The main module (C++ class) which perform calculations of donor/acceptor coupling is ETCoupl class. As all computational modules it is derived from HaCompMod and HaTextCmdTarget classes. There are three dialogs associated with ETCoupl: ChooseRedox - dialog to interactively choose donor and acceptor groups, PathwaysDlg - dialog to perform PATHWAYS calculations for donor/acceptor coupling, ETEffHamDlg - dialog class to manage calculations of donor/acceptor electronic coupling with divide-and-conquer method. ETCoupl class performs PATHWAYS calculations of three types: 1.BestPath calculations finding the best coupling between donor and acceptor atoms using Diijkstra algorithm 2. Coupling Map calculations when PATHWAYS couplings from the donor to all other atoms of the system are calculated. 3. Identification of atoms which belong to the PATHWAYS with coupling values within certain threshold of the best path. For this purpose coupling from the donor and acceptor to all other atoms in the system are calculated. An atoms is selected if the product of its couplings to the donor and acceptor exceed a threshold value. Divide-and-Conquer calculation of the donor/acceptor coupling are performed in ETCoupl class and ETHeffHF class, the letter is an abstraction for effective hamiltonian in Hartree- Fock approximation. An instance of ETHeffHF class is contained in the ETCoupl class. To calculate effective hamiltonian on active orbitals first Green function matrix on the active orbitals is calculated given the molecular orbitlas and molecular energies of the system. This matrix is then inverted to get an effective hamiltonian matrix. The effective hamil- tonian matrix is logically disected into interaction submatricies between active orbitals of different atomic groups. Submatricies of the effective hamiltonian are stored in a database file using functions of Berkeley Database library encapsulated in the class HaMatDB. When storing a group- group submatrix of the effective hamiltonian, the program check if the submatrix between group with the same IDs already exist in the database (from the calulations on another overlapping fragment of the system). If such a matrix exists, the products of protection 124 factors of the groups for the submatrix stored in the database and for the submatrix about to be saved are calculated. The new submatrix is stored if the product of the protection factors of its atomic groups are larger then that of the stored submatrix. The less the protection factor of an atomic group the more we expect the electronic structure of the group is perturbed in the fragment compare to the intact structure of the system. The effective hamiltonian of the system accumulated in the database is restored and donor/acceptor coupling is calculated. Two methods of the donor/acceptor electronic coupling calculations are currently supported. In the first method the energy splitting of eigen states of the effective hamiltonian is minimized by the application of the electrical field between donor and acceptor. This acomplished by 1. The matricies of components of electrical dipole operator with an origin in the midpoint between donor and acceptor are calculated using class HaOperR. 2. Dipole operator matricies are premultipled by cosines of the direction from the donor to acceptor and the value of the strength of the electrical field. 3. The energy splitting between donor and acceptor localized eigenstates is minimized using conjugate gradient method, changing the strength of the applied electrical field and diagonalizing the matrix of the effective hamiltonian. The eignestates localized in the donor and acceptor can be chosen interactively using 3D contour representation of isodensity levels of the eigenstates. The second method of donor/acceptor coupling calculations, calculate Green-Function ma- trix elements between donor and acceptor localized states and described in the chapter ??. The user interactively chooses donor/acceptor localized eigenstates of the e ective hamil- tonian. The program truncates these states to be localized only on the donor or acceptor atoms to obtain localized donor and acceptor states. Green-function matrix elements be- tween these states are calculated and the obtained 2x2 matrix is inverted to give e ective donor/acceptor interaction. The second method is more than an order of magnitude faster than the method based on energy splitting calculations. In the nearest future we will modify the program to derive approximate localized donor and acceptor states from the calculations on fragments, and will calculate donor/acceptor Green Function elements with iterative methods instead of using the inversion of the whole e ective hamiltonian matrix, which should the calculations dramatically faster for very large ET system. Outer sphere reorganization energies in HARLEM are calculated with the help of ElectrostMod class which manages electrostatic tinteractions solving 3D Poisson-Boltzmann equation. These types of calculations are accessed through the dialog class ElectrostDlg. The program setup two Electrostatic calculations. One with dielectric con- stants of the media set to its satic value (. = 80 for water and . = 4 for the protein. In both calculations +1e charge uniformly distributed over atoms of the donor and (-1e) charge distributed over atoms of the acceptor. This is very crude representation of the changes of the charge distribution if the system upon the electron transfer. However this approxi- mation doesn't typically cause as great error in the calculated reorganization energy value while make calculations very easy for the user of the program. The user need just choose interactively donor and acceptor and run reorganization energy calculations with a press of a button. The calculations take just seconds for default 65x65x65 grid.
Example of PATHWAYS calculation in Gray's Horse Cyt-C HIS-33-Ru-bpy complex:
1. Start HARLEM and load PDB file of the complex:
Easiest way probably will be to drop the icon of PDB file (in this case cytc_33_1.pdb) on harlem.exe icon. Another method will be to use File->Open Menu in HARLEM (one should choose PDB file option in Open Dialog).
2. Specify donor and acceptor in Edit Redox Centers Dialog:
a)Open dialog by ET->'Edit Redox Centers' b)choose DONOR or ACCEPTOR toggle buttons. c)Fill list of atoms of donor and acceptor by clicking on the desired atom and pressing INCLUDE button. Selected atoms are seen as small spheres. One also could choose the whole residue by choosing selection level RESIDUE toggle button and clicking on the desired residue (one can also just type in the prompt). In the example case of cyt one may wish to choose donor as HEM105 and acceptor RBP200(Ru-bpy). first one can choose whole HEM105 as a donor ( choose selection level residue, click on some HEM atom and press INCLUDE), then when you press ACCEPTOR toggle button and back DONOR toggle button list of donor atoms (all atoms belonging to HEM group will appear). One may delete from the donor atoms of propionates and methyl groups by selecting them in the list and pressing DELETE button.
All atoms of the donor(acceptor) assumed coupled with the value 1.0 (short-circuited).
3. Run Pathways:
Choose ET->"Run Pathways" which will open PATHWAYS Dialog.
One can do three types of calculations currently:
3 a) Best Path calculations( should take about 30s on Pentium-133 IBM-PC)
Choose BEST_PATH toggle button and press RUN Description of the BEST PATH between specified Donor and acceptor will appear in HARLEM CONSOLE Window. Best Path member atoms will be denoted by spheres on the molecular image.
3 b) Coupling Map: Coupling of all atoms to the donor
Choose Coupling Map option and press RUN button. Coupling map will be printed to HARLEM Console Window. and Protein will be coloured by coupling values (red- max, blue- min)
If one save the molecule in pdb format ( currently one need to open HARLEM command line window and type command at HARLEM> prompt like: save pdb cyt33_2.pdb
the last name of the file in arbitrary of course) the ln of coupling values will be in the temperature factors of the atoms in the pdb file.
3 c) 3-rd type of PATHWAYS calculations is the selection of all atoms which belong to the paths which have coupling vlaued within certain threshold value from the BEST PATH say within a facot of 0.5 or 0.1. These calculations give you an estimate which residues are important for mediating ET coupling between Donor and Acceptor.
One runs these calculations by selecting threshold value in the prompt and press "SELECT COUPLED" button. (In the case of cyt this will be atoms of HIS33, Arg38, Leu23)
Identifiers of atoms on the important paths will be printed to HARLEM Console Window. Atoms on the important paths and donor and acceptor will be plotted as tubes. One can get idea what atoms are important by clicking on selected atoms - their identifiers will appear in HARLEM CONSOLE window.
la-la
1.3.6