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/*******************************************************************************
* McStas, neutron ray-tracing package
* Copyright 1997-2003, All rights reserved
* Risoe National Laboratory, Roskilde, Denmark
* Institut Laue Langevin, Grenoble, France
*
* Component: SANSNanodiscs
*
* %I
* Written by: Martin Cramer Pedersen (mcpe@nbi.dk)
* Date: October 17, 2012
* Origin: KU-Science
*
* A sample of monodisperse phospholipid bilayer nanodiscs in solution (water).
*
* %D
* A component simulating the scattering from a box-shaped, thin solution (water)
* of monodisperse phospholipid bilayer nanodiscs.
*
* %P
* AxisRatio: [] Axis ratio of the bilayer patch.
* NumberOfLipids: [] Number of lipids per nanodisc.
* AreaPerLipidHeadgroup: [AA^2] Area per lipid headgroup - default is POPC.
* HeightOfMSP: [AA] Height of the belt protein - default is MSP1D1.
* VolumeOfOneMSP: [AA^3] Volume of one belt protein - default is MSP1D1.
* VolumeOfHeadgroup: [AA^3] Volume of one lipid headgroup - default is POPC.
* VolumeOfCH2Tail: [AA^3] Volume of the CH2-chains of one lipid - default is POPC.
* VolumeOfCH3Tail: [AA^3] Volume of the CH3-tails of one lipid - default is POPC.
* ScatteringLengthOfOneMSP: [cm] Scattering length of one belt protein - default is MSP1D1 in D2O.
* ScatteringLengthOfHeadgroup: [cm] Scattering length of one lipid headgroup - default is POPC in D2O.
* ScatteringLengthOfCH2Tail: [cm] Scattering length of the CH2-chains of one lipid - default is POPC in D2O.
* ScatteringLengthOfCH3Tail: [cm] Scattering length of the CH3-tails of one lipid - default is POPC in D2O.
* Roughness: [] Factor used to smear the interfaces of the nanodisc.
* Concentration: [mM] Concentration of sample.
* RhoSolvent: [cm/AA^3] Scattering length density of solvent - default is D2O.
* AbsorptionCrosssection: [1/m] Absorption cross section of the sample.
* xwidth: [m] Dimension of component in the x-direction.
* yheight: [m] Dimension of component in the y-direction.
* zdepth: [m] Dimension of component in the z-direction.
* SampleToDetectorDistance: [m] Distance from sample to detector (for focusing the scattered neutrons).
* DetectorRadius: [m] Radius of the detector (for focusing the scattered neutrons).
*
* %E
*******************************************************************************/
DEFINE COMPONENT SANSNanodiscs
SETTING PARAMETERS (AxisRatio = 1.4, NumberOfLipids = 130.0, AreaPerLipidHeadgroup = 65.0, HeightOfMSP = 24.0,
VolumeOfOneMSP = 26296.5, VolumeOfHeadgroup = 319.0, VolumeOfCH2Tail = 818.8, VolumeOfCH3Tail = 108.6,
ScatteringLengthOfOneMSP = 8.8E-10, ScatteringLengthOfHeadgroup = 7.05E-12, ScatteringLengthOfCH2Tail = -1.76E-12, ScatteringLengthOfCH3Tail = -9.15E-13,
Roughness = 5.0, Concentration = 0.01, RhoSolvent = 6.4e-14, AbsorptionCrosssection = 0.0,
xwidth, yheight, zdepth, SampleToDetectorDistance, DetectorRadius)
DEPENDENCY " @GSLFLAGS@ "
NOACC
SHARE
%{
#include <gsl/gsl_sf_bessel.h>
// Functions used for compution the intensity from a given liposome
double FormfactorCylinder(double q, double MajorSemiAxis, double MinorSemiAxis, double Height, double Alpha, double Beta)
{
double const ProjectedRadius = sqrt(pow(MajorSemiAxis * sin(Beta), 2) + pow(MinorSemiAxis * cos(Beta), 2));
double const Formfactor1 = gsl_sf_bessel_J1(q * ProjectedRadius * sin(Alpha)) / (q * ProjectedRadius * sin(Alpha));
double const Formfactor2 = sin(q * Height * cos(Alpha) / 2.0) / (q * Height * cos(Alpha) / 2.0);
return 2 * Formfactor1 * Formfactor2;
}
double IntensityOfEmptyNanodiscs(double q, double MajorSemiAxis, double MinorSemiAxis, double ThicknessOfBelt,
double HeightOfBelt, double HeightOfLipids, double HeightOfTails, double HeightOfCH3,
double DeltaRhoBelt, double DeltaRhoHead, double DeltaRhoCH2Tail, double DeltaRhoCH3Tail)
{
// Declaration
double Intensity;
double IntensityPart;
double AmplitudeOfBelt;
double AmplitudeOfHeads;
double AmplitudeOfCH2Tail;
double AmplitudeOfCH3Tail;
double FormfactorOfBelt;
double FormfactorOfHeads;
double FormfactorOfCH2Tail;
double FormfactorOfCH3Tail;
const double OuterMajorSemiAxis = MajorSemiAxis + ThicknessOfBelt;
const double OuterMinorSemiAxis = MinorSemiAxis + ThicknessOfBelt;
const double VolumeOfBelt = PI * HeightOfBelt * OuterMajorSemiAxis * OuterMinorSemiAxis - PI * HeightOfBelt * MajorSemiAxis * MinorSemiAxis;
const double VolumeOfHeads = PI * HeightOfLipids * MajorSemiAxis * MinorSemiAxis - PI * HeightOfTails * MajorSemiAxis * MinorSemiAxis;
const double VolumeOfCH2Tail = PI * HeightOfTails * MajorSemiAxis * MinorSemiAxis - PI * HeightOfCH3 * MajorSemiAxis * MinorSemiAxis;
const double VolumeOfCH3Tail = PI * HeightOfCH3 * MajorSemiAxis * MinorSemiAxis;
// Variables needed for integration over alpha
int i;
const int NumberOfStepsInAlpha = 50;
double Alpha;
const double AlphaMin = 0.0;
const double AlphaMax = PI / 2.0;
const double AlphaStep = (AlphaMax - AlphaMin) / (1.0 * NumberOfStepsInAlpha);
// Variables needed in integration over beta
int j;
const int NumberOfStepsInBeta = 50;
double Beta;
const double BetaMin = 0.0;
const double BetaMax = PI / 2.0;
const double BetaStep = (BetaMax - BetaMin) / (1.0 * NumberOfStepsInBeta);
// Computation
Intensity = 0.0;
for (i = 0; i < NumberOfStepsInAlpha; ++i) {
Alpha = (i + 0.5) * AlphaStep;
for (j = 0; j < NumberOfStepsInBeta; ++j) {
Beta = (j + 0.5) * BetaStep;
// Compute formfactors
FormfactorOfBelt = (PI * HeightOfBelt * OuterMajorSemiAxis * OuterMinorSemiAxis * FormfactorCylinder(q, OuterMajorSemiAxis, OuterMinorSemiAxis, HeightOfBelt, Alpha, Beta) -
PI * HeightOfBelt * MajorSemiAxis * MinorSemiAxis * FormfactorCylinder(q, MajorSemiAxis, MinorSemiAxis, HeightOfBelt, Alpha, Beta)) /
(PI * HeightOfBelt * OuterMajorSemiAxis * OuterMinorSemiAxis - PI * HeightOfBelt * MajorSemiAxis * MinorSemiAxis);
FormfactorOfHeads = (PI * HeightOfLipids * MajorSemiAxis * MinorSemiAxis * FormfactorCylinder(q, MajorSemiAxis, MinorSemiAxis, HeightOfLipids, Alpha, Beta) -
PI * HeightOfTails * MajorSemiAxis * MinorSemiAxis * FormfactorCylinder(q, MajorSemiAxis, MinorSemiAxis, HeightOfTails , Alpha, Beta)) /
(PI * HeightOfLipids * MajorSemiAxis * MinorSemiAxis - PI * HeightOfTails * MajorSemiAxis * MinorSemiAxis);
FormfactorOfCH2Tail = (PI * HeightOfTails * MajorSemiAxis * MinorSemiAxis * FormfactorCylinder(q, MajorSemiAxis, MinorSemiAxis, HeightOfTails, Alpha, Beta) -
PI * HeightOfCH3 * MajorSemiAxis * MinorSemiAxis * FormfactorCylinder(q, MajorSemiAxis, MinorSemiAxis, HeightOfCH3 , Alpha, Beta)) /
(PI * HeightOfTails * MajorSemiAxis * MinorSemiAxis - PI * HeightOfCH3 * MajorSemiAxis * MinorSemiAxis);
FormfactorOfCH3Tail = FormfactorCylinder(q, MajorSemiAxis, MinorSemiAxis, HeightOfCH3, Alpha, Beta);
// Compute amplitudes
AmplitudeOfBelt = DeltaRhoBelt * VolumeOfBelt * FormfactorOfBelt;
AmplitudeOfHeads = DeltaRhoHead * VolumeOfHeads * FormfactorOfHeads;
AmplitudeOfCH2Tail = DeltaRhoCH2Tail * VolumeOfCH2Tail * FormfactorOfCH2Tail;
AmplitudeOfCH3Tail = DeltaRhoCH3Tail * VolumeOfCH3Tail * FormfactorOfCH3Tail;
// Perform integration
IntensityPart = pow(AmplitudeOfBelt + AmplitudeOfHeads + AmplitudeOfCH2Tail + AmplitudeOfCH3Tail, 2);
Intensity += 2 / PI * sin(Alpha) * IntensityPart * AlphaStep * BetaStep;
}
}
return Intensity;
}
%}
DECLARE
%{
// Declarations
double Absorption;
double q;
double NumberDensity;
// Scattering lengths
double RhoBelt;
double RhoHead;
double RhoCH2Tail;
double RhoCH3Tail;
double DeltaRhoHead;
double DeltaRhoBelt;
double DeltaRhoCH2Tail;
double DeltaRhoCH3Tail;
// Geometric properties
double MajorSemiAxis;
double MinorSemiAxis;
double ThicknessOfBelt;
double HeightOfBelt;
double HeightOfLipids;
double HeightOfTails;
double HeightOfCH3;
%}
INITIALIZE
%{
// Rescale concentration into number of aggregates per m^3 times 10^-4
NumberDensity = Concentration * 6.02214129e19;
// Computations
if (!xwidth || !yheight || !zdepth) {
printf("%s: Sample has no volume, check parameters!\n", NAME_CURRENT_COMP);
}
Absorption = AbsorptionCrosssection;
// Scattering properties of different components
DeltaRhoBelt = RhoBelt - RhoSolvent;
DeltaRhoHead = RhoHead - RhoSolvent;
DeltaRhoCH2Tail = RhoCH2Tail - RhoSolvent;
DeltaRhoCH3Tail = RhoCH3Tail - RhoSolvent;
// Geometric properties of different components
const double AreaOfLipids = NumberOfLipids * AreaPerLipidHeadgroup / 2.0;
MinorSemiAxis = sqrt(AreaOfLipids / (PI * AxisRatio));
MajorSemiAxis = MinorSemiAxis * AxisRatio;
HeightOfLipids = 2.0 * (VolumeOfHeadgroup + VolumeOfCH2Tail + VolumeOfCH3Tail) / AreaPerLipidHeadgroup;
HeightOfTails = 2.0 * (VolumeOfCH2Tail + VolumeOfCH3Tail) / AreaPerLipidHeadgroup;
HeightOfCH3 = 2.0 * VolumeOfCH3Tail / AreaPerLipidHeadgroup;
ThicknessOfBelt = sqrt(pow(MinorSemiAxis + MajorSemiAxis, 2) / 4.0 + 2.0 * VolumeOfOneMSP / (PI * HeightOfMSP)) - (MajorSemiAxis + MinorSemiAxis) / 2.0;
%}
TRACE
%{
// Declarations
double t0;
double t1;
double l_full;
double l;
double l1;
double Intensity;
double Weight;
double IntensityPart;
double SolidAngle;
double qx;
double qy;
double qz;
double v;
double dt;
double vx_i;
double vy_i;
double vz_i;
char Intersect = 0;
// Computation
Intersect = box_intersect(&t0, &t1, x, y, z, vx, vy, vz, xwidth, yheight, zdepth);
if (Intersect) {
if (t0 < 0.0) {
fprintf(stderr, "Neutron already inside sample %s - absorbing...\n", NAME_CURRENT_COMP);
ABSORB;
}
// Compute properties of neutron
v = sqrt(pow(vx, 2) + pow(vy, 2) + pow(vz, 2));
l_full = v * (t1 - t0);
dt = rand01() * (t1 - t0) + t0;
PROP_DT(dt);
l = v * (dt - t0);
// Store properties of incoming neutron
vx_i = vx;
vy_i = vy;
vz_i = vz;
// Generate new direction of neutron
randvec_target_circle(&vx, &vy, &vz, &SolidAngle, 0, 0, SampleToDetectorDistance, DetectorRadius);
NORM(vx, vy, vz);
vx *= v;
vy *= v;
vz *= v;
// Compute q
qx = V2K * (vx_i - vx);
qy = V2K * (vy_i - vy);
qz = V2K * (vz_i - vz);
q = sqrt(pow(qx, 2) + pow(qy, 2) + pow(qz, 2));
// Compute scattering
l1 = v * t1;
Intensity = exp(- pow(q * Roughness, 2)) * IntensityOfEmptyNanodiscs(q, MajorSemiAxis, MinorSemiAxis, ThicknessOfBelt, HeightOfMSP, HeightOfLipids,
HeightOfTails, HeightOfCH3, DeltaRhoBelt, DeltaRhoHead, DeltaRhoCH2Tail, DeltaRhoCH3Tail);
p *= l_full * SolidAngle / (4.0 * PI) * NumberDensity * Intensity * exp(- Absorption * (l + l1) / v);
SCATTER;
}
%}
MCDISPLAY
%{
box(0, 0, 0, xwidth, yheight, zdepth,0, 0, 1, 0);
%}
END
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