Theoretical Aspects

Summary

How to use MODULE
 

Required Material

Starting the Program

Input File Format

Initial Display

Displaying the Primary Sequence

Selection of Type of Coupling

Setting Internuclear Distances

Fitting Single Modules

Fitting the Alignment Tensor

Correlation Plots

Comparision of Calculated and Experimental Couplings

Monte Carlo Error Analysis

Test Sample 1

Choice of Modules from Primary Sequence

Fitting the Alignment Tensors

Correlation Plots

Comparision of Calculated and Experimental Couplings

Monte Carlo Error Analysis

Common Alignment Frame

Degenerate Orientations

Automatic Calculation of Molecular Architecture

Covalent Bonds

Test Sample 2

Special Cases

Axially Symmetric Alignment Tensor.

Highly Rhombic Alignment Tensor.

 
Distance Constraints

Creating and Reading Work Folders

Simulating Datasets

Hammerhead Ribozyme - Orientation of Secondary Structural Motifs.

Test Sample 3

Protein-Protein Complexes.

Test Sample 4

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MODULE is a novel program developed to allow the determination of alignment tensor parameters for individual or multiple domains in macromolecules from residual dipolar couplings and to facilitate their manipulation to construct low-resolution models of macromolecular structure.

For multi-domain systems the program determines the relative orientation of individual structured domains, and provides graphical user-driven rigid-body modeling of the different modules relative to the common tensorial frame.

Translational freedom in the common frame, and equivalent rotations about the diagonalized (x,y,z) axes, are used to position the different modules in the common frame to find a model in best agreement with experimentally measured couplings alone or in combination with additional experimental or covalent information.
 
 

Required Material

Silicon Graphics running IRIX 6.5 or higher, PC Linux running RedHat 5.2 or higher, or SUN SPARC running Solaris 2.6 or higher.

Starting the Program

The program is started by typing the command module. Data and coordinate files can be read using either the name of the files -

or by reading the files in the File menu -:

Input File Format

Module requires two sources of input information: the measured residual dipolar coupling values D_ij, their associated uncertainty s_ij and an estimation of the order parameter S (for many application this will of course be assumed to be 1), and a standard coordinate file from the Brookhaven data bank containing the structure under investigation (protein or nucleic acid).
 

_{The data file must be of the form -}

3 CA 3 C     -2.127479 0.195 1.00

4 CA 4 C     1.182786 0.349 1.00

5 CA 5 C     3.222452 0.245 1.00

- - - - - - -

- - - - - - -

2 N 2 HN     10.013671 0.500 1.00

3 N 3 HN      6.264468 0.500 1.00

4 N 4 HN     15.149721 0.500 1.00

5 N 5 HN     -8.166057 0.500 1.00

- - - - - - -

- - - - - - -

These lines can be entered in any order. The program will recognise any atoms whose equivalent names are present in the pdb file, so no sub-headings are required.
 

Initial Display

The initial display of the program shows the molecular structure in the pdb reference frame:

Displaying the Primary Sequence
 
 

The molecular sequence can be displayed by selecting the option Definition from the Visualisation menu -
 
 

Selection of Type of Coupling
 

MODULE can treat different couplings simultaneously or in combination. To select the couplings to be treated for a given tensor calculation select Couplings Choice from the Control menu : The available couplings in the data file will be already highlighted and can be selectively removed by clicking on the illuminated box.
 
 

Setting Internuclear Distances
 

The couplings are calculated with the appropriate pre-factors including the gyromagnetic ratio and the inter-nuclear distance; this can be chosen to be a either a standard fixed distance from an interactive table, or the actual distance (Å) present in the coordinate file (select Inter-Atom Distances from the Control menu)
 
 

While the program has been specifically designed to treat multiple structures simultaneously, in the simplest case the whole molecule will be considered to be a single module, and a single tensor will be fitted - all amino acids for which data are available have a dot above the appropriate letter in the primary sequence.
 

Fitting the Alignment Tensor

To fit the tensor to the selected couplings with this parameter set simply click on Fit in the main MODULE window - This should take a few seconds on a R10000 SGI processor (approximately equivalent to a 400MHz PC)
 
 

Having fitted the tensor, the axial and radial components (A_a and A_r) and the euler angles describing the orientation of the tensor relative to the pdb frame, are shown in the background window - NOTE that the axial and rhombic components are quoted and treated in absolute order units throughout the program (normally 10^-4 is cited).

The tensor can then be visualised with respect to the pdb coordinates (Orientation in the Visualisation menu) -
 
 

Correlation Plots

To check the quality of the fit, or to identify outliers, correlations of calculated and experimental couplings can be viewed, either separately or for all couplings together by selecting the option Back-Corr in the Visualisation menu:

Selecting Separate Couplings gives the correlations between calculated and experimental for each different type of coupling, defined by the different atom types -
 
 

The correlation for each particular coupling type can be viewed in detail using the same menu. The cursor can be used to identify the specific couplings (for example the outlier shown here).

In example shown below we have selected the CO-N coupling :
 
 

Note that in each of these options the local chi2 is shown (in blue at the bottom of the plot), with respect to the individual points. This allows outliers or problematic couplings to be identified easily. A text line in the window (at the top) gives the name, chi2 and calculated and experimental values of the coupling corresponding to the cursor poisition (yellow line).
 
 
 

Comparision of Calculated and Experimental Couplings
 

Similarly, the experimental and calculated couplings can be visualised with respect to the primary sequence, either separately or for all couplings together by selecting the option Back-Diff in the Visualisation menu:
 
 

Separate Couplings -
 
 

HN-CO Couplings

Monte Carlo Error Analysis

The uncertainty associated with the orientation of the tensor axes, and the values of the axial and rhombic components can be estimated using a Monte-Carlo based error analysis.

This analysis takes the best-fit tensor and back-calculates simulated datsets from this using a Gaussian noise distribution.

The noise distribution is based on the data uncertainty in the initial input file.

The Monte Carlo analysis can be selected using the button in the main display window.
 
 

The angular dispersion is small in this case - the noise which was simulated for this 'Dataset' was based on an uncertainty of 5% so this is perhaps not surprising.

The dispersion in the magnituide of Da and Dr can be visualised using the Monte Carlo in the Visualisation menu
 
 

In the example shown below the tensor has axial symmetry, so the transverse components of the tensor are equivalent (Axx-Ayy=0). The results of the monte-carlo simulation reflect this; the dispersion in the transverse plane is continuous, while the direction of the Azz component is well defined. Note that there are points in both positive and negative z-directions.
 
 

Test Sample 1 - The files used for this example are enclosed with the downloaded package and are called -
 
 

sample1.pdb

sample1.dat

One of the main uses of MODULE, in our hands at least, is the ability to fit multiple different modules and treat them as rigid oriented objects in a common reference frame of the alignment tensor, this part of the manual will explain how to do this and illustrate some of the features we have included to help treat this kind of orientational molecular modelling.
 

Choice of Modules from Primary Sequence

The regions of primary sequence to be used for the different modules can be selected using the cursor once the pdb file has been read : In this case two helices and the central beta sheet of our model system have been selected as representing different regions of known structure. The rest of the molecule represents the third module (yellow).
 
 

Note that the 2nd Display can be used to visualise the molecule while selecting the regions from the primary sequence.

The Select button on the bottom left of the interface allows residues or atoms to be identified with the cursor.
 
 
 

Fitting the Alignment Tensors

To fit the tensors to the selected couplings click on Fit in the main MODULE window - This should take a few seconds per module on a R10000 SGI processor (approximately equivalent to a 400MHz PC)
 
 

Having fitted the tensor, the axial and radial components (A_a and A_r) and the euler angles describing the orientation of the tensor relative to the pdb frame, are shown in the background window.

The tensors can then be visualised with respect to the pdb coordinates (Orientation in the Visualisation menu) -
 
 

Correlation Plots

To inspect the quality of the fits, or to identify outliers, correlations of calculated and experimental couplings can be viewed, either separately or for all couplings together by selecting the option Back-Corr in the Visualisation menu:
 
 

Selecting Separate Couplings gives the correlations between calculated and experimental for each different type of coupling, defined by the different atom types.
The data from each different module are coloured with respect to the colour of the particular module M1-M6.
 
 

The correlation for each particular coupling type can be viewed in detail using the same menu. The cursor can be used to identify the specific couplings.

Note that in each of these options the local chi2 is shown with respect to the individual points on the x-axis. This allows outliers or problematic couplings to be identified easily. A text line in the window gives the name, chi2 and calculated and experimental values of the coupling corresponding to the cursor poisition (yellow line).

In the example shown below we have selected the CA-CO :
 
 

Comparision of Calculated and Experimental Couplings

Similarly, the experimental and calculated couplings can be visualised with respect to the primary sequence, either separately or for all couplings together by selecting the option Back-Diff in the Visualisation menu:
 
 

Again the data from each different module are coloured with respect to the colour of the particular module M1-M6.
 

Separate Couplings -

HN-N Couplings

Monte Carlo Error Analysis

The uncertainty associated with the orientation of the tensor axes, and the values of the axial and rhombic components can be estimated using a Monte-Carlo based error analysis.

This analysis takes the best-fit tensor and back-calculates a simulated datset for each set of couplings. A gaussian noise distribution is then centred on these values, based on the uncertainty in the initial input data file.

The Monte Carlo analysis can be applied to all, or only one single module, and is selected using the button in the main display window.
 
 

As described above the dispersion in the magnitude of Da and Dr can be visualised using Monte Carlo in the Visualisation menu
 

So far we have only described the determination of alignment tensors, in this section we will show how MODULE can be used to provide molecular modelling of structures consisting of different subunits oriented using residual dipolar couplings.

In the first example we have chosen an extended molecule, in this case a double module of Cadherin, for which the modular structure is known but overall orientation of the different domains is difficult to determine using local structural information.

We have simulated data from throughout the two modules in the crystal conformation, and have used a .pdb file with a different relative orientation as input for MODULE in combination with this data.

As in the previous example the different modules are selected from the primary sequence:

Note that the amino acids in the linker region of the molecule have been 'unselected' using the white button on the right hand side of the main window. When this is done all couplings from these residues are taken out of the calculation (the amino acid letter has a dash instead of a dot over it in this case).

Couplings can be chosen and internuclear distances set as described above.

The two modules are fitted using the button Fit in the main window.
 
 

The tensors are superimposed on the structures in the original orientation as read in the inital .pdb file.

Common Alignment Frame

The modules can then be aligned using the button Align in the main window, such that the axes of the tensors for the different domains are coaxial.

The relative geometry of the two domains can be changed by clicking on the button Fix.

In the Align mode, the modules only have the degrees of freedom which retain the common axis definition.

In other words the modules have translational freedom, and can undergo rotations of 180° about the x, y and z axes of the common alignment frame.

Translational freedom is accessed using the cursor; this will select the module closest to the cursor. Translation in the z-dimension can be accessed by moving the cursor in the 2nd Display (orthogonal to the main window view).

Degenerate Orientations.

Rotation about the x, y and z axes can be performed in the window Rotations/Distance in the Control menu.
 
 

The180° rotations about the axes of the alignment tensor generate multiple solutions for the relative orientations of the two modules. The four different orientations of module 1 relative to module 2 are shown below. The dotted line between the modules indicates the covalent junction; and the distance between the modules is given in the Rotations/Distance window found in the Control menu.

In favourable cases covalent and non-bonded information will allow rejection of some solutions : For example in the case shown here the two bottom solutions have covalent distances which are too far apart, unless one of the modules sits on top of the other.

In order to check for this kind of steric clash, it is possible to calculate the overlap of van der Waals radii of atoms in different modules for a given geometry, using the Critical Distance option in the main window.
 
 

This mode highlights parts of the molecule in pink for the residues which have inter-module non-bond contacts which are less then the critical distance shown the window (this can be controlled using the slider).
 
 

Clearly in the figure shown here the two molecules are strongly overlapped if this solution is used.

The two solutions in the top part of the figure above are nevertheless still possible. These are related by a 180° rotation about the z-axis for module 1.

These two solutions are impossible to distinguish in this case, both can equally well fulfill the orientational data and the covalent geometry.

The program will automatically calculate the position of the two modules to fulfill both of these criteria, by selecting the button Position in the main window.

One of the degenerate solutions in shown below -
 
 

Test Sample 2 - The files used for this example are enclosed with the downloaded package and are called -
 

sample2.pdb

sample2.dat

In the first case we have selected all of the secondary structural elements to be part of the same module.
 
 

If we fit this selection (see explanation above), the fit is already quite good, as shown from the correlation plots for the different coupling types; nevertheless there are significant differences between calculated and experimental values:
 
 

We now divide the secondary structural elements into four separate modules - the three helices and the central beta-sheet;
 
 

This clearly gives a better correlation overall, if we look at the orientation of the tensors relative to the separate structural elements in the pdb frame we can see why this might be -
 
 

All four modules are now aligned with the same tensor axes. They can be manipulated (assuming the molecular geometry Fix button has been switched off) so that each module can be rotated around the x, y and z axes (Control menu - Rotation/Distances), and each module has complete translational freedom in all three directions.

In this case there will clearly be a large number of possible solutions for the different orientations of the 4 modules due to the 4-fold degeneracy for each motif about the tensor axes.
 
 

Automatic Calculation of Molecular Architecture

Covalent Bonds

MODULE can automatically test all of these different possibilities to find the geometry which is in best agreement with the original Covalent structure of the molecule. This is read in the initial pdb file and kept in memory for this purpose.

Using the align mode MODULE will automatically test the different possibilities to find the geometry which is in best agreement with the original Covalent structure of the molecule. This is read in the initial pdb file and kept in memory for this purpose.

A similar calculation is performed using the Position button in the main window, and the Covalent option although in this case the nearest solution is proposed:

Special Cases

The File menu can also be used to save a Folder for future use.
 

Simulating Datasets

Residual dipolar couplings can be simulated for a given structure and a defined tensor using the menu Control and the option DefineTensor

Two further examples have been chosen to illustrate the use of the Module: these are the examples shown in our recent article describing the program. In both cases we have simulated data from theoretical alignment tensors in systems where orientational information would be particularly valuable.
 
 

The first is the hammerhead ribozyme, whose three-dimensional structure has been determined using X-ray crystallography (Pley et al 1994). This small catalytic RNA comprises three canonical regions of consensus secondary structure in the form of A-type helices, with, in the case of stem II, an additional GAAA tetraloop configuration, folded around the central core of the molecule.

It has recently been demonstrated that residual dipolar couplings can contribute important information to the determination of RNA global fold determination (Mollova et al 2000) precisely because of the complementarity of this long-range structural order, with the local secondary structure which can often be identified from well-established experimental procedures (Saenger 1984).

Similarly, in this example we have simulated dipolar couplings measured in both sugars and bases (assuming a ¹³C labelled sample to be available) from the hammerhead ribozyme, by calculating C-H couplings from the crystallographic structure (pdb code 1mmh) and adding 8% stochastic noise to the simulated values. The alignment tensor was assumed to be

and S assumed to be equal to 1 throughout the molecule. The molecule was then "unwound" using the Discover-derived program SCULPTOR (Hus et al 2000) using a high temperature restrained molecular dynamics calculation, such that the orientation of the helices was no longer native, but the secondary structural regions remained intact.

Comparison of the X-ray crystallographic structure of RNA/DNA ribozyme inhibitor (left pdb code 1mmh) and the structure used as initial model for the simulated experiment using Module (right). The native structure was partially unfolded using high-temperature restrained molecular dynamics as described in the text. The three stem regions are shown in blue (I), orange (II) and red (III), while the core is shown in grey. The heavy atoms from the core region were used for the superposition of the two structures. The rmsd of the heavy atoms between the two models is 10.5Å.
 
 

The different regions of the molecule to be treated as individual domains are selected from the primary sequence. The three stem regions are shown in blue (I), orange (II) and red (III), while the core is shown in yellow.

This non-native structure (heavy atom rmsd of 10.5Å compared to the initial, correct structure) and the simulated couplings were then used to reconstruct a model of the molecule using Module.

The alignment tensors are fitted for the stem regions (I-III); which are then automatically aligned in the reference frame of a common tensor.

In this case the tensors are virtually identical as the data are all calculated assuming the same simulated system.

Comparison of noise — simulated and fitted data from the 3 stem regions of the ribozyme — The blue data correspond to points from stem I, orange from stem II and red from stem III .

It is then possible to organise the three oriented domains relative to the core, either manually or automatically, to find a model in agreement with the orientational data and preserving the known covalence (heavy atom rmsd of 2.5Å compared to the initial, correct structure).
 

I -The alignment tensors of the different modules are determined and their eigenvectors superposed on the structures in their original (unwound) orientation.
 
 

II - The modules are then oriented so that the tensors all have the same alignment in the frame indicated by the tensor directions. The dotted lines indicate the distances between the covalently bound atoms. The substructures can then be manipulated individually on the screen, using only translational degrees of freedom and 180° rotations about A_xx, A_yy and A_zz. to find the most feasible model.
 
 

III - The optimal position of the different modules can also be calculated automatically, as described in the text, and this, or the manually adjusted orientation, can then be fixed and written in standard coordinate format.
 
 

IV - The final structure was calculated automatically using MODULE, by selecting the relative orientation of the different domains which minimises the function

The final model has a backbone rmsd of 2.5 Å compared to the initial crystal structure.

Test Sample 3 - The files used for this example are enclosed with the downloaded package and are called -
 

sample3.pdb

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Protein-Protein Complexes.

The second example concerns a recently published molecular complex between the minor coat protein from Gene III in phage M13 (G3P) (86 amino acids) and the C-terminal domain of E.Coli protein Tol-A (126 amino acids).

Again this complex has recently been crystallised, and its structure determined using X-ray diffraction (Lubkowski et al. 1999). This structure was used to simulate experimental residual dipolar coupling data from NH sites distributed throughout the two molecules and 5% stochastic noise added to these simulated values. The tensor used in this case has eigenvalues

and S was again assumed to be equal to 1 in all cases.
 
 

Determination of the relative orientations of the complexed proteins Tol-a III and GP3.

The two proteins are treated as individual domains — again selected from the primary sequence (blue — GP3, yellow —Tol-a III).

The alignment tensors of the proteins are determined and their eigenvectors superposed on the structures in their original (pdb) orientation:
 
 

The individual protein structures were then aligned using Align as shown below. In this case the degeneracy of relative orientation plays a  significant role, as there is no covalence between the two partners
 
 

The proteins are rotated so that the tensors all have the same orientation in the alignment tensor frame indicated by the tensor directions. The proteins can be manipulated separately in this frame, using only translational freedom and rotations about A_xx, A_yy and A_zz.

There is no covalent interaction between the proteins, so in order to select between the multiple possible solutions, the user can select points on preferred interaction surfaces of the two molecules to aid the model-building. These may be experimental, such as intermolecular nOe measured between interacting surfaces, or predicted from existing structural information, for example electrostatic or hydrophobic surface calculations. Here we have kept the orientation of the Tol-a constant and show the 4 equivalent orientations of the GP3 protein, due to the inherent degeneracy of p rotations about A_xx, A_yy and A_zz.

Distance Restraints

Alternatively, if chemical shift mapping or inter-protein nOe have been measured distance constraints can be read (using the File menu and the Open Constraints option).

The constraints can be visualised using the constraints button which will appear in the main window when the distances have been successfully read -
 
 

 
 

The Position/Dist.Constraints command can then be used to calculate, and display a relative position of the modules which is in agreement with the measured distances and the residual dipolar coupling :

 
 

 The complex can be written to a coordinate file, for further refinement using molecular dynamics or more specific modelling procedures, using the File menu and Save PDB File As;
 
 

 
 
 

Test Sample 4 - The files used for this example are enclosed with the downloaded package and are called -
 
 

sample4.pdb

sample4.dat
 

Acknowledgements.

This work was supported by the Commisariat à l’Energie Atomique and the Centre National de la Recherche Scientifique.

References.

Hus, J.-C., Marion, D. and Blackledge, M. (2000) J. Mol. Biol. 298, 927-936.

Lubkowski, J., Hennecke, F., Pluckthun, A. and Wlodawer, A. (1999) Structure, 7 711-722.

Mollova, E.T., Hansen, M.R. and Pardi, A. (2000) J. Am. Chem. Soc. 122, 11561-11562.

Pley, H.W., Flaherty, K.M. and McKay, D.B. (1994) Science, 372, 68-74.

Saenger, W. ( 1984) Principles of Nucleic Acid Structure. Springer-Verlag, New York