Modulation of primary radical pair kinetics and energetics in photosystem II by the redox state of the quinone electron acceptor Q(A)

Time-resolved photovoltage measurements on destacked photosystem II membranes from spinach with the primary quinone electron acceptor Q(A) either singly or doubly reduced have been performed to monitor the time evolution of the primary radical pair P680(+)Pheo(-). The maximum transient concentration of the primary radical pair is about five times larger and its decay is about seven times slower with doubly reduced compared with singly reduced Q(A). The possible biological significance of these differences is discussed. On the basis of a simple reversible reaction scheme, the measured apparent rate constants and relative amplitudes allow determination of sets of molecular rate constants and energetic parameters for primary reactions in the reaction centers with doubly reduced Q(A) as well as with oxidized or singly reduced Q(A). The standard free energy difference DeltaG degrees between the charge-separated state P680(+)Pheo(-) and the equilibrated excited state (Chl(N)P680)* was found to be similar when Q(A) was oxidized or doubly reduced before the flash (approximately -50 meV). In contrast, single reduction of Q(A) led to a large change in DeltaG degrees (approximately +40 meV), demonstrating the importance of electrostatic interaction between the charge on Q(A) and the primary radical pair, and providing direct evidence that the doubly reduced Q(A) is an electrically neutral species, i.e., is doubly protonated. A comparison of the molecular rate constants shows that the rate of charge recombination is much more sensitive to the change in DeltaG degrees than the rate of primary charge separation.     

The molecular code for hemoglobin allostery revealed by linking the thermodynamics and kinetics of quaternary structural change. 1. Microstate linear free energy relations

A novel model linking the thermodynamics and kinetics of hemoglobin's allosteric (R --> T) and ligand binding reactions is applied to photolysis data for human HbCO. To describe hemoglobin's kinetics at the microscopic level of structural transitions and ligand-binding events for individual [ij]-ligation microstates ((ij)R --> (ij)T, (ij)R + CO --> ((i)(+1))(k)R, and (ij)T + CO --> ((i)(+1))(k)T), the model calculates activation energies, (ij)DeltaG(++), from previously measured cooperative free energies of the equilibrium microstates (Huang, Y., and Ackers, G. K. (1996) Biochemistry 35, 704-718) by using linear free energy relations ((ij)DeltaG(++) - (01)DeltaG(++) = alpha[(ij)DeltaG - (01)DeltaG], where the parameter alpha, describing the variation of activation energy with reaction energy perturbation, can depend on the natures of both the reaction and the perturbation). The alpha value measured here for the allosteric dynamics, 0.21 +/- 0.03, corresponds closely to values observed previously, strongly suggesting that the thermodynamic microstate energies directly underlie the allosteric kinetics (as opposed to the alpha((ij)DeltaG(RT)) serving merely as arbitrary fitting parameters). Besides systematizing the study of hemoglobin kinetics, the utility of the microstate linear free energy model lies in the ability to test microscopic aspects of allosteric dynamics such as the "symmetry rule" for quaternary change deduced previously from thermodynamic evidence (Ackers, G. K., et al. (1992) Science 255, 54-63). Reflecting a remarkably detailed correspondence between thermodynamics and kinetics, we find that a kinetic model that includes the large free energy splitting between doubly ligated T microstates implied by the symmetry rule fits the data significantly better than one that does not.     

Alkaline conformational transition and gated electron transfer with a Lys 79 --> his variant of iso-1-cytochrome c

To probe the mechanism of the alkaline conformational transition and its effect on the dynamics of gated electron transfer (ET) reactions, a Lys 79 --> His (K79H) variant of iso-1-cytochrome c has been prepared. Guanidine hydrochloride denaturation monitored by circular dichroism and absorbance at 695 nm indicates that this variant unfolds from a partially unfolded state. The conformation of the wild type (WT) and K79H proteins was monitored at 695 nm from pH 2 to 11. These data indicate that acid unfolding is multi-state for both K79H and WT proteins and that the His 79-heme alkaline conformer is more stable than a previously reported His 73-heme alkaline conformer. Fast and slow phases are observed in the kinetics of the alkaline transition of the K79H variant. The pH dependence of the fast phase kinetic data shows that ionizable groups with pKa values near 6.8 and 9 modulate the formation of the His 79-heme alkaline conformer. The slow phase kinetic data are consistent with a single ionizable group with a pKa near 9.5 promoting the Lys 73-heme alkaline transition. In the broader context of data on the alkaline transition, ionization of the ligand replacing Met 80 appears to play a primary role in promoting the formation of the alkaline conformer, with other ionizable groups acting as secondary modulators. Intermolecular ET with hexaammineruthenium(II) chloride shows conformational gating due to both His 79-heme and Lys 73-heme alkaline conformers. Both the position and the nature of the alkaline state ligand modulate the dynamics of ET gating.     

Probing protein dynamics using temperature jump relaxation spectroscopy

There have been recent advances in initiating and perturbing chemical reactions on very fast timescales, as short as picoseconds, thus making it feasible to study a vast range of chemical kinetics problems that heretofore could not be studied. One such approach is the rapid heating of water solutions using laser excitation. Laser-induced temperature jump relaxation spectroscopy can be used to determine the dynamics of protein motion, an area largely unstudied for want of suitable experimental and theoretical probes, despite the obvious importance of dynamics to protein function. Coupled with suitable spectroscopic probes of structure, relaxation spectroscopy can follow the motion of protein atoms over an enormous time range, from picoseconds to minutes (or longer), and with substantial structural specificity.     

Thermodynamic interpretation of protein dynamics from NMR relaxation measurements

Protein dynamics and thermodynamics can be characterized through measurements of relaxation rates of side chain (2)H and (13)C, and backbone (15)N nuclei using NMR spectroscopy. The rates reflect protein motions on timescales from picoseconds to milliseconds. Backbone and methyl side chain NMR relaxation measurements for several proteins are beginning to reveal the role of protein dynamics in protein stability and ligand binding.     

Correlation of electron transfer rate in photosynthetic reaction centers with intraprotein dielectric properties

A number of the electrogenic reactions in photosystem I, photosystem II, and bacterial reaction centers (RC) were comparatively analyzed, and the variation of the dielectric permittivity (ε) in the vicinity of electron carriers along the membrane normal was calculated. The value of ε was minimal at the core of the complexes and gradually increased towards the periphery. We found that the rate of electron transfer (ET) correlated with the value of the dielectric permittivity: the fastest primary ET reactions occur in the low-polarity core of the complexes within the picosecond time range, whereas slower secondary reactions take place at the high-polarity periphery of the complexes within micro- to millisecond time range. The observed correlation was quantitatively interpreted in the framework of the Marcus theory. We calculated the reorganization energy of ET carriers using their van der Waals volumes and experimentally determined ε values. The electronic coupling was calculated by the empirical Moser-Dutton rule for the distance-dependent electron tunneling rate in nonadiabatic ET reactions. We concluded that the local dielectric permittivity inferred from the electrometric measurements could be quantitatively used to estimate the rate constant of ET reactions in membrane proteins with resolved atomic structure with the accuracy of less than one order of magnitude.     

Effects of kinetic coupling on experimentally determined electron transfer parameters

Coupled electron transfer (ET) occurs when a relatively slow nonadiabatic ET reaction is preceded by a rapid but unfavorable adiabatic reaction that is required to activate the system for ET. As a consequence of this, the observed ET rate constant (k(ET)) is an apparent value equal to the product of the true k(ET) and the equilibrium constant for the preceding reaction step. Analysis of such reactions by ET theory may yield erroneous values for the reorganizational energy (lambda), electronic coupling (H(AB)), and ET distance that are associated with the true k(ET). If the DeltaG degrees dependence of the rate of a coupled ET reaction is analyzed, an accurate value of lambda will be obtained but the experimentally determined H(AB) will be less than the true H(AB) and the ET distance will be greater than the true distance. If the temperature dependence of the rate of a coupled ET reaction is analyzed, the experimentally determined value of lambda will be greater than the true lambda. The magnitude of this apparent lambda will depend on the magnitude of DeltaH degrees for the unfavorable reaction step that precedes ET. The experimentally determined values of H(AB) and distance will be accurate if DeltaS degrees for the preceding reaction is zero. If DeltaS degrees is positive, then H(AB) will be greater than the true value and the distance will be less than the true value. If DeltaS degrees is negative, then H(AB) will be less than the true value and the distance will be greater than the true value. Data sets for coupled ET reactions have been simulated and analyzed by ET theory to illustrate these points.     

Amplitudes and time scales of picosecond-to-microsecond motion in proteins studied by solid-state NMR: a critical evaluation of experimental approaches and application to crystalline ubiquitin

Solid-state NMR provides insight into protein motion over time scales ranging from picoseconds to seconds. While in solution state the methodology to measure protein dynamics is well established, there is currently no such consensus protocol for measuring dynamics in solids. In this article, we perform a detailed investigation of measurement protocols for fast motions, i.e. motions ranging from picoseconds to a few microseconds, which is the range covered by dipolar coupling and relaxation experiments. We perform a detailed theoretical investigation how dipolar couplings and relaxation data can provide information about amplitudes and time scales of local motion. We show that the measurement of dipolar couplings is crucial for obtaining accurate motional parameters, while systematic errors are found when only relaxation data are used. Based on this realization, we investigate how the REDOR experiment can provide such data in a very accurate manner. We identify that with accurate rf calibration, and explicit consideration of rf field inhomogeneities, one can obtain highly accurate absolute order parameters. We then perform joint model-free analyses of 6 relaxation data sets and dipolar couplings, based on previously existing, as well as new data sets on microcrystalline ubiquitin. We show that nanosecond motion can be detected primarily in loop regions, and compare solid-state data to solution-state relaxation and RDC analyses. The protocols investigated here will serve as a useful basis towards the establishment of a routine protocol for the characterization of ps–μs motions in proteins by solid-state NMR.     

Correlation of electron transfer rate in photosynthetic reaction centers with intraprotein dielectric properties

A number of the electrogenic reactions in photosystem I, photosystem II, and bacterial reaction centers (RC) were comparatively analyzed, and the variation of the dielectric permittivity (epsilon) in the vicinity of electron carriers along the membrane normal was calculated. The value of epsilon was minimal at the core of the complexes and gradually increased towards the periphery. We found that the rate of electron transfer (ET) correlated with the value of the dielectric permittivity: the fastest primary ET reactions occur in the low-polarity core of the complexes within the picosecond time range, whereas slower secondary reactions take place at the high-polarity periphery of the complexes within micro- to millisecond time range. The observed correlation was quantitatively interpreted in the framework of the Marcus theory. We calculated the reorganization energy of ET carriers using their van der Waals volumes and experimentally determined epsilon values. The electronic coupling was calculated by the empirical Moser-Dutton rule for the distance-dependent electron tunneling rate in nonadiabatic ET reactions. We concluded that the local dielectric permittivity inferred from the electrometric measurements could be quantitatively used to estimate the rate constant of ET reactions in membrane proteins with resolved atomic structure with the accuracy of less than one order of magnitude.     

Consideration of the Possibility that the slow step in protein denaturation reactions is due to cis-trans isomerism of proline residues.

A model is proposed to account for the observation that the denaturation of small proteins apparently occurs in two kinetic phases. It is suggested that only one of these phases--the fast one--is actually an unfolding process. The slow phase is assumed to arise from the cis-trans isomerism of proline residues in the denaturated protein. From model compound data, it is shown that the expected rate for isomerism is in satisfactory agreement with the rates actually observed for protein folding. It is also shown that a simple model of protein unfolding based on the isomerism concept is very successful in accounting for many known experimental characteristics of the kinetics and thermodynamic of protein denaturation. Thus, the model is able to predict that two kinetic phases will be seen in the transition region while none are seen in the base-line regions, that both the fast and slow refolding phases lead to the native protein as the product, that the fast phase becomes the only observable phase for jumps ending far in the denatured base-line region, that most or all small proteins show a limiting low-temperature activation energy of ca. 20,000 cal, and that the relaxtion time for the slow phase seen in cytochrome c denaturation is much shorter than for all other small proteins. By utilizing "double-jump" experiments, it is shown directly that the slow phase is not part of the unfolding process but that it corresponds to a transition among two or more denatured forms which have identical spectroscopic (286.5 nm) properties. Thus, the slow relaxation is "invisible" except in the transition region where it couples to the fast unfolding equilibrium. Finally, since the present model assumes that only one of the major kinetic phases seen in denaturation reactions is concerned with the denaturation process per se, it is in agreement with numerous thermodynamic studies which show consistency with the two-state model for unfolding.     

Protein flexibility from the dynamical transition: a force constant analysis

A standard analysis of the scattered neutron incoherent elastic intensity measured with very good energy resolution yields elastic scans, i.e., mean-square displacements of atomic motions (in a pico to nanosecond time scale) in a sample as a function of temperature. This provides a quick way for characterizing the dynamical behavior of biological macromolecules, such behavior being correlated with biological function and activity. Elastic scans of proteins exhibit a dynamical transition at approximately 200 K, marking a cross-over in molecular fluctuations between harmonic and nonharmonic dynamical regimes. This paper presents an approach allowing analysis of the elastic scan in terms of force constants and related parameters, such as the free energy barrier DeltaG at the transition. We find that the increased protein flexibility beyond the dynamical transition is associated with DeltaG approximately equals RT and effective force constants of the order of 0.1-3 N/m. The analysis provides a set of parameters for characterizing molecular resilience and exploring relations among dynamics, function, and activity in proteins.     

Delayed fluorescence from the photosynthetic reaction center measured by electronic gating of the photomultiplier

The decay of the delayed fluorescence (920 nm) of reaction centers from the photosynthetic bacterium Rhodobacter sphaeroides R26 in the P(+)Q(A)(-) charge-separated state (P and Q(A) are the primary donor and quinone, respectively) has been monitored in a wide (100 ns to 100 ms) time range. The photomultiplier (Hamamatsu R3310-03) was protected from the intense prompt fluorescence by application of gating potential pulses (-280 V) to the first, third, and fifth dynodes during the laser pulse. The gain of the photomultiplier dropped transiently by a factor of 1 x 10(6). The delayed fluorescence showed a smooth but nonexponential decay from 100 ns to 1 ms that was explained by the relaxation of the average free energy between P* and P(+)Q(A)(-) changing from -580 to -910 meV. This relaxation is due to the slow protein response to charge separation and can be described by a Kohlrausch relaxation function with time constant of 65 micros and a stretching exponent of alpha = 0.45.     

Electron transfer and protein dynamics in the photosynthetic reaction center.

We have measured the kinetics of electron transfer (ET) from the primary quinone (Q(A)) to the special pair (P) of the reaction center (RC) complex from Rhodobacter sphaeroides as a function of temperature (5-300 K), illumination protocol (cooled in the dark and under illumination from 110, 160, 180, and 280 K), and warming rate (1.3 and 13 mK/s). The nonexponential kinetics are interpreted with a quantum-mechanical ET model (Fermi's golden rule and the spin-boson model), in which heterogeneity of the protein ensemble, relaxations, and fluctuations are cast into a single coordinate that relaxes monotonically and is sensitive to all types of relaxations caused by ET. Our analysis shows that the structural changes that occur in response to ET decrease the free energy gap between donor and acceptor states by 120 meV and decrease the electronic coupling between donor and acceptor states from 2.7 x 10(-4) cm(-1) to 1.8 x 10(-4) cm(-1). At cryogenic temperatures, conformational changes can be slowed or completely arrested, allowing us to monitor relaxations on the annealing time scale (approximately 10(3)-10(4) s) as well as the time scale of ET (approximately 100 ms). The relaxations occur within four broad tiers of conformational substates with average apparent Arrhenius activation enthalpies of 17, 50, 78, and 110 kJ/mol and preexponential factors of 10(13), 10(15), 10(21), and 10(25) s(-1), respectively. The parameterization provides a prediction of the time course of relaxations at all temperatures. At 300 K, relaxations are expected to occur from 1 ps to 1 ms, whereas at lower temperatures, even broader distributions of relaxation times are expected. The weak dependence of the ET rate on both temperature and protein conformation, together with the possibility of modeling heterogeneity and dynamics with a single conformational coordinate, make RC a useful model system for probing the dynamics of conformational changes in proteins.     

Charge Movement of a Voltage-Sensitive Fluorescent Protein

The N-terminus of Ciona intestinalis (Ci-VSP) is a voltage-sensing domain (VSD) controlling the activity of a phosphatase domain on the C terminus. By replacing the phosphatase domain with a tandem of fluorescent proteins, CFP and YFP, a family of fluorescence resonance energy transfer-based, genetically encoded voltage-sensing fluorescent protein (VSFP) was created. VSFP2.3, one of the latest versions of this family, showed large changes in YFP emission upon changes in membrane potential with CFP excitation when expressed in Xenopus laevis oocytes. The time course of the fluorescence has two components: the fast component correlates with the time course of sensing current produced by the charge movement, while the slow component is at least one order-of-magnitude slower than the sensing current. This suggests that the tandem of fluorescent proteins reports a secondary conformational transition of the VSD which resembles the relaxation of the VSD of Ci-VSP described in detail for the Ci-VSP. This observation indicates that the relaxation of the VSD of VSFP2.3 is a global conformational change that encompasses the entire S4 segment.     

Fluorescence decay kinetics of chlorophyll in photosynthetic membranes

The absorption of light by the pigments of photosynthetic organisms results in electronic excitation that provides the energy to drive the energy-storing light reactions. A small fraction of this excitation gives rise to fluorescence emission, which serves as a sensitive probe of the energetics and kinetics of the excited states. The wavelength dependence of the excitation and emission spectra can be used to characterize the nature of the absorbing and fluorescing molecules and to monitor the process of sensitization of the excitation transfer from one pigment to another. This excitation transfer process can also be followed by the progressive depolarization of the emitted radiation. Using time-resolved fluorescence rise and decay kinetics, measurements of these processes can now be characterized to as short as a few picoseconds. Typically, excitation transfer among the antenna or light harvesting pigments occurs within 100 psec, whereupon the excitation has reached a photosynthetic reaction center capable of initiating electron transport. When this trap is functional and capable of charge separation, the fluorescence intensity is quenched and only rapidly decaying kinetic components resulting from the loss of excitation in transit in the antenna pigment bed are observed. When the reaction centers are blocked or saturated by high light intensities, the photochemical quenching is relieved, the fluorescence intensity rises severalfold, and an additional slower decay component appears and eventually dominates the decay kinetics. This slower (1-2 nsec) decay results from initial charge separation followed by recombination in the blocked reaction centers and repopulation of the excited electronic state, leading to a rapid delayed fluorescence component that is the origin of variable fluorescence. Recent growth in the literature in this area is reviewed here, with an emphasis on new information obtained on excitation transfer, trapping, and communication between different portions of the photosynthetic membranes.     

Structural relaxation and nonexponential kinetics of CO-binding to horse myoglobin. Multiple flash photolysis experiments.

The geminate recombination kinetics of CO-myoglobin strongly deviates from single exponential behavior in contrast to what is expected for unimolecular reactions (1). At low temperatures, this result was attributed to slowly exchanging conformational states which differ substantially in barrier height for ligand binding. Above 160 K the kinetics apparently slow down with temperature increase. Agmon and Hopfield (2) explain this result in terms of structural relaxation perpendicular to the reaction coordinate, which enhances the activation energy. In their model, structural relaxation homogenizes the kinetic response. Recently, Steinbach et al. (3) proposed a relaxation model which conserves the kinetic inhomogeneity. Below we test these conjectures by single and multiple excitation experiments. This method allows for discrimination between parallel (inhomogeneous) and sequential (homogeneous) kinetic schemes. The kinetic anomaly above 160 K is shown to result from a homogeneous, structurally relaxed intermediate. However a second anomaly is found above 210 K concerning the inhomogeneous phase which may indicate either a shift in activation energy or entropy.     

Thermodynamic and kinetic analysis of sensitivity amplification in biological signal transduction

Based on a thermodynamic analysis of the kinetic model for the protein phosphorylation-dephosphorylation cycle, we study the ATP (or GTP) energy utilization of this ubiquitous biological signal transduction process. It is shown that the free energy from hydrolysis inside cells, DeltaG (phosphorylation potential), controls the amplification and sensitivity of the switch-like cellular module; the response coefficient of the sensitivity amplification approaches the optimal 1 and the Hill coefficient increases with increasing DeltaG. We discover that zero-order ultrasensitivity is mathematically equivalent to allosteric cooperativity. Furthermore, we show that the high amplification in ultrasensitivity is mechanistically related to the proofreading kinetics for protein biosynthesis. Both utilize multiple kinetic cycles in time to gain temporal cooperativity, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein.     

A measure of conformational entropy change during thermal protein unfolding using neutron spectroscopy

Thermal unfolding of proteins at high temperatures is caused by a strong increase of the entropy change which lowers Gibbs free energy change of the unfolding transition (DeltaG(unf) = DeltaH - TDeltaS). The main contributions to entropy are the conformational entropy of the polypeptide chain itself and ordering of water molecules around hydrophobic side chains of the protein. To elucidate the role of conformational entropy upon thermal unfolding in more detail, conformational dynamics in the time regime of picoseconds was investigated with neutron spectroscopy. Confined internal structural fluctuations were analyzed for alpha-amylase in the folded and the unfolded state as a function of temperature. A strong difference in structural fluctuations between the folded and the unfolded state was observed at 30 degrees C, which increased even more with rising temperatures. A simple analytical model was used to quantify the differences of the conformational space explored by the observed protein dynamics for the folded and unfolded state. Conformational entropy changes, calculated on the basis of the applied model, show a significant increase upon heating. In contrast to indirect estimates, which proposed a temperature independent conformational entropy change, the measurements presented here, demonstrated that the conformational entropy change increases with rising temperature and therefore contributes to thermal unfolding.