Shaila C. Rossle¹, Irmgard Frank²

1 Department of Chemistry and Biochemistry, Center for Nanoscience and Nanosystems Initiative Munich, Ludwig-Maximilians-University Munich, Butenandtstr. 11, 81377 Munich, ² Institut für Physikalische Chemie und Elektrochemie, Callinstr. 3A, 30167 Hannover

TABLE OF CONTENTS

1. Abstract

2. Introduction

3. Density functional theory for excited states

4. Applications

4.1. Photoactive yellow protein

4.2. Green fluorescent protein

4.3. Rhodopsin

4.4. Bacteriorhodopsin

5. Perspectives

6. Acknowledgements

7. References

1. ABSTRACT

First-principles simulations start to be applicable to the photochemistry and photophysics in biological systems. In this review the prerequisites for investigating such excited state phenomena in large systems are outlined. Generally, a quantum mechanical description of the electronic structure is combined with molecular dynamics simulations, which allows to describe the motion of the atoms in the field produced by the quantum-mechanical potential. Like this, bonds can be formed and broken, that is, chemical reactions can be simulated. The review focuses on applications of first-principles molecular dynamics to photoactive proteins.

2. INTRODUCTION

The enormous advances in the field of computational chemistry, allied to the advent of high speed and parallel computing technologies, have encouraged the development and application of computational simulations for the comprehension of structure, dynamics and chemical reactions of complex molecular systems. Most of these studies are based on molecular dynamics simulations where the systems are described by classical, quantum mechanics or a combined approach, depending on the phenomena investigated.

The theoretical approach most broadly applied to biological systems is classical molecular dynamics. This method allows the investigation of structure, dynamics and thermodynamics of inorganic, organic, and biological systems, including proteins, membranes and nucleic acids. It solves the classical Newtonian equations of motion, whereby the forces are calculated from an empirical force field. Molecules are described as atoms being connected by 'springs' that oscillate at finite temperature, typically 300 K. Since many biological systems are composed of but a few different moieties, in particular of amino acids and nucleic acids, this approach is most successful in the application to biosystems, where very good parametrizations exist. The approximations which render the method so extremely efficient, result however in an insufficient description of systems where charge transfer, electronic excitation, bond-breaking or bond-formation take place. For describing such phenomena where details of the electronic structure are essential, it is necessary to include quantum mechanical (QM) calculations in the simulation schemes. Therefore the introduction of density functional theory (DFT) based simulations in biology was motivated by the need of a first-principles description for the interatomic interactions whenever a classical force-field description is not sufficient. An advantage of the first-principles molecular dynamics approach is the fact that it does not make use of atom-type dependent parameters. That is, there is only one type of carbon atoms instead of sp² carbons and sp³ carbons etc. The atoms may change their connectivity and hybridization at any time. This fact in combination with the use of quantum mechanically computed potentials renders the study of quantum phenomena such as bond formation and bond breaking processes possible.

In a first-principles MD simulation, which is capable of combining dynamics and quantum mechanics, the forces acting on the nuclei are iteratively obtained from an electronic structure calculation in every time step, corresponding to an "on the fly" treatment. Pioneering work in this field was done by Car and Parrinello in 1985 (1,2,3). Car-Parrinello molecular dynamics (CPMD) has seen widespread use in materials science, chemistry, and condensed matter physics, but also offers an ideal method which combines the accuracy of DFT and the power of MD necessary for biological systems which are intrinsically dynamical (4). The basic concept is simple: instead of trying to compute the potential energy surface of the system in as many dimensions as possible and performing dynamics on this surface in a second step, the on-the-fly methods consider only those points that are reached during a molecular dynamics run. Only for these structures, the energy and the energy gradient are determined by a quantum-chemical method during the simulation. It is apparent that this approach has the advantage to allow very complex systems to be treated without prior knowledge of the possible reaction pathways. A disadvantage is that relatively high demands have to be made concerning the quantum-chemical method used. The development of modern density functionals (5) represented an important step in the development of practical on-the-fly schemes. The most successful on-the-fly concept is still the one originally developed by Car and Parrinello (see for example (3)):

Description of the valence electrons by density functional theory (6, 7) using a plane-wave basis set and periodic boundary conditions;

Description of the inner electrons by previously computed, fixed pseudopotentials;

Simultaneous motion of electrons and nuclei according to the Car-Parrinello equations (1).

Density functional theory in such simulations - like in most practical calculations - is always used within the Kohn-Sham formalism and may hence also - more accurately - be called Kohn-Sham theory. The Kohn-Sham formalism involves the decomposition of the total density into molecular orbitals (approximate single electron functions). This decomposition leads to approximate functionals but also to a very simple and illustrative picture of the electronic structure in terms of orbitals.

A serious limitation of first-principles MD techniques is the CPU cost which essentially limits the size of tractable systems to some hundred atoms. An extension of the method to a mixed quantum-classical (QM/MM) hybrid scheme is particularly attractive for the investigation of biochemical reactions. QM/MM methods divide the system into a chemically active part, treated by first-principles QM methods, whereas the effect of the protein environment is modeled by a classical force field (8-10). Such an approach has the advantage that the computational effort can be focused on the part of the system where it is most needed, whereas the effects of the surroundings are taken into account with a more expedient model. In this way, large biomolecular systems can be treated in a computationally efficient manner. In addition, long range effects which are important for a proper modeling of protein structures, are better described by a classical parametrization than by present-day density functionals. Several mixed QM/MM Car-Parrinello approaches have been implemented (11,12), in which the steric and electrostatic effects of the surroundings are explicitly taken into account. For recent reviews of applications of QM/MM simulations using the Car-Parrinello scheme, see (4, 13,14).

Very attractive applications of first principles molecular dynamics get into reach by extending the scheme to the treatment of electronically excited states. Particularly the description of photochemical reactions which occur upon electronic excitation by photon absorption, is very appealing because there the full power of the approach can be exploited. Photoreactions usually occur on the timescales that are accessible to free (unconstrained) first principles molecular dynamics simulations. The complex dynamics of photoreactions is an actual field of intense experimental studies (15-20).

For the theoretical investigation of the electronically excited states of molecular systems a large variety of quantum chemical approaches is available. These methods comprise ab initio methods such as configuration interaction singles (CIS) (21,22), complete active space self-consistent field theory (CASSCF) (23,24), complete active space perturbation theory in second order (CASPT2) (25-27), and multi-reference configuration interaction (MRD-CI) (28,29), as well as density functional theory (DFT) approaches such as time-dependent density functional theory (TDDFT) (30-33). For a recent overview of the quantum chemical methods which are most frequently used for the investigation of excited states in biological systems see (34). Most of these methods, however, are not suitable for on-the-fly simulations. This is due to the fact that they are either not fast enough or cannot be used as black-box methods for the automated calculation of thousands of points on a potential energy surface during a simulation. In addition, particularly for the more accurate methods like multi-reference configuration interaction, it is very difficult to obtain analytic energy gradients to compute the forces on the nuclei. Furthermore the quantum chemical approach should be applicable with moderate effort in connection with plane wave basis sets. This latter requirement excludes all methods except DFT methods. The use of delocalized plane waves which have no origin in space, is advantageous for the computation of energies and forces during dynamics simulations. In addition, plane wave basis sets allow the treatment of individual molecules and condensed phases such as solids, surfaces, and solutions, on an equal footing.

To the aim of treating photoreactions restricted open-shell Kohn-Sham (ROKS) was developed in 1998 (35,36). Later the TDDFT gradients were programmed and it became possible to do geometry optimizations and molecular dynamics with this method (37,38). TDDFT is the superior method for describing electronic spectra. However, severe problems occur when moving on excited-state potential energy surfaces, which renders ROKS the better alternative for simulating photoreactions.

In the next section, we briefly introduce the most important concepts of excited state DFT methods and describe the advancements that are relevant for the application of the methodologies to photo-biological processes. Thereafter, we report a few applications and illustrate what can be achieved with first principles molecular dynamics simulations.

3. DENSITY FUNCTIONAL THEORY FOR EXCITED STATES

According to Kohn and Sham (7) the exact ground state density, and with it all observable quantities, of the many-body problem can be obtained in principle from a single set of molecular orbitals. In the simplest case of non-degenerate orbitals and an even number of electrons, this means that each orbital is filled with one electron with alpha spin and one electron with beta spin. To satisfy the Pauli principle, these orbitals are not just multiplied to yield the total wavefunction, but are composed to an antisymmetric Slater determinant. In practical applications, always approximate solutions are obtained due to the fact that the exact density functional is unknown.

If one wants to extend the theory to the simulation of photoreactions, the question arises: What are excited states? And: Which excited states are relevant for the description of photoreactions? The first question is not as trivial as it might seem and different communities tend to answer this question in a different way. Particularly in molecular physics the description of the electronically excited states via a perturbation from the ground state is very common. In quantum chemistry, methods starting from a reoccupation of orbitals have been more broadly used for many years. For vertical excitations this usually leads to equivalent results, meaning that the results from the different approaches can directly be compared. In both descriptions the excited states are orthogonal to the corresponding ground state. Let us, however, consider the situation of two states adopting the same energy which usually occurs during a photoreaction. Now it is a matter of definition what is the ground state and how the excited states are numbered. One might speak of a degenerate ground state at this point and renumber the excited states. In a simulation of a photoreaction, however, one has to decide how to handle this situation in an automated way. Present implementations of perturbation theory based methods tend to fail in such situations.

A second problem arises at this point, namely the way how the electronic and nuclear degrees of freedom are separated. The approximation usually employed in molecular calculations is the adiabatic approximation in which the nuclei are fixed in space and the electrons are fully relaxed. This approximation which is based on the paper of Born and Oppenheimer (39) leads to the picture of Born-Oppenheimer potential energy surfaces (Figure 1). In this adiabatic approximation (a-diabatic: 'non-intersecting'), electronic states 'hardly ever cross' (more precisely: states of different spin symmetry or different spatial symmetry do not cross). In the early days of quantum chemistry, this led to the discussion, how molecular systems may return to the ground state as efficiently as it is observed in photoreactions. In the past decades it has been noted on the basis of ab-initio calculations that also in the adiabatic approximation there are so-called conical intersections (40) between ground and excited states present in most molecular systems (41). These conical intersections have been discussed as the points through which the systems proceed during photoreactions on their way back to the ground state. Today it is commonly known that the conical intersections are in general multidimensional objects (conical seams, conical intersection spaces).

An alternative description represents the diabatic approximation for which no unique definition exists. The simplest way to arrive at diabatic surfaces is by making an additional approximation, namely the single-configuration approximation. This approximation forces a system to remain in a certain electronic configuration (for example in a ionic configuration), while during the motion on an adiabatic surface the character of a state may change (for example from ionic to radicalic). In the diabatic approximation crossings between states of the same symmetry are no longer forbidden and a one-dimensional conical intersection is replaced by a two-dimensional crossing.

A complete solution of the problem is possible by using adiabatic approximations (i.e. not diabatic approximations (42)) and computing the non-adiabatic coupling elements. Such powerful calculations which yield the complete picture, are possible for small molecules (see for example 43,44). For larger systems simplifications are desirable.

We consider the simplest situation of a molecular system that has all electrons paired in energetically non-degenerate molecular orbitals in its ground state and has singlet spin symmetry (S₀). If it is irradiated with light, it is transfered to some energetically higher-lying singlet state, depending on the energy of the absorbed photon. The transition to triplet states is symmetry forbidden since the photon does not transfer spin. According to Kasha's rule (45), deactivation to the lowest excited singlet state (S₁) is very fast, so that usually no photochemistry takes place in the higher-lying excited states.

The S₁ state may be long-lived enough for photoreactions to occur - if there is no close-lying conical intersection through which the system is rapidly transfered back to its ground state. Also, there is a finite probability for conversion to the close-lying triplet state T_{1 (}intersystem crossing). Since the transition from the triplet state back to the singlet ground state is forbidden, T₁ is usually long-lived and photoreactions may occur in this state. So the states that are most relevant for describing photoreactions in organic and biological systems are S₁ and T₁.

Which quantum chemical methods may be used to describe these states? As mentioned before, one possibility is to obtain an electronic spectrum as response to a perturbation of the ground state. This concept is most successfully realized with TDDFT in the approximation developed by Casida (32), which has become the standard method to compute spectra of medium-sized to large molecules. Electronic spectra are usually reliably obtained with TDDFT with shortcomings particularly in the description of charge transfer states. Generally, for excited states, one cannot expect the same accuracy as for ground states and comparison to other theoretical and/or experimental results is necessary. Nevertheless, in combination with modern density functionals like B3LYP, a remarkably high accuracy is reached with TDDFT. When dealing with photoreactions, the question arises if TDDFT should be considered as a diabatic or adiabatic approach and how conical intersections should be treated. In a recent publication the TDDFT surfaces were compared to adiabatic surfaces (33).

The second approach mentioned above is used by the restricted open-shell methods, restricted open-shell Hartree-Fock (ROHF) and restricted open-shell Kohn-Sham (ROKS). Here, excited states are constructed by reoccupying orbitals. This allows to propagate the system in the excited state without keeping the knowledge of the corresponding ground state. In the example of a ground-state singlet with all orbitals doubly occupied, the excited state S₁ is generated by removing one electron from the highest occupied molecular orbital (HOMO) and putting it in the lowest unoccupied molecular orbital (LUMO). To describe the spin symmetry correctly, such a situation must in general be described not only by a single Slater determinant but by a linear combination of Slater determinants, namely a spin-adapted configuration. Due to the single-configuration approximation, the restricted open-shell methods are diabatic. With such a restricted open-shell approach, only the few lowest open-shell states can be described, typically S₁ and T₁. To obtain more states of the spectrum, the concept can be extended in the case of Hartree-Fock theory to a linear combination of many configurations, leading to the adiabatic multi-configuration self-consistent field (MCSCF) theories like CASSCF. At present, such an extension is not possible in Kohn-Sham theory in a satisfying way. However, Kohn-Sham theory offers the advantage of having electron correlation included already in a single configuration description. The different treatments of electron correlation in CASSCF and ROKS lead to different restrictions. In CASSCF the correlation caused by the few orbitals in the active space ('static correlation') is very well considered, while the contributions of all the other virtual orbitals ('dynamic correlation') is completely neglected. This may lead to an unbalanced treatment of correlation unless a large part of the electronic system is included in the active space. Hence CASSCF calculations can be done in a very accurate way for small molecules, but for larger systems a reasonable choice of the active space becomes difficult. In ROKS the correlation of all orbitals is considered in an averaged way through the exchange-correlation term of Kohn-Sham theory. This may lead to qualitatively wrong results if static correlation is of high relevance for the description of S₁. In practical applications it turned out, however, that a precise description of static correlation is not critical for surprisingly many cases (46,47), quite in contrast to what has been concluded from Hartree-Fock based calculations. Empirically, the "Kohn-Sham hope" that a simpler description of the many-body problem is possible on the basis of a single set of orbitals with integer (or rational) occupation numbers holds for low-lying excited states, too. However, a red-shift of typically 0.5-0.7 eV of the ROKS results was observed which is due to an insufficient description of the exchange interaction in connection with the functionals employed (GGA functionals). This usually does not influence the motion on the excited state potential energy surface, but prevents the determination of absolute excitation energies.

One of the nice features of ROKS is the possibility of a simple return to an open-shell ground state (Figure 1): If there is a crossing to an open-shell ground state, the simulation will continue diabatically from the excited to the ground state. This turned out to be a good approximation already in medium-size systems (47). In larger systems the kinetic energy is even easier distributed among the vibrational degrees of freedom and the behaviour is even more diabatically. Note that, when passing such a crossing, the ROKS singlet state becomes the ground state while the restricted closed shell state becomes the excited state. In other words, if talking about restricted and restricted open-shell methods, instead of discriminating between ground and excited states, one might just as well discriminate between restricted closed-shell states, restricted open-shell states, and 'real' excited states (the latter being not easily accessible to a single-configuration method). In this framework, Kasha's rule reads: Photoreactions hardly ever take place in real excited states.

As discussed before, the description of the nuclear dynamics is approximated by the classical equations of motion. Thus quantum effects on nuclear motion are ignored (but could also be described in a CPMD manner (48)). Particularly for photoreactions which usually involve high kinetic energies and negligible barriers, these effects are not relevant. Classical Newton dynamics is simple, but affords the knowledge of the energy gradients. The computation of the gradients for ROKS is straightforward using the Hellmann-Feynman theorem as it is usually done in CPMD calculations; TDDFT gradients have been implemented in several program packages some years ago (37, 38). As is shown in the Applications section, many studies still do not attempt to compute excited-state gradients and excited-state structures, but use ground state structures as obtained for example from DFT-QM/MM calculations. This is significantly simpler to do than QM/MM calculations in the excited states, but gives an information only about the first instances after excitation, i. e. before significant relaxation can take place in the excited state. In a real excited-state dynamics not only the initial relaxation of the system but eventually also photoreactions can be observed. As ultrafast photoreactions typically occur far from equilibrium at high kinetic energies, dynamical effects are most relevant and unconstrained excited-state molecular dynamics represents an irreplacable tool for the description of such phenomena. It will be seen in the next section, however, that it is not an easy task to simulate spontaneous photoreactions in biological systems due to limitations in accuracy and in CPU time, and but a few successful cases are reported in the literature.

4. APPLICATIONS

Several applications of first principles molecular dynamics in a variety of systems of chemical importance and under a broad range of thermodynamic conditions were reviewed quite recently in (49). The comprehensive review illustrates the broad applicability of first-principles molecular dynamics calculations in the study of structures, reaction mechanisms, and electronic properties for both isolated molecules and condensed phases.

Examples for biological systems are reviewed in (4,14). Most studies of such large systems use the QM/MM implementations in CPMD (11,12). These applications include for example the investigation of the catalytic mechanisms and structural features of a variety of enzymes (50-59) and the selectivity mechanism of ion channels (60). Also interactions between a ligand and its target in a cis-platin-DNA adduct (61), and DNA-binding organo-ruthenium compounds (62) were investigated, as well as the DNA damage caused by radicals (63).

In the present review we concentrate on the application of first-principles molecular dynamics to photoreactions in biological systems. Photoactive proteins fulfill important biological functions. They represent a specific class of proteins which give to different organisms the capability to absorb and convert light. Small organic molecules, known as chromophores, are bound to these proteins to do the first task in the light transduction pathway. Upon absorption of a photon, these chromophores may undergo photochemical reactions which alter their conformation or chemical composition.

Here, we present a short overview of recent applications of DFT-QM/MM approaches to the most important photoactive proteins with chromophores absorbing in the visible region, namely photoactive yellow protein, green fluorescent protein, rhodopsin, and bacteriorhodopsin. In all these systems the chromophores contain extended PI systems with double bonds which eventually rotate in the excited state from their cis to their trans forms or vice versa (photoisomerization). To understand the specific behavior of these photoactive proteins, it is necessary to understand the photoisomerizations in the particular PI systems and how they are influenced by the particular protein environments. We report the present state of first-principles simulations on these systems which will show that there are still quite a few open questions. Particularly it turns out that observing a spontaneous (photo)reaction in a biological system and thus determining every detail - the mechanism, the reaction time, etc. - still remains a formidable task for modern quantum chemical simulations.

4.1. Photoactive yellow protein

Photoactive yellow protein (PYP) is a small and structurally well characterized protein (Figure 2A), which has a relatively simple light-initiated photocycle with features in common with the visual pigments and other photoactive proteins. For this reason, PYP has extensively been studied, using numerous experimental techniques (64-72). PYP is a water-soluble photoreceptor protein, first isolated from Ectothiorhodospira halophila (64,65). The protein is believed to serve as the photosensor initiating the negative phototactic response to blue light (66). It contains the chromophore para-coumaric acid which gives the protein its characteristic yellow color. This chromophore is bound via a thiol ester linkage to the only cysteine residue in the protein (67,68). Upon excitation, it undergoes an isomerization reaction from its trans to its cis form (Figure 2B, 2C), leading to a photocycle consisting of several transient intermediates, and recovers the initial state on a subsecond time scale (69). It is sometimes claimed that PYP has properties which make it a candidate for application in photobioelectronics and as a consequence is a potential biomaterial for the next generation of electronic devices.

Several computational studies describe the isomerization of the chromophore (73-79). The isomerization of the isolated chromophore as well as the isomerization of the chromophore in its binding pocket have been studied using static DFT calculations (73). For the isolated chromophore, the computations show that the trans configuration is lowest in energy, both for the neutral and for the deprotonated system. The negative charge is found to induce modifications in the structure of the molecule and, specifically, a significant elongation of the isomerizable double bond. Such an elongation of a chemical bond usually correlates to a lowering of the rotational barrier which was also found for the PYP ground state. It was also confirmed that the protein environment induces an out-of-plane torsion in the ground state trans pCA chromophore. By means of TDDFT calculations, the electronic excitation relevant for the photochemistry of PYP was determined to be dominated by the HOMO-LUMO transition. Computation of the excited-state potential energy curves using ground state structures with TDDFT (76) yielded a small barrier in the excited state of a few kcal/mol. Note however, that for a more precise determination the structures would have to be relaxed in the excited state. This latter paper is also an example how difficult it can be to make clear statements about protonation states of biological moieties on the basis of DFT calculations which may render an assignment to the spectroscopically observed intermediates difficult.

The protonation of pCA after excitation and isomerization of this chromophore was studied using classical molecular dynamics and DFT-QM/MM (79). It was shown that the stabilization of the charge is a very important factor, indicating that the direct environment of the chromophore is highly important for this reaction. In pure DFT simulations of the chromophore binding pocket in vacuum, very frequent proton transfer was observed in contrast to the QM/MM simulations. This difference was attributed to rearrangements in the environment after isomerization which could not be modelled on the timescale accessible to QM/MM simulations.

Even if we want to restrict our review to DFT calculations, a CASSCF-QM/MM study must be mentioned at this point (78). To our knowledge this remarkable study represents the first simulation of a spontaneous isomerization of PYP. A rather small CASSCF space was chosen (6 electrons in 6 orbitals, 3-21G basis set) which however seems to be sufficient to get the essential features of the photoreaction (reaction time, quantum yield) with very good accuracy. Switching to the ground state was allowed if a conical intersection was reached, thus conserving the total energy during the dynamics. The change of the internal degrees of freedom, that is, the full motion of the chromophore as it occurs spontaneously upon excitation, was monitored at this high theoretical level. The simulations show how the isomerizing double bond is rotated from 180 degrees (trans form) to about 90 degrees in the excited state and continues the rotation to a value of about 0 degrees (cis form) after return to the ground state.

4.2. Green fluorescent protein

Green fluorescent protein (GFP), an intrinsically fluorescent protein (IFP) isolated from coelenterates, such as the Pacific jellyfish Aequorea Victoria (80), is one of the most widely studied and exploited proteins in biochemistry and cell biology. It is used as a marker of gene expression and protein targeting in intact cells and organisms (81-83). Efforts to improve and vary the properties of GFP were made for its application as a pH sensor or in microscopy with the generation of GFP mutants. Many different mutants of GFP were engineered with new spectroscopic properties by mutating amino acids in either the chromophore or in the surrounding part of the protein (84-86).

The cylindrical beta-barrel structure (Figure 3A) formed by 11 beta-strands constitutes a perfect cylinder structure containing in its center the fluorescent chromophore p-hydroxybenzylidene-imidazolinone. This fluorophore is derived from post-translational cyclization of a serine-tyrosine-glycine tripeptide, followed by dehydrogenation of the tyrosine (Figure 3B). The chromophore shows two thermodynamically stable protonation states, corresponding to two absorption peaks of the protein spectrum. The wild-type exhibits two absorption maxima at 395 and 475 nm which relax to an emission maximum around 508 nm, emitting a greenish yellow light. The 395 nm peak is associated with the protonated (neutral or A) form, whereas the 475 nm peak is associated with the deprotonated (anionic or B) form. The equilibrium between the two states can be controlled by external factors such as pH and mutations which affect the chromophore environment (84,87).

TDDFT calculations of neutral and anionic chromophore structures determined from ground state QM/MM calculations have been performed and good agreement with experiment was found (88). Another study presents DFT calculations (using TDDFT for the description of the excited states) of the structural and electronic properties of the chromophore in presence of close residues (89). A relationship between optical and structural properties of the chromophore was found. The same approach was also extended to the whole series of the IFP chromophores (90). TDDFT proves to be appropriate to accurately analyze the absorption properties of a large family of molecules.

The excited-state dynamics of a fluorescing protein cannot be expected to be very exciting, as fluorescence usually means that there is no major excited-state motion in the system. Otherwise in most systems a conical intersections would be reached which would allow a radiation-less return to the ground state. More interesting than GFP for performing excited-state MD simulations is asFP595. This protein can repeatedly be switched from a non-fluorescent state to a fluorescent one. The chromophore in the protein environment and its isomerized state were investigated using QM/MM and TDDFT (91). The authors discuss the difficulty of assigning the protonation states for different intermediates, a problem which is ubiquitous in DFT-QM/MM. The shallow potentials of hydrogen bonds in biological systems and the delicate equilibria are difficult to describe in an accurate way with present-day density functionals. Further method development is needed.

4.3. Rhodopsin

Rhodopsin is a highly specialized G protein-coupled receptor (GPCR) which detects photons in the rod photoreceptor cell. Studies on rhodopsin have unveiled many structural and functional features that are common to the large and pharmacologically important group of the GPCR superfamily, of which rhodopsin is the best-studied member (92,93). Rhodopsin is composed of the protein opsin linked to 11-cis retinal, a polyene chromophore bound through a protonated Schiff base linkage to Lys-296 (92) (Figure 4). Rhodopsin is involved in the transduction of light into visual signals, i.e. nerve impulses, in the visual system of the central nervous system (94).

The first step of vision consists in absorption of a photon by the rhodopsin chromophore which causes its isomerization to the all-trans form in an extremely fast and efficient process (Figure 4B). This photoisomerization initiates a photocycle during which a series of interconversions between different conformational states happens. These structural changes are driven by the release of the photon energy which is in part stored in the system as chemical energy (95-99). Many experimental and theoretical studies have been devoted to the understanding of the underlying mechanism which is of fundamental importance for the process of human vision (100-112).

The isolated chromophore and the chromophore plus counterion were investigated using static ROKS calculations in (102), showing the strong dependence of the reaction on the environment. While for the isolated molecule a significant barrier was observed, the presence of the counterion reduces this barrier significantly. This is in agreement with the observation that in solution the isomerization is slower and less specific, meaning that also other double bonds rotate. In a subsequent study (111), the combination of the QM/MM approach with the ROKS method was used for describing the dynamics in the first excited-singlet state of rhodopsin. Such a QM/MM study became possible after the first X-ray structure of rhodopsin was published (104). A model system (106) consisting of rhodopsin, the chromophore, a hydrophobic membrane, and a saline solution was employed. No photoisomerization could be observed in the ROKS-QM/MM simulations at ambient temperatures. Obviously a small free energy barrier remained also in the protein environment. Exactly the same behavior was observed in TDDFT-QM/MM simulations of the system. Hence shortcomings in the description of the interaction with the environment are a very probable reason. Nevertheless, spontaneous ultrafast isomerization was obtained with ROKS-QM/MM when the local temperature of the chromophore was artificially increased. Then, it could be shown (Figure 5) how the environment induces the selective isomerization from the 11-cis to the all-trans form of retinal which is possible with surprisingly small atom displacements (111). With this minimum motion, the photoisomerization leads to formation of a strongly distorted trans form of the chromophore ('molecular spring'). The release of the strain then induces consecutive reactions. The resulting intermediates have been investigated with ground state dynamics in (112).

4.4. Bacteriorhodopsin

Bacteriorhodopsin (bR), a photoactive trans-membrane protein, is a light driven pump which transports protons across the cell membrane of the halophilic organism Halobacterium salinarum (113,114). bR has some features which render an investigation (113-121) more attractive than that of rhodopsin: The extraction from bacteria is much simpler and it seems more suitable for technical applications. It is the best understood ion transport protein and has become a paradigm for membrane proteins in general and transporters in particular (116). bR contains seven trans-membrane helices that enclose a cavity in which a retinal is contained (Figure 6A). Much like in rhodopsin, the retinal moiety which acts as the chromophore, is covalently bound via a Schiff base linkage to the Lys-216 residue. However, in dark state of bacteriorhodopsin the chromophore is not in the 11-cis, but in the all-trans form.

Absorption of light energy leads to an isomerization of the retinal chromophore from the all-trans to the 13-cis configuration (Figure 6B), which induces a series of further conformational changes in bR. The resulting photocycle intermediates are characterized as the sequence of K, L, M, N and O. All steps are well characterized by spectroscopic methods (113,114). From the last intermediate, bR returns to the original conformation, completing the photocycle (115). In the transition from the L to M intermediate, bR releases a proton into the extracellular space, and in the subsequent transition from the M to the N state, a proton is taken up from the cytoplasm. The uptake and release of protons increase the trans-membrane electrochemical H⁺ gradient (proton-motive force), converting light energy into biologically processes, like ATP production and the maintenance of iso-osmolarity of the cytoplasm during cell growth. Most of the structures involved have been determined with crystallographic methods (117,119).

It was proposed that water networks are involved in the vectorial proton translocation and release (120), contrary to the model that proposes that amino acid side chains are mainly responsible for the proton transport mechanism. Ground-state DFT-QM/MM dynamics simulations were applied to a model of bR in a solvated lipid bilayer membrane where the protonated water network within a hydrophilic pocket on the extracellular side of bR was treated as the QM part (120,121). Simulations of the photoreaction which induces the proton translocation are not yet available. Simulating the photoreaction of bR and comparison to the rhodopsin simulations would be particularly interesting, as the chromophores isomerize at different positions within the conjugated chains which must be due to the protein environment. Comparison of the X-ray structures shows that in both proteins the counterions are close to the respective isomerizing bond, which suggests that this interaction with the protein environment determines which bonds are isomerized in a longer conjugated chain.

5. PERSPECTIVE

The simulations of chemical reactions in biological systems represent a big challenge to theoretical approaches. The need for an accurate quantum mechanical description of the electronic structure combined with the description of the nuclear dynamics at finite temperature leads to enormous requirements concerning computer time. Nevertheless it is nowadays feasible to do Car-Parrinello simulations for systems of about 1000 atoms (122).

Particularly fascinating but even more difficult than ground state dynamics is the investigation of excited state motion of large molecular systems. The first successful unconstrained simulations of ultrafast photoreactions in biological systems have been published in recent years and there is more to come. Proceeding in this direction, however, will afford further developments not only concerning efficiency but also concerning accuracy.

6. ACKNOWLEDGMENT

This work has been supported by the Deutsche Forschungsgemeinschaft (SFB 486 'Manipulation von Materie auf der Nanometerskala' and SFB 749 'Dynamik und Intermediate molekularer Transformationen') and by the Excellence Cluster 'Nanosystems Initiative Munich'.

7. REFERENCES

1. Car R, M. Parrinello: Unified approach for molecular-dynamics and density-functional theory. Phys Rev Lett 55, 2471-2474 (1985).
doi:10.1103/PhysRevLett.55.2471
PMid:10032153

2. Parrinello M: From silicon to RNA: The coming of age of ab initio molecular dynamics. Solid State Commun 102, 107-120 (1997)
doi:10.1016/S0038-1098(96)00723-5

3. Marx D, J. Hutter: Ab Initio Molecular Dynamics: Theory and Implementation, in Modern Methods and Algorithms of Quantum Chemistry, Ed: J. Grotendorst, John von Neumann Institute for Computing, Julich (2000)

4. Andreoni W, A. Curioni, T. Mordasini: DFT-based molecular dynamics as a new tool for computational biology: First applications and perspective. IBM J Res Dev 45, 397-407 (2001)

5. Becke A. D: Density-functional exchange-energy approximation with correct assymptotic behavior. Phys Rev A 38, 3098-3100 (1988)
doi:10.1103/PhysRevA.38.3098
PMid:9900728

6. Hohenberg P. C, W. Kohn: Inhomogeneous electron gas. Phys Rev B 136, 864-871 (1964)
doi:10.1103/PhysRev.136.B864

7. Kohn W., J. L. Sham: Self-Consistent Equations Including Exchange and Correlation Effects. Phys Rev 140, 1133-1138 (1965)
doi:10.1103/PhysRev.140.A1133

8. Warshel A, L. Michael: Theoretical studies of enzymatic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J Mol Biol 103, 227-249 (1976)
doi:10.1016/0022-2836(76)90311-9
PMid:985660

9. Singh U. C, P. A. Kollman: A combined ab initio quantum mechanical and molecular mechanical method for carrying out simulations on complex molecular systems: Applications to the CH3Cl + Cl- exchange reaction and gas phase protonation of polyethers. J Comp Chem 7, 718-730 (1986)
doi:10.1002/jcc.540070604

10. Field M. J, P. A. Bash, M. Karplus: A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations. J Comp Chem 11, 700-733 (1990)
doi:10.1002/jcc.540110605

11. Eichinger M, P. Tavan, J. Hutter, M. Parrinello: A hybrid method for solutes in complex solvents: Density functional theory combined with empirical force fields. J Chem Phys 110, 10452-10467 (1999)
doi:10.1063/1.479049

12. Laio A, J. VandeVondele, U. Rothlisberger: A Hamiltonian electrostatic coupling scheme for hybrid Car-Parrinello molecular dynamics simulations. J Phys Chem 116, 6941-6947 (2002)
doi:10.1063/1.1462041

13. Carloni P, U. Rothlisberger, M. Parrinello: The role and perspective of ab initio molecular dynamics in the study of biological systems. Acc Chem Res 35, 455-464 (2002)
doi:10.1021/ar010018u
PMid:12069631

14. Dal Peraro M, P. Ruggerone, S. Raugei, F. L. Gervasio, P. Carloni: Investigating biological systems using first principles Car-Parrinello molecular dynamics simulations. Curr Opin Struct Biol 17, 147-268 (2007)
doi:10.1016/j.sbi.2007.03.007

15. Koller F, W. J. Schreier, T. E. Schrader, A. Sieg, S. Malkmus, C. Schulz, S. Dietrich, K. Ruck-Braun, W. Zinth, M. Braun: Ultrafast structural dynamics of photochromic indolylfulgimides studied by vibrational spectroscopy and DFT calculations. J Phys Chem A 110, 12769-12776 (2006)
doi:10.1021/jp0657787

16. Heinz B, S. Malkmus, S. Laimgruber, S. Dietrich, C. Schulz, K. Ruck-Braun, M. Braun, W. Zinth, P. Gilch: Comparing a photoinduced pericyclic ring opening and closure: Differences in the excited state pathways. J Am Chem Soc 129, 8577 (2007)
doi:10.1021/ja071396i
PMid:17567132

17. Schreier W. J, T. E. Schrader, F. Koller, P. Gilch, C. E. Crespo-Hernández, V. N. Swaminathan, T. Carell, W. Zinth, B. Kohler: Thymine dimerization in DNA is an ultrafast photoreaction. Science 315, 625 (2007)
doi:10.1126/science.1135428
PMid:17272716

18. Lochbrunner S, C. Schriever, E. Riedle: Direct observation of the nuclear motion during ultrafast intramolecular proton transfer in hydrogen-transfer reactions, Eds: J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen, Wiley-VCH, Weinheim (2006)

19. Zinth W, J. Wachtveitl: The first picoseconds in bacterial photosynthesis - ultrafast electron transfer for the efficient conversion of light energy. ChemPhysChem 6, 871-880 (2005)
doi:10.1002/cphc.200400458
PMid:15884069

20. Lenz M. O, R. Huber, B. Schmidt, P. Gilch, R. Kalmbach, M. Engelhard, J. Wachtveitl: First steps of retinal photoisomerization in proteorhodopsin. Biophys J. 91, 255-262 (2006)
doi:10.1529/biophysj.105.074690
PMid:16603495    PMCid:1479053

21. Del Bene J, R. Ditchfield, J. A. Pople: Self-consistent molecular orbital methods. X. Molecular orbital studies of excited states with minimal and extended basis sets. J Chem Phys 55, 2236-2241 (1971)
doi:10.1063/1.1676398

22. Foresman J. B, M. Head-Gordon, J. A. Pople, M. J. Frisch: Toward a systematic molecular orbital theory for excited states. J Phys Chem 96, 135-149 (1992)
doi:10.1021/j100180a030

23. Hegarty D, M. A. Robb: Application of Unitary Group-Methods to Configuration-Interaction-Calculations. Mol Phys 38, 1795-1812 (1979)
doi:10.1080/00268977900102871

24. Eade R. H, M. A. Robb: Direct minimization in MCSCF theory: The quasi-newton method. Chem Phys Lett 83, 362-368 (1981)
doi:10.1016/0009-2614(81)85480-2

25. Roos B. O, K. Andersson, M. P. Fulscher: Towards an accurate molecular orbital theory for excited states: The benzene molecule. Chem Phys Lett 192, 5-13 (1992)
doi:10.1016/0009-2614(92)85419-B

26. Andersson K, P.-A. Malmqvist, B. O. Roos: Second-order perturbation theory with a complete active space self-consistent field reference function. J Chem Phys 96, 1218-1228 (1992)
doi:10.1063/1.462209
Can't connect to PubMed

27. Roos B. O, K. Andersson: Modern electron structure theory, In: Advanced Series in Physical Chemistry. Ed: D. R. Yarkony, World Scientific, Singapore (1995)

28. Buenker R. J, S. D. Peyerimhoff: Individualized configuration selection in CI calculations with subsequent energy extrapolation. Theor Chim Acta 33, 35-58 (1974)

29. Buenker R. J, S. D. Peyerimhoff: Energy extrapolation in CI calculations. Theor Chim Acta 217, 217-228 (1975)
doi:10.1007/BF00555301
Can't connect to PubMed

30. Ghosh S. K, B. M. Deb: Dynamic polarizability of many-electron systems within a time-dependent density-functional theory. Chem Phys 71, 295-306 (1982)
doi:10.1016/0301-0104(82)87030-4
Can't connect to PubMed

31. Runge E, E. K. U. Gross: Density-functional theory for time-dependent systems. Phys Rev Lett 52, 997-1000 (1984)
doi:10.1103/PhysRevLett.52.997
Can't connect to PubMed

32. Casida M. E : Recent advances in density functional methods, Ed: D. P. Chong, World Scientific, Singapore (1995)

33. Cordova F, L. J. Doriol, A. Ipatov, M. E. Casida, C. Filippi, A. Vela: Troubleshooting time-dependent density-functional theory for photochemical applications: Oxirane. J. Chem. Phys. 127, 164111-164118 (2007)
doi:10.1063/1.2786997
Can't connect to PubMed

34. Dreuw A: Quantum chemical methods for the investigation of photoinitiated processes in biological systems: Theory and applications. ChemPhysChem 7, 2259-2274 (2006)
doi:10.1002/cphc.200600064
Can't connect to PubMed

35. Frank I, J. Hutter, D. Marx, M. Parrinello: Molecular dynamics in low-spin excited states. J Chem Phys 108, 4060-4069 (1998)
doi:10.1063/1.475804
Can't connect to PubMed

36. J. Friedrichs, K. Damianos, I. Frank: Solving restricted open-shell equations in excited-state molecular dynamics simulations. Chem Phys 347, 17-24 (2008)
doi:10.1016/j.chemphys.2007.09.035
Can't connect to PubMed

37. Furche F, R. Ahlrichs: Adiabatic time-dependent density functional methods for excited state properties. J Chem Phys 117, 7433-7447 (2002)
doi:10.1063/1.1508368
Can't connect to PubMed

38. Hutter J: Excited state nuclear forces from the Tamm-Dancoff approximation to time-dependent density functional theory within the plane wave basis set framework. J Chem Phys 118, 3928-3934 (2003)
doi:10.1063/1.1540109
Can't connect to PubMed

39. Born M, J. R. Oppenheimer: Zur Quantentheorie der Molekeln. Ann Phys 84, 457-484 (1927)
doi:10.1002/andp.19273892002
Can't connect to PubMed

40. Koppel H, W. Domcke, L. S. Cederbaum: Multi-mode molecular dynamics beyond the Born-Oppenheimer approximation. Adv Chem Phys 57, 59 (1984).
doi:10.1002/9780470142813.ch2
Can't connect to PubMed

41. Bernardi F, M.Olivucci, M. A. Robb: Potential energy surface crossings in organic photochemistry. Chem Soc Rev 25, 321-328 (1996)
doi:10.1039/cs9962500321
Can't connect to PubMed

42. Doltsinis N. L, D. Marx: Nonadiabatic Car-Parrinello molecular dynamics. Phys Rev Lett 88 166402, 1-4 (2002)

43. Viel A, R. P. Krawczyk, U. Manthe, W. Domcke: Photoinduced dynamics of ethene in the N, V, and Z valence states: A six-dimensional nonadiabatic quantum dynamics investigation. J. Chem. Phys. 120, 11000-11010 (2004)
doi:10.1063/1.1740696
Can't connect to PubMed

44. Lan Z, W. Domcke: Role of vibrational energy relaxation in the photoinduced nonadiabatic dynamics of pyrrole at the pi-sigma-S0 conical intersection. Chem. Phys. In press (2008)
doi:10.1016/j.chemphys.2008.01.049
Can't connect to PubMed

45. Kasha M: Characterization of electronic transitions in complex molecules. Faraday Discuss. Chem. Soc. 9, 14-19 (1950)
doi:10.1039/df9500900014
Can't connect to PubMed

46. Grimm S, C. Nonnenberg, I. Frank: Restricted open-shell Kohn-Sham theory for pi-pi* transitions. I. Polyenes, cyanines, and protonated imines. J Chem Phys 119, 11574 (2003)
doi:10.1063/1.1623742
Can't connect to PubMed

47. Frank I, K. Damianos: Restricted open-shell Kohn-Sham theory: Simulation of the pyrrole photodissociation. J Chem Phys 126, 125105-1-5 (2007)

48. Marx D, M. Parrinello: Ab initio path integral molecular dynamics. Z. Phys. B Con. Mat. 95, 143-144 (1994).

49. Tse J. S: Ab initio molecular dynamics with density functional theory. Annu Rev Phys Chem 53, 249-290 (2002)
doi:10.1146/annurev.physchem.53.090401.105737
PMid:11972009

50. Dal Peraro M, L. I. Llarrull, U. Rothlisberger, A. J. Vila, P. Carloni: Water assisted reaction mechanism of monozinc b-lactamases. J Am Chem Soc 126, 12661-12668 (2004)
doi:10.1021/ja048071b
PMid:15453800

51. Dal Peraro M, A. J. Vila, P. Carloni, M. L. Klein: Role of zinc content on the catalytic efficiency of B1 metallo beta-lactamases. J Am Chem Soc 129, 2808-2816 (2007)
doi:10.1021/ja0657556
PMid:17305336

52. De Vivo M, B. Ensing, M. Dal Peraro, G. A. Gomez, D. W. Christianson, M. L. Klein: Proton shuttles and phosphatase activity in soluble epoxide hydrolase. J Am Chem Soc 129, 387-394 (2007)
doi:10.1021/ja066150c
PMid:17212419

53. Boero M, T. Ikeda, E. Ito, K. Terakura: Hsc70 ATPase: An insight into water dissociation and joint catalytic role of K+ and Mg2+ metal cations in the hydrolysis reaction. J Am Chem Soc 128, 16798-16807 (2006)
doi:10.1021/ja064117k
PMid:17177430

54. Rovira C, M. Alfonso-Prieto, X. Biarnes, X. Carpena, I. Fita, P. C. Loewen: A first principles study of the binding of formic acid in catalase complementing high resolution X-ray structures. Chem Phys 323, 129-137 (2006)
doi:10.1016/j.chemphys.2005.08.049

55. Alfonso-Prieto M, A. Borovik, X. Carpena, G. Murshudov, W. Melik-Adamyan, I. Fita, C. Rovira, P. C. Loewen: The structures and electronic configuration of compound I intermediates of Helicobacter pylori and Penicillium vitale catalases determined by X-ray crystallography and QM/MM DFT calculations. J Am Chem Soc 129, 4193-4205 (2007)
doi:10.1021/ja063660y
PMid:17358056

56. Raugei S, P. Carloni: Structure and function of vanadium haloperoxidases. J Phys Chem B 110, 3747-3758 (2006)
doi:10.1021/jp054901b
PMid:16494433

57. Boero M, M. Tateno, K. Terakura, A. Oshiyama: Double-metal-ion/ single-metal-ion mechanisms of the cleavage reaction of ribozymes: first-principles molecular dynamics simulations of a fully hydrated model system. J Chem Theory Comput 1, 925-934 (2005)
doi:10.1021/ct050066q

58. Vidossich P, P. Carloni: Binding of phosphinate and phosphonate inhibitors to aspartic proteases: A first principles study. J Phys Chem B 110, 1437-1442 (2006)
doi:10.1021/jp0544639
PMid:16471695

59. Cascella M, C. Micheletti, U. Rothlisberger, P. Carloni: Evolutionarily conserved functional mechanics across pepsin-like and retroviral aspartic proteases. J Am Chem Soc 127, 3734-3742 (2005)
doi:10.1021/ja044608+
PMid:15771507

60. Bucher D, S. Raugei, L. Guidoni, M. Dal Peraro, U. Rothlisberger, P. Carloni, M. L. Klein: Polarization effects and charge transfer in the KcsA potassium channel. Biophys Chem 124, 292-301 (2006)
doi:10.1016/j.bpc.2006.04.008
PMid:16737771

61. Carloni P, M. Sprik, W. Andreoni: Key steps of the cis-platin-DNA interaction: Density functional theory-based molecular dynamics simulations. J Phys Chem B 104, 823-835 (2000)
doi:10.1021/jp992590x

62. Gossens C, I. Tavernelli, U. Rothlisberger: Rational design of organo-ruthenium anticancer compounds. Chimia 59, 81-84 (2005)
doi:10.2533/000942905777676795

63. Gervasio F. L, A. Laio, M. Iannuzzi, M. Parrinello: Influence of DNA structure on the reactivity of the guanine radical cation. Chemistry 10, 4846-4852 (2004)

64. Meyer T. E: Isolation and characterization of soluble cytochromes, ferredoxins and other chromophoric proteins from the halophilic phototropic bacterium Ectothiorhodospira halophila. Biochim Biophys Acta 806, 175- 183 (1985)
doi:10.1016/0005-2728(85)90094-5

65. Meyer T. E, E. Yakali, M. A. Cusanovich, G. Tollin: Properties of a water-soluble, yellow protein isolated from a halophilic phototrophic bacterium that has photochemical activity analogous to sensory rhodopsin. Biochemistry 26, 418-423 (1987)
doi:10.1021/bi00376a012
PMid:3828315

66. Sprenger W. W, W. D. Hoff, J. P. Armitage, K. J. Hellingwerf: The eubacterium Ectothiorhodospira halophila is negatively phototactic, with a wavelength dependence that fits the absorption spectrum of the photoactive yellow protein. J Bacteriol 175, 3096-3104 (1993)

67. Hoff W. D, P. Dux, K. Hard, B. Devreese, I. M. Nugteren-Roodzant, W. Crielaard, R. Boelens, R. Kaptein, J. van Beeumen, K. J. Hellingwerf: Thiol ester-linked p-coumaric acid as a new photoactive prosthetic group in a protein with rhodopsin-like photochemistry. Biochemistry 33, 13959-13962 (1994)
doi:10.1021/bi00251a001
PMid:7947803

68. Baca M, G. E. O. Borgstahl, M. Boissinot, P. M. Burke, D. R. Williams, K. A. Slater, E. D. Getzoff: Complete chemical structure of photoactive yellow protein: Novel thioester-linked 4-hydroxycinnamyl chromophore and photocycle chemistry. Biochemistry 33, 14369-14377 (1994)
doi:10.1021/bi00252a001
PMid:7981196

69. Hellingwerf K. J, W. D. Hoff, W. Crielaard: Photobiology of microorganisms: How photosensors catch a photon to initialize signalling. Mol Microbiol 21, 683-693 (1996)
doi:10.1046/j.1365-2958.1996.411402.x
PMid:8878032

70. Genick U. K, S. M. Soltis, P. Kuhn, I. L. Canestrelli, E. D. Getzoff: Structure at 0.85 A resolution of an early protein photocycle intermediate. Nature, 392, 206-209 (1998).
doi:10.1038/32462
PMid:9515969

71. Getzoff E. D, K. N. Gutwin, U. K. Genick: Anticipatory active-site motions and chromophore distortion prime photoreceptor PYP for light activation. Nat Struct Biol 10, 663-668 (2003)
doi:10.1038/nsb958
PMid:12872160

72. Kort R, K. J. Hellingwerf, R. B. G. Ravelli: Initial events in the photocycle of photoactive yellow protein. J Biol Chem 279, 26417-26424 (2004)
doi:10.1074/jbc.M311961200
PMid:15026418

73. Sergi A, M. Gruning, M. Ferrario, F. Buda: Density functional study of the photoactive yellow protein's chromophore. J. Phys. Chem. B 105, 4386-4391 (2001)
doi:10.1021/jp002270+

74. Groenhof G, M. F. Lensink, H. J. C. Berendsen, A. E. Mark: Signal transduction in the photoactive yellow protein. I. Photon absorption and the isomerization of the chromophore. Proteins 48, 202-211 (2002)
doi:10.1002/prot.10136

75. Groenhof G, M. F. Lensink, H. J. C. Berendsen, A. E. Mark: Signal transduction in the photoactive yellow protein. II. Proton transfer initiates conformational changes. Proteins 48, 212-219 (2002)
doi:10.1002/prot.10135

76. Thompson M. J, D. Bashford, L. Noodleman, E. D. Getzoff: Photoisomerization and Proton Transfer in Photoactive Yellow Protein. J Am Chem Soc 125, 8186-8194 (2003)
doi:10.1021/ja0294461
PMid:12837088

77. Yoda M, Y. Inoue, M. Sakurai: Effect of Protein Environment on pKa Shifts in the Active Site of Photoactive Yellow Protein. J Phys Chem B 107, 14569-14575 (2003)
doi:10.1021/jp0364102

78. Groenhof G. M, M. Bouxin-Cademartory, B. Hess, S. P. de Visser, H. J. C. Berendsen, M. Olivucci, A. E. Mark, M. A. Robb: Photoactivation of the photoactive yellow protein: Why photon absorption triggers a trans-to-cis isomerization of the chromophore in the protein. J Am Chem Soc 126, 4228-4233 (2004)
doi:10.1021/ja039557f
Can't connect to PubMed

79. Leenders E. J. M, L. Guidoni, U. Rothlisberger, J. Vreede, P. G. Bolhuis, E. Jan Meijer: Protonation of the Chromophore in the photoactive yellow protein. J. Phys. Chem. B 111, 3765-3773 (2007)
doi:10.1021/jp067158b
Can't connect to PubMed

80. Prendergast F. G, K. G. Mann: Chemical and physical properties of aequorin and the green fluorescent protein isolated from Aequorea forskalea. Biochemistry 17, 3448-3453 (1978)
doi:10.1021/bi00610a004
Can't connect to PubMed

81. Philips G. N: Structure and dynamics of green fluorescent protein. Curr Opin Struct Biol 7, 821-827 (1997)
doi:10.1016/S0959-440X(97)80153-4
Can't connect to PubMed

82. Tsien R. Y: The green fluorescent protein. Annu Rev Biochem 67, 509-544 (1998)
doi:10.1146/annurev.biochem.67.1.509
Can't connect to PubMed

83. Prendergast F. G: Biophysics of the green fluorescent protein. Methods Cell Biol 58, 1-18 (1999)
doi:10.1016/S0091-679X(08)61945-7
Can't connect to PubMed

84. Creemers T.M.H, A. J. Lock, V. Subramaniam, T. M. Jovin, S. Voelker: Photophysics and optical switching in green fluorescent protein mutants. PNAS 97, 2974-2978 (2000)
doi:10.1073/pnas.050365997
Can't connect to PubMed

85. Shaner N. C, P. A. Steinbach, R. Y. Tsien: A guide to choosing fluorescent proteins. Nat Methods 2, 905-909 (2005)
doi:10.1038/nmeth819
Can't connect to PubMed

86. Jung G, J. Wiehler, A. Zumbusch: The photophysics of the green fluorescent protein: Influence of the key amino acids at positions 65, 203, and 222. Biophys J 88, 1932-1947 (2005)
doi:10.1529/biophysj.104.044412
Can't connect to PubMed

87. Haupts U, S. Maiti, P. Schwille, W. W. Webb: Dynamics of fluorescence fluctuations in green fluorescent protein observed by fluorescence correlation spectroscopy. PNAS 95, 13573-13578 (1998)
doi:10.1073/pnas.95.23.13573
Can't connect to PubMed

88. Marques M. A. L, X. Lopez, D. Varsano, A. Castro, A. Rubio: Time-dependent density-functional approach for biological chromophores: The case of green fluorescent protein. Phys Rev Lett 90, 258101-258104 (2003)
doi:10.1103/PhysRevLett.90.258101
Can't connect to PubMed

89. Laino T, R. Nifosi, V. Tozzini: Relationship between structure and optical properties in green fluorescent proteins: A quantum mechanical study of the chromophore environment. Chem Phys 298, 17-28 (2004)
doi:10.1016/j.chemphys.2003.10.040
Can't connect to PubMed

90. Nifosi R, P. Amat, V. Tozzini: Variation of spectral, structural, and vibrational properties within the intrinsically fluorescent proteins family: A density functional study. J Comp Chem 28, 2366-2377 (2007)
doi:10.1002/jcc.20764
Can't connect to PubMed

91. Schaefer L. V, G. Groenhof, A. R. Klingen, G. M. Ullmann, M. Boggio-Pasqua, M. A. Robb, H. Grubmuller: Photoswitching of the fluorescent protein asFP595: Mechanism, proton pathways, and absorption spectra. Angew Chem 46, 530-536 (2007)
doi:10.1002/anie.200602315
Can't connect to PubMed

92. Hargrave P. A, J. H. McDowell, D. R. Curtis, J. K. Wang, E. Juszczak, S.-L. Fong, J. K. Rao, P. Argos: The structure of bovine rhodopsin. Biophys Struct Mech 9, 235-244 (1983)
doi:10.1007/BF00535659
Can't connect to PubMed

93. Sakmar T. P, S. T. Menon, E. P. Marin, E. S. Awad: Rhodopsin: Insights from recent structural studies. Annu Rev Biophys Biomol Struct 31, 443-84 (2002)
doi:10.1146/annurev.biophys.31.082901.134348
Can't connect to PubMed

94. Palczewski K: G protein-coupled receptor rhodopsin. Annu Rev Biochem 75, 743-767 (2006)
doi:10.1146/annurev.biochem.75.103004.142743
Can't connect to PubMed

95. Lewis J. W, I. Pinkas, M. Sheves, M. Ottolenghi, D. S. Kliger: Structural changes in early photolysis intermediates of rhodopsin from time-resolved spectral measurements of artificial pigments sterically hindered along the chromophore chain. J Am Chem Soc 117, 918-923 (1995)
doi:10.1021/ja00108a008
Can't connect to PubMed

96. Han M, M. Groesbeek, T. P. Sakmar, S. O. Smith: The C9 methyl group of retinal interacts with glycine-121 in rhodopsin. PNAS 94, 13442-13447 (1997)
doi:10.1073/pnas.94.25.13442
Can't connect to PubMed

97. Borhan B, M. L. Souto, H. Imai, Y. Shichida, K. Nakanishi: Movement of retinal along the visual transduction path. Science 288, 2209-2212 (2000)
doi:10.1126/science.288.5474.2209
Can't connect to PubMed

98. Jang G.-F, V. Kuksa, S. Filipek, F. Bartl, E. Ritter, M. H. Gelb, K. P. Hofmann, K. Palczewski: Mechanism of rhodopsin activation as examined with ring constrained retinal analogs and the crystal structure of the ground state protein. J Biol Chem 276, 26148-26153 (2001)
doi:10.1074/jbc.M102212200
Can't connect to PubMed

99. Pan D, R. A. Mathies: Chromophore structure in lumirhodopsin and metarhodopsin I by time-resolved resonance Raman microchip spectroscopy. Biochemistry 40, 7929-7936 (2001)
doi:10.1021/bi010670x
Can't connect to PubMed

100. Warshel A, N. Barboy: Energy storage and reaction pathways in the first step of the vision process. J Am Chem Soc 104, 1469-1476 (1982)
doi:10.1021/ja00370a003
Can't connect to PubMed

101. Kochendoerfer G. G, P. J. E. Verdegem, I. van der Hoef, J. Lugtenburg, R. A. Mathies: Retinal analog study of the role of steric interactions in the excited state isomerization dynamics of rhodopsin. Biochemistry 35, 16230-16240 (1996)
doi:10.1021/bi961951l
Can't connect to PubMed

102. Molteni C, I. Frank, M. Parrinello: An excited state density functional theory study of the Rhodopsin Chromophore J Am Chem Soc 121, 12177-12183 (1999)
doi:10.1021/ja983708a
Can't connect to PubMed

103. Mathies R. A, J. Lugtenburg: The Primary Photoreaction of Rhodopsin, in Handbook of Biological Physics, Eds. D. G. Stavenga, W. J. DeGrip, and E. N. Pugh Jr., Elsevier Science Press, 55-90 (2000)

104. Palczewski K, T. Kumasaka, T. Hori, C. A. Behnke, H. Motoshima, B. A. Fox, I. Le Trong, D. C. Teller, T. Okada, R. E. Stenkamp, M. Yamamoto, M. Miyano: Crystal Structure of rhodopsin: A G protein-coupled receptor Science 289, 739-745 (2000)
doi:10.1126/science.289.5480.739
Can't connect to PubMed

105. Teller D. C, T. Okada, C. A. Behnke, K. Palczewski, R. E. Stenkamp: Advances in determination of a high-resolution three-dimensional structure of rhodopsin, a model of G-protein-coupled receptors GPCRs. Biochemistry 40, 7761-7772 (2001)
doi:10.1021/bi0155091
Can't connect to PubMed

106. Rohrig U, L. Guidoni, U. Rothlisberger: Early steps of the intramolecular signal transduction in rhodopsin explored by molecular dynamics simulations. Biochemistry 41, 10799-10809 (2002)
doi:10.1021/bi026011h
Can't connect to PubMed

107. Saam J, E. Tajkhorshid, S. Hayashi, K. Schulten: Molecular dynamics investigation of primary photoinduced events in the activation of rhodopsin. Biophys J 83, 3097-3112 (2002)

108. Sugihara M, V. Buss, P. Entel, M. Elstner, T. Frauenheim: 11-cis-retinal protonated Schiff base: Influence of the protein environment on the geometry of the rhodopsin chromophore. Biochemistry 41, 15259-15266 (2002)
doi:10.1021/bi020533f
Can't connect to PubMed

109. Birge R. R, B. E. Knox: Perspectives on the counterion switch-induced photoactivation of the G protein-coupled receptor rhodopsin. PNAS 100, 9105-9107 (2003)
doi:10.1073/pnas.1733801100
Can't connect to PubMed

110. Sinicropi A, A. Migani, L. De Vico, M. Olivucci: Photoisomerization acceleration in retinal protonated Schiff-base models. Photochem Photobiol Sci 2, 1250-1255 (2003)
doi:10.1039/b307333p
Can't connect to PubMed

111. Rohrig U, L. Guidoni, A. Laio, I. Frank, U. Rothlisberger: A molecular spring for vision. J Am Chem Soc 126, 15328-15329 (2004)
doi:10.1021/ja048265r
PMid:15563129

112. Rohrig U, L. Guidoni, U. Rothlisberger: Solvent and protein effects on the structure and dynamics of the rhodopsin chromophore, ChemPhysChem 6, 1836-1847 (2005)
doi:10.1002/cphc.200500066
PMid:16110519

113. Lozier R. H, R. A. Bogomolni, W. Stoeckenius: Bacteriorhodopsin: A light-driven proton pump in Halobacterium halobium. Biophys J 15, 955-963 (1975)

114. Mathies R. A, S. W. Lin, J. B. Ames, W. T. Pollard: From femtoseconds to biology: Mechanism of bacteriorhodopsin's light-driven proton pump. Annu. Rev Biophys Biophys Chem 20, 491-518 (1991)
doi:10.1146/annurev.bb.20.060191.002423
PMid:1867724

115. Lanyi J. K: Proton translocation mechanism and energetics in the light-driven pump bacteriorhodopsin. Biochim Biophys Acta 1183, 241-261 (1993)
doi:10.1016/0005-2728(93)90226-6

116. Haupts U, J. Tittor, D. Oesterhelt: Closing in on bacteriorhodopsin: Progress in understanding the molecule. Annu Rev Biophys Biomol Struct 28, 367-399 (1999)
doi:10.1146/annurev.biophys.28.1.367
PMid:10410806

117. Edman K, P. Nollert, A. Royant, H. Belrhali, E. Pebay-Peyroula, J. Hajdu, R. Neutze, E. M. Landau: High-resolution X-ray structure of an early intermediate in the bacteriorhodopsin photocycle. Nature 401, 822-826 (1999)
doi:10.1038/44623
PMid:10548112

118. Luecke H, B. Schobert, H.-T. Richter, J.-P. Cartailler, J. K. Lanyi: Structural changes in bacteriorhodopsin during ion transport at 2 Angstrom resolution. Science 286, 255-260 (1999)
doi:10.1126/science.286.5438.255
PMid:10514362

119. Lanyi J. K: What is the real crystallographic structure of the L photointermediate of bacteriorhodopsin? Biochim Biophys Acta 1658, 14-22 (2004)
doi:10.1016/j.bbabio.2004.03.018

120. Rousseau R, V. Kleinschmidt, U. W. Schmitt, D. Marx: Modeling protonated water networks in bacteriorhodopsin. Phys Chem Chem Phys 6, 1848-1859 (2004)
doi:10.1039/b313220j

121. Mathias G, D. Marx: Structures and spectral signatures of protonated water networks in bacteriorhodopsin. PNAS 104, 6980-6985 (2007)
doi:10.1073/pnas.0609229104

122. Gervasio F. L, P. Carloni, M. Parrinello: Electronic structure of wet DNA. Phys Rev Lett 89, 108102-1-4 (2002)

Abbreviations: QM: quantum mechanics; DFT: density functional theory; CPMD: Car Parrinello molecular dynamics; QM/MM: quatum mechanics/molecular modeling; CIS: configuration interaction singles; CASSCF: complete active space self-consistent field theory; CASPT2: complete active space perturbation theory, second order; MRD-CI: multi-reference (doubles) configuration interaction; TDDFT: time-dependent density functional theory; ROKS: restricted open-shell Kohn-Sham; ROHF: restricted open-shell Hartree-Fock; HOMO: highest occupied molecular orbital; LUMO: lowest occupied molecular orbital; MCSCF: multi-configuration self-consistent field; PYP: photoactive yellow protein; GFP: green fluorescent protein; GPCR: G protein-coupled receptor; IFP: intrinsically fluorescent protein; bR: bacteriorhodopsin

Key Words: Density Functional Calculations, CPMD, QM/MM, Photoactive Proteins, Fluorescent Proteins, Reaction mechanisms, Review

Send correspondence to: Irmgard Frank, Institut für Physikalische Chemie und Elektrochemie, Callinstr. 3A, 30167 Hannover, Tel: 49(511)762-17893, Fax: 49(511)762-4009, E-mail:irmgard.frank@theochem.uni-hannover.de

Figure 1. Schematic representation of typical potential energy surfaces (PES) that are relevant for photoreactions. Plotted is the potential energy E vs. some reaction coordinate R. Vibrational levels are neglected, that is, nuclear motion is considered to be classical. Depending on the energy of the photon, the electronic excitation of the singlet ground state (S₀) leads vertically from the educt minimum to one of the excited singlet states. In the scheme, fast deactivation to the first excited singlet state S₁ may occur diabatically through the diabatic crossing D1. The system may continue its motion in the S₁ state till it reaches the diabatic crossing D2. From there it may return diabatically to the ground state S₀ and relax in the product state minimum (photoreaction). A back reaction to the ground-state minimum of the educt may occur thermally across the ground-state barrier on longer time scales. If the velocity along the relevant coordinate is too high for a diabatic return to the ground state, the system may continue its motion in the excited state till it reaches the depicted conical intersection through which return to the ground state can occur. Note that this two-dimensional sketch can just give a first idea of the different possibilities in a 3N-6 dimensional PES space. (In particular, it does not show that moving along a diabatic crossing space usually leads to a conical intersection space.) The green line marks the process which is described by the diabatic ROKS approximation.

Figure 2. A) Ribbon representation of PYP. The protein consists of a single polypeptide chain of 125 residues. The chromophore consists of a para-hydroxy cinnamic acid molecule represented by balls and sticks. B) Chemical structure of the para-coumaric acid. C) PYP's chromophore binding pocket. The para-coumaric acid is attached via a thioester linkage to the only cysteine residue (Cys69) in the protein. In the pG state of the photocycle, the chromophore (red) is in the trans conformation and is deprotonated. The structure of the intermediate is shown in blue. The buried charge on the chromophore is stabilized by hydrogen bonds from Tyr42 and Glu46.

Figure 3. A) Cartoon representation of GFP containing the chromophore (in red) in its center. B) Chemical structure of the chromophore p-hydroxybenzylidene-imidazolinone that originates from an internal Ser-Tyr-Gly sequence which is post-translationally modified.

Figure 4. A) Ribbon representation of rhodopsin containing the protonated Schiff base of retinal as chromophore (in red). The chromophore is a derivative of vitamin A1 (retinol) with a total of 20 carbon atoms. C) Upon absorption of a photon in the visible range, 11-retinal can isomerize to all-retinal. Retinal is covalently bound to the nitrogen atom of a lysine residue (Lys296) and Glu113 stabilizes the protonated state of retinal.

Figure 5. ROKS-QM/MM simulation of rhodopsin. Upper row: change of dihedral angles and displacements during the isomerization. Lower row: the chromophore in the binding pocket during the three stages of the simulation. I: Ground state, cis form, II: excited state, III: ground state, formation of trans form. In the excited state, the C₁₁-C₁₂ bond rotates to 90 degrees and continues this rotation in the ground state, while all other bonds remain essentially unchanged. This rapid rotation is possible with very minor atom displacements in the specific environment of the binding pocket.