QSAR

9       Performing Molecular Field Analysis

Molecular field analysis (MFA) is a method for quantifying the interaction energy between a probe molecule and a set of aligned target molecules in QSAR. Interaction energies measured and analyzed for a set of 3D structures can be useful in establishing structure-activity relationships.

To generate an energy field (also known as a probe map), a probe molecule is placed at a random location, then moved about a target molecule within a defined 3D grid. At each defined point in the grid, an energy calculation is performed, measuring the interaction energy between the probe and the target molecule. Atoms in the target molecule are fixed, so that the intramolecular energy in the target is ignored. When a complete probe map is calculated for each molecule in the target set, energy values for each point in the grid can be reported in columns added to the study table.

For a set of structures for which energy fields are generated, some or all of the grid data points can be used as descriptors in generating QSARs and analyzing structure-activity relationships.

This chapter describes the procedures in MFA for generating energy fields and for incorporating field data into QSARs. The following topics are discussed in this chapter:

This chapter describes

Accessing molecular field analysis (page 166)

Creating a field (page 167)

Setting MFA preferences (page 169)

Managing independent variables (page 171)

Managing fields (page 174)

Generating a QSAR using field data (page 175)

Predicting biological activity (page 175)

Before you begin

• You must have a properly licensed copy of the appropriate Cerius2 software, including copies of QSAR+, Alignment or HipHop, Molecular Field Analysis, Open Force Field (OFF), and Force Field Editor installed on your system. If you have any questions about your system setup or your software license, please talk to your system administrator.
• You should be familiar with the Cerius2 interface and tools. For an introduction to the interface and the Visualizer tools, please see the Cerius2 Modeling Environment.

Also, be sure you are familiar with QSAR+ and an alignment program (Alignment or HipHop). For information on these modules, see Cerius² Hypothesis and Receptor Models.

1.   Generate or load the models that you want to study into the Model Manager.

2.   Display the study table and load the models into it. By default, hydrogens are added, charges are calculated, and structures are minimized as part of this process. If you have already done work on these structures and want to change the defaults, select Preferences/Molecules... on the Study Table menu bar. For information about preferences, see Setting molecule-processing preferences on page 113. For information on loading models, see Loading molecules into Cerius2 on page 111.

3.   Use the Alignment or HipHop module to align the models in the study table. The module that you use depends on what is available on your system and what your study objectives are. For information about Alignment or HipHop see the corresponding sections in Cerius2 Hypothesis and Receptor Models.

To start MFA, go to the QSAR deck of cards, then choose the FIELD ANALYSIS (MFA) card from the deck.

The FIELD ANALYSIS (MFA) card contains selections designed to perform MFA calculations on a set of molecules to generate QSARs. This module is similar in some functions to Field Calculation, a Cerius2 core module that calculates and visualizes energy fields (probe maps) for single molecules.

Creating a field

As part of the calculation, the 3D region in which the probe moves and the points at which calculations are performed are defined. Calculations are performed at each point in the grid for the interaction energy between each probe and each structure in the study set.

To create a field

To create a field, follow these steps:

1.   Select Create Field from the FIELD ANALYSIS (MFA) card. The Create Field control panel appears.

2.   If you want to use all the default settings, click Create. MFA calculates fields for each model listed in the study table.

For each model two fields are generated, one with a proton probe and one with an uncharged methyl probe. Each calculation uses a cubic grid with 2-Å spacing. Energy calculations are made between -30 and 30 kcal.

For each map, point values are added to the study table, one value per column. Each column is labeled using the probe name and point number. A typical map contains several hundred points. Each new column is labeled as an independent (X) variable.

If you double-click a column containing a field value, the location of the point where this value was calculated is marked in the model window by a 3D cross and a name label.

Determining the set of target molecules

To determine the set of target molecules, adjust the set of study molecules using the Field popups. The first popup gives choices for what set of molecules you want to designate as the target set: All, Selected, or Current. The models are taken from the study table.

Using existing grids

You can use an existing grid that you have defined in the Field Calculation module by checking the Use Current Field Points checkbox. You must have grid data loaded in the Define Grid control panel. For more information on defining a grid in the Field Calculation module, see the Cerius2 Hypothesis and Receptor Models.

To report the number of grid points

You can see the current dimensions of the field by clicking Show # of Field Points. The number of field points is shown to the right of the label and the field is displayed in the Cerius² graphics window. Some information about the field is written to the text window, giving the total number of field points, the field name, the extent of the field on each axis (in angstroms), the step size (in angstroms), and the number of steps along each axis (that is, if there are N steps, there are N + 1 field points):

There are 27 sample points
Sample points Field-1: 
X: [-2.000, 2.000] (2.000) 3 steps 
Y: [-2.000, 2.000] (2.000) 3 steps 
Z: [-2.000, 2.000] (2.000) 3 steps

You can choose the shape of the field by setting the popup to RECTANGULAR for the usual parallelepiped field or SPHERICAL for a spherical field.

To change the bounding box (grid) size

You can adjust the size of the bounding box that contains the field points by setting the EXPAND/CONTRACT/RESET popup menu, then choose an axis from the XYZ/X/Y/Z popup (XYZ adjusts the box simultaneously in all directions). To make the adjustment, click the pushbutton to the left of the EXPAND popup. The bounding box changes size by one Stepsize increment and the new dimensions are printed in the text window.

Selecting Probes

To define a probe, check or uncheck the appropriate checkboxes H+, Donor/Acceptor, CH3, CH3-, CH3+, and Generic Probe.

A Generic probe is defined as a sphere with adjustable charge and radius. The default charge is zero and the default radius is 4.20 Å. You can adjust these values by entering new numbers in the appropriate entry boxes.

The Other probe selection allows you to define a probe from Cerius2 molecule files. When you make this probe selection, a list of files is displayed in a file browser on the right side of the control panel. Select a probe by selecting a file from this list. Field calculations are computationally demanding, and probe size can have a significant effect on computation time and resources.

Setting MFA preferences

Setting preferences

To set preferences, select Preferences from the Field Analysis (Mfa) card. The MFA Preferences control panel appears.

The following parameters can be specified as described:

Adjusting grid size

The controls that adjust the Field size depend on which Field Geometry you chose in the Create Field control panel. For a rectangular grid you may set the Stepsize, which is the distance in angstroms between field points.

For a spherical grid you may specify the Number of Polar Steps, the Starting Radius, and the Stepsize (in angstroms). The spherical grid consists of a set of concentric spheres centered at the center of the set of molecular models under consideration. The Starting Radius sets the diameter of the innermost sphere, and Radius Step Size sets the distance between adjacent cells. The Number of Polar Steps determines the density of field points on each concentric shell. It is the number of points on the equator of each sphere (each sphere has the same number of points on it) so the number of points on each sphere is proportional to the square of Number of Polar Steps.

The number of nested spheres in the grid depends on the greatest extent of the largest model. You can modify this with the EXPAND/CONTRACT popup.

Selecting a charge method

To select a charge method, select the charge algorithm that you want to apply to the probes and target molecules from the popup. The choices are:

• As Is -- Use this if you prepared the charges of the target molecules and probes in other Cerius² modules and want to retain and use these charges in the field calculation.
• OFF QEQ -- This selection uses the dynamic charge equilibration algorithm that is part of Open Force Field (OFF). The charges of probes and target molecules are adjusted by the QEQ algorithm as a probe is moved during calculation. Using this algorithm increases the length of field calculation.
• Gasteiger -- This selection computes charges for probes and target molecules at the beginning of the calculation by applying the Gasteiger algorithm.

Note

To add field data to the study table, check the Add Field to Study Table checkbox if you want the energy values for each field point to be added to the study table when a field calculation is completed. For each field, point values are added as columns, one value per column. Each column is labeled using the probe name and point number. A typical map contains several hundred points.

Determining the variable status of new columns

If it is checked, Mark New Field Columns Independent marks the new columns created by the field calculation as independent X variables, according to the settings specified in the Manage Independent Columns control panel.

When checked, Auto Unmark New Columns unmarks all new columns before they are re-marked by the functionality in the Manage Independent Columns control panel (to open the Manage Independent Columns panel, select the Variables/Manage Independent menu item in the study table).

If Auto Unmark New Columns is checked, all the new columns added to the study table are sorted and labelled the same way, as specified in the Manage Independent Columns control panel.

For information on using the Manage Independent Columns control panel, see Managing independent variables on page 171.

Setting an energy calculation range

Check the Truncate Energy checkbox to determine the energy range of acceptable calculations. Put the minimum and maximum values that you want for the range in the appropriate entry boxes. The default range is -30-30 kcal.

Randomizing grid points

Randomize grid points by checking the Randomize Grid Points checkbox. This checkbox applies to the way that MFA establishes the location of calculations in a grid. Grid points are defined by x, y, and z coordinates within defined boundaries and by the step size for each dimension. When you check the Randomize Grid Points checkbox, the point value is not calculated at a defined point, but in the area around the point (less than half a step length from it). The actual location of each calculation is random within this space. This calculation method generally gives results that are statistically better than those generated using fixed grid points.

Minimizing probes

To minimize probes, check the Minimize Probes checkbox if you are using a multi-atom probe. This option fixes one atom of the probe at the field calculation point, then minimizes the probe. The atom that is fixed at the calculation point is the first atom in the probe.

Managing independent variables

1.   Select Change Independent from the FIELD ANALYSIS (MFA) card. The Manage Independent Columns control panel appears.

Mark -- A marked column is labeled as an independent variable. By default, field columns added to the study table are marked.

Unmark -- An unmarked column has no variable label and is not used in QSAR calculations.

Delete -- A deleted column is removed from the study table. Deleted columns can be recovered only by recreating a field.

To select the affected columns, choose Independent, Selected, or All from the Columns popup. The columns included in your selection are affected by any radio button choices you have made when you click Change.

Performing a global change in column status

To perform a global change in column status:

1.   Click the Columns radio button on the Manage Independent Columns control panel.

2.   Choose Unmark, Mark or Delete from the popup.

3.   Click Change. The columns you have specified in the popup on the top line of the control panel are marked, unmarked, or deleted according to your specification.

To change the status according to a specified variance value:

1.   Click the second radio button on the Manage Independent Columns control panel.

2.   Choose Unmark, Mark, or Delete from the first popup.

3.   Choose Variance from the second popup.

4.   Specify whether the variance criterion is to be less than (<) or greater than (>) the specified numerical value by choosing from the third popup.

5.   Select a variance value by entering a number in the data entry box.

6.   Click Change. The column group you selected in the top line are marked, unmarked, or deleted according to the variance criterion you specified.

To change the status according to a specified correlation:

1.   Click the second radio button on the Manage Independent Columns control panel.

2.   Choose Unmark, Mark, or Delete from the first popup.

3.   Choose Correlation^2 from the second popup.

4.   Indicate if the correlation criterion is to be less than (<) or greater than (>) the specified numerical value by choosing from the third popup.

5.   Select a correlation value between zero and one by entering a number in the entry box.(The default value of 4 applies only to variance and is not an appropriate value for correlation calculations.)

6.   Click Change. The columns you selected in the top line are marked, unmarked, or deleted according to the variance criterion you specified.

To select column subgroups of defined size:

1.   Click the third radio button on the Manage Independent Columns control panel.

2.   Choose Unmark, Mark, or Delete from the first popup.

3.   Choose Percent or Columns from the second popup and enter an appropriate numeric value in the entry box to the left of the popup. This sets the group size (absolutely or relatively).

4.   Select Lowest or Highest from the third popup, then choose Variance or Correlation^2 from the fourth popup. This sets the selection parameter and range.

Managing fields

Accessing field maps

To access field maps:

Select Field Manager from the FIELD ANALYSIS (MFA) menu card. The Field Manager control panel appears.

The control panel includes a browser that lists maps you created in Field Analysis or Field Calculation.

After you select a map by highlighting it in the browser, you can manage it in several ways>

Listing map information in the text window

To list map information in the text window:

Click the Describe button in the Field Manager control panel. The following information is listed in the text window:

• The probemap name as shown in the Field Manager.
• The name of the grid onto which the probes were placed.
• The type of probe that was used.
• The dimensions and resolution of the grid.

To visualize a map, click the Visualize button. The Probe Surface Generation control panel appears. Use this panel to create a probe surface that visualizes your field map in the model window. For information on the Probe Surface Generation control panel, see the Field Calculation chapter in the Cerius² Hypothesis and Receptor Models.

Deleting a map

To delete a map, click the Delete button. The map you have selected is deleted permanently.

Saving a map

To save a map, click the Output to map.mbk button. The map is saved to a file named map.mbk. Only one map can be saved by this mechanism. If you selection another map and click this button, the first map.mbk is overwritten.

Generating a QSAR using field data

Generating a QSAR -equation

1.   Select the G/PLS or the Stepwise method for generating a QSAR. The PLS method is not available for use with field data.

2.   Click the RUN button at the top of the study table.

A QSAR equation or set of equations is generated and displayed in the Equation Viewer.

3.   Validate the equation-building process by clicking the Validate icon on the study table (the button marked "OK").

4.   Run the randomization and crossvalidation tests by clicking the appropriate buttons in the Validate control panel. For more information on this process, see Validating QSAR equations and data on page 223.

Predicting biological activity

Predicting activity

1.   Select and add the molecule in which you are interested to the study table.

2.   Select Create Field from the FIELD ANALYSIS (MFA) card to open the Create Field control panel.

3.   Uncheck all probes so that no new field value columns are added to the study table.

4.   Click Create. MFA generates field data, predicted activity, and residuals data for all models in the study table, including the model you added.

When field and QSAR calculations are complete, you can mark the field points used in the QSAR in the model window:

Open the Equation Viewer and check the Plot Equation button. Field descriptors used in the QSAR equation are marked in the Study Table, and the grid points are displayed in the model window with a 3D cross and a name label. Additional information is also printed in the text window. For information about the Equation Viewer, see Chapter 14, Using the Equation Viewer.