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Biological Small Angle Scattering |
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LIPMIX manualWritten by P.V. Konarev, and D.I. Svergun. © ATSAS Team, 2003-2021 Table of ContentsManualProgram LIPMIX allows one to restore the electron density of a lipid bilayer and simultaneously generate the corresponding size distribution and multilamellar organization of the lipid vesicles. If you use results from LIPMIX in your own publication, please cite: IntroductionThe SAXS data collected from symmetric lipid vesicles can be well approximated by a product of the formfactor of a thin spherical shell FTS (defining the vesicle size) and the formfactor of a flat lipid bilayer FFB (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 [1-2]. The ordered behavior of multiple bilayers inside the vesicle can be taken into account by an additional interbilayer structure factor multiplier term [3]. The intensity from a dilute polydisperse mixture of the multi-lamellar vesicles (MLVs) can be represented as follows: 
where s=4πsin(θ) / λ, 2θ is the scattering angle, λ is the X-ray wavelength, N is the number of MLV particles with different bilayer structures, νk and Ik(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 
where DV(r)k is the volume size distribution of vesicles, FTS(s,r)k is the form-factor of a thin spherical shell with radius r, FFB(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, SiFB(s) is the interbilayer structure factor of evenly spaced flat bilayers and wi is the occupancy factor for MLV particles with a given number of ordered lipid bilayers. The volume distribution of MLVs DV(r) can be parametrized by a monomodal Gauss or Schulz distribution with a mean radius R and width σ [4]. The form-factor FFB(s,r) is the Fourier transform of the electron density profile of the bilayer, which can be approximated by five Gaussian functions similar to [5,6]: 
where the first four Gaussians terms of width Hi centered at ZHi (i=1,2) represent the hydrophilic phospholipid polar headgroups to model both symmetric and asymmetric density profiles. The fifth Gaussian term of width σC at the centre of the bilayer shell accounts for the hydrophobic hydrocarbon chains and ρr is the ratio of the electron density of the hydrocarbon chains to that of the headgroups. The interbilayer structure factor SFB(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 [7,8]: 
where L is the total number of ordered flat bilayers in the vesicle, d is the bilayer thickness and η is the Caille parameter, which is a measure for the bilayer bending fluctuations, γ is Euler's constant. LIPMIX allows one to model mixtures containing up to ten different components (i.e. different types of particles) Running LIPMIXConfigurationBelow there is the list of the fitting parameters for SFF approximation from MLV mixtures: SPHERE, FTS(s) term from SFF approximation
DIFFUSE, FFB(s) term from SFF approximation
Running OutputTo start the program one has to have both lipmix.exe and lipmix.cmd (see LIPMIX Input Files ) files in one directory and run with the following command: LIPMIX.EXE < LIPMIX.CMD _/_/ _/_/_/_/_/ _/_/_/_/_/_/ _/_/_/_/_/_/ _/_/_/_/ _/_/_/_/_/
_/_/ _/_/ _/_/ _/_/ _/_/ _/_/ _/_/ _/_/
_/_/ _/_/ _/_/ _/_/ _/_/ _/_/ _/_/
_/_/ _/_/ _/_/ _/_/ _/_/ _/_/ _/_/_/_/_/
_/_/ _/_/ _/_/_/_/_/_/ _/_/ _/_/ _/_/
_/_/ _/_/ _/_/ _/_/ _/_/ _/_/ _/_/
_/_/_/_/_/ _/_/ _/_/ _/_/_/_/ _/_/_/_/_/ _/_/
DIALOGUE SERVICE PROGRAM FOR MINIMIZATION OF NONLINEAR MULTIVARIATE
FUNCTIONS.
Program LIPMIX uses the optimization program suite OPTIS written by V.V. Volkov (Institute of Crystallography, Moscow, Russia) e-mail: vvo@ns.crys.ras.ru
Dialogue mode [ Interactive / PASSive ] ...... < Inter. >:
OPTIS: OPTIS: Welcome to user's problem
Enter the series title .................................: Enter comment line
.....................................: Enter Number of phases ................
< 0 >: Enter concentration of the system ...... < 0.0 >:
Choose type of data file format:.
1: OTOKO format
2: ASCII format
Enter the format code .................. < 2 >: Enter INTENSITY fil
name .............. < .dat >: 339703.100000000 10.4556000000
00
Angular units in the input file :
4*pi*sin(theta)/lambda [1/angstrom] (1)
4*pi*sin(theta)/lambda [1/nm ] (2)
2* sin(theta)/lambda [1/angstrom] (3)
2* sin(theta)/lambda [1/nm ] (4) < 1 >: Enter Fraction of t
e curve ............ < 0.0 >: 75 101
I(1), I(last) : 339703.100000000 10.7711200000000
s(1), s(last) : 3.229300000000000E-002 0.421600000000000
Err(1), Err(last): 10191.0900000000 0.323133500000000
15-dimensional user's problem
OPTIS: OPTIS: OPTIS: ///////////////////////////////////////////////////////
//////////////
This is the information which was read from the command file. OPTIS --- Version 5.6 rev. 09 May 02 03:30 reports current information:
08-Oct-2009 time 10:42:37
Objective function -- : User's problem (15-dimensional): 0
Chosen algorithm ---- : B-F-G-S with simple bounds
number of performed function evaluations ----- : 1
number of performed iterations --------------- : 0
number of performed gradient estimations ----- : 0
maximum number of function evaluations ------- : 5250
maximum number of search iterations ---------- : 40
total number of problem variables ------------ : 15
number of problem variables to be varied ----- : 15
maximum allowed number of variables ---------- : 512
function value ------------------------------- : 5.678e-2
rel/abs function tolerance to be attained ---- : 0.0
tolerance multiplier switch ------------------ : 0.0 (OFF)
upper bound on hessian condition number ------ : 0.0 (OFF)
temperature and scedule factor --------------- : 0.0, 0.0
function computation noise (rel/abs) --------- : 0.0
relative machine precision ------------------- : 2.22e-16
message level -------------------------------- : 1
===> Press CR to continue: ---------------------------------------------------
------------------
fixative-vector
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1
----------------------------------------------------------------------
argument values
0.500000 0.00000 0.00000 48.0000 1.00000
5.00000 55.0000 0.00000 0.500000 0.00000
0.00000 40.0000 1.00000 3.00000 300.000
----------------------------------------------------------------------
lower bounds on variables
0.00000 0.00000 0.00000 40.0000 1.00000
0.100000 48.0000 0.00000 0.00000 0.00000
0.00000 30.0000 1.00000 2.10000 300.000
----------------------------------------------------------------------
upper bounds on variables
1.00000 0.00000 0.00000 60.0000 1.00000
25.0000 85.0000 0.00000 1.00000 0.00000
0.00000 60.0000 1.00000 10.1000 300.000
//////////////////////////////////////////////////////////////////////
The information about minimization method (it uses B-F-G-S with simple bounds) and the argument values (its initial values, lower and upper boundaries). CPU time used: 0 min 0.02 sec Final Function value. (In ideal fit it should approach to zero) Produced function minimum is equal to 0.1162144E-02 at the point: 0.987769 0.00000 0.00000 54.1704 1.00000 7.11431 55.0000 0.00000 0.614604 0.00000 0.00000 45.2565 1.00000 4.02500 300.000 Optimized values for the arguments.
after 301 function evaluations,
0 gradient evaluations,
0 iterations
CPU time used: 0 min 4.61 sec
E4MAIN --- Normal termination
LIPMIX Input FilesFor running the program LIPMIX it is necessary to prepare the command file where one has to specify your model and initial values of parameters for this model, i.e. the number of "phases" (components), the type for each component (SPHERE, DIFFUSE), dimension parameters (relative volume fraction, average sphere radius, its polydispersity, type of distribution function (Gauss or Schultz) etc., the upper and lower boundary values for all fitting parameters. Below there is an example of command file for the model containing different types of MLV particles, one can design the model containing several components of the same type (for example large and small MLV, unilamellar and multilamellar vesicles etc.), but in all cases one has to follow the thumb rule of describing the model parameters as it is done in this example command file: Below symbols !! are used for comments. For your convienence it is recommended to keep the comments on each line, the program will automatically detect them. Example Command File 1 (MLVs particles)i !! Two initialising !!!!!!!!!!!!!!!!!!!!!!!!! !! strings pro us !! Command "Problem user" Series titles !! Comment Line 1 (done by user ) Partial data titles !! Comment Line 2 (done by user ) EXPERIMENT !! MODE FOR FITTING DATA, "TEST" MODE FOR EXPERTS 2 !! Number of Phases (2 for this example) 0.2000 !! System Concentration DIFFUSE !! Type of the DIFFUSE 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) 2 !! ASCII format file 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) meth sb !! Minimization method sb - "simple bounds" loa maxit 1000 !! maximum number of iterations 40 run !! run minimisation process y !! confirm running y !! confirm running mess 15 !! message for saving the output data eva !! write data mes 1 !! prepare for next set data ex !! exit the program y !! confirm exit y !! confirm exit To start the program one has to have both lipmix.exe and lipmix.cmd files in one directory and run with the following command: LIPMIX.EXE < LIPMIX.CMD LIPMIX Output FilesThe output files of the program LIPMIX 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 lipmix.log file
lipmix.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 LIPMIX adds information to this file, so you will have the whole history of running the program in this file. References:[1] Pencer J., Krueger S., Adams C. P., Katsaras J. Method of separated form factors for polydisperse vesicles // Journal of Applied Crystallography. 2006, Vol. 39, Pp. 293-303. [2] Kiselev M.A., Lesieur P., Kisselev A.M. et al. Model of separated form factors for unilamellar vesicles // Applied Physics A: Materials Science & Processing. 2002, Vol. 74. Pp. s1654-s1656. [3] Heftberger P., Kollmitzer B., Heberle F. A. et al. // Journal of Applied Crystallography. 2014, Vol. 47, Pp. 173-180. [4] Schulz G.V., Ueber die Beziehung zwischen Reaktiongeschwindigkeit und Zusammensetzung des Reaktionproduktes Macropolymerisationsvorgaemgen // Z. Phys. Chem. Abt. B. 1935, Vol. 30, Pp. 379. [5] Pabst G., Rappolt M., Amenitsch H., Laggner P., Structural information from multilamellar liposomes at full hydration: full q-range fitting with high quality x-ray data // Phys Rev E. 2000, Vol. 62, Pp. 4000-4009. [6] Pabst G., Koschuch R., Pozo-Navas B. et al. Structural analysis of weakly ordered membrane stacks // Journal of Applied Crystallography. 2003. Vol. 36, Pp. 1378-1388. [7] Caille A., Remarques sur la diffusion des rayons X dans les smectiques // C. R. Acad. Sci. Paris (Ser. B). 1972, Vol. 274, Pp. 891-893. [8] Zhang R.T., Suter R.M., Nagle J.F., Theory of the Structure Factor of Lipid Bilayers // Phys Rev E. 1994, Vol. 50, Pp. 5047-5060. |
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Last modified: February 12, 2020
© BioSAXS group 2020