DNA Repair Mechanism by Photolyase: Electron Transfer Path from the Photolyase Catalytic Cofactor FADH−to DNA Thymine Dimer

J. theor. Biol. (2001) 210, 237}248 doi:10.1006/jtbi.2001.2291, available online at http://www.idealibrary.com on

DNA Repair Mechanism by Photolyase: Electron Transfer Path from the Photolyase Catalytic Cofactor FADH ⴚ to DNA Thymine Dimer DMITRY MEDVEDEV AND ALEXEI A. STUCHEBRUKHOV* Department of Chemistry, ;niversity of California, Davis, CA 95616, ;.S.A. (Received on 18 January 2000, Accepted in revised form on 2 February 2001)

Photolyase is an enzyme that catalyses photorepair of thymine dimers in UV damaged DNA by electron transfer reaction. The structure of the photolyase/DNA complex is unknown at present. Using crystal structure coordinates of the substrate-free enzyme from E. coli, we have recently built a computer molecular model of a thymine dimer docked to photolyase catalytic site and studied molecular dynamics of the system. In this paper, we present analysis of the electronic coupling and electron transfer pathway between the catalytic cofactor FADH\ and the pyrimidine dimer by the method of interatomic tunneling currents. Electronic structure is treated in the extended HuK ckel approximation. The root mean square transfer matrix element is about 6 cm\, which is consistent with the experimentally determined rate of transfer. We "nd that electron transfer mechanism responsible for the repair utilizes an unusual folded conformation of FADH\ in photolyases, in which the isoalloxazine ring of the #avin and the adenine are in close proximity, and the peculiar features of the docked orientation of the dimer. The tunneling currents show explicitly that despite of the close proximity between the donor and acceptor complexes, the electron transfer mechanism between the #avin and the thymine bases is not direct, but indirect, with the adenine acting as an intermediate. These calculations con"rm the previously made conclusion based on an indirect evidence for such mechanism.  2001 Academic Press

1. Introduction Photolyase is an enzyme that catalyses photorepair of DNA thymine dimer lesions (Friedberg et al., (1995). The structure and function of this enzyme has been actively investigated in the past few years (Heelis et al., 1995; Sancar, 1994; Kim & Sancar, 1993). With high e$ciency photolyase binds to thymine (T12T) and other pyrimidine (Pyr12Pyr) dimers on DNA, and splits the dimers when exposed to UV}visible light. The key element in the repair mechanism is electron transfer from one of the two cofactors of photolyase, an excited #avin molecule of *FADH\, to the pyrimidine dimer on DNA. As a consequence *Corresponding author. 0022}5193/01/100237#12 $35.00/0

of this electron transfer reaction, the two bonds between the pyrimidine bases break up. The excitation of the FADH\ occurs either directly by light or after the second chromophore (MTHF in the folate and 8-HDF in the deaza#avin class) absorbs a photon and transfers excitation energy by FoK rster's mechanism to FADH\. Upon dimer splitting the electron is transferred back to the oxidized #avin, and the enzyme and the repaired DNA dissociate. Recently, the crystal structures of photolyase from Escherichia coli (Park et al., 1995) and Anacystis nidulans (Tamada et al., 1997) have been resolved. The structure of the photolyase/DNA complex, however, which is the key to understanding the mechanism of repair, is  2001 Academic Press

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unknown at present. The mutagenesis studies identi"ed several amino acid residues that are involved in di!erent aspects of the enzymatic function (Kim et al., 1992b; Li et al., 1991; Li & Sancar, 1990). The binding of DNA to the enzyme has been studied for native (Sancar et al., 1985) and synthetic (Husain & Sancar, 1987; Husain et al., 1987) systems. It was found that the enzyme binds speci"cally to UV-irradiated DNA in a sequence-independent way regardless of whether the DNA is in the superhelical, open circular, or linear form or whether the DNA is single or double stranded. This latter result strongly suggests that the enzyme predominantly recognizes the dimer rather than any distortion of the helix (Sancar et al., 1985). The rate and e$ciency of single electron transfer from *FADH\ to Pyr12Pyr have been investigated by time-resolved #uorescence, absorbance (Langenbacher et al., 1997; Kim et al., 1994, 1992a, 1991; Okamura et al., 1991), and EPR spectroscopies (Kim et al., 1992c). Although the natural substrate for photolyase is a Pyr12Pyr in a duplex DNA, photolyase also binds, though with smaller a$nity, to dinucleotide dimers and splits them with the same quantum yield as in the oligonucleotide form (i.e. when the dimer is a part of duplex DNA) and with a similar rate (Kim & Sancar, 1991; Langenbacher et al., 1997). The similarity of electron transfer rates and quantum yields for the dinucleotide and oligonucleotide forms of a pyrimidine dimer implies that the dimer has the same position in the enzymes active site in both cases (Kim & Sancar, 1991). This "nding provides the basis for studies of both the binding and the dimer-splitting electron transfer reaction in a model photolyase/substrate system where the substrate is just the dinucleotide Pyr12Pyr dimer. We have recently studied the formation of photolyase/(dinucleotide pyrimidine dimer) complex by using computer simulation program DOCK 4.0, obtained the structure of the dimer bound in the catalytic site of the enzyme, studied molecular dynamics of the system, and calculated electronic coupling between the FADH\ cofactor and the dimer (Antony et al., 2000). The general position of the dimer obtained resembles the one proposed on the basis of the active site

structure by Park et al. (1995), and average electronic coupling is about 6 cm\, which agrees with the experimentally measured rate of electron transfer (Langenbacher et al., 1997). The sensitivity analysis has shown that despite the close proximity of the dimer to FADH\ in the catalytic site, the electron transfer mechanism between the #avin and the pyrimidine bases is not direct, but indirect, with the adenine acting as an intermediate. Such a mode of electron transfer utilizes the unusual conformation of FADH\ in photolyases, which brings the isoalloxazine ring of the #avin and adenine in close proximity (Park et al., 1995; Tamada et al., 1997; Hahn et al., 1998), and the peculiar features of the docked orientation of the dimer in the catalytic site. In this paper, we study the details of electron transfer path between FADH\ catalytic cofactor of photolyase and the thymine dimer T12T for the con"guration obtained in our previous work (Antony et al., 2000), using the method of interatomic tunneling currents (Stuchebrukhov, 1997, 1996a, b). Electronic structure of the complex is treated at the semi-empirical extended HuK ckel level (Yates, 1978). In our other study (Cheung et al., 1999), the same method has been used for the analysis of Trp306 to FADH electron transfer, which is responsible for the reactivation of the enzyme when FADH\ loses an electron crucial for its catalytic activity. The paper is structured as follows. In the next section, the computational methods that were used for the determination of the docked orientation and studying the dynamic behavior of the system are brie#y reviewed. A more detailed account is given in our recent paper (Antony et al., 2000). We then brie#y describe the method of tunneling currents for studying the electron transfer pathways. In Section 3, con"gurations obtained are discussed, donor and acceptor states are identi"ed, and results of calculation of the pathways are presented. The discussion in Section 4 concludes the paper.

2. Methods 2.1. DOCKING

Due to the lack of experimental data on the structure of the photolyase/dimer complex, we

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recently modeled (Antony et al., 2000) the binding geometry of a pyrimidine dimer in the active site of DNA photolyase using molecular simulation program DOCK 4.0 (Kuntz et al., 1994; Kuntz, 1992). DOCK generates many possible orientations and conformations of the ligand within a selected region of the receptor structure. These orientations can be scored using several schemes designed to measure steric and/or chemical complementarity of the receptor-ligand complex. These scores can be used to evaluate likely orientations of a single ligand, or to rank molecules from a database (DOCK, 1997). As a descriptor matching method, DOCK matches the shape of the ligand with that of the receptors binding site. In the simulation the coordinates of chain A in the crystal structure of the enzyme (Park et al., 1995) without crystallographic water and the structure of a thymine dimer detached from a piece of damaged DNA obtained with a molecular dynamics simulation (Miaskiewicz et al., 1996) were used. The docking was performed under the assumption of no deformation of the binding site of the enzyme upon the substrate binding (Park et al., 1995).

calculations were performed for the singlet ground state of both FADH\ and thymine dimer with the restricted Hartree}Fock method using the 6-31G* basis set. The charges were determined by "tting to the electrostatic potential found in the quantum chemical calculations using the program RESP (Bayly et al., 1993; Cornell et al., 1993), which is a part of Amber 5.0, as recommended. The procedure of adding water molecules is described in our previous work (Antony et al., 2000). After water molecules were added, the energy minimization was performed. During it the bonds involving hydrogen atoms were relaxed. The structure obtained as a result of energy minimization was used as the starting point for the equilibration run, which lasted 100 ps. It started with zero kinetic energy and "nished with kinetic energy of atoms corresponding to temperature ¹"300 K. From this stage on, all the bonds in the system were constrained. Following the equilibration procedure, the main molecular dynamics run with constant temperature ¹"300 K, was performed. It lasted 1 ns. 2.3. ELECTRONIC COUPLING AND TUNNELING CURRENTS

2.2. MOLECULAR DYNAMICS

Molecular dynamics simulation was performed using the simulation package Amber 5.0 (Case et al., 1997; Pearlman et al., 1995) and is described in more detail in our previous work (Antony et al., 2000). The initial structure was the one obtained in the docking procedure, and water molecules were added to account for the e!ect of solvent. On all stages of the simulation the movable parts were atoms of the dimer, the FAD, and added water molecules. The protein was substituted by its active site, and its atoms were not allowed to move. For molecular dynamics simulation we used Amber94 force "eld (Cornell et al., 1995). It requires partial charges to be assigned to all atoms of the system to perform the simulation. For atoms of protein and water they were assigned by the program xLEaP (part of Amber 5.0). For the dimer and FAD ab initio quantum chemical calculations were performed, using the Gaussian 94 (Frisch et al., 1995) package. These

The electronic structure of the protein is described by the extended HuK ckel theory (Yates, 1978; Antony et al., 2000; Cheung et al., 1999). The coupling between two electronic states "D2 and "A2 with overlap S is given by the matrix " element (Daizadeh et al., 1997a; Newton, 1991) H !ES " . ¹ " " " 1!S "

(1)

¹ is the half energy splitting between the two " delocalized states "t 2 and "t 2 resulting from > \ diagonalization of H, if the two localized states "D2 and "A2 are in resonance at energy E. When there is no resonance, the states "D2 and "A2 can be approximated by two eigenstates of the entire system. These two eigenstates are identi"ed by projecting all eigenstates of the system onto zeroth-order donor and acceptor states ("d2 and "a2), which are obtained by diagonalization of the isolated donor and acceptor complexes, respectively. The donor and acceptor complexes are

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prede"ned sets of atoms, on which the states "D2 and "A2 are likely to be localized. Usually, the overlap of only one of the eigenstates of the entire system with zeroth-order state "d2 or "a2 is close to unity, while all other eigenstates have nearly zero overlaps. The interaction of the zeroth-order donor and acceptor states with the protein environment results only in a slight delocalization. However, this delocalization causes the e!ective interaction between the donor and acceptor states. Since the e!ective coupling between donor and acceptor states is of the order of 1}30 cm\ and small on the scale of molecular orbital energies (order of an eV), the nuclear con"gurations of the system derived from its crystal structure or from molecular dynamics simulation are unlikely to be in a transition state ful"lling the resonance condition of electron tunneling. In electron transfer reactions, the donor and acceptor states are brought into resonance by motion of the protein coordinates and #uctuations of the solvent (Marcus & Sutin, 1985). Here we model the former e!ect by adding energies to the Hamiltonians of the donor or/and acceptor complexes. The additional energies give rise to a shift of the electronic spectra of the donor and acceptor complexes. In particular, states "D2 and "A2 are moved and eventually brought into resonance. Fluctuations of the solvent can be modeled similarly by application of a homogeneous electric "eld in a direction from the donor to the acceptor site (Katz & Stuchebrukhov, 1998). The electron transfer pathways are calculated by the method of interatomic tunneling currents (Stuchebrukhov, 1997, 1996a, b). The matrix of interatomic tunneling currents is de"ned by 1 J " J " NO NGOH

GZN HZO GZN HZO ;(H !ES )(c" c !c c" ). NGOH NGOH OH NG OH NG

(2)

Here c" and c are the molecular orbital expansion coe$cients of the donor and acceptor states, respectively, E is the tunneling energy, which was taken to be equal to the average of the energies of donor and acceptor states. Indices p and q label di!erent atoms in the complex, while indices

i and j refer to atomic orbitals centered on atoms p and q, respectively. The matrix J is the NGOH representation of the quantum probability #ux associated with the electron tunneling process in an atomic orbital basis. The tunneling matrix element is related to the total tunneling #ux through a dividing surface S by "






¹ "! max J . " NO 1" NZ1" O,1"

(3)

The dividing surface is de"ned in a way that it includes most of electron density in donor state, but excludes most of electron density in acceptor state. Here it is chosen as a sphere around the geometrical center of the donor complex. Similarly, for a dividing surface S around acceptor:  ¹

"






" max J . NO NZ1 O,1 1

(4)

The above formulas provide a method to calculate the electronic coupling strength, which employs only one diagonalization. No precise resonance between "D2 and "A2 is required in this method, it is su$cient to adjust their zerothorder approximations, "d2 and "a2. Importance of individual atoms in the tunneling process (i.e. the atomic level of resolution of the tunneling pathway; Cheung et al., 1999) is evaluated by the total tunneling #ux through an atom, normalized by the total #ux from donor to acceptor described above:

 J O NO , N " N "¹ " "

(5)

where the summation is only over those atoms q for which J '0. The physical meaning of NO N is the average number of times an electron N will pass a given atom p during the tunneling process. This number is not necessarily smaller than one (Stuchebrukhov, 1996a). Since at least one diagonalization is required for the application of the method of tunneling currents, the system, or the important part of it, should be reasonably small. This is usually the case since tunneling currents are concentrated in

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a relatively small region around the straight line connecting donor and acceptor. Those parts of the protein that are not involved in electron transfer process can be eliminated by a sensitivity analysis of the electronic coupling, such as, e.g. our protein pruning method (Cheung et al, 1999).

Results CONFIGURATION OF THE DIMER IN THE CATALYTIC SITE

In the docking procedure, both the energy of the con"guration and the electronic coupling between FADH\ and the dimer have been taken into account to "nd the &&best'' con"guration of the dimer in the catalytic site of the photolyase (Antony et al., 2000). The con"guration with the strongest electronic coupling has the highest probability of transferring an electron. On the other hand, con"gurations with too high energy are thermodynamically unlikely. The search was made over many possible con"gurations generated by the DOCK program. The structure obtained in docking was later re"ned by molecular dynamics simulation. The complex consisting of the whole protein and a thymine dimer contains 7636 atoms with 19 312 valence orbitals. In order to obtain a system that is accessible to direct diagonalization and retain the part that is important for electron transfer, we substitute the protein by its reasonably large part around the active site. The truncation of the protein results in a complex with 44 residues (including donor and acceptor complexes), containing 850 atoms with 2224 valence orbitals. Later, it will be obvious that such a truncation is indeed permissible to study electronic coupling of our interest. The details of the docking procedure and molecular dynamics simulation, as well as a detailed description of the geometry of the con"guration of the dimer in the active site are given elsewhere (Antony et al., 2000). In Fig. 1, the retained amino acids around the active site of the protein, together with the dimer docked to the protein are shown. The found orientation of the thymine dimer resembles the one that could be inferred from the analysis of the shape and polarity distribution of

the active site in the #ipped out conformation of the dimer of Park et al. (1995). It is also very similar to the position of the pyrimidine dimer docked in the modeled active site of Saccharomyces cerevisiae (Berg & Sancar, 1998), if the appropriate translations between the residues of S. cerevisiae and E. coli are made. A noticeable feature of the docked con"guration is that the dimer sits deep inside the catalytic cavity, and the exocyclic amine of the adenine base in FADH and the O4 oxygen atom of the 5 base form a close contact. This contact turns out to be essential for establishing the e!ective coupling between the LUMOs of the dimer and the #avin. 3.2. DONOR AND ACCEPTOR STATES

The catalytic cofactor of photolyase is a #avin adenine dinucleotide (Sancar, 1994) (FAD). It is bound to the enzyme in a U-shaped conformation, opening a hole on the #at surface of the helical domain of the protein (Park et al., 1995). In order to be catalytically active, the cofactor has to be in the reduced form FADH\ and in its excited singlet state (Hartzfeld & Rose, 1993; Kim et al., 1993). The zeroth-order donor state "d2 was determined in separate calculation of electronic structure of FADH\ isolated from the enzyme. The geometry was taken the same as in crystal structure of DNA photolyase from E. coli (Park et al., 1995), with hydrogen atoms added by the InsightII program (Molecular Simulations Inc., 1996b). The highest occupied molecular orbital (HOMO) of the cofactor FADH\ is well above the other "lled orbitals (+1.25 eV) and is well localized on the #avin moiety of the cofactor. It is assumed that in the repair redox reaction, the electron from this orbital will be excited (either directly by light, or by the energy transfer from the second chromophore in the enzyme) to one of the lowest unoccupied orbitals of the #avin. Electron transfers from several such states were tested (Antony et al., 2000). In these calculations the donor state "d2 was represented by the LUMO of the #avin molecule. The main amplitude of LUMO resides on its isoalloxazine ring. Since the #avin is nearly planar, both HOMO and LUMO are n-orbitals. For all the structures derived in

FIG. 1. Truncated part of photolyase with the thymine dimer docked to its catalytic site. In the repair reaction that splits the dimer, an electron from the excited #avin molecule of *FADH\, shown as donor, is transferred to the dimer, shown as acceptor. Electron transfer path is shown in red color with coloring scheme described in the text.

FIG. 3. The FADH/T12T complex in which the electron transfer of the dimer splitting reaction occurs, and the details of the electron transfer path between *FADH\ and the thymine dimer in the structure shown in Fig. 1. Atomic numbers correspond to data shown in Fig. 2. The major transfer #uxes are shown by arrows. The intensity of red color of di!erent atoms corresponds to calculated values of N shown in Fig. 2. The main transfer (tunneling) path is APBPCPD with the N adenine of FADH playing the role of a virtual intermediate in electron transfer reaction.

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the molecular dynamics simulation, the LUMO of the #avin was taken as the donor state. The electron acceptor in the repair reaction is the thymine dimer. The geometry of the dimer was taken from the result of a molecular dynamics simulation on a segment of damaged DN A duplex (Miaskiewicz et al., 1996). As for the donor, the zeroth-order acceptor orbital was calculated for an isolated acceptor complex. The two highest occupied and four lowest unoccupied MOs of the thymine dimer are localized on the thymine bases. The four lowest unoccupied orbitals are grouped in two pairs of closely spaced levels. The doublets are due to mixing of corresponding n-orbitals on the individual thymine rings. The LUMO and LUMO#1 of the dimer are mostly combinations of the orbitals of 5 and 3 thymines. Their ratio is changing in the course of molecular vibrations but is always of order of unity. Surprisingly, we "nd that in the initial structure of the dimer LUMO and LUMO#1 are separated by only 0.03 eV, i.e. they are almost degenerated. In the course of molecular vibrations this degeneracy is lifted, and in the majority

of structures derived from molecular dynamics simulation, energies of LUMO and LUMO#1 of the dimer are separated by values of 0.1 eV or more. Both LUMO and LUMO#1 of the dimer have their main amplitudes at the C2"O2 and C4"O4 carbonyl groups of both rings. A detailed analysis of the electronic states of both FADH\ and the thymine dimer is given elsewhere (Antony et al., 2000). Both LUMO and LUMO # 1 of the dimer were considered as the acceptor states in our calculations. 3.3. TUNNELING CURRENTS AND ELECTRON TRANSFER PATHWAYS

Here we present the analysis of interatomic currents in the structure found in docking. This picture of currents does not change signi"cantly in the structures derived from molecular dynamics simulation, that followed the docking procedure. The distribution of the normalized atomic tunneling currents N is shown in Figs 1 and 2. In N Fig. 2 the numerical data for distribution of

FIG. 2. Normalized total atomic currents calculated according to eqn (5). The atomic numbers on the horizontal axis are identi"ed in Fig. 3.

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N for most important atoms in the complex is N shown, whereas in Fig. 1, the values of N are N coded with various degrees of intensity of the red color. The bright red corresponds to a large value of N . Figure 3 shows the correspondence beN tween the atomic numbers that are used in Fig. 2 and the atoms of the system. All other atoms, that are present in Fig. 1 and are not shown in Fig. 2, have negligible contributions. As clearly seen in Fig. 1, only a few elements in the structure are involved in the electron transfer process. These are the #avin part of FAD, the electron donor, the adenine part of FAD, obviously an intermediate, and the dimer itself, the acceptor of the transferring electron. No side chains of the protein were found to play any signi"cant role in the electronic coupling. As we found previously (Antony et al., 2000), the average electronic coupling between FADH\ and the dimer is about 6 cm\, which is consistent with the measured rate of electron transfer in this system (Langenbacher et al., 1997). On the other hand, the contribution of the side chains of the protein into the coupling is about two orders of magnitude smaller. This contribution was evaluated by calculating the coupling in the system found in docking with the direct interaction between the orbitals of the dimer and those of FADH\ turned o!. Thus, the role of the catalytic site in photolyase seems only to host FADH\ cofactor in a speci"c conformation, and to provide a docking site for the dimer, which perfectly "ts into the hole leading to electron donor FADH\, in a speci"c orientation. The detailed picture of the tunneling currents is shown in Fig. 3. As in Fig. 1, the intensity of red color of individual atoms and their half bonds represents the N values given in Fig. 2. Although N the whole information about the tunneling process is contained in the matrix J , the full graphiNO cal representation of this matrix would be too cumbersome*all pairs of atoms in such a picture would be connected by arrows, representing probability #uxes J in the system as electron NO tunnels from donor to acceptor, with numbers corresponding to numerical values of J atNO tached to each arrow. The direction of the arrows is associated with the sign of J . If J is positive NO NO the current is from q to p, and in the opposite direction if the sign of J is negative. Among all NO

243

interatomic currents we can distinguish, however, the largest ones that show the main pattern of quantum mechanical #ow. The arrows in Fig. 3 indicate the directions of only such major currents. Initially, electron (probability) density is localized on the isoalloxazine ring of the #avin, i.e. the lower right-hand part of Fig. 3, mainly on the carbon atom 764 and on the carbonyl group 742, 743. In the end of the transfer, the electron is localized on the two rings of the thymine dimer, mainly on the carbonyl groups of the bases (atoms 806, 807, 838 and 839). Due to conservation of quantum probability, the decrease of probability on one atom results in the increase of probability on some other neighboring atom, or several such atoms. The main tunneling path in the structure found in docking is shown as APBPCPD. In those structures found in molecular dynamics simulation that have signi"cant (such as 5 cm\ or larger) electronic coupling the main path is largely the same. The most important di!erence is that not only the oxygen 807 of the 5 thymine, but also the oxygen 839 of the 3 thymine, serves as the main acceptor of electrons from the adenine. As seen from Fig. 3, in the structure found in docking the major part of the electron probability density "rst #ows from the #avin molecule through nitrogen atom 763 to carbon 765 and, then, through hydrogen 766, in a through-space tunneling, is transferred to carbon atom 728 of the adenine ring. In structures found in molecular dynamics simulation the current may leave #avin through several di!erent atoms, so that it is delocalized. The pathway running from #avin to adenine via oxygen 774 and hydrogen 775, which is found in the crystallographic structure and shown in Figs 1 and 3, however, is questionable. This hydrogen, which is not seen in the crystal structure analysis, may be involved in a hydrogen bond with the nitrogen 737 on the #avin (Park et al., 1995), and if this is correct, then the pathway going through this hydrogen to the adenine may be turned o!. In our molecular dynamics simulations we did not "nd this hydrogen bond, but this, however, does not allow us to make the conclusion that it does not exist. Since the bond lengths were constrained during the simulation, the hydrogen bond formation may have been

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hindered. But, in the structures, obtained in the molecular dynamics simulation, the current going from #avin to adenine is strongly delocalized, this possible hydrogen bond does not change the overall pattern of tunneling currents. Once the #ow has reached the adenine ring it equilibrates there, and there are circular currents in the aromatic rings of the adenine. From the adenine of FADH, through nitrogen 729 and its hydrogens, the major tunneling #ow is directed to carbonyl oxygens of the bases of the thymine dimer. There is also weak direct coupling between the #avin and the adenine, and part of electron density may also go directly from donor to acceptor, by-passing the adenine intermediate. The intensity of currents in these direct pathways is usually several times smaller than that in the major path, though. These direct paths include through-space jumps from the C8m methyl group (carbon 756) of the #avin to the methyl group (carbon 834) on the 3 thymine, from the carbon 760 on the #avin and its hydrogen to the carbonyl group (atoms 838 and 839) on the 3 thymine, and from the carbon 765 and its hydrogens to the same carbonyl group. The relative magnitudes of the direct coupling and the indirect one are determined by the geometry of the complex. In the docking simulation (Antony et al., 2000) we "nd that the dimer simply cannot get too close to the #avin, due to geometrical constraints of the docking site, while in the course of molecular dynamics the dimer is on average slightly farther from the #avin than in the structure found in docking (Antony et al., 2000). Therefore, indirect coupling dominates. Interestingly, the small direct coupling between the donor and the acceptor may destructively interfere with the major coupling path through N729 of the adenine and the carbonyl groups of thymines. Such a destructive quantum interference between tunneling paths is not uncommon in donor}acceptor interactions of large systems (see, e.g. Stuchebrukhov, 1996a). In the language of tunneling #uxes, the destructive interference is re#ected in opposite signs (i.e. the directions) of the currents of the two interfering paths. In our case, the small direct current may have the opposite direction to the main current from adenine nitrogen 729 to oxygen thymines.

Since the electron probability density of the transferring electron is strongly delocalized between two thymine bases in the "nal (acceptor) state, there are strong currents within the acceptor complex that describe, obviously, the redistribution of electron density once it enters the dimer. Since the coupling between the bases is much stronger than that between the dimer and the adenine, the relatively small #ux entering the dimer is followed by much stronger circular currents between the rings. This is re#ected in the strong picks of atomic currents in Fig. 2 corresponding primarily to carbonyl atoms of two bases of the dimer. Finally, using expressions (3) and (4) relating the total tunneling current to the transfer matrix element, the overall electronic coupling between FADH\ and the dimer was evaluated. Results of such calculations are shown in Fig. 4. The resulting coupling in the structure found in docking is about 10 cm\, while in the structures found in molecular dynamics simulations the average electronic coupling is about 6 cm\, which is consistent with experimentally determined rate of electron transfer, k"(100 ps)\ (Langenbacher et al., 1997; Antony et al., 2000). The tunneling matrix element #uctuates strongly in the course of dynamics of the system, with amplitude of #uctuations in the range of 30 cm\, and its variance is of the order of the root mean square matrix element itself (Antony et al., 2000). 4. Summary and Conclusions Electron transfer from an excited FADH\ to T12T dimer in a damaged DNA is the key step in the DNA repair mechanism by photolyase. To obtain insights about the functional mechanism of this enzyme, a model system*photolyase plus a dinucleotide T12T dimer*has been analysed in this and in the previous paper (Antony et al., 2000). The work was motivated by recent experimental studies of the same system, see e.g. (Langenbacher et al., 1997). Two questions of crucial importance have been addressed: "rst, what is the orientation of the dimer in the catalytic site of photolyase, and second, what is the mechanism of electron transfer. Using the molecular simulation program DOCK 4.0 (Kuntz et al., 1994; Kuntz, 1992)

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245

FIG. 4. Saturation of the total tunneling #ux through a dividing surface between donor and acceptor. The maximum of absolute value of the tunneling #ux in this "gure, according to eqns. (3) and (4), gives the value of the transfer matrix element ) donor; ( ) acceptor. ¹ . Calculations are shown for both donor and acceptor complexes. ( "

and molecular dynamics simulation, we explored di!erent con"gurations of a T12T dimer within the active site of the photolyase molecule from E. coli (Park et al., 1995). For various positions of the T12T dimer within the catalytic site, we calculated the electronic coupling matrix element between the catalytic cofactor FADH\ and the dimer, and examined electron transfer pathways with the method of tunneling currents (Stuchebrukhov, 1997, 1996a, b). The electronic structure of the system was treated within the extended HuK ckel approximation. The con"guration with the strongest coupling has a transfer matrix element of about 10 cm\. This structure was used as a starting point for a molecular dynamics simulation, which allowed us to re"ne the position of the dimer in the catalytic site. The average value of the transfer matrix element along the dynamics trajectory is about 6 cm\, which is consistent with the experimentally determined rate of transfer. In the average con"guration the docked thymine dimer is sitting deep in the catalytic site, with the distance between the #avin and the base pair less

than 3 As , the closest contact being established by the hydrogens that belong to the C9m methyl group of the #avin (carbon 756) and the methyl group of the 3 thymine (carbon 834), Fig. 3. This con"guration of the dimer in the catalytic site resembles the one that could be inferred from the analysis of Park et al. (1995). We "nd that the side chains of photolyase practically do not contribute into electronic coupling. This situation is opposite to that in electron transfer processes in redox membrane enzymes, where electrons tunnels larger distances of the order 15}20 As through the protein medium intervening between donor and acceptor, and the protein structural elements are necessary for electronic coupling (Moser et al., 1992; Scott, 1997). Here the dimer can approach the catalytic cofactor FADH\ directly. The role of the enzyme in this case seems to be only to host the reduced FAD in a speci"c folded con"guration, and to provide a docking site for the dimer (a hole leading to FADH\), into which the latter "ts perfectly, also in a speci"c orientation, with carbonyl oxygens of the dimer, that needs to be reduced

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for the splitting, directed towards the reducing element. Despite the close distance between the dimer and FADH\ in the catalytic site, we "nd that the electron transfer is not direct, but indirect, with the adenine moiety of FADH playing the role of a virtual intermediate. It is assumed that initially electron is localized on the #avin part of FADH. Such a mode of electron transfer is a direct consequence of the speci"c folded state of FADH\ and the peculiar relative orientation of the dimer in the catalytic site. Tunneling currents, described in this paper, provide the details of the pathway, Fig. 3. In a recent experimental study (Langenbacher et al., 1997) the rate of electron transfer for di!erent pyrimidine dimers T12T, T12U, U12T, and U12U has been measured. It was found that the rate depends upon the nature of the pyrimidine dimer. It is 10 s\ at 275 K for the case of a thymine}thymine dimer, and 3 times faster for a uracil}uracil dimer. The mixed dimer T12U acts like the symmetric thymine dimer, the U12T like the symmetric uracil dimer (Langenbacher et al., 1997). The experimentally observed threefold increase of the rate when the 5 methyl group is substituted by hydrogen corresponds to a factor 1.7 variation in the coupling strength. In our study the average matrix element was approximately the same for all four dimers. Since the variance of matrix element along the dynamics trajectory is of the order of the matrix element itself, and geometrical changes as small as 0.5 As lead, typically, to a pronounced change in the value of matrix element, it is di$cult to reproduce such a small change in the rate of reaction, given the accuracy of the extended HuK ckel description of the electronic structure and molecular dynamics simulations used in our model. To obtain a complete picture, perhaps more accurate electronic structure calculations would be required. We should, of course, emphasize that the accuracy of the extended HuK ckel method employed here for calculation of the electronic coupling is very di$cult to assess. It is empirically known that the method sometimes &&works'' and sometimes does not. The reason that it is still in use is that more accurate methods of calculation, that are currently being developed, (see e.g. Kim

& Stuchebrukhov, 2000; Stuchebrukhov, 2001), are yet di$cult to apply to extended systems, such as we are dealing with here. Our previous tests showed that for small organic redox systems, which do not contain transition metal ions, the extended HuK ckel method can give results within a factor of 2-4 to ab initio calculations. It is clear, however, that the results for such a subtle characteristics as the tunneling matrix element should be veri"ed, if possible, when the new ab initio techniques become available. Finally, the found electronic coupling of the order of 10 cm\ between FAD and the thymine dimer indicates that the latter should be located pretty closely to FAD in a docked con"guration, to ensure the high rate of electron transfer observed in the experiments. To achieve such a conformation in the DNA/photolyase complex, the dimer should be #ipped out from the double helix of DNA. We believe such deformation occurs upon photolyase binding. However, the detailed mechanism of how such a con"guration can be induced in the binding process is unknown at present (Antony et al., 2000). Our work in computational molecular biology is a result of stimulating cross-disciplinary environment created at the UC Davis Institute of Theoretical Dynamics by Joel Keizer. His own success and enthusiasm were inspiration for us, Physicists and Chemists, to undertake an adventure into new areas, and to discover an amazing world of Biology. We are forever indebted to Joel for this intellectual gift. We would like to thank Dr Jens Antony for stimulating discussions of the material of the paper, and for his help with computer calculations. We would also like to acknowledge Dr Jianxin Guo for his help with molecular dynamics simulations. This work was supported by the research grant from the National Institutes of Health (GM54052-02) and by the fellowships from the Sloan and Beckman Foundations. Computer support of JPL/Caltech Supercomputing Center is gratefully acknowledged.

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DNA REPAIR

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