotypes with VS < 0.5 as these varieties are insensitive and calculated rates of MaxDVrn1 are simply amplifying noise
// Maximum upregulation delta Vrn1 (MaxDVrn1)
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
if (VS > 0)
{
Params.MaxDVrn1 = DVrn1AtVrnTreatTemp / Math.Exp(camp.k * EnvData.VrnTreatTemp);
}
else
{
Params.MaxDVrn1 = 0.0;
}
// Genotypic variation in MaxDVrn1 combine with BaseDVrn1 to determine cold temperature vernalisatin sensitiviy
// A genotype with low BaseDVrn1 and high MaxDVrn1 will show high vernalisation sensitivity and sensitivity will decline
// either BaseDVrn1 increasees of MaxDVrn1 decreases.
////////////////////////////////////////////////////////////////////////////
// Photoperiod effects on vernalisation
////////////////////////////////////////////////////////////////////////////
// The parameters calculated above deal with photoperiod sensitivity in fully vernalised crops and vernalisation sensitivity
// under short photoperiod where cold is the only factor driving vernalisation response.
// Under long days photoperiod can also interact with vernalisation, either slowing the rate of vernalisation or speding it up
// Vernalisation photoperiod sensitivy parameter (VPPS) is calculated to determine what effect photoperiod will have.
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
double VPPS = 1 - ((VSBP_LN + EmergBP) * Params.BaseDVrn1);
// Genotypes that have a negative VPPS demonstrate short day vernalisation. Under long days vernalisation requirement is reduced
// This is caused by the expression of Vrn2 which must be blocked by additional expression of Vrn1 meaning vernalisation takes longer.
// The assumed mechanisum for Vrn2 is that it is expressed to a potential level and that one unit of Vrn1 will block the effective
// expression of Vrn2 so actual Vrn2 expression will always be lower than potential
// We can make some assumptions about the amounts of Vrn2 expression under long Pp conditions to calcualte rates
// Firstly, under un-vernalised conditions we can calculate the potential Vrn2 expression simply from
// the amount of BaseVrn1 expression up to VSBP
// Potential Vern2 expression at VS under long Pp UnVerrnalised treatment (pVrn2AtVSBP_LV)
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
double pVrn2AtVSBP_LN = (VSBP_LN + EmergBP) * Params.BaseDVrn1;
// Under full vernalised treatment Vrn2 expression must be less than or equal to VernalisationThreshold at the time of VS.
// If we assume it is equal to VernalisationThreshold this provides us with another amount of pVrn2
// Potential Vern2 expression at VS under long Pp Vernalised treatment (pVrn2AtVSBP_LV)
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
double pVrn2AtVSBP_LV = camp.VrnSatThreshold;
// If we regress these two potential Vrn2 amounts against their durations to VS the slope give us a rate of Vrn2 expression
// The resulting rate needs to always be less than BaseDVrn1 so Vrn1 can catch up with Vrn2 to cause vernalisation
// the amount of Vrn2 needs to quickly exceed BaseDVrn1 soon after emergence to achieve a delay in VS.
// The intercept of the regression quantifys how much Vrn2 would be expressed at emergence.
// Initial potential Vrn2 at emergence (IPVrn2) and potential Vrn2 rate there after (DpVrn2)
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Params.MaxIpVrn2 = 0;
Params.MaxDpVrn2 = 0;
//Vrn2 parameters only relevent for genotypes with nevaitve VPPS and a low BaseDVrn1. Genotypes with a high base
if (VPPS < 0) //and (BaseDVrn1 < 0.4):
{
if (VSBP_LN - VSBP_LV == 0)
{
Params.MaxIpVrn2 = pVrn2AtVSBP_LN;
}
else
{
Params.MaxDpVrn2 = Math.Max(0, (pVrn2AtVSBP_LN - pVrn2AtVSBP_LV) / (VSBP_LN - VSBP_LV));
Params.MaxIpVrn2 = (pVrn2AtVSBP_LV) - (VSBP_LV * Params.MaxDpVrn2);
if (Params.MaxDpVrn2 >= (Params.BaseDVrn1 * 0.99)) //If DpVrn2 exceeds baseVrn1 we need to do some forcing so it doesn't
{
double BaseVrn1AtVSBP_LV = (VSBP_LV + EmergBP) * Params.BaseDVrn1;
Params.MaxDpVrn2 = Math.Max(0, (pVrn2AtVSBP_LN - (BaseVrn1AtVSBP_LV * 1.2)) / (VSBP_LN - VSBP_LV));
Params.MaxIpVrn2 = (pVrn2AtVSBP_LN) - (VSBP_LN * Params.MaxDpVrn2);
}
}
}
// Genotypes that have a positive VPPS show an acelleration of vernalisation under long day conditions.
// The molecular mechanium for this is uncertain so we attrubute it to VrnX
// Under Long Pp unvernalised varieties will reach VS BP sooner than BaseVrn1 expresion determines.
// BaseVrn1 expression at VS under long Pp unvernalised treatment (BaseVrn1AtVSBP_LN)
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
double BaseVrn1AtVSBP_LN = Math.Min(camp.VrnSatThreshold, (VSBP_LN + EmergBP) * Params.BaseDVrn1);
// If we assume the expression of VrnX upregulates Vrn1 an equivelent amount then the amount of VrnX expression can be
// Estimated as the difference between Base Vrn1 at VS and the Vernalisation threshold. The duration of expression is
// VSBP assuming VrnX is expressed from emergence until VS.
// Maximum rate of Vrnx Expression (MaxDVrnX)
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Params.MaxDVrnX = (camp.VrnSatThreshold - BaseVrn1AtVSBP_LN) / (VSBP_LN);
return(Params);
}
/// <summary>
/// works through calculation scheme and assigns values to each parameter
/// </summary>
/// <param name="FLNset">Final leaf number set observations (or estimations) for cultivar</param>
/// <param name="TreatmentTtDuration">Thermal time duration of vernalisation treatment</param>
/// <param name="TtEmerge">Thermal time from imbibing to emergence</param>
/// <param name="Tt">Temperature during vernalisatin treatment</param>
/// <returns></returns>
public CultivarRateParams CalcCultivarParams(
FinalLeafNumberSet FLNset,
double TreatmentTtDuration, double TtEmerge, double Tt)
{
CultivarRateParams Params = new CultivarRateParams();
//Haun stage duration of vernalisation treatment period
double VernTreatHS = TreatmentTtDuration / (camp.BasePhyllochron * 0.75);
// Haun stage equivelents from imbibing to Emergence
double EmergHS = TtEmerge / (camp.BasePhyllochron * 0.75);
// Haun stage duration from vernalisation saturation to terminal spikelet under long day conditions
double L_HSVsTs = 3.0;
// Calculate TSHS for each envronment set from FLNData
double TSHS_LV = camp.calcTSHS(FLNset.LV);
double TSHS_LN = camp.calcTSHS(FLNset.LN);
double TSHS_SV = camp.calcTSHS(FLNset.SV);
double TSHS_SN = camp.calcTSHS(FLNset.SN);
// Photoperiod sensitivity (PPS)
// the difference between TSHS at 8 and 16 h pp under
//full vernalisation.
double PPS = Math.Max(0, TSHS_SV - TSHS_LV);
// Maximum delta for Upregulation of Vrn3 (MaxDVrn3)
// Occurs under long Pp conditions
// Assuming Vrn3 increases from 0 - 1 between VS to TS and this takes
// 3 HS under long Pp conditions.
double MaxDVrn3 = 1.0 / L_HSVsTs;
// Base delta for upredulation of Vrn3 (BaseDVrn3)
// Occurs under short Pp conditions
// Assuming Vrn3 infreases from 0 - 1 from VS to TS
// and this take 3 HS plus the additional HS from short Pp delay.
Params.BaseDVrn3 = 1.0 / (L_HSVsTs + PPS);
// Vernalistion Saturation Haun Stage under 8h Nil vern conditins (VSHS8hNil)
// Determine how many HS it would take to express Vrn3 == 1.0
// and subtract this from TSHS8hNill.
// Bound to CompetenceHS as Vernalisation won't occur before this.
double VSHS_SN = Math.Max(camp.CompetenceHS, TSHS_SN - (L_HSVsTs + PPS));
// Base delta for upregulation of Vrn1 (BaseDVrn1)
// Occurs under non vernalising conditions
// Assuming Vernalisation saturation occurs when Vrn1 == Vrn1Target
// under short Pp (no Vrn2) Vrn1Target = 1.0.
// Need to include time from imbib to emerge in duration
Params.BaseDVrn1 = 1.0 / (VSHS_SN + EmergHS);
// Vernalisation Saturation Haun Stage under 16h Nil vern conditions (VSHS16hNil)
// Assuming Vern saturation occurs 3.0 HS before TSHS16hNil
// 3.0 is HS from VS to TS under long Pp conditions
// Bound to CompetenceHS as Vernalisation won't occur before this.
double VSHS_LN = Math.Max(camp.CompetenceHS, TSHS_LN - L_HSVsTs);
// Long day Increase in Vrn1Target (Vrn1TargetInc)
// The extention in VSHS due to the action of Vrn2 under long days
// Work out how much VSHS is delayed under long Pp conditions.
// Multiply this by BaseDVrn1 to get how much more Vrn1 was
// expressed before vernalisation
double L_Vrn1TargetInc = (VSHS_LN - VSHS_SN) * Params.BaseDVrn1;
// Maximum delta for upregulation of Vrn2 (MaxDVrn2)
// Occurs under long day conditions
// LDVrnTargetInc is divided by the HS duration of Vrn2 expression
// which goes from CompetenceHS to VS.
Params.MaxDVrn2 = Math.Max(0.0, MathUtilities.Divide(L_Vrn1TargetInc, (VSHS_LN - camp.CompetenceHS), 0));
// Vernalistion Saturation Haun Stage under 8h Full vern conditions (VSHS8hFull)
// Assuming VSHS occurs 3 HS pluss the HS delay from short Pp prior
// prior to TSHS
// Bound to CompetenceHS as Vernalisation won't occur before this.
double VSHS_SV = Math.Max(camp.CompetenceHS, TSHS_SV - (L_HSVsTs + PPS));
// Number of Haun stages from the end of treatment until Vernalisation saturation
// Under 8 H full vern conditions (TransToVSHS8hFull)
double TransToVSHS_SV = Math.Max(0, VSHS_SV + EmergHS - VernTreatHS);
// The amount of methalated Vrn1 at the time of transition from vern treatment (MethVern1@Trans)
// Under 8h when VrnTarget will be 1.0
// VrnTarget less the amount of Vrn1 that expressed after transition
double MethVern1AtTrans = Math.Max(0, 1.0 - TransToVSHS_SV * Params.BaseDVrn1);
// BaseVer1 expressed at transition from vernalisation treatment
double BaseVrn1AtTrans = Math.Min(0, VernTreatHS * Params.BaseDVrn1);
// Methalated Cold upredulated Vrn1 expression at the time of transition (MethColdVrn1@Trans)
// Subtract out BasedVrn1 expression up to transition
double MethColdVrn1AtTrans = Math.Max(0.0, MethVern1AtTrans - BaseVrn1AtTrans);
// The timing at which methalation started
// relative to transition from vernalising treatments (RelativeMethTiming)
double RelativeMethTiming = 1.0 - MethColdVrn1AtTrans;
// The amount of BaseVrn1 that had expressed at the time methalation of ColdVrn1 started
double BaseVern1AtMeth = BaseVrn1AtTrans * RelativeMethTiming;
// Cold induced delta upregulation of Vrn1 at treatment temperature ('DVrn1@Tt')
// Methalation of Cold upregulated Vrn1 occurs when
// ColdUpRegVrn1 > Vrn1Target
// Vrn1Target will be 1.0 in 8 hour conditions
// so ColdUpRegVrn1 at transition will be:
// 1.0 - BaseVern1@Meth + MethColdVrn1@Trans.
// divide by treatment HS duration to give rate
double DVrn1AtTt = MathUtilities.Divide((1.0 - BaseVern1AtMeth + MethColdVrn1AtTrans), VernTreatHS, 0);
// Maximum upregulation delta Vrn1 (MUdVrn1)
// The rate of dVrn1/HS at 0oC. Calculate by rearanging UdVrn1 equation
// UdVrn1 = MUdVrn1 * np.exp(k*Tt) as UdVrn1@Tt is known
Params.MaxDVrn1 = MathUtilities.Divide(DVrn1AtTt, Math.Exp(camp.k * Tt), 0);
return(Params);
}