Low frequency vibrational modes in proteins: changes induced by point-mutations in the protein-cofactor matrix of bacterial reaction centers

Low-Frequency Coherent Raman Imaging Robust to Optical Scattering

We demonstrate low-frequency interferometric impulsive stimulated Raman scattering (ISRS) imaging with high robustness to distortions by optical scattering. ISRS is a pump-probe coherent Raman spectroscopy that can capture Raman vibrational spectra. Recording of ISRS spectra requires isolation of a probe pulse from the pump pulse. While this separation is simple in nonscattering specimens, such as liquids, scattering leads to significant pump pulse contamination and prevents the extraction of a Raman spectrum. We introduce a robust method for ISRS microscopy that works in complex scattering samples. High signal-to-noise ISRS spectra are obtained even when the pump and probe pulses pass through many scattering layers.

End-to-End Protein Normal Mode Frequency Predictions Using Language and Graph Models and Application to Sonification

The prediction of mechanical and dynamical properties of proteins is an important frontier, especially given the greater availability of proteins structures. Here we report a series of models that provide end-to-end predictions of nanodynamical properties of proteins, focused on high-throughput normal mode predictions directly from the amino acid sequence. Using neural network models within the family of Natural Language Processing and graph-based methods, we offer atomistically based mechanistic predictions of key protein mechanical features. The models include an end-to-end long short-term memory (LSTM) model, an end-to-end transformer model, a graph-based transformer model, and an equivariant graph neural network. All four models show exceptional performance, with the graph-based transformer architecture offering the best results but at the cost of requiring a graph structure as input. Conversely, the LSTM and transformer models offer end-to-end sequence-to-property prediction capabilities, providing efficient avenues for protein engineering, analysis, and design. We compare our results against published data based on a Principal Neighborhood Aggregation graph neural network, revealing that the transformer model offers better performance while also being able to predict a large set of the first 64 normal mode frequencies, simultaneously. The use of the end-to-end transformer model may facilitate other downstream applications through the use of transfer learning, and it offers a comprehensive prediction of dynamical properties without any structural knowledge, directly from the amino acid sequence. We demonstrate a potential application in scientific sonification, where the normal mode frequencies are transposed to generate audible signals for a detailed analysis of subtle changes of protein sequences.

Rapid prediction of protein natural frequencies using graph neural networks

Natural vibrational frequencies of proteins help to correlate functional shifts with sequence or geometric variations that lead to negligible changes in protein structures, such as point mutations related to disease lethality or medication effectiveness. Normal mode analysis is a well-known approach to accurately obtain protein natural frequencies. However, it is not feasible when high-resolution protein structures are not available or time consuming to obtain. Here we provide a machine learning model to directly predict protein frequencies from primary amino acid sequences and low-resolution structural features such as contact or distance maps. We utilize a graph neural network called principal neighborhood aggregation, trained with the structural graphs and normal mode frequencies of more than 34 000 proteins from the protein data bank. combining with existing contact/distance map prediction tools, this approach enables an end-to-end prediction of the frequency spectrum of a protein given its primary sequence.

Machine learning model for fast prediction of the natural frequencies of protein molecules

Natural vibrations and resonances are intrinsic features of protein structures and enable differentiation of one structure from another. These nanoscale features are important to help to understand the dynamics of a protein molecule and identify the effects of small sequence or other geometric alterations that may not cause significant visible structural changes, such as point mutations associated with disease or drug design. Although normal mode analysis provides a powerful way to accurately extract the natural frequencies of a protein, it must meet several critical conditions, including availability of high-resolution structures, availability of good chemical force fields and memory-intensive large-scale computing resources. Here, we study the natural frequency of over 100 000 known protein molecular structures from the Protein Data Bank and use this dataset to carefully investigate the correlation between their structural features and these natural frequencies by using a machine learning model composed of a Feedforward Neural Network made of four hidden layers that predicts the natural frequencies in excellent agreement with full-atomistic normal mode calculations, but is significantly more computationally efficient. In addition to the computational advance, we demonstrate that this model can be used to directly obtain the natural frequencies by merely using five structural features of protein molecules as predictor variables, including the largest and smallest diameter, and the ratio of amino acid residues with alpha-helix, beta strand and 3–10 helix domains. These structural features can be either experimentally or computationally obtained, and do not require a full-atomistic model of a protein of interest. This method is helpful in predicting the absorption and resonance functions of an unknown protein molecule without solving its full atomic structure.

Natural vibrations and resonances are intrinsic features of protein structures and can be learnt from existing structures.

A Self-Consistent Sonification Method to Translate Amino Acid Sequences into Musical Compositions and Application in Protein Design Using Artificial Intelligence

We report a self-consistent method to translate amino acid sequences into audible sound, use the representation in the musical space to train a neural network, and then apply it to generate protein designs using artificial intelligence (AI). The sonification method proposed here uses the normal mode vibrations of the amino acid building blocks of proteins to compute an audible representation of each of the 20 natural amino acids, which is fully defined by the overlay of its respective natural vibrations. The vibrational frequencies are transposed to the audible spectrum following the musical concept of transpositional equivalence, playing or writing music in a way that makes it sound higher or lower in pitch while retaining the relationships between tones or chords played. This transposition method ensures that the relative values of the vibrational frequencies within each amino acid and among different amino acids are retained. The characteristic frequency spectrum and sound associated with each of the amino acids represents a type of musical scale that consists of 20 tones, the "amino acid scale". To create a playable instrument, each tone associated with the amino acids is assigned to a specific key on a piano roll, which allows us to map the sequence of amino acids in proteins into a musical score. To reflect higher-order structural details of proteins, the volume and duration of the notes associated with each amino acid are defined by the secondary structure of proteins, computed using DSSP and thereby introducing musical rhythm. We then train a recurrent neural network based on a large set of musical scores generated by this sonification method and use AI to generate musical compositions, capturing the innate relationships between amino acid sequence and protein structure. We then translate the de novo musical data generated by AI into protein sequences, thereby obtaining de novo protein designs that feature specific design characteristics. We illustrate the approach in several examples that reflect the sonification of protein sequences, including multihour audible representations of natural proteins and protein-based musical compositions solely generated by AI. The approach proposed here may provide an avenue for understanding sequence patterns, variations, and mutations and offers an outreach mechanism to explain the significance of protein sequences. The method may also offer insight into protein folding and understanding the context of the amino acid sequence in defining the secondary and higher-order folded structure of proteins and could hence be used to detect the effects of mutations through sound.

Analysis of the vibrational and sound spectrum of over 100,000 protein structures and application in sonification

We report a high-throughput method that enables us to automatically compute the vibrational spectra of more than 100,000 proteins available in the Protein Data Bank to date, in a consistent manner. Using this new algorithm we report a comprehensive database of the normal mode frequencies of all known protein structures, which has not been available before. We then use the resulting frequency spectra of the proteins to generate audible sound by overlaying the molecular vibrations and translating them to the audible frequency range using the music theoretic concept of transpositional equivalence. The method, implemented as a Max audio device for use in a digital audio workstation (DAW), provides unparalleled insights into the rich vibrational signatures of protein structures, and offers a new way for creative expression by using it as a new type of musical instrument. This musical instrument is fully defined by the vibrational feature of almost all known protein structures, making it fundamentally different from all the traditional instruments that are limited by the material properties of a few types of conventional engineering materials, such as wood, metals or polymers.

Characterization of Vibrational Coherence in Monomeric Bacteriochlorophyll a by Two-Dimensional Electronic Spectroscopy

Bacteriochlorophyll a (BChla) is the most abundant pigment found in the Bacterial Reaction Center (BRC) and light-harvesting proteins of photosynthetic purple and green bacteria. Recent two-dimensional electronic spectroscopy (2DES) studies of photosynthetic pigment-protein complexes including the BRC and the Fenna-Matthews-Olson (FMO) complex have shown oscillatory signals, or coherences, whose physical origin has been hotly debated. To better understand the observations of coherence in larger photosynthetic systems, it is important to carefully characterize the spectroscopic signatures of the monomeric pigments. Prior spectroscopic studies of BChla have differed significantly in their observations, with some studies reporting little to no coherence. Here we present evidence of strong coherences in monomeric BChla in isopropanol using 2DES at 77 K. We resolve many modes with frequencies that correspond well with known vibrational modes. We confirm their vibrational origin by comparing the 2D spectroscopic signatures with expectations based on a purely vibrational model.

Ultrafast X-Ray Crystallography and Liquidography

Time-resolved X-ray diffraction provides direct information on three-dimensional structures of reacting molecules and thus can be used to elucidate structural dynamics of chemical and biological reactions. In this review, we discuss time-resolved X-ray diffraction on small molecules and proteins with particular emphasis on its application to crystalline (crystallography) and liquid-solution (liquidography) samples. Time-resolved X-ray diffraction has been used to study picosecond and slower dynamics at synchrotrons and can now access even femtosecond dynamics with the recent arrival of X-ray free-electron lasers.

Spectral exhibition of electron-vibrational relaxation in P* state of Rhodobacter sphaeroides reaction centers

Electron-vibrational relaxation in the excited state of the primary electron donor, bacteriochlorophyll dimer P, in the reaction centers (RCs) of purple photosynthetic bacteria Rhodobacter sphaeroides is modeled. A multimode model of three states (i.e., the ground state Pg, initially excited P1*, and relaxed excited P2*) is used to calculate the incoherent dynamics of the difference (ΔA) spectra on a femtosecond timescale for the YM210 W mutant RCs. The relaxation processes are described by the step-ladder model. The model shows that the electron-vibrational relaxation in the excited state of P is visualized by the transient red shift of the stimulated emission from P*. The dynamics of this shift is observed as a change in the ΔA spectrum shape in its red-most part, within a few hundreds of femtoseconds after excitation. As a result, an initial rise in the red-side ΔA kinetics is delayed with respect to the blue-side kinetics. The time constant of the P1* → P2* electronic relaxation (54 fs) and the Pg, P1*, and P2* vibrational relaxations (120 fs), used in the model, provided the best fit of the experimental time-resolved ΔA spectra and kinetics at 90 and 293 K. The possible nature of the P1* → P2* electronic relaxation is discussed.

Visualizing a protein quake with time-resolved X-ray scattering at a free-electron laser

We describe a method to measure ultrafast protein structural changes using time-resolved wide-angle X-ray scattering at an X-ray free-electron laser. We demonstrated this approach using multiphoton excitation of the Blastochloris viridis photosynthetic reaction center, observing an ultrafast global conformational change that arises within picoseconds and precedes the propagation of heat through the protein. This provides direct structural evidence for a 'protein quake': the hypothesis that proteins rapidly dissipate energy through quake-like structural motions.

Modeling of reversible charge separation in reaction centers of photosynthesis: an incoherent approach

Primary charge separation in reaction centers (RCs) of bacterial photosynthesis is modeled in this work. An incoherent population dynamics of RCs states is formulated by kinetic equations. It is assumed that charge separation is accompanied by regular motion of the system along additional coordinates. This motion modulates an energetics of the reactions, and this modulation causes femtosecond oscillations in the population of the states. The best qualitative and quantitative accordance with experimental data on native, modified and mutant RCs of Rba. sphaeroides is achieved in the five states model that includes two excited states P(*)905BAHA and P(*)940BAHA and three charge separated states I, P(+)BA(-)HA and P(+)BAHA(-) (P is a primary electron donor, bacteriochlorophyll dimer, BA and HA are electron acceptors, monomeric bacteriochlorophyll and bacteriopheophytin in active A-branch respectively). The excited states emit at 905 and 940 nm and have approximately the same energy and high interaction rate. The intermediate state I is populated earlier than the P(+)BA(-)HA state and has energy close to the energy of the excited states, a high rate of population and depopulation and spectral identity to the BA(-). A sum of the I and P(+)BA(-)HA populations fits the experimental kinetics of the BA(-) absorption band at 1020 nm. The model explains an oscillatory phenomenon in the kinetics of the P(*) stimulated emission and of the BA(-) absorption. In the schemes without the I state, accordance with the experiment is achieved at unreal parameter values or is not achieved at all. A qualitative agreement of the model with the experiment can be achieved at a wide range of parameter values. The nature of the states I and P(*)940BAHA is discussed in terms of partial charge separation between P and BA and inside P respectively.

Solid-State NMR of Nanomachines Involved in Photosynthetic Energy Conversion

Magic-angle spinning NMR, often in combination with photo-CIDNP, is applied to determine how photosynthetic antennae and reaction centers are activated in the ground state to perform their biological function upon excitation by light. Molecular modeling resolves molecular mechanisms by way of computational integration of NMR data with other structure-function analyses. By taking evolutionary historical contingency into account, a better biophysical understanding is achieved. Chlorophyll cofactors and proteins go through self-assembly trajectories that are engineered during evolution and lead to highly homogeneous protein complexes optimized for exciton or charge transfer. Histidine-cofactor interactions allow biological nanomachines to lower energy barriers for light harvesting and charge separation in photosynthetic energy conversion. In contrast, in primordial chlorophyll antenna aggregates, excessive heterogeneity is paired with much less specific characteristics, and both exciton and charge-transfer character are encoded in the ground state.

Fluorescence of tryptophan in designed hairpin and Trp-cage miniproteins: measurements of fluorescence yields and calculations by quantum mechanical molecular dynamics simulations

The quantum yield of tryptophan (Trp) fluorescence was measured in 30 designed miniproteins (17 β-hairpins and 13 Trp-cage peptides), each containing a single Trp residue. Measurements were made in D(2)O and H(2)O to distinguish between fluorescence quenching mechanisms involving electron and proton transfer in the hairpin peptides, and at two temperatures to check for effects of partial unfolding of the Trp-cage peptides. The extent of folding of all the peptides also was measured by NMR. The fluorescence yields ranged from 0.01 in some of the Trp-cage peptides to 0.27 in some hairpins. Fluorescence quenching was found to occur by electron transfer from the excited indole ring of the Trp to a backbone amide group or the protonated side chain of a nearby histidine, glutamate, aspartate, tyrosine, or cysteine residue. Ionized tyrosine side chains quenched strongly by resonance energy transfer or electron transfer to the excited indole ring. Hybrid classical/quantum mechanical molecular dynamics simulations were performed by a method that optimized induced electric dipoles separately for the ground and excited states in multiple π-π* and charge-transfer (CT) excitations. Twenty 0.5 ns trajectories in the tryptophan's lowest excited singlet π-π* state were run for each peptide, beginning by projections from trajectories in the ground state. Fluorescence quenching was correlated with the availability of a CT or exciton state that was strongly coupled to the π-π* state and that matched or fell below the π-π* state in energy. The fluorescence yields predicted by summing the calculated rates of charge and energy transfer are in good accord with the measured yields.

Mechanism and Reaction Coordinate of Directional Charge Separation in Bacterial Reaction Centers

Using first-principles molecular dynamics, we predict the reaction coordinate and mechanism of the first charge-separation step in the reaction center of photosynthetic bacteria in a model including the special pair (P) and closest relevant residues. In the ground state, a dynamical localization of the highest occupied orbital is found to be a defining characteristic of P. This feature is linked to the tuning of the orbital energy levels by the coupling with two collective low-frequency vibrational modes. After electronic excitation, we demonstrate one specific mode that couples to P*, representing the reaction coordinate along which the excited state develops. The characteristic vibrational coordinate we predict to be the rotation of an axial histidine (HisM202), which selectively lowers the energy of one (PM) of the two bacteriochlorophylls in P. This leads to a unidirectional displacement of electron density to establish PL(+)PM(-) charge-transfer character, a hypothesis well-supported by an extensive framework of experimental evidence.

Coherent phenomena of charge separation in reaction centers of LL131H and LL131H/LM160H/FM197H mutants of Rhodobacter sphaeroides

Primary stage of charge separation and transfer of charges was studied in reaction centers (RCs) of point mutants LL131H and LL131H/LM160H/FM197H of the purple bacterium Rhodobacter sphaeroides by differential absorption spectroscopy with temporal resolution of 18 fsec at 90 K. Difference absorption spectra measured at 0-4 psec delays after excitation of dimer P at 870 nm with 30 fsec step were obtained in the spectral range of 935-1060 nm. It was found that a decay of P* due to charge separation is considerably slower in the mutant RCs in comparison with native RCs of Rba. sphaeroides. Coherent oscillations were found in the kinetics of stimulated emission of the P* state at 940 nm. Fourier analysis of the oscillations revealed a set of characteristic bands in the frequency range of 20-500 cm(-1). The most intense band has the frequency of ~130 cm(-1) in RCs of mutant LL131H and in native RCs and the frequency of ~100 cm(-1) in RCs of the triple mutant. It was found that an absorption band of bacteriochlorophyll anion B(A)(-) which is registered in the difference absorption spectra of native RCs at 1020 nm is absent in the analogous spectra of the mutants. The results are analyzed in terms of the participation of the B(A) molecule in the primary electron transfer in the presence of a nuclear wave packet moving along the inharmonic surface of P* potential energy.

Excited-state vibrational coherence in methanol solution of Zn(II) tetrakis(N-methylpyridyl)porphyrin: charge-dependent intermolecular mode frequencies and implications for electron-transfer dynamics in photosynthetic reaction centers

The nature of the intermolecular vibrational modes between the redox-active chromophores and the protein medium in the photosynthetic reaction center is central to an understanding of the structural origin of the quantum efficiency of the light-driven charge-separation reactions that result in storage of solar energy. In recent work on this issue, we have characterized the low-frequency vibrational coherence of Zn(II) meso-tetrakis(N-methylpyridyl)porphyrin (ZnTMPyP) and compared it to that from bacteriochlorophyll a in polar solution and in the small light-harvesting subunits B820 and B777. The charge-transfer character of ZnTMPyP's π* excited states afford us the opportunity to characterize how the intermolecular vibrational modes and potential with the surrounding medium are affected by the charge on the porphyrin macrocycle. The excited-state vibrational coherence observed with Q-band (S(1) state) excitation at 625 nm of ZnTMPyP in methanol solution contains dominant contributions from a pair of rapidly damped (effective damping time γ < 400 fs) components that are assigned to the hindered translational and librational porphyrin-solvent intermolecular modes. The 256 cm(-1) mean frequency of the intermolecular modes is significantly higher than that observed previously in the ground state, 79 cm(-1), with Soret-band excitation at 420 nm [Dillman et al., J. Phys. Chem. B. 2009, 113, 6127-6139]. The increased mode frequency arises from the activation of the ion-dipole and ion-induced-dipole terms in the intermolecular potential. In the ground state, the π-electron density of ZnTMPyP is mostly confined to the region of the porphyrin macrocycle. In the excited state, the π-electron density is extensively delocalized from the porphyrin out to two of the peripheral N-methylpyridyl rings, each of which carries a single formal charge. The charge-dependent terms contribute to a significant stabilization of the equilibrium geometry of the porphyrin-solvent complex in the excited state. In the photosynthetic reaction center, these terms will play an important role in trapping the charged products of the forward, charge-separation reactions, and the location of the bacteriopheophytin acceptor in a nonpolar region of the structure enhances the rate of the secondary charge-separation reaction.

Primary electron transfer in reaction centers of YM210L and YM210L/HL168L mutants of Rhodobacter sphaeroides

The role of tyrosine M210 in charge separation and stabilization of separated charges was studied by analyzing of the femtosecond oscillations in the kinetics of decay of stimulated emission from P* and of a population of the primary charge separated state P(+)B(A)(-) in YM210L and YM210L/HL168L mutant reaction centers (RCs) of Rhodobacter sphaeroides in comparison with those in native Rba. sphaeroides RCs. In the mutant RCs, TyrM210 was replaced by Leu. The HL168L mutation placed the redox potential of the P(+)/P pair 123 mV below that of native RCs, thus creating a theoretical possibility of P(+)B(A)(-) stabilization. Kinetics of P* decay at 940 nm of both mutants show a significant slowing of the primary charge separation reaction in comparison with native RCs. Distinct damped oscillations in these kinetics with main frequency bands in the range of 90-150 cm(-1) reflect mostly nuclear motions inside the dimer P. Formation of a very small absorption band of B(A)(-) at 1020 nm is registered in RCs of both mutants. The formation of the B(A)(-) band is accompanied by damped oscillations with main frequencies from ~10 to ~150 cm(-1). Only a partial stabilization of the P(+)B(A)(-) state is seen in the YM210L/HL168L mutant in the form of a small non-oscillating background of the 1020-nm kinetics. A similar charge stabilization is absent in the YM210L mutant. A model of oscillatory reorientation of the OH-group of TyrM210 in the electric fields of P(+) and B(A)(-) is proposed to explain rapid stabilization of the P(+)B(A)(-) state in native RCs. Small oscillatory components at ~330-380 cm(-1) in the 1020-nm kinetics of native RCs are assumed to reflect this reorientation. We conclude that the absence of TyrM210 probably cannot be compensated by lowering of the P(+)B(A)(-) free energy that is expected for the double YM210L/HL168L mutant. An oscillatory motion of the HOH55 water molecule under the influence of P(+) and B(A)(-) is assumed to be another potential contributor to the mechanism of P(+)B(A)(-) stabilization.

EvoRSR: an integrated system for exploring evolution of RNA structural robustness

Background

Robustness, maintaining a constant phenotype despite perturbations, is a fundamental property of biological systems that is incorporated at various levels of biological complexity. Although robustness has been frequently observed in nature, its evolutionary origin remains unknown. Current hypotheses suggest that robustness originated as a direct consequence of natural selection, as an intrinsic property of adaptations, or as a congruent correlate of environment robustness. To elucidate the evolutionary origins of robustness, a convenient computational package is strongly needed.

Results

In this study, we developed the open-source integrated system EvoRSR (Evolution of RNA Structural Robustness) to explore the evolution of robustness based on biologically important landscapes induced by RNA folding. EvoRSR is object-oriented, modular, and freely available at under the GNU/GPL license. We present an overview of EvoRSR package and illustrate its features with the miRNA gene cel-mir-357.

Conclusion

EvoRSR is a novel and flexible package for exploring the evolution of robustness. Accordingly, EvoRSR can be used for future studies to investigate the evolution and origin of robustness and to address other common questions about robustness. While the current EvoRSR environment is a versatile analysis framework, future versions can include features to enhance evolutionary studies of robustness.

Electron and nuclear dynamics in many-electron atoms, molecules and chlorophyll-protein complexes: a review

It has been shown [V.A. Shuvalov, Quantum dynamics of electrons in many-electron atoms of biologically important compounds, Biochemistry (Mosc.) 68 (2003) 1333-1354; V.A. Shuvalov, Quantum dynamics of electrons in atoms of biologically important molecules, Uspekhi biologicheskoi khimii, (Pushchino) 44 (2004) 79-108] that the orbit angular momentum L of each electron in many-electron atoms is L=mVr=nPlanck's and similar to L for one-electron atom suggested by N. Bohr. It has been found that for an atom with N electrons the total electron energy equation E=-(Z(eff))(2)e(4)m/(2n(2)Planck's(2)N) is more appropriate for energy calculation than standard quantum mechanical expressions. It means that the value of L of each electron is independent of the presence of other electrons in an atom and correlates well to the properties of virtual photons emitted by the nucleus and creating a trap for electrons. The energies for elements of the 1st up to the 5th rows and their ions (total amount 240) of Mendeleev' Periodical table were calculated consistent with the experimental data (deviations in average were 5 x 10(-3)). The obtained equations can be used for electron dynamics calculations in molecules. For H(2) and H(2)(+) the interference of electron-photon orbits between the atoms determines the distances between the nuclei which are in agreement with the experimental values. The formation of resonance electron-photon orbit in molecules with the conjugated bonds, including chlorophyll-like molecules, appears to form a resonance trap for an electron with E values close to experimental data. Two mechanisms were suggested for non-barrier primary charge separation in reaction centers (RCs) of photosynthetic bacteria and green plants by using the idea of electron-photon orbit interference between the two molecules. Both mechanisms are connected to formation of the exciplexes of chlorophyll-like molecules. The first one includes some nuclear motion before exciplex formation, the second one is related to the optical transition to a charge transfer state.

Intermolecular Vibrational Coherence in Bacteriochlorophyllawith Clustered Polar Solvent Molecules

We show that resonant impulsive excitation of the Qy absorption band of bacteriochlorophyll a (BChl) launches a rapidly damped (gamma < 200 fs) ground-state coherent wave-packet motion that arises from intermolecular modes with clustered solvent molecules. Femtosecond pump-probe, dynamic-absorption signals were obtained at room temperature with BChl solutions in pyridine, acetone, and 1-propanol. The vibrational coherence observed in the 0-800-fs regime is modeled in the time domain by two (or three, in the case of 1-propanol) modulation components with asymmetric, inhomogeneously broadened line shapes and frequencies in the 100-200-cm(-1) range. The mean frequency of the vibrational coherence exhibits at least a quadratic dependence on the dipole moment of the solvent molecules and a y-intercept in the 100-cm(-1) regime. This trend is modeled by an expression for the natural frequency of a "6-12" potential composed of attractive terms from van der Waals forces and a repulsive term from the exchange (Pauli exclusion) force. The model suggests that comparable contributions to the potential are provided by the dipole-dipole and London dispersion interactions. These results support the hypothesis that the low-frequency vibrational modes in the 100-cm(-1) regime that are coupled to the light-driven charge-separation reactions in the reaction center from purple bacteria are derived from intermolecular vibrational modes between the chromophores and the surrounding protein medium.

Direct evolution of genetic robustness in microRNA

Genetic robustness, the invariance of the phenotype in the face of genetic perturbations, can endow the organism with reduced susceptibility to mutations. A large body of work in recent years has focused on the origins, mechanisms, and consequences of robustness in a wide range of biological systems. Despite the apparent prevalence of mutational robustness in nature, however, its evolutionary origins are still unclear. Does robustness evolve directly by natural selection or is it merely a correlated byproduct of other phenotypic traits? By examining microRNA (miRNA) genes of several eukaryotic species, we show that the structure of miRNA precursor stem-loops exhibits a significantly high level of mutational robustness in comparison with random RNA sequences with similar stem-loop structures. Hence, this excess robustness of miRNA goes beyond the intrinsic robustness of the stem-loop hairpin structure. Furthermore, we show that it is not the byproduct of a base composition bias or of thermodynamic stability. These findings suggest that the excess robustness of miRNA stem-loops is the result of direct evolutionary pressure toward increased robustness. We further demonstrate that this adaptive robustness evolves to compensate for structures with low intrinsic robustness.

Characterization of protein matrix motions in the Rb. sphaeroides photosynthetic reaction center

We use Normal Mode Analysis to investigate motions in the photosynthetic reaction center (RC) protein. We identify the regions involved in concerted fluctuations of the protein matrix and analyze the normalized amplitudes and the directionality of the first few dominant modes. We also seek to quantify the coupling of normal modes to long-range electron transfer (ET). We find that a quasi-continuous spectrum of protein motions rather than one individual mode contributes to light-driven electron transfer. This is consistent with existing theoretical models (e.g. the spin-boson/dispersed polaron model) for the coupling of the protein and solvent "bath" to charge separation events. [Figure: see text].

Role of intramolecular vibrations in long-range electron transfer between pheophytin and ubiquinone in bacterial photosynthetic reaction centers

The dynamics of the elementary electron transfer step between pheophytin and primary ubiquinone in bacterial photosynthetic reaction centers is investigated by using a discrete state approach, including only the intramolecular normal modes of vibration of the two redox partners. The whole set of normal coordinates of the acceptor and donor groups have been employed in the computations of the Hamiltonian matrix, to reliably account both for shifts and mixing of the normal coordinates, and for changes in vibrational frequencies upon ET. It is shown that intramolecular modes provide not only a discrete set of states more strongly coupled to the initial state but also a quasicontinuum of weakly coupled states, which account for the spreading of the wave packet after ET. The computed transition probabilities are sufficiently high for asserting that electron transfer from bacteriopheophytin to the primary quinone can occur via tunneling solely promoted by intramolecular modes; the transition times, computed for different values of the electronic energy difference and coupling term, are of the same order of magnitude (10(2) ps) of the observed one.

Structural, dynamic, and energetic aspects of long-range electron transfer in photosynthetic reaction centers

Intramolecular electron transfer within proteins plays an essential role in biological energy transduction. Electron donor and acceptor cofactors are bound in the protein matrix at specific locations, and protein-cofactor interactions as well as protein conformational changes can markedly influence the electron transfer rates. To assess these effects, we have investigated charge recombination from the primary quinone acceptor to the special pair bacteriochlorophyll dimer in wild-type reaction centers of Rhodobacter sphaeroides and four mutants with widely modified free energy gaps. After light-induced charge separation, the recombination kinetics were measured in the light- and dark-adapted forms of the protein from 10 to 300 K. The data were analyzed by using the spin-boson model, which allowed us to self-consistently determine the electronic coupling energy, the distribution of energy gaps, the spectral density of phonons, and the reorganization energy. The analysis revealed slow changes of the energy gap after charge separation. Interesting correlations of the control parameters governing electron transfer were found and related to structural and dynamic properties of the protein.

Vibrational coherence from the dipyridine complex of bacteriochlorophyll a: intramolecular modes in the 10-220-cm(-1) regime, intermolecular solvent modes, and relevance to photosynthesis

We present the first observations of vibrational coherence in the 10-220-cm-1 region from bacteriochlorophyll a (BChl) in solution. A distinction can be made for the first time between BChl's intramolecular normal modes and intermolecular modes between BChl and solvent. The results show that the low-frequency vibrations that accompany the initial electron-transfer reaction from the paired BChl primary electron donor, P, in photosynthetic reaction centers arise predominantly from intramolecular modes of histidine-ligated BChl macrocycles. The results also suggest that polar-solvent interactions can significantly perturb the electronic properties of BChl in a manner that might have important functional consequences.

Energetics and mechanisms of high efficiency of charge separation and electron transfer processes in Rhodobacter sphaeroides reaction centers

Effects of environmental changes due to D(2)O/H(2)O substitution and cryosolvent addition on the energetics of the special pair and the rate constants of forward and back electron transfer reactions in the picosecond-nanosecond time domain have been studied in isolated reaction centers (RC) of the anaxogenic purple bacterium Rhodobacter sphaeroides. The following results were obtained: (i). replacement of H(2)O by D(2)O or addition of either 70% (v/v) glycerol or 35% (v/v) DMSO do not influence the absorption spectra; (ii). in marked contrast to this invariance of absorption, the maxima of fluorescence spectra are red shifted relative to control by 3.5, 6.8 and 14.5 nm for RCs suspended in glycerol, D(2)O or DMSO, respectively; (iii). D(2)O/H(2)O substitution or DMSO addition give rise to an increase of the time constants of charge separation (tau(e)), and Q(A)(-) formation (tau(Q)) by a factors of 2.5-3.1 and 1.7-2.5, respectively; (iv). addition of 70% glycerol is virtually without effect on the values of tau(e) and tau(Q); (v). the midpoint potential E(m) of P/P(+) is shifted by about 30 and 45 mV towards higher values by addition of 70% glycerol and 35% DMSO, respectively, but remains invariant to D(2)O/H(2)O exchange; and (vi). an additional fast component with tau(1)=0.5-0.8 ns in the kinetics of charge recombination P(+)H(A)(-)-->P*(P)H(A) emerges in RC suspensions modified either by D(2)O/H(2)O substitution or by DMSO treatment. The results have been analysed with special emphasis on the role of deformations of hydrogen bonds for the solvation mechanism of nonequilibrium states of cofactors. Reorientation of hydrogen bonds provides the major contribution of the very fast environmental response to excitation of the special pair P. The Gibbs standard free energy gap between 1P* and P(+)B(A)(-) due to solvation is estimated to be approximately 70, 59 and 48 meV for control, D(2)O- and DMSO-treated RC samples, respectively.

Tuning of the optical and electrochemical properties of the primary donor bacteriochlorophylls in the reaction centre from Rhodobacter sphaeroides: spectroscopy and structure

A series of mutations have been introduced at residue 168 of the L-subunit of the reaction centre from Rhodobacter sphaeroides. In the wild-type reaction centre, residue His L168 donates a strong hydrogen bond to the acetyl carbonyl group of one of the pair of bacteriochlorophylls (BChl) that constitutes the primary donor of electrons. Mutation of His L168 to Phe or Leu causes a large decrease in the mid-point redox potential of the primary electron donor, consistent with removal of this strong hydrogen bond. Mutations to Lys, Asp and Arg cause smaller decreases in redox potential, indicative of the presence of weak hydrogen bond and/or an electrostatic effect of the polar residue. A spectroscopic analysis of the mutant complexes suggests that replacement of the wild-type His residue causes a decrease in the strength of the coupling between the two primary donor bacteriochlorophylls. The X-ray crystal structure of the mutant in which His L168 has been replaced by Phe (HL168F) was determined to a resolution of 2.5 A, and the structural model of the HL168F mutant was compared with that of the wild-type complex. The mutation causes a shift in the position of the primary donor bacteriochlorophyll that is adjacent to residue L168, and also affects the conformation of the acetyl carbonyl group of this bacteriochlorophyll. This conformational change constitutes an approximately 27 degrees through-plane rotation, rather than the large into-plane rotation that has been widely discussed in the context of the HL168F mutation. The possible structural basis of the altered spectroscopic properties of the HL168F mutant reaction centre is discussed, as is the relevance of the X-ray crystal structure of the HL168F mutant to the possible structures of the remaining mutant complexes.

Modeling the bacterial photosynthetic reaction center. 4. The structural, electrochemical, and hydrogen-bonding properties of 22 mutants of Rhodobacter sphaeroides

Site-directed mutagenesis has been employed by a number of groups to produce mutants of bacterial photosynthetic reaction centers, with the aim of tuning their operation by modifying hydrogen-bond patterns in the close vicinity of the "special pair" of bacteriochlorophylls P identical with P(L)P(M). Direct X-ray structural measurements of the consequences of mutation are rare. Attention has mostly focused on effects on properties such as carbonyl stretching frequencies and midpoint potentials to infer indirectly the induced structural modifications. In this work, the structures of 22 mutants of Rhodobacter sphaeroides have been calculated using a mixed quantum-mechanical molecular-mechanical method by modifying the known structure of the wild type. We determine (i) the orientation of the 2a-acetyl groups in the wild type, FY(M197), and FH(M197) series mutants of the neutral and oxidized reaction center, (ii) the structure of the FY(M197) mutant and possible water penetration near the special pair, (iii) that significant protein chain distortions are required to assemble some M160 series mutants (LS(M160), LN(M160), LQ(M160), and LH(M160) are considered), (iv) that there is competition for hydrogen-bonding between the 9-keto and 10a-ester groups for the introduced histidine in LH(L131) mutants, (v) that the observed midpoint potential of P for HL(M202) heterodimer mutants, including one involving also LH(M160), can be correlated with the change of electrostatic potential experienced at P(L), (vi) that hydrogen-bond cleavage may sometimes be induced by oxidation of the special pair, (vii) that the OH group of tyrosine M210 points away from P(M), and (viii) that competitive hydrogen-bonding effects determine the change in properties of NL(L166) and NH(L166) mutants. A new technique is introduced for the determination of ionization energies at the Koopmans level from QM/MM calculations, and protein-induced Stark effects on vibrational frequencies are considered.

Reaction centres of purple bacteria

The bacterial reaction centre is undoubtedly one of the most heavily studied electron transfer proteins and, as this article has tried to describe, it has made some unique contributions to our understanding of biological electron transfer and coupled protonation reactions, and has provided fascinating information in areas that concern basic properties such as protein heterogeneity and protein dynamics. Despite intensive study, much remains to be learned about how this protein catalyses the conversion of solar energy into a form that can be used by the cell. In particular, the dynamic roles played by the protein are still poorly understood. The wide range of time-scales over which the reaction centre catalyses electron transfer, and the relative ease with which electron transfer can be triggered and monitored, will ensure that the reaction centre will continue to be used as a laboratory for testing ideas about the nature of biological electron transfer for many years to come.

Coherent reaction dynamics in a bacterial cytochrome c oxidase

Biological reactions in protein complexes involve structural dynamics spanning many orders of magnitude in time. In standard descriptions of catalysis by enzymes, the transition state between reactant and product is reached by thermal, stochastic motion. In the ultrashort time domain, however, the protein moiety and cofactor motions leading to altered conformations can be coherent rather than stochastic in nature. Such coherent motions may play a key role in controlling the accessibility of the transition state and explain the high efficiency of the reaction. Here we present evidence for coherent population transfer to the product state during an ultrafast reaction catalysed by a key enzyme in aerobic organisms. Using the enzyme cytochrome c oxidase aa3 from the bacterium Paracoccus denitrificans, we have studied haem dynamics during the photo-initiated ultrafast transfer of carbon monoxide from haem a3 to CuB by femtosecond spectroscopy. The ground state of the unliganded a3 species is populated in a stepwise manner in time, indicating that the reaction is mainly governed by coherent vibrations (47cm(-1)). The reaction coordinate involves conformational relaxation of the haem group and we suggest that ligand transfer also contributes.