2. Applying Constraints

This chapter describes the options in QUANTA used to define and apply various constraints for CHARMm calculations. Read this chapter if you want to apply constraints to structures undergoing CHARM-based operations.

For information on the definition and analysis of constraints used specifically for NMR structure determination, consult another volume in the QUANTA documentation set NMR Structure Determination.

Four kinds of constraints are described in this chapter:

Atom constraints - Used to fix or harmonically constrain an atom or set of atoms to their current positions during energy minimization or dynamics calculations.

Distance constraints - Used to apply a square-well constraining potential between one atom or set of atoms and a second atom or set of atoms to limit the distance between them to specified bounds. Where the constraint involves a collection of atoms (protons of a methyl group, for example), distances are measured from an average position.

Dihedral constraints - Used to apply a harmonic constraint to restrict a dihedral (torsion angle) to a specified value.

Stochastic boundary constraints - Used to simulate forces arising from average properties of the system outside a specified boundary.

Access to the tools for defining and applying constraints is through the CHARMm menu. From the CHARMm menu, select Constraints Options to display a pull-right menu containing selections for each type of constraint option. Table 7 lists the selections and provides a brief description of each.

Table 7. Constraints Options Menu
Selection Description

Select Atom Constraints

Provides palette choices for defining atom constraints and for selecting atoms to which the constraints are applied.

Atom Constraints On

Turns on the atom constraints selected for the current session and stored in an .atc file.

Atom Constraints Off

Turns off the atom constraints selected for the current session and stored in an .atc file.

Dihedral/Distance

Provides palette choices for defining dihedral and distance constraints and preparing a Constraints Table.

Dihedral On

Turns on the dihedral constraints selected for the current session and stored in the Constraints Table.

Dihedral Off

Turns off the dihedral constraints selected for the current session and stored in the Constraints Table.

Distance On

Turns on distance constraints selected for the current session and stored in the Constraints Table.

Distance Off

Turns off the distance constraints selected for the current session and stored in the Constraints Table.

Stochastic Bdry Settings

Provides choices for defining deformable boundary forces used to study an active site.

Stochastic Bdry Settings On

Turns on stochastic boundary settings selected for the current session.

Stochastic Bdry Settings Off

Turns off stochastic boundary settings selected for the current session.

Table 7. Constraints Options Menu
Selection	Description
Select Atom Constraints	Provides palette choices for defining atom constraints and for selecting atoms to which the constraints are applied.
Atom Constraints On	Turns on the atom constraints selected for the current session and stored in an .atc file.
Atom Constraints Off	Turns off the atom constraints selected for the current session and stored in an .atc file.
Dihedral/Distance	Provides palette choices for defining dihedral and distance constraints and preparing a Constraints Table.
Dihedral On	Turns on the dihedral constraints selected for the current session and stored in the Constraints Table.
Dihedral Off	Turns off the dihedral constraints selected for the current session and stored in the Constraints Table.
Distance On	Turns on distance constraints selected for the current session and stored in the Constraints Table.
Distance Off	Turns off the distance constraints selected for the current session and stored in the Constraints Table.
Stochastic Bdry Settings	Provides choices for defining deformable boundary forces used to study an active site.
Stochastic Bdry Settings On	Turns on stochastic boundary settings selected for the current session.
Stochastic Bdry Settings Off	Turns off stochastic boundary settings selected for the current session.

Defining and applying atom constraints

Atom constraints are first defined, then applied. To define a constraint:

1. Set the force constant.

2. Select the atoms to which this particular force constant applies.

Start the process by selecting Constraints Options from the CHARMm menu. Then select Select Atom Constraints from the pull-right menu. Two palettes open, the Set Atom Constraints and Atom Constraints Utilities palettes. These palettes are similar to those used throughout QUANTA for atom selection. For example, see the description of the Active Atoms and Active Atoms Utilities palettes in Chapter 2 of QUANTA Basic Operations.

Table 8 and Table 7 list the selections in the Set Atom Constraints and Atom Constraints Utilities palettes, respectively, and provide a brief description of each selection.

Table 8. Set Atom Constraints palette
Selection Description

All MSFs

Selects all MSFs that have been chosen on the Molecule Management Table if each MSF has <500 atoms. This option is turned off if one MSF has >500 atoms.

One MSF...

Selects the atoms contained in the specified MSF. Only the selected MSF is displayed.

Apply to All MSFs

Applies specified selections of one MSF to all active MSFs.

Color by Value

Assigns a color to each atom according to the force constant that is associated with the atom. Helps ensure that constraints are properly set.

Show Force Constants

Labels each atom with the force constant assigned to it. Helps establish proper constraints.

Harmonic Force...

Opens dialog box to set a force-constant value. Default value is 100.00. The force constant remains in effect until it is changed.

Fix

Constrains selected atoms to their current position.

Free

Sets force constant to zero.

All Atoms

Selects all atoms in the structure. Can be used to restore a structure after using other atom selection options.

All Non-Hydrogen Atoms

Selects all atoms except hydrogen atoms.

Solvent

Selects all residues of type: WAT, HOH, TIP, TIP3, SOL, SOLV, ST2, NON, H2O, TIP4.

Alpha-Carbon Atoms

Selects only protein alpha-carbon atoms.

Protein Backbone

Selects only protein backbone atoms.

Nucleic Acid Backbone

Selects only nucleic acid backbone atoms.

Residue Range...

Active residue range selected by completing information in a dialog box. The process can be repeated.

Residue Type...

Active residue type selected by completing information in a dialog box. The process can be repeated.

Atom Type...

Active atom type selected by completing information in a dialog box. The process can be repeated.

Pick Molecule

Using the mouse, selection of a molecule is made from the active MSFs on the screen.

Pick Segment

Using the mouse, selection of a segment is made by picking an atom in the segment from the active MSFs on the screen.

Pick Residue

Using the mouse, selection of a residue is made by picking an atom in the residue from the active MSFs on the screen.

Pick Residue Range

Using the mouse, selection of a residue range is made by picking two atoms from the active MSFs on the screen.

Pick Atom

Using the mouse, selection of an atom is made by picking it from the active MSFs on the screen.

Proximity Tools

Opens the Proximity Tools palette containing multiple choices for selecting a central atom and nearby portions of a molecule.

Type in a Selection

A dialog box is used to enter Selection-Commands.

Undo

Returns the viewing area to the state before the previous command.

Clear

Deletes all selections. Resets to defaults.

Revert

Returns the viewing area to the initial state when Select Atom Constraints was selected.

Quit

Exits Select Atom Constraints without saving changes and reverts to the original .atc file.

Finish

Exits Select Atom Constraints and writes the changes to a temporary .atc file. At least one atom of the active molecule must be selected to use this option.

Table 8. Set Atom Constraints palette
Selection	Description
All MSFs	Selects all MSFs that have been chosen on the Molecule Management Table if each MSF has <500 atoms. This option is turned off if one MSF has >500 atoms.
One MSF...	Selects the atoms contained in the specified MSF. Only the selected MSF is displayed.
Apply to All MSFs	Applies specified selections of one MSF to all active MSFs.
Color by Value	Assigns a color to each atom according to the force constant that is associated with the atom. Helps ensure that constraints are properly set.
Show Force Constants	Labels each atom with the force constant assigned to it. Helps establish proper constraints.
Harmonic Force...	Opens dialog box to set a force-constant value. Default value is 100.00. The force constant remains in effect until it is changed.
Fix	Constrains selected atoms to their current position.
Free	Sets force constant to zero.
All Atoms	Selects all atoms in the structure. Can be used to restore a structure after using other atom selection options.
All Non-Hydrogen Atoms	Selects all atoms except hydrogen atoms.
Solvent	Selects all residues of type: WAT, HOH, TIP, TIP3, SOL, SOLV, ST2, NON, H2O, TIP4.
Alpha-Carbon Atoms	Selects only protein alpha-carbon atoms.
Protein Backbone	Selects only protein backbone atoms.
Nucleic Acid Backbone	Selects only nucleic acid backbone atoms.
Residue Range...	Active residue range selected by completing information in a dialog box. The process can be repeated.
Residue Type...	Active residue type selected by completing information in a dialog box. The process can be repeated.
Atom Type...	Active atom type selected by completing information in a dialog box. The process can be repeated.
Pick Molecule	Using the mouse, selection of a molecule is made from the active MSFs on the screen.
Pick Segment	Using the mouse, selection of a segment is made by picking an atom in the segment from the active MSFs on the screen.
Pick Residue	Using the mouse, selection of a residue is made by picking an atom in the residue from the active MSFs on the screen.
Pick Residue Range	Using the mouse, selection of a residue range is made by picking two atoms from the active MSFs on the screen.
Pick Atom	Using the mouse, selection of an atom is made by picking it from the active MSFs on the screen.
Proximity Tools	Opens the Proximity Tools palette containing multiple choices for selecting a central atom and nearby portions of a molecule.
Type in a Selection	A dialog box is used to enter Selection-Commands.
Undo	Returns the viewing area to the state before the previous command.
Clear	Deletes all selections. Resets to defaults.
Revert	Returns the viewing area to the initial state when Select Atom Constraints was selected.
Quit	Exits Select Atom Constraints without saving changes and reverts to the original .atc file.
Finish	Exits Select Atom Constraints and writes the changes to a temporary .atc file. At least one atom of the active molecule must be selected to use this option.

Table 9. Atom Constraints Utilities palette
Selection Description

Retrieve Labeled from MSF

Recovers labeled constraints from MSF created in QUANTA 3.3 or older. Atom constraints for QUANTA are stored as a set of commands in an .atc file.

Read Selection-Commands

Reads command from file.atc and updates the viewing area to select the new set of commands.

Append Selection-Commands

Appends the current file.atc with a set of commands from another file2.atc and updates the viewing area to reflect the new combined set of commands.

Save Selection-Commands

Saves the current set of commands to a new file.

List Selection-Commands

Lists the current set of commands in the Textport window.

Edit File Manually

Allows an .atc file to be manually edited. A window is opened, which uses the vi editor for editing the file¹.

Help on Commands

Provides a list of all commands and their functions in the Textport.

¹You can change the default editor by using the setenv command before QUANTA is started. The syntax is: setenv EDITOR (name of system editor to be used).

Table 9. Atom Constraints Utilities palette
Selection	Description
Retrieve Labeled from MSF	Recovers labeled constraints from MSF created in QUANTA 3.3 or older. Atom constraints for QUANTA are stored as a set of commands in an .atc file.
Read Selection-Commands	Reads command from file.atc and updates the viewing area to select the new set of commands.
Append Selection-Commands	Appends the current file.atc with a set of commands from another file2.atc and updates the viewing area to reflect the new combined set of commands.
Save Selection-Commands	Saves the current set of commands to a new file.
List Selection-Commands	Lists the current set of commands in the Textport window.
Edit File Manually	Allows an .atc file to be manually edited. A window is opened, which uses the vi editor for editing the file¹.
Help on Commands	Provides a list of all commands and their functions in the Textport.

To set a particular force constant, select Harmonic Force... from the Set Atom Constraints palette. Or select Fix or Free to fix atoms or free them, respectively.

When you have completed the task of setting a force constant, select the set of atoms to which this force is to apply, using one of the selections in the Set Atom Constraints palette. Selections are automatically written to a filename.atc file.

The Atom Constraints Utilities palette provides tools to save a particular selection scheme to an .atc file. This file can then be read and used in subsequent sessions.

To use your constraints selections in CHARMm energy calculations, select Finish from the Set Atom Constraints palette. The current set of selection commands in the .atc file is translated, and a value for each atom is stored in the appropriate MSF. A status flag is set on, and the constraints are communicated directly to CHARMm for all subsequent energy calculations. These constraints remain active until explicitly turned off using the Atom Constraints Off selection in the Constraints Options pullright menu or until the QUANTA session is ended.

If a second molecule is added to an ongoing session, the .atc file is updated to include the new molecule. But you must apply the Atom Constraints On selection to inform CHARMm of the change.

Sample procedure - Defining and applying atom constraints

Complete the next exercise to become familiar with the procedures for defining and applying atom constraints. This exercise uses mypeptide.msf generated in Chapter 4 of QUANTA Generating and Displaying Molecules. If you have not done so, complete Chapter 4 before proceeding.

1. Open an MSF.

From the File menu, select Open. A File Librarian dialog box is displayed.

Select the file mypeptide.msf. Select Replace then the Open button. The structure is displayed in the viewing area.

2. Define atom constraints.

From the CHARMm menu, select Constraints Options. From the pull-right menu, select Select Atom Constraints. The Select Atom Constraints and Atom Constraints Utilities palettes are displayed over the Geometry palette. The Modeling palette is removed. The molecule is displayed in light green

From the Set Atom Constraints palette, select Show Force Constants. Color by Value and Fix are default selections. The message line reports the force constant as -1.00.

From the Set Atom Constraints palette, select Alpha-carbon Atoms. The alpha carbons are displayed in light green, and the force constant -1.00 is displayed in a label on each carbon. The rest of the molecule is displayed in blue.

3. Exit from Select Atom Constraints.

From the Set Atom Constraints palette, select Finish. The palette is removed and the Modeling palette is redisplayed. The structure returns to standard colors. A textport message reads:

The file mypeptide.msf contains the following extra information: Next energy calculation will use constraints.

4. Apply constraints.

From the modeling palette, select CHARMm Energy. An energy value is calculated and displayed in the upper-right corner of the viewing area.

From the CHARMm menu, select Minimization Options. A dialog box is displayed allowing you to select a minimization method and to specify associated parameters controlling the calculation

Select the option:

Steepest Descents

Enter the values:

Number of Minimization Steps: 50
Coordinate Update Frequency: 5
Energy Gradient Tolerance: 0.00001
Energy Value Tolerance: 0.000
Initial Step Size: 0.020
Step Value Tolerance: 0.000

Select OK. The minimization technique and associated parameters are defined, and the dialog box is cleared from the screen.

From the Modeling palette, select CHARMm Minimization. The cursor changes from an arrow to a watch while the minimization calculation runs.

At the end of the calculation, the structure is displayed with new coordinates. The energy is displayed in the upper- right corner of the viewing area.

5. Rerun minimization without constraints.

From the CHARMm menu, select Constraint Options. From the pull-right menu, select Atom Constraints Off.

Rerun an energy minimization exactly as in Step 4.

Compare the data from the calculations in Steps 4 and 5.

6. Reject changes.

Select Reject Changes from the Modeling palette.

Defining and applying distance constraints

Distance constraints are used most frequently to represent interatomic distances determined experimentally by measurement of the nuclear Overhauser effect. NOE interactions or general distance constraints used in CHARMm calculations can be defined as described below. The NMR Constraints Editor and NMR Structure Determination applications of QUANTA provide additional tools to be used with the X-PLOR interface. They are described in the book NMR Structure Determination.

A subset of the options used in the NMR application is available for use in general modeling problems. As with atom constraints, distance constraints first must be defined then applied.

The subset of distance constraints described in this section is accessed using the Edit Constraints palette that opens when Distance/Dihedral is selected from the Constraints Options pull-right menu that is opened from the CHARMm menu. This palette is also used to apply dihedral constraints. Table 8, lists and briefly describes the palette selections.

Table 10 . Edit Constraints palette
Selection Description

Read Constraints

Reads a Constraints Table created in a previous session or in NMR Workbench.

Import Constraints...

Provides an interface to alternative constraint file formats. The CHARMm format reads and writes constraints in a format that can be read into CHARMm when used in the stand-alone mode. The Xplor format reads or generates constraints suitable for the XPLOR program. Several other constraint formats are supported for the NMR-Structure Determination package and are described elsewhere.

Export Constraints...

Provides an interface (same as import) to move files into alternative constraint file formats.

Define Dihedral Constraint(s)

Defines a dihedral constraint when four connected atoms are picked. These atoms are taken to be definitions of the end atoms of the constraint. A constraint thus defined is added to the Constraints Table. There is no provision to define a constraint for unconnected atoms.

Propagate a Dihedral Pick

Attempts to find all possible occurrences of the dihedral defined by the atom names of the four picked atoms. This selection is valid only for polymers in which atom names repeat from residue to residue.

Dihedral Families

Opens a dialog box where dihedral family constraints are defined.

Generate Dihedral Constraints

Used in conjunction with the NMR workbench. Reads a table of experimentally determined NMR coupling constants of the type JNH_HA and JHA-HB and converts these to constraints for torsion angles Phi and Chi1, respectively. Operation of this selection is described in the book NMR Structure Determination.

Dihedral Options

Sets defaults to use in defining dihedral constraints.

Define Distance Constraint(s)

Defines a constraint by picking two atoms from the active molecule on the screen. There are six picking modes (listed below) available.

Individual Atom

Picks just the atom that is selected. Default mode.

Protons Bound to Picked Atom

Defines a constraint to a pseudo atom whose position is defined as the average of the positions of all protons bound to the picked atom. For example, the protons of a methyl group can be simultaneously picked by picking the methyl carbon atom.

Atoms of Picked Residue

Defines a constraint for a pseudoatom whose position is determined by the average of all atoms in the picked residue.

Protons of Picked Residue

Defines a constraint to a pseudoatom whose position is determined by the average of all protons in the picked residue.

Atom of Picked Segment

Defines a constraint for a pseudoatom whose position is determined by the average of all atoms in the picked segment. Limited to 500 atoms.

Protons of Picked Segment

Defines a constraint for a pseudoatom whose position is determined by the average of all protons with the average taken over the entire segment. Limited to 500 atoms.

Distance Options

Opens a dialog box containing distance constraints defaults, and options for changing those values. The options assign values to constraint types, class, upper and lower bounds, activity status, and constraints display.

Select Constraints

Allows selection of a subset of constraints to be active and displayed. Additional selections can be made using table selection mechanisms.

Delete Selected Constraints

Allows an entire set of selected constraints to be deleted. A single constraint can be deleted by selecting it then deleting it.

Show Violation Labels

Displays constraints on the screen using a color code to indicate the extent to which each constraint satisfies boundaries imposed upon it. For those constraints that are not satisfied, the violation label reports the extent to which the bound is violated.

Show Constraints

Toggles the display of constraints on the structure in the viewing. Constraints are also listed in the Constraints table.

Save Constraints

Saves the current constraints in table form and supplies a .con file extension as a means to identify it as a Constraints table. This is the recommended format to use for communicating with NMR Workbench.

Save Constrains As...

Saves the current constraints in table form and supplies a .con file extension to identify it as a Constraints table. Allows new filename to be assigned. This is the recommended format to use for communicating with NMR Workbench.

Exit Edit Constraints

Exits the Edit Constraints palette for distance and dihedral constraint definition and application. Returns to molecular modeling mode where CHARMm energy calculations can be carried out. Contacts displayed on the model are removed, but the table remains displayed. The table must be present in order to send Constraint commands to CHARMm.

Table 10 . Edit Constraints palette
Selection	Description
Read Constraints	Reads a Constraints Table created in a previous session or in NMR Workbench.
Import Constraints...	Provides an interface to alternative constraint file formats. The CHARMm format reads and writes constraints in a format that can be read into CHARMm when used in the stand-alone mode. The Xplor format reads or generates constraints suitable for the XPLOR program. Several other constraint formats are supported for the NMR-Structure Determination package and are described elsewhere.
Export Constraints...	Provides an interface (same as import) to move files into alternative constraint file formats.
Define Dihedral Constraint(s)	Defines a dihedral constraint when four connected atoms are picked. These atoms are taken to be definitions of the end atoms of the constraint. A constraint thus defined is added to the Constraints Table. There is no provision to define a constraint for unconnected atoms.
Propagate a Dihedral Pick	Attempts to find all possible occurrences of the dihedral defined by the atom names of the four picked atoms. This selection is valid only for polymers in which atom names repeat from residue to residue.
Dihedral Families	Opens a dialog box where dihedral family constraints are defined.
Generate Dihedral Constraints	Used in conjunction with the NMR workbench. Reads a table of experimentally determined NMR coupling constants of the type JNH_HA and JHA-HB and converts these to constraints for torsion angles Phi and Chi1, respectively. Operation of this selection is described in the book NMR Structure Determination.
Dihedral Options	Sets defaults to use in defining dihedral constraints.
Define Distance Constraint(s)	Defines a constraint by picking two atoms from the active molecule on the screen. There are six picking modes (listed below) available.
Individual Atom	Picks just the atom that is selected. Default mode.
Protons Bound to Picked Atom	Defines a constraint to a pseudo atom whose position is defined as the average of the positions of all protons bound to the picked atom. For example, the protons of a methyl group can be simultaneously picked by picking the methyl carbon atom.
Atoms of Picked Residue	Defines a constraint for a pseudoatom whose position is determined by the average of all atoms in the picked residue.
Protons of Picked Residue	Defines a constraint to a pseudoatom whose position is determined by the average of all protons in the picked residue.
Atom of Picked Segment	Defines a constraint for a pseudoatom whose position is determined by the average of all atoms in the picked segment. Limited to 500 atoms.
Protons of Picked Segment	Defines a constraint for a pseudoatom whose position is determined by the average of all protons with the average taken over the entire segment. Limited to 500 atoms.
Distance Options	Opens a dialog box containing distance constraints defaults, and options for changing those values. The options assign values to constraint types, class, upper and lower bounds, activity status, and constraints display.
Select Constraints	Allows selection of a subset of constraints to be active and displayed. Additional selections can be made using table selection mechanisms.
Delete Selected Constraints	Allows an entire set of selected constraints to be deleted. A single constraint can be deleted by selecting it then deleting it.
Show Violation Labels	Displays constraints on the screen using a color code to indicate the extent to which each constraint satisfies boundaries imposed upon it. For those constraints that are not satisfied, the violation label reports the extent to which the bound is violated.
Show Constraints	Toggles the display of constraints on the structure in the viewing. Constraints are also listed in the Constraints table.
Save Constraints	Saves the current constraints in table form and supplies a .con file extension as a means to identify it as a Constraints table. This is the recommended format to use for communicating with NMR Workbench.
Save Constrains As...	Saves the current constraints in table form and supplies a .con file extension to identify it as a Constraints table. Allows new filename to be assigned. This is the recommended format to use for communicating with NMR Workbench.
Exit Edit Constraints	Exits the Edit Constraints palette for distance and dihedral constraint definition and application. Returns to molecular modeling mode where CHARMm energy calculations can be carried out. Contacts displayed on the model are removed, but the table remains displayed. The table must be present in order to send Constraint commands to CHARMm.

When the Define Distance Constraints selection is active, any two picks are taken to be definitions of the end atoms of the constraint. A constraint thus defined is added to a table of constraints labeled Constraints_Database.con. This table opens in a separate window over the window for the Molecule Management table. It is stored in a .con file when the Edit Constraints palette is exited.

As each constraint is defined, a colored dashed line on the screen connects the end atoms of the constraint. If the actual interatomic distance in the model falls within specified bounds, the contact line is displayed in blue. If the distance exceeds the upper bound, it is drawn in red, and if less than the lower bound, in yellow.

Constraint properties are assigned current default values. These defaults can be changed using the dialog box that is displayed when Distance Options is selected from the Edit Constraints palette. After a constraint is defined and appears in the table, its properties can be edited directly in the table using table edit procedures. The atom identifiers in columns End 1 and End 2 of the table cannot be edited.

The options defined in this dialog box include:

Type -A code used primarily to distinguish distance constraints (defined by two atoms) from torsion constraints (defined by four atoms). For distance constraints in most applications, set the type to NOE.

Class- Four-letter code used to distinguish various kinds of distance interactions from one another. Its primary use is in the NMR Structure Determination application, where different potential functions are assigned to different types of interactions. The class assigned here is useful only as a tag for selection.

Targeted Distance (Target)- The optimal distance between two picked atoms.

Upper Bound and Lower Bound -Values that define the range for which a constraint is satisfied. These correspond to R_MAX and R_MIN parameters, respectively, in the CHARMm NOE potential function. They determine the width of the square well.

CHARMm Force Constant KMIN and KMAX - Force constants that determine the steepness of the potential outside the R_MIN and R_MAX ranges.

Activity Setting - Determines if a constraint in the Constraints table is sent to CHARMm. If the toggle is set to Inactive, the constraint can be defined but not used in CHARMm calculations.

The Constraints table contains columns for each parameter described above, plus several that are specific to the NMR Structure Determination application. Full column display is achieved in an expanded window.

The Constraints table also includes its own set of menus that can be used to manipulate table data and edit constraints. These pull-down menus are accessed from the menu bar at the top of the table and include:

File - Manages import and export of table files. Limited use recommended. Instead use the Import, Export, and Save selections in the Edit Constraints palette.

Edit - Manages constraint subsets. Also provides tools to define and edit rows.

Format - Customizes appearance of the table.

Data - Manipulates table entries.

Special Tools - Defines and manages constraint subsets.

Initially, all constraints are selected and highlighted in blue, both in the Constraints table and on the screen,. When many constraints are defined, it may be useful to select or delete a subset of them as an aid to viewing. Constraints can be selected by using options in the Select Constraints palette. This palette is displayed when you select Select Constraints in the Edit Constraints palette.

You also may select constraints from the Constraints table. Selections in the table are made by clicking or double-clicking the row number of the constraint you want to select, by using Select All in the table Edit menu, by using Find in the table Data menu, or by using selections in the Special Tools menu.

If the <Shift> key is depressed as a row is selected, the row is added to the current constraints list. If the <Ctrl> key is depressed as a row is selected, all rows between the current row and the previously selected row are selected.

In the CHARMm Constraints Options pull-right menu, Distance On and Distance Off are used to communicate selected constraints to CHARMm. In addition, the Status column (activity setting) in the Constraints table can be used to toggle individual constraints on or off. When changes are made in the table, turn all constraints off then on again to make sure the changes are sent to CHARMm.

Each time constraints are sent to CHARMm, a dialog box appears requesting values for a scaling factor to be used in the CHARMm NOE constraint potential function. The functional form of this potential is described in the CHARMm documentation.

Defining and applying torsion constraints

A torsion (dihedral) constraint is defined by picking four connected atoms after selecting Define Dihedral Constraint in the Edit Constraints palette. No provision is made to define a constraint for unconnected atoms.

The atom identifiers that appear in the Constraints table are the end atoms of the torsion. The constraints that you define are listed in the table and also displayed on the model as a small ring around the middle bond of the torsion. The ring is blue if the value of the torsion in the model lies within the specified upper and lower bounds. Red indicates a violated upper bound and yellow indicates a violated lower bound.

Default values for constraint parameters can be modified by selecting Dihedral Options in the Edit Constraints palette. The parameters in the dialog box that opens include:

type - Used do distinguish dihedral constraints from distance constraints when interacting with CHARMm.

Constrain to - Provides options for defining the optimal constraint value.

Current value - Constrains the torsion to stay at or near its current value.

Specified Target - Defines the optimal value and its upper and lower bounds.

Solve Karplus Equation - Each time a dihedral is picked, activates a dialog box that presents coefficients for the Karplus equation and solutions that would be generated by a particular value of an experimentally determined coupling constant. Both the coefficient and the coupling constant can be changed.

CHARMm Force Constant - Sets a default value that appears in the Constraints table for the force constant The CHARMm potential function used for torsion constraints is a simple harmonic function containing force constant K.

Activity Setting - Determines if a constraint in the Constraints table is sent to CHARMm. If the toggle is set to Inactive, the constraint can be defined but not used in CHARMm calculations.

The Edit Constraints palette selection, Propagate a Dihedral Pick, attempts to find all possible occurrences of the torsion defined by the atom names of the four picked atoms. If, for example, the atoms C, N, Ca, and C are picked in a residue of a polypeptide chain, all occurrences of this torsion are found and defined. This selection is valid only for polymers in which atom names repeat from residue to residue.

As with Propagate a Dihedral Pick, the Dihedral Families selection is useful only in molecules that contain repeating subunits. Dihedral Families allows quick definition of commonly occurring dihedrals such as phi, psi, and omega in proteins. For example, the selection could be useful in setting up simulations of proteins in which all omega torsions are restricted to the trans configuration.

In the CHARMm Constraints Options pull-right menu, Dihedral On and Dihedral Off are used to communicate selected constraints to CHARMm. In addition, the Status column (activity setting) in the Constraints table can be used to toggle a single constraint on or off. When changes are made in the table, turn all constraints off then on again to make sure the changes are sent to CHARMm.

Sample procedure - Defining and applying distance and torsion constraints

Complete the following exercise to become familiar with the procedure for defining and applying distance and torsion constraints. Continue using mypeptide for this exercise.

1. Define distance constraints.

From the CHARMm menu, select Constraints Options. Then select Dihedral/Distance from the pull-right menu that opens. The Edit Constraints palette opens and the Modeling palette is removed.

From the Edit Constraints palette, select Define Distance Constraints . In the palette, Individual Atom is highlighted as a default selection.

Pick any two pairs of atoms as end atoms in the mypeptide molecule to define two distance constraints. A dashed line appears connecting each pair of atoms. If the distances are within default bounds, the line is blue. If not, the line is either red (too far) or yellow (too near).

The Constraints table entitled Constraints_database.con is displayed in a separate window. The distance constraints are listed in the table.

2. Define dihedral constraints.

From the Edit Constraints palette, select Define Dihedral Constraints .

Pick any four connected atoms to define a torsion angle in the mypeptide molecule. The torsion constraint data is added to the Constraints table.

3. Exit the Edit Constraints palette.

From the Edit Constraints palette, select Finish. The palette is removed and the Modeling palette is redisplayed. The Constraints table remains on display. A File Librarian dialog box opens.

Enter:

mypeptide

Select the Save button. The distance constraints are saved to a .con file.

4. Apply constraints.

From the CHARMm menu, select Constraint Options. From the pull-right menu that opens, select Distance Constraints On and Dihedral Constraints On.

From the Modeling palette, select CHARMm Energy. An energy value is calculated and displayed in the upper right corner of the viewing area.

From the CHARMm menu, select Minimization Options. A dialog box is displayed allowing you to select a minimization method and to specify associated parameters controlling the calculation

Select the option:

Steepest Descents

Enter the values:

Number of Minimization Steps: 50
Coordinate Update Frequency: 5
Energy Gradient Tolerance: 0.00001
Energy Value Tolerance: 0.000
Initial Step Size: 0.020
Step Value Tolerance: 0.000

Select OK. The minimization technique and associated parameters are defined, and the dialog box is cleared from the screen.

From the Modeling palette, select CHARMm Minimization. The cursor changes from an arrow to a watch while the minimization calculation runs. The distance and torsion constraints that you defined are applied during the calculations.

At the end of the calculation, the structure is displayed with new coordinates. The energy is displayed in the upper right corner of the viewing area.

From the Modeling palette, select Reject Changes. The molecule is redisplayed using the most recently stored coordinates.

5. Rerun minimization without constraints.

From the CHARMm menu, select Constraint Options. From the pull-right menu that opens, select Distance Off and Dihedral Off.

Rerun an energy minimization exactly as in Step 4.

Compare the visual and written data from the calculations in Steps 4 and 5.

Select Reject Changes from the Modeling palette.

Applying stochastic boundary constraints

Deformable boundary forces are used in studying small localized regions of solvent (the reaction zone) around an active site. The program assumes that either the entire molecule or the region of the active site is solvated. Outside the reaction zone, atoms of the solvent and solute are either fixed or ignored. Boundary forces are applied to the solvent atoms inside the zone and serve to contain the reaction zone.

In QUANTA, boundary forces generally are computed from the deformable boundary method of Brooks and Karplus. (See References) These forces are computed in 1-Å increments for solvent spheres 8-25 Å in diameter.

To select and apply these forces, select Constraint Options from the CHARMm menu. From the Constraints Options pull-right menu that opens, select Stochastic Bdry Settings. A dialog box opens from which you select options and specify parameters.

Summary

This chapter describes the options in QUANTA used to define and apply various constraints for CHARMm calculations. Access to the tools for defining and applying constraints is through the CHARMm menu.

Four kinds of constraints are described:

Atom constraints - Used to fix or harmonically constrain an atom or set of atoms to their current positions during energy minimization or dynamics calculations.

Distance constraints - Used to apply a square-well constraining potential between one atom or set of atoms and a second atom or set of atoms to limit the distance between them. Distance constraints are used most frequently to represent interatomic distances determined experimentally by measurement of the nuclear Overhauser effect

Torsion constraints - Used to apply a harmonic constraint to restrict a torsion angle to a specified value.

Stochastic boundary constraints - Used to simulate forces arising from average properties of the system outside a specified boundary. In QUANTA, boundary forces generally are computed from the deformable boundary method of Brooks and Karplus.

Initially all constraints are selected and displayed both in the Constraints table and on the screen. The Constraints table contains columns for each constraint parameter. It also includes its own set of menus that can be used to manipulate table data and edit constraints.

1. C. L. Brooks III and M. Karplus. 1983. J. Chem. Phys. 79, 6312.