mixtures
Manual
The following sections briefly describe the method implemented in MIXTURES, then how to run MIXTURES from the command- line and describe the required input and the produced output files.
Introduction
The MIXTURES program fits experimental scattering curves by modeling multicomponent systems represented by simple geometrical bodies, considering their polydispersity and interparticle interactions.
Additionally, MIXTURES can reconstruct the electron density of a lipid bilayer while simultaneously generating the size distribution and multilamellar organization of lipid vesicles. It also enables the reconstruction of the electron density of a lipid bilayer and the generation of the size distribution of unilamellar lipid vesicles. The presence of proteins on the inner or outer surface of the unilamellar lipid vesicle can be modeled by introducing asymmetry into the electron density profile. Micelle structures can be modeled using a polydisperse ellipsoidal core-shell approximation.
MIXTURES significantly enhances and extends the functionality of the programs MIXTURE, LIPMIX, and BILMIX available in earlier ATSAS releases. MIXTURES employs an efficient DN2FB minimization algorithm, which significantly improves fit quality. The advantage of the DN2FB algorithm is that it includes boundary constraints for the model parameters within the Levenberg-Marquardt algorithm. In contrast, in the programs MIXTURE, LIPMIX, and BILMIX, boundary constraints were added as penalty terms to a target minimization function, which was less efficient in many cases.
Geometrical Bodies
The model scattering intensity may be represented by a linear combination of up to four types of particles:
The total scattering intensity can be expressed as follows:
\[I(s) = \sum_{k=1}^{K} \nu_k I_k(s),\]where \(\nu_k\) and \(I_k(s)\) are the volume fraction and the scattering intensity from the \(k\)-th component respectively, and \(K\) is the number of particles. For mixtures of different types of particles with possible polydispersity and interactions between particles of the same component, the scattering intensity from a component can be represented as
\[I_k(s) = S_k(s) \int_{0}^{\infty} D_k(R) V_k(R) \left[ \Delta \rho_k(R) \right]^2 i_{0k}(s, R) \, \mathrm{d}R,\]where \(\Delta \rho_k(R)\), \(\nu_k(R)\) and \(i_{0k}(s,R)\) denote the contrast, volume, and normalized scattering intensity (form factor) of the particle with size \(R\), respectively.
These functions are defined by the shape and internal structure of the particles, and \(i_{0k}(0,R)=1\), while \(S_k(s)\) is the structure factor describing the interference effects for the \(k\)-th component. Each component can be monodisperse or polydispers. In the latter case the size polydispersity \(D_k(R)\) is described by a two-parametric monomodal Gaussian or Schultz distribution characterized by the average dimension \(R_{0k}(R)\) and dispersion \(\Delta R_k(R)\).
Spheres and cylinders may have the following features:
- Polydispersity in radius with Gaussian or Schultz distribution
- Two shells with different contrasts, where a contrast of 0.0 in the inner shell indicates a hollow sphere or cylinder
Interparticle interactions between spherical particles can be described by a structure factor calculated using the Percus-Yevick approximation for a hard-sphere or sticky hard-sphere potential. This potential is described by two parameters: the hard-sphere interaction radius \(R_k^{hs}\) and the “stickiness” parameter \(\tau_k\).
The following sections describe the fitting parameters for each of the four body types.
Spheres
| Parameters | Description |
|---|---|
| Volume fraction | \(0 < \nu_k < 1\) |
| Internal Shell Radius | \(0 \leq R_{\mathrm{in}}\); if \(R_{\mathrm{in}} = 0\), the sphere is solid |
| Internal Shell Contrast | \(\rho_{\mathrm{in}}\); if \(\rho_{\mathrm{in}} = \rho_{\mathrm{out}}\), the sphere is uniform |
| External Shell Radius | \(0 \leq R_{\mathrm{out}}\) |
| External Shell Contrast | \(\rho_{\mathrm{out}}\) |
| Polydispersity | \(dR_{\mathrm{out}}\) |
| Volume concentration | Proportion of volume taken by all particles (from 0 to 1), required to calculate the structure factor |
| Hard sphere radius | \(0 \leq R_{\mathrm{hs}} < R_{\mathrm{out}}\) |
| Stickiness parameter | \(0 \leq \tau < 100\); \(\tau = 0\) no interaction, \(\tau = 100\) hard sphere |
Possible variants:
- monodisperse or polydisperse spheres,
- solid spheres or spheres with hollows
- interactive or non-interactive spheres
Cylinders
| Parameters | Description |
|---|---|
| Volume fraction | \(0 < \nu_k < 1\) |
| Internal Shell Radius | \(0 \leq R_{\mathrm{in}}\); if \(R_{\mathrm{in}} = 0\), the cylinder is solid |
| Internal Shell Contrast | \(\rho_{\mathrm{in}}\); if \(\rho_{\mathrm{in}} = \rho_{\mathrm{out}}\), the cylinder is uniform |
| External Shell Radius | \(0 \leq R_{\mathrm{out}}\) |
| External Shell Contrast | \(\rho_{\mathrm{out}}\) |
| Polydispersity of the radius | \(dR_{\mathrm{out}}\) |
| Height | \(0 < H_{\mathrm{cyl}}\), fixed |
Possible variants:
- monodisperse or polydisperse cylinders,
- solid cylinders or hollwo cylinders
Ellipsoids of Rotation
Note: ellipsoid of rotation with semiaxis of \(R\), \(R\), and \(v*R\).
| Parameters | Description |
|---|---|
| Volume fraction | \(0 < \nu_k < 1\) |
| Semiaxis of ellipsoid | \(0 < R\) |
| Ellipsoid ratio | \(0 < vR\) |
Possible variants:
- monodisperse ellipsoids
Dumbbells
Note: two stuck together spheres; parameters are the same as for spheres.
Multilamellar Vesicles
The SAXS data collected from symmetric lipid vesicles can be well approximated by a product of the form factor of a thin spherical shell \(F_{TS}\) (defining the vesicle size) and the form factor of a flat lipid bilayer \(F_{FB}\) (containing information about the electron density across the bilayer). This so-called separated form factor (SFF) approximation is valid when the vesicle size is much larger than the bilayer thickness. The ordered behavior of multiple bilayers inside the vesicle can be taken into account by an additional interbilayer structure factor multiplier term.
The intensity from a dilute polydisperse mixture of the multi-lamellar vesicles (MLVs) can be represented as follows:
\[I(s) = \sum_{k=1}^{N} \nu_k I_k(s)\]where \(s = 4\pi \sin(\theta)/\lambda\), \(2\theta\) being the scattering angle, \(\lambda\) the scattering wavelength, \(N\) is the number of MLV particles with different bilayer structures, \(\nu_k\) and \(I_k(s)\) are the volume fractions and the partial scattering intensities from these MLVs, respectively. Using the above SFF approximation and taking into account vesicle size polydispersity and variability of multilamellar organization, each partial intensity can be expressed as
\[I_k(s) \approx \frac{1}{s^2} \left| \int F_{TS}(s, r)_k D_V(r)_k \, dr \right|^2 \times \left| F_{FB}(s)_k \right|^2 \times \sum_{i=1}^{M} w_i S_i^{FB}(s)\]where \(D_V(r)_k\) is the volume size distribution of vesicles, \(F_{TS}(s,r)_k\) is the form factor of a thin spherical shell with radius \(r\), \(F_{FB}(s)_k\) is the form factor of the flat lipid bilayer of the \(k\)-th component in the mixture, \(M\) is the total number of MLV particles with different multilamellar organization, \(S_i^{FB}(s)\) is the interbilayer structure factor of evenly spaced flat bilayers and \(w_i\) is the occupancy factor for MLV particles with a given number of ordered lipid bilayers. The volume distribution of MLVs \(D_V(r)\) can be parameterized by a monomodal Gaussian or Schulz distribution with a mean radius \(R\) and width \(\sigma\). The form factor \(F_{FB}(s)\) is the Fourier transform of the electron density profile of the bilayer, which can be approximated by five Gaussian functions:
\[\rho(z) = \sum_{i=1}^{2} A_i \left[ \exp \left( \frac{-(z - z_{H_i})^2}{2 \sigma_{H_i}^2} \right) + \exp \left( \frac{-(z + z_{H_i})^2}{2 \sigma_{H_i}^2} \right) \right] - \rho_r \exp \left( \frac{-z^2}{2 \sigma_C^2} \right)\]where the first two Gaussians terms of width \(H_i\) centered at \(Z_{H_i}\), (i=1,2) represent the hydrophilic phospholipid polar headgroups to model both symmetric and asymmetric density profiles. The fifth Gaussian term of width \(\sigma_C\) at the center of the bilayer shell accounts for the hydrophobic hydrocarbon chains and \(\rho_r\) is the ratio of the electron density of the hydrocarbon chains to that of the headgroups. The interbilayer structure factor \(S^{FB}(s)\) from \(L\) evenly spaced flat bilayers of finite size resulting in the appearance of Bragg peaks is calculated according to the modified Caille theory:
\[S^{FB}(s) = L + 2 \sum_{k=1}^{L-1} (L - k) \cos(ksd) \exp \left( - \left( \frac{d}{2\pi} \right)^2 s^2 \eta \left[ \gamma + \ln(\pi k) \right] \right)\]where \(L\) is the total number of ordered flat bilayers in the vesicle, \(d\) is the bilayer thickness and \(\eta\) is the Caille parameter, which is a measure for the bilayer bending fluctuations, where \(\gamma\) is Euler’s constant.
The following sections describe the fitting parameters for the SFF approximation of MLV mixtures.
Sphere
\(F_{TS}(s)\) term of the SFF approximation.
| Parameters | Description |
|---|---|
| Volume fraction | \(0 < \nu_k < 1\) |
| Internal Shell Radius | \(0 \leq R_{\mathrm{in}}\); if \(R_{\mathrm{in}} = 0\), the sphere is solid |
| Internal Shell Contrast | \(\rho_{\mathrm{in}}\); if \(\rho_{\mathrm{in}} = \rho_{\mathrm{out}}\), the sphere is uniform |
| External Shell Radius | \(0 \leq R_{\mathrm{out}}\) |
| External Shell Contrast | \(\rho_{\mathrm{out}}\) |
| Polydispersity | \(dR_{\mathrm{out}}\) |
| Volume concentration | Proportion of volume taken by all particles (from 0 to 1), required to calculate the structure factor |
| Hard sphere radius | \(0 \leq R_{\mathrm{hs}} < R_{\mathrm{out}}\) |
| Stickiness parameter | \(0 \leq \tau < 100\); \(\tau = 0\) no interaction, \(\tau = 100\) hard sphere |
Diffusen
\(F_{FB}(s)\) term of the SFF approximation.
| Parameters | Description |
|---|---|
| Volume fraction | \(0 < \nu_k < 1\) |
| Peak1 position of hydrophilic phospholipid polar headgroup (positive density) | \(Z_{H_1}\) |
| Width of Peak1 of hydrophilic phospholipid polar headgroup (positive density) | \(\sigma_{H_1}\) |
| Peak2 position of hydrophilic phospholipid polar headgroup (positive density) | \(Z_{H_2}\) |
| Width of Peak2 of hydrophilic phospholipid polar headgroup (positive density) | \(\sigma_{H_2}\) |
| Amplitude ratio of Peak2/Peak1 (positive density) | \({A_2}/{A_1}\) |
| Width of Peak3 of the hydrophobic hydrocarbon chains (negative density) | \(\sigma_{C}\) |
| Amplitude ratio of Peak3/Peak1 (negative density) | \(\rho_r\) |
| Caille parameter (measure for the bilayer bending fluctuations) | \(\eta\) |
| Total number of multilayer vesicles (always FIXED) | \(L\) |
| Number of layers for the \(i\)-th multilayer vesicle | \(L_i\) |
| Weight contribution for the \(i\)-th multilayer vesicle | \(w_i\) |
Unilamellar Vesicles and Micelles
The SAXS data collected from globular lipid vesicles can be well approximated by a product of the form factor of a thin spherical shell \(F_{TS}\) (defining the vesicle size) and the form factor of a flat lipid bilayer \(F_{FB}\) (containing information about the electron density across the bilayer). This so-called separated form factor (SFF) approximation is valid when the vesicle size is much larger than the bilayer thickness.
The intensity from a dilute polydisperse mixture of the unilamellar vesicles (ULVs) can be represented as follows:
\[I(s) = \sum_{k=1}^{N} \nu_k I_k(s)\]where \(s = 4\pi \sin(\theta)/\lambda\), \(2\theta\) being the scattering angle, \(\lambda\) the scattering wavelength, \(N\) is the number of ULV particles with different bilayer structures, \(\nu_k\) and \(I_k(s)\) are the volume fractions and the partial scattering intensities from these ULVs, respectively. Using the above SFF approximation and taking into account vesicle size polydispersity, each partial intensity can be expressed as
\[I_k(s) \approx \left| \int F_{TS}(s, r) D_V(r) \, dr \right|^2 \times \left| \frac{F_{FB}(s, r)}{s} \right|^2\]where \(D_V(r)\) is the volume size distribution of vesicles, \(F_{TS}(s,r)\) is the form factor of a thin spherical shell with radius \(r\), \(F_{FB}(s,r)\) is the form factor of the flat lipid bilayer. The volume distribution of ULVs \(D_V(r)\) can be parameterized by a monomodal Gaussian or Schulz distribution with a mean radius \(R\) and width \(\sigma\).
The form factor \(F_{FB}(s, r)\) is the Fourier transform of the electron density profile of the bilayer, which can be approximated by four Gaussian functions:
\[\rho(z) = \exp \left( \frac{-(z - z_{H_1})^2}{2 \sigma_{H_1}^2} \right) + \exp \left( \frac{-(z + z_{H_1})^2}{2 \sigma_{H_1}^2} \right) - \rho_r \exp \left( \frac{-z^2}{2 \sigma_C^2} \right) + A_2 \exp \left( \frac{-(z + z_{H_2})^2}{2 \sigma_{H_2}^2} \right)\]where the first two Gaussian terms of width \(\sigma_{H_1}\) centered at \(Z_{H_1}\) and \(Z_{H_1}\) represent the hydrophilic phospholipid polar headgroups. The third Gaussian term of width \(\sigma_C\) at the center of the bilayer shell accounts for the hydrophobic hydrocarbon chains and \(\rho_r\) is the ratio of the electron density of the hydrocarbon chains to that of the headgroups. Finally, the fourth Gaussian term (with the width \(\sigma_{H_2}\) centered at \(Z_{H_2}\) and the amplitude ratio \(A_2\)) can account for the asymmetry in the electron density profile which can be caused either by the complicated rafted structure of the different types of lipids and/or by the presence of the membrane protein on the inner or outer surface of the lipid vesicle.
The shape of the vesicle can also be approximated by an ellipsoid of revolution by substituting the form factor of a thin spherical shell in the SFF approximation with the form factor of a core-shell ellipsoid of revolution.
MIXTURES allows the modeling of mixtures with up to ten different components, i.e., different types of particles.
The following sections describe the fitting parameters for the SFF approximation of ULV mixtures using either the spherical or ellipsoidal shape of the vesicle
Sphere
\(F_{TS}(s)\) term of the SFF approximation.
| Parameters | Description |
|---|---|
| Volume fraction | \(0 < \nu_k < 1\) |
| Internal Shell Radius | \(0 \leq R_{\mathrm{in}}\); if \(R_{\mathrm{in}} = 0\), the sphere is solid |
| Internal Shell Contrast | \(\rho_{\mathrm{in}}\); if \(\rho_{\mathrm{in}} = \rho_{\mathrm{out}}\), the sphere is uniform |
| External Shell Radius | \(0 \leq R_{\mathrm{out}}\) |
| External Shell Contrast | \(\rho_{\mathrm{out}}\) |
| Polydispersity | \(dR_{\mathrm{out}}\) |
| Volume concentration | Proportion of volume taken by all particles (from 0 to 1), required to calculate the structure factor |
| Hard sphere radius | \(0 \leq R_{\mathrm{hs}} < R_{\mathrm{out}}\) |
| Stickiness parameter | \(0 \leq \tau < 100\); \(\tau = 0\) no interaction, \(\tau = 100\) hard sphere |
Ellipsoid
\(F_{TS}(s)\) term of the SFF approximation.
| Parameters | Description |
|---|---|
| Volume fraction | \(0 < \nu_k < 1\) |
| SemiAxis R for Ellipsoid (R,R,v*R) (inner value) | \(0 \leq R\); if \(R=0\) and \(t>0\), the ellipsoid is solid |
| Ratio v of samiaxes for Ellipsoid, anisometry degree | \(0 < v\); with \(v < 1\) oblate ellipsoid, \(v = 1\) sphere, \(v > 1\) prolate ellipsoid |
| Thickness t of the Ellipsoid shell | \(0 \leq t\); if \(R>0\) and \(t=0\), the ellipsoid is solid |
| Polydispersity of the Ellipsoid | \(dR_{\mathrm{ell}}\) |
| Internal Shell Contrast | \(\rho_{\mathrm{in}}\); if \(\rho_{\mathrm{in}} = \rho_{\mathrm{out}}\), the ellipsoid is uniform |
| External Shell Contrast | \(\rho_{\mathrm{out}}\) |
Diffuse
\(F_{FB}(s)\) term of the SFF approximation.
| Parameters | Description |
|---|---|
| Volume fraction | \(0 < \nu_k < 1\) |
| Peak1 position of hydrophilic phospholipid polar headgroup (positive density) | \(Z_{H_1}\) |
| Width of Peak1 of hydrophilic phospholipid polar headgroup (positive density) | \(\sigma_{H_1}\) |
| Peak2 position of hydrophilic phospholipid polar headgroup (positive density, inner surface of lipid vesicle) | \(Z_{H_2}\) (in) |
| Width of Peak2 of hydrophilic phospholipid polar headgroup (positive density, inner surface of lipid vesicle) | \(\sigma_{H_2}\) (in) |
| Amplitude ratio of Peak2/Peak1 (positive density, left side) | \({A_2}/{A_1}\) (in) |
| Peak2 position of hydrophilic phospholipid polar headgroup (positive density, outer surface of lipid vesicle) | \(Z_{H_2}\) (out) |
| Width of Peak2 of hydrophilic phospholipid polar headgroup (positive density, outer surface of lipid vesicle) | \(\sigma_{H_2}\) (out) |
| Amplitude ratio of Peak2/Peak1 (positive density, outer surface of lipid vesicle) | \({A_2}/{A_1}\) (out) |
| Width of Peak3 of the hydrophobic hydrocarbon chains (negative density) | \(\sigma_{C}\) |
| Amplitude ratio of Peak3/Peak1 (negative density) | \(\rho_r\) |
| Number of layers of lipid vesicles (1 - unilamellar lipid vesicles) | \(L\) |
Running MIXTURES
Usage:
Usage: mixtures [OPTIONS]
OPTIONS known by MIXTURES are described in next section.
Command-Line Arguments and Options
MIXTURES does not accept any command line arguments. Instead the configuration is done interactively.
MIXTURES recognizes the following command-line options.
| Short Option | Long Option | Description |
|---|---|---|
| -h | --help | Print a summary of arguments, options, and exit. |
| -v | --version | Print version information and exit. |
Interactive Configuration
While the configuration can be done interactively at the command-line, due to the complexity of the configuration options it is highly advisable to prepare a command file instead. This command file can then be provided to MIXTURES via input redirection. For example on Linux, macOS and cmd.exe on Windows:
$ mixtures < user.txt
Powershell users on Windows have to use:
% Get-Content user.txt | mixtures
The file name and extension used for the command file are not important and can be anything that makes it memorable for the user.
The command file has to specify the model and initial values of parameters for the model, i.e. the number of “phases” (components), the type for each component (SPHERE, CYLINDER, ELLIPSOID, DUMBBELL, ELLIPSOIDP, DIFFUSE, DIFFUSEN), their dimension parameters as described in the introduction, the polydispersity, type of distribution function (Gaussian or Schultz), as well as the upper and lower boundary values for all fitting parameters.
It is possible to design a model with several components of the same type, for example, large and small MLV, unilamellar and multilamellar vesicles, and more.
Anything after !! is treated as a comment and ignored by the program.
It is recommended that users document each input value in this way.
Detailed examples of command files can be found below.
Runtime Output
After configuration, MIXTURES first traces the progres sof the minimization, where typical output may look like:
IT NF F RELDF RELDX MODEL STPPAR D*STEP NRELDF
60 107 0.137E-02 0.36E-10 0.41E-08 G 0.91E-08 0.54E-05-0.66E-05
61 118 0.137E-02 0.70E-13 0.39E-08 G 0.15E-03 0.15E-04-0.17E-05
62 128 0.137E-02 0.95E-15 0.87E-12 G 0.19E+00 0.72E-08-0.97E-06
63 133 0.137E-02 -0.25E-14 0.46E-14 G 0.99E+02 0.23E-10-0.16E-05
Here the value in the column F should tend to 0 over time.
Eventually, MIXTURES will report the final, optimized values. For example:
Arguments and bounds:
X[ 1 ] = 6.725979456680084E-02 expected (no bounds): 1.00000000000000
Bounds: 0.00000000000000 1.00000000000000
X[ 2 ] = 0.00000000000000 expected (no bounds): 1.00000000000000
Bounds: 0.00000000000000 0.00000000000000
X[ 3 ] = 0.00000000000000 expected (no bounds): 1.00000000000000
Bounds: 0.00000000000000 0.00000000000000
X[ 4 ] = 4.85082806945562 expected (no bounds): 1.00000000000000
Bounds: 1.00000000000000 22.0000000000000
X[ 5 ] = 1.00000000000000 expected (no bounds): 1.00000000000000
Bounds: 1.00000000000000 1.00000000000000
X[ 6 ] = 4.85082806082969 expected (no bounds): 1.00000000000000
Bounds: 0.300000000000000 5.50000000000000
X[ 7 ] = 55.0000000000000 expected (no bounds): 1.00000000000000
Bounds: 5.00000000000000 55.0000000000000
X[ 8 ] = 0.00000000000000 expected (no bounds): 1.00000000000000
Bounds: 0.00000000000000 0.00000000000000
X[ 9 ] = 9.708822986140732E-02 expected (no bounds): 1.00000000000000
Bounds: 0.00000000000000 1.00000000000000
MIXTURES Input Files
MIXTURES Output Files
Mixtures.log file contains information about the file name of experimental data and obtained fitting parameters for your model for each component. After each run the program MIXTURES adds information to this file, so you will have the whole history of running the program in this file.
Geometrical Bodies
In the case of geometrical bodies the output files of the program MIXTURES are the following: 3 files with extensions *.fit, *.pam, *.str, where the names of files coincide with the file name of experimental data as well as mixtures.log file
| File extensions | Description |
|---|---|
| .fit | Fit of the model scattering versus the experimental data. |
| .pam | Partial intensities of each component in the model. |
| .str | Structure Factor information. |
Multilamellar Vesicles
In the case of MLV mixtures the output files of the program MIXTURES are the following: 3 files with extensions *.fit, *.den, *.vr, where the names of files coincide with the file name of experimental data as well as mixtures.log file
| File extensions | Description |
|---|---|
| .fit | Fit of the model scattering versus the experimental data. |
| .den | Electron density of lipid bilayer profile of the model. |
| .vr | Volume size distribution of MLV particles. |
Unilamellar Vesicles and Micelles
In the case ULV mixtures/ellipsoidal micelles the output files of the program MIXTURES are the following: 3 files with extensions *.fit, *.den, *.vr, where the names of files coincide with the file name of experimental data as well as mixtures.log file
| File extensions | Description |
|---|---|
| .fit | Fit of the model scattering versus the experimental data. |
| .den | Electron density of lipid bilayer profile of the model. |
| .vr | Volume size distribution of ULV particles (globular or ellipsoidal). |
Examples
Mixtures of geometric bodies (spheres + cylinders)
Some description !! Comment Line 1 (done by user)
Some description !! Comment Line 2 (done by user)
2 !! Number of Phases (2 for this example)
0.20 !! System Concentration
SPHERE !! Type of the first Phase
0.25 0.0 1.0 !! sphere volume Fraction
0.0 0.0 0.0 !! inner shell sphere radius
0.0 0.0 0.0 !! density (contrast) for inner shell (if hollow sphere)
48.0 40.0 60.0 !! outer shell sphere radius
1.0 1.0 1.0 !! density (contrast) for outer shell
5.0 0.1 25.0 !! sphere polydispersity
75.0 55.0 95.0 !! interaction radius for spheres (hard sphere radius)
2 !! type of distributions for spheres (1 - Gauss, 2 - Schultz)
0.0 0.0 0.0 !! sticky parameter (0.1 < tau < 100), if tau=0 no interactions
CYLINDER !! Type of the second Phase
0.25 0.0 1.0 !! cylinder volume Fraction
0.0 0.0 0.0 !! inner shell cylinder radius
0.0 0.0 0.0 !! density (contrast) for inner shell
40.0 30.0 60.0 !! outer shell cylinder radius
1.0 1.0 1.0 !! density (contrast) for outer shell
3.0 2.1 10.1 !! cylinder outer shell radius polydispersity
2 !! type of distributions for cylinders (1 - Gauss, 2 - Schultz)
300.0 !! cylinder length
test1.dat !! experimental file data
test1-output_name !! output prefix name
1 !! scale for s-vector in A*(-1) (1 for 1.0 coefficient)
1.0 !! fraction of data taken for evaluation
Mixtures of geometric bodies (ellipsoids + dumbbells)
Some description !! Comment Line 1 (done by user)
Some description !! Comment Line 2 (done by user)
2 !! Number of Phases (2 for this example)
0.20 !! System Concentration
ELLIPSOID !! Type of the third Phase
0.25 0.0 1.0 !! ellipsoid Fraction
90.0 20.0 100.0 !! SemiAxis for Ellipsoid (Radius r)
1.5 0.5 3.0 !! Ratio of SemiAxes "v" for Ellipsoid (semiaxes r, r, v*r)
DUMBBELL !! Type of the fourth Phase
0.25 0.0 1.0 !! volume Fraction of dumbbells
0.0 0.0 0.0 !! inner sphere radius
0.0 0.0 0.0 !! density (contrast) for inner shell
62.3 40.0 80.0 !! outer sphere radius
1.0 1.0 1.0 !! density (contrast) for outer shell
2.0 0.1 25.0 !! sphere polydispersity
2 !! type of distributions for spheres in dumbbell
test1.dat !! experimental file data
test1-output_name !! output prefix name
1 !! scale for s-vector in A*(-1) (1 for 1.0 coefficient)
1.0 !! fraction of data taken for evaluation
Mixtures of multilamellar vesicles
Series titles !! Comment Line 1 (done by user)
Partial data titles !! Comment Line 2 (done by user)
2 !! Number of Phases (2 for this example)
0.2000 !! System Concentration
DIFFUSEN !! Type of the DIFFUSEN Phase (SFF approximation)
0.50 0.0000 100.000 !! Volume fraction of the bilayer component
2.131 1.421 2.141 !! Peak1 position (positive density)
0.213 0.103 0.323 !! Width of peak1 position (positive density)
1.650 1.440 2.160 !! Peak2 position (positive density)
0.329 0.120 0.340 !! Width of peak2 position (positive density)
0.172 0.000 1.780 !! Amplitude ratio (Peak2/Peak1) (positive density)
0.396 0.280 0.450 !! Width of peak3 position (negative density)
0.884 0.270 3.890 !! Amplitude ratio (Peak3/Peak1) (negative density)
0.05 0.01 0.20 !! Callie parameter (measure for the bilayer bending fluctuations)
5 5 5 !! Total Number of multilayer vesicles (alwayed FIXED)
1 1 1 !! Number of layers for vesicle type1
473. 173. 1073. !! Weight contribution of vesicle type 1
2 2 2 !! Number of layers for vesicle type2
41. 11. 121. !! Weight contribution of vesicle type 2
3 3 3 !! Number of layers for vesicle type3
30.0 10.0 80.0 !! Weight contribution of vesicle type 3
4 4 4 !! Number of layers for vesicle type4
18.5 4.5 69.5 !! Weight contribution of vesicle type 4
5 5 5 !! Number of layers for vesicle type5
12.47 2.47 52.47 !! Weight contribution of vesicle type 5
SPHERE !! Type of the SPHERE Phase (SFF approximation)
0.5000 0.0000 100.000 !! Volume fraction of the component (vesicle/micelle)
0.0000 0.0000 0.0000 !! Inner (core) radius of the sphere
0.0000 0.0000 0.0000 !! Inner (core) contrast of the sphere
83.4598 34.7678 262.1518 !! Outer (core+shell) radius of the sphere
1.0000 1.0000 1.0000 !! Outer (shell) contrast of the sphere
8.6920 1.1730 17.3839 !! Polydisperstiry on the sphere radius
400.000 400.000 400.000 !! Hard-sphere radius (for interactions only)
2 !! Schulz distribution 2 (Gauss distribution 1)
0.0000 0.0000 0.0000 !! stickiness parameter (for interactions only)
test_lipmix.dat !! Experimental data file
test_lipmix_output_name !! Output prefix name
1 !! Angular scale (1/2/3/4) as in GNOM
1.0 !! Exp. data portion to fit (from beginning)
Mixtures of Unilamellar Vesicles (globular)
Series titles !! Comment Line 1 (done by user)
Partial data titles !! Comment Line 2 (done by user)
2 !! Number of Phases (2 for this example)
0.2000 !! System Concentration
SPHERE !! Type of the first Phase (SFF approximation)
0.5000 0.0000 100.0000 !! Volume fraction of the component (vesicle/micelle)
0.0000 0.0000 0.0000 !! Inner (core) radius of the sphere
0.0000 0.0000 0.0000 !! Inner (core) contrast of the sphere
29.4598 20.7678 62.1518 !! Outer (core+shell) radius of the sphere
1.0000 1.0000 1.0000 !! Outer (shell) contrast of the sphere
2.6920 1.1730 17.3839 !! Polydisperstiry on the sphere radius
86.9196 86.9196 86.9196 !! Hard-sphere radius (for interactions only)
2 !! Schulz distribution 2 (Gauss distribution 1)
0.0000 0.0000 0.0000 !! stickiness parameter (for interactions only)
DIFFUSE !! Type of the second Phase (SFF approximation)
0.5 0.1 100.0 !! Volume fraction of the bilayer component
1.76 1.72 1.80 !! Peak1 position (positive density)
0.57 0.55 0.59 !! Width of peak1 position (positive density)
6.04 5.04 7.04 !! Peak2 position (positive density, inner surface of lipid vesicle)
1.13 0.83 1.13 !! Width of peak2 position (positive density, inner surface of lipid vesicle)
0.05 0.03 0.50 !! Amplitude ratio (Peak2/Peak1) (positive density, inner surface of lipid vesicle)
6.04 5.04 7.04 !! Peak2 position (positive density, outer surface of lipid vesicle)
1.13 0.83 1.13 !! Width of peak2 position (positive density, outer surface of lipid vesicle)
0.00 0.00 0.00 !! Amplitude ratio (Peak2/Peak1) (positive density, outer surface of lipid vesicle)
0.67 0.37 0.77 !! Width of peak3 position (negative density)
1.36 1.06 1.46 !! Amplitude ratio (Peak3/Peak1) (negative density)
1 !! Number of layers (1 - means only diffuse scattering from a single bilayer)
test_bilmix.dat !! Experimental data file
test_bilmix_output_name !! Output prefix name
1 !! Angular scale (1/2/3/4) as in GNOM
0.8 !! Exp. data portion to fit (from beginning)
Mixtures of Unilamellar Vesicles (ellipsoidal)
Series titles !! Comment Line 1 (done by user)
Partial data titles !! Comment Line 2 (done by user)
2 !! Number of Phases (2 for this example)
0.2000 !! System Concentration
ELLIPSOIDP !! Type of the fourth Phase ( sph, cyl, dmb, ell)
1.0 0.0 1.0 !! ellipsoid Fraction
60.0 50.0 70.0 !! SemiAxis for Ellipsoid (b,b,v*b) (inner value)
1.0 0.9 1.15 !! Ratio of SemiAxes for Ellipsoid
1.0 1.0 1.0 !! Thickness of the shell Ellipsoid
5.0 1.0 20.0 !! Polydispersity of the ellipsoid
1.0 1.0 1.0 !! Inner contrast of ellipsoid
1.0 1.0 1.0 !! Outer contrast of ellipsoid
1 !! Type distribution
DIFFUSE !! Type of the second Phase (SFF approximation)
0.5 0.1 100.0 !! Volume fraction of the bilayer component
1.76 1.72 1.80 !! Peak1 position (positive density)
0.57 0.55 0.59 !! Width of peak1 position (positive density)
6.04 5.04 7.04 !! Peak2 position (positive density, inner surface of lipid vesicle)
1.13 0.83 1.13 !! Width of peak2 position (positive density, inner surface of lipid vesicle)
0.05 0.03 0.50 !! Amplitude ratio (Peak2/Peak1) (positive density, inner surface of lipid vesicle)
6.04 5.04 7.04 !! Peak2 position (positive density, outer surface of lipid vesicle)
1.13 0.83 1.13 !! Width of peak2 position (positive density, outer surface of lipid vesicle)
0.00 0.00 0.00 !! Amplitude ratio (Peak2/Peak1) (positive density, outer surface of lipid vesicle)
0.67 0.37 0.77 !! Width of peak3 position (negative density)
1.36 1.06 1.46 !! Amplitude ratio (Peak3/Peak1) (negative density)
1 !! Number of layers (1 - means only diffuse scattering from a single bilayer)
test_bilmix.dat !! Experimental data file
test_bilmix_output_name !! Output prefix name
1 !! Angular scale (1/2/3/4) as in GNOM
0.8 !! Exp. data portion to fit (from beginning)