DSPC Custom Layers#
This shows an example of using a custom layers model to analyse reflectivity from a supported bilayer of DSPC.
In this example, we can make use of the fact that the volumes, and of course the atomistic composition are known. So, for lipid tails for example, then we can take a literature value for the tails volume, have a fittable parameter for the lipid area per molecule, and then the tail thickness will simply be
\[Tail Thick = Tail Volume / Lipid APM.\]
Since the volume is known, then the SLD of the tails is also obviously easily calculable.
In addition, the datasets for this example, have a resolution (per point) in their fourth column. We use this resolution in our analysis, rather than declaring a constant, fittable one.
This example can be run as a script or interactively using the instructions below.
Note
The custom model used is a MATLAB model - examples/normalReflectivity/customLayers/customBilayerDSPC.m.
Run Script:
root = getappdata(0, 'root');
cd(fullfile(root, 'examples', 'normalReflectivity', 'customLayers'));
customLayersDSPCScript
Run Interactively:
root = getappdata(0, 'root');
cd(fullfile(root, 'examples', 'normalReflectivity', 'customLayers'));
edit customLayersDSPCSheet.mlx
Custom Layers Example for Supported DSPC layer.
Example of using Custom layers to model a DSPC supportd bilayer.
Start by making the class and setting it to a custom layers type:
problem = createProject(name='oDSPC - Custom Layers', calcType='normal', model='custom layers', geometry='substrate/liquid', absorption=false);
problem.showPriors = true;
For a custom layers model, rather than being forced to define out layers as [Thick SLD Rough.... etc], we can parameterise however we like and then use a function to calculate the [d rho sigma] arrangement for each layer. So for example, if the volume of lipid tails are known (from the literature), then all we need is the Area per molecule, because then....
,where d is the thickness and V is the volume.
Likewise, the SLD is
as usual.
In this folder there is a pre-prepared Matlab custom model for a DSPC on a Silicon substrate. We can display it here to see what we mean.....
type('customBilayerDSPC')
We need to add the parameters we are going to need to define the model (note that Substrate Roughness' always exists as parameter 1 as before, and that we are setting a Gaussian prior on Head Hydration here).
Parameters = {
% Name min val max fit?
{'Oxide thick', 5, 20, 60, true };
{'Oxide Hydration' 0, 0.2, 0.5, true };
{'Lipid APM' 45 55 65 true };
{'Head Hydration' 0 0.2 0.7 true 'gaussian' 0.3 0.03};
{'Bilayer Hydration' 0 0.1 0.2 true };
{'Bilayer Roughness' 2 4 8 true };
{'Water Thickness' 0 2 10 true };
};
problem.addParameterGroup(Parameters);
problem.setParameter(1,'min',1,'max',10); % Change the substrate roughness limits
Need to add the relevant Bulk SLD's. Change the bulk in from air to silicon, and add two additional water contrasts:
% Change bulk in from air to silicon....
problem.setBulkIn(1,'name','Silicon','min',2.07e-6,'value',2.073e-6,'max',2.08e-6,'fit',false);
% Add two more values for bulk out....
problem.addBulkOut('SLD SMW',1e-6,2.073e-6,3e-6,true);
problem.addBulkOut('SLD H2O',-0.6e-6,-0.56e-6,-0.3e-6,true);
problem.setBulkOut(1,'fit',true,'min',5e-6);
Now add the datafiles. We have three datasets we need to consider - the bilayer against D2O, Silicon Matched water and H2O. Load these datafiles in and put them in the data block....
% Read in the datafiles
D2O_data = dlmread('c_PLP0016596.dat');
SMW_data = dlmread('c_PLP0016601.dat');
H2O_data = dlmread('c_PLP0016607.dat');
% Add the data to the project
problem.addData('Bilayer / D2O', D2O_data);
problem.addData('Bilayer / SMW', SMW_data);
problem.addData('Bilayer / H2O', H2O_data);
problem.setData(2,'dataRange',[0.013 0.37]);
problem.setData(3,'dataRange',[0.013 0.32996]);
problem.setData(4,'dataRange',[0.013 0.33048]);
Add the custom file to the project....
problem.addCustomFile('DSPC Model', 'customBilayerDSPC.m', 'matlab', pwd);
Also, add the relevant background parameters - one each for each contrast:
% Change the name of the existing parameters to refer to D2O
problem.setBackgroundParam(1,'name','Backs par D2O','fit',true,'min',1e-10,'max',1e-5,'value',1e-6);
% Add two new backs parameters for the other two..
problem.addBackgroundParam('Backs par SMW',1e-10,1e-6,1e-5,true);
problem.addBackgroundParam('Backs par H2O',1e-10,1e-6,1e-5,true);
% And add the two new constant backgrounds..
problem.addBackground('Background SMW','constant','Backs par SMW');
problem.addBackground('Background H2O','constant','Backs par H2O');
% And edit the other one....
problem.setBackground(1,'name','Background D2O','source','Backs par D2O');
% Finally modify some of the other parameters
% Set the scalefactor...
problem.setScalefactor(1,'Value',1,'min',0.5,'max',2,'fit',true);
We need to use the data resolution (i.e. the fourch column of our datafiles). Do do this, we need to add a 'Data' resolution object to our resolutions table...
problem.addResolution('Data Resolution','data');
Now add the three contrasts as before. To set the model, we point to the custom file we've just added to the project:
% D2O contrast..
problem.addContrast('name', 'Bilayer / D2O',...
'background', 'Background D2O',...
'resolution', 'Data Resolution',...
'scalefactor', 'Scalefactor 1',...
'BulkOut', 'SLD D2O',...
'BulkIn', 'Silicon',...
'data', 'Bilayer / D2O',...
'model', 'DSPC Model');
% SMW contrast..
problem.addContrast('name', 'Bilayer / SMW',...
'background', 'Background SMW',...
'resolution', 'Data Resolution',...
'scalefactor', 'Scalefactor 1',...
'BulkOut', 'SLD SMW',...
'BulkIn', 'Silicon',...
'data', 'Bilayer / SMW',...
'model', 'DSPC Model');
% SMW contrast..
problem.addContrast('name', 'Bilayer / H2O',...
'background', 'Background H2O',...
'resolution', 'Data Resolution',...
'scalefactor', 'Scalefactor 1',...
'BulkOut', 'SLD H2O',...
'BulkIn', 'Silicon',...
'data', 'Bilayer / H2O',...
'model', 'DSPC Model');
Look at the complete model definition before sending it to RAT;
disp(problem)
To run it, we need to make a controls block....
controls = controlsClass()
And send this to RAT...
[problem,results] = RAT(problem,controls);
plotRefSLD(problem,results);
Our guess values were not too bad here. We can proceed directly to the Bayesian Analysis.....
controls.procedure = 'dream';
controls.nSamples = 25000;
controls.parallel = 'contrasts';
controls.adaptPCR = true
Send this to RAT....
[problem,results] = RAT(problem,controls);
Now plot our the results....
h1 = figure;
bayesShadedPlot(problem, results,'KeepAxes',true,'interval',65,'q4',false);
h2 = figure;
plotHists(results,'figure',h2,'smooth',true);
h3 = figure
plotChain(results);
h4 = figure
cornerPlot(results,'figure',h4,'smooth',false);
...and we're done.