Charge recombination time distributions in photosynthetic reaction centers exposed to alternating intervals of photoexcitation and dark relaxation.

The charge recombination lifetime of photosynthetic reaction centers (RCs) increases significantly upon lengthy illumination, revealing nonequilibrium structural transitions in the protein-cofactor system. This paper analyzes the charge recombination kinetics measured in isolated RCs following a systematic variation of actinic illumination times (pulses) from 0.1 s to hundreds of seconds. The maximum entropy method (MEM) was utilized for optimizing the fitting procedure to retrieve the relaxation spectrum from the experimental recombination kinetics curves. The MEM-assisted analysis reveals that each relaxation curve contains at least three peaks in the relaxation time-distribution domain. Two peaks are always observed, one near 0.1 s and the other near 1 s recombination times. A third peak appears after prolonged photoexcitation with a relaxation time significantly greater than 1 s, and the time of this peak increases further in recombination time as the photoexcitation pulse duration is increased. In addition to the shifts of the time constant distributions, the amplitudes of the distributions in the time domain spectrum demonstrate a variation in the quinone occupancy of the RCs. The results reported here support our previous claim that accumulation of slow conformational changes, triggered by charge separation events in the RCs, controls system dynamics and favors stabilization of more efficient functioning regimes of the RCs.

Approximation of super-ions for single-file diffusion of multiple ions through narrow pores.

The general theory of the single-file multiparticle diffusion in the narrow pores could be greatly simplified in the case of inverted bell-like shape of the single-particle energy profile, which is often observed in biological ion channels. There is a narrow and deep groove in the energy landscape of multiple interacting ions in such profiles, which corresponds to the pre-defined optimal conduction pathway in the configurational space. If such groove exists, the motion of multiple ions can be reduced to the motion of single quasiparticle, called the superion, which moves in one-dimensional effective potential. The concept of the superions dramatically reduces the computational complexity of the problem and provides very clear physical interpretation of conduction phenomena in the narrow pores.

Theory of single-file multiparticle diffusion in narrow pores.

Single-file diffusion of multiple strongly interacting particles in a one-dimensional pore is described within a general analytical framework. The theory accounts for nonequilibrium conditions, explicit particle-particle interactions, external potential acting on the particles and the fluctuations of the number of particles due to their exchange with external equilibrium reservoirs. It is shown that the problem can be reduced to a closed hierarchical set of partial differential equations of increasing dimensionality, which can be solved numerically. Our framework allows computing any macroscopic characteristic of multiparticle diffusion in the pore. It is shown that the pore occupancy probabilities and the current are rational functions of external concentrations in the steady state. The theory is tested on a simplified model of the narrow rigid pore inspired by the selectivity filter of biological ion channel. Perspectives and limitations of the theory are discussed.

Equilibration kinetics in isolated and membrane-bound photosynthetic reaction centers upon illumination: a method to determine the photoexcitation rate.

Kinetics of electron transfer, following variation of actinic light intensity, for photosynthetic reaction centers (RCs) of purple bacteria (isolated and membrane-bound) were analyzed by measuring absorbance changes in the primary photoelectron donor absorption band at 865 nm. The bleaching of the primary photoelectron donor absorption band in RCs, following a sudden increase of illumination from the dark to an actinic light intensity of I(exp), obeys a simple exponential law with the rate constant alphaI(exp) + k(rec), in which alpha is a parameter relating the light intensity, measured in mW/cm(2), to a corresponding theoretical rate in units of reciprocal seconds, and k(rec) is the effective rate constant of the charge recombination in the photosynthetic RCs. In this work, a method for determining the alpha parameter value is developed and experimentally verified for isolated and membrane-bound RCs, allowing for rigorous modeling of RC macromolecule dynamics under varied photoexcitation conditions. Such modeling is necessary for RCs due to alterations of the forward photoexcitation rates and relaxation rates caused by illumination history and intramolecular structural dynamics effects. It is demonstrated that the classical Bouguer-Lambert-Beer formalism can be applied for the samples with relatively low scattering, which is not necessarily the case with strongly scattering media or high light intensity excitation.

Fuzzy domains: new way of describing flexibility and interdependence of the protein domains.

We proposed the innovative method of domain identification based on the concept of the fuzzy domains. In this method each residue of the protein can belong to several domains simultaneously with certain weights, which reflect to what extent this residue shares the motion pattern of the given domain. Our method allows describing the fuzzy boundaries between the domains and the gradual changes of the motion pattern from one domain to the other. It provides the reasonable compromise between the continuous change of the protein dynamics from one residue to the other and the discrete description of the structure in terms of small number of domains. We suggested quantitative criterion, which shows the overall degree of domain flexibility in the protein. The concept of the fuzzy domains provides an innovative way of visualization of domain flexibility, which makes the gradual transitions between the domains clearly visible and comparable to available experimental and structural data. In the future, the concept of the fuzzy domains can be used in the coarse-grained simulations of the domain dynamics in order to account for internal protein flexibility.

Is the mobility of the pore walls and water molecules in the selectivity filter of KcsA channel functionally important?

We performed in-depth analysis of the forces which act on the K(+) ions in the selectivity filter of the KcsA channel in order to estimate the relative importance of static and dynamic influence of the filter wall and water molecules on ion permeation and selectivity. The forces were computed using the trajectories of all-atom molecular dynamics simulations. It is shown that the dynamics of the selectivity filter contributes about 3% to the net force acting on the ions and can be neglected in the studies focused on the macroscopic properties of the channel, such as the current. Among the filter atoms, only the pore-forming carbonyl groups can be considered as dynamic in the studies of microscopic events of conduction, while the dynamic effects from all other atoms are negligible. We also show that the dynamics of the water molecules in the filter can not be neglected. The fluctuating forces from the water molecules can be as strong as net forces from the pore walls and can effectively drive the ions through the local energy barriers in the filter.

The blind search for the closed states of hinge-bending proteins.

The hinge-bending proteins provide the most pronounced example of the large-amplitude slow motions in a number of proteins, which are critical for their functioning. They are often used as the test ground for developing novel approaches to the simulation of slow protein dynamics. In the present study, we present the algorithm, which allows physically-consistent simulations of slow protein dynamics in globular proteins. Our algorithm is based on the hierarchical clustering of the correlation patterns (HCCP) technique of domain identification, which allows subdividing the protein into the hierarchy of the rigid-body-like clusters. The clusters are allowed to rotate relative to one another on the automatically identified hinges. The clusters are found in the course of automated, objective and well-tested procedure. In the present communication, our technique is applied to 10 hinge-bending proteins. For each of the proteins, we performed the blind search for the closed conformation, staring from the open one. Resulting closed conformations are compared with the closed states observed in crystallographic structures. It is shown that our technique produces realistic closed conformations for 8 out of 10 studied proteins. This demonstrates that HCCP technique can be used for finding alternative protein conformations and for sampling the slow motions in proteins.

The change of protein intradomain mobility on ligand binding: is it a commonly observed phenomenon?

Analysis of changes in the dynamics of protein domains on ligand binding is important in several aspects: for the understanding of the hierarchical nature of protein folding and dynamics at equilibrium; for analysis of signal transduction mechanisms triggered by ligand binding, including allostery; for drug design; and for construction of biosensors reporting on the presence of target ligand in studied media. In this work we use the recently developed HCCP computational technique for the analysis of stabilities of dynamic domains in proteins, their intrinsic motions and of their changes on ligand binding. The work is based on comparative studies of 157 ligand binding proteins, for which several crystal structures (in ligand-free and ligand-bound forms) are available. We demonstrate that the domains of the proteins presented in the Protein DataBank are far more robust than it was thought before: in the majority of the studied proteins (152 out of 157), the ligand binding does not lead to significant change of domain stability. The exceptions from this rule are only four bacterial periplasmic transport proteins and calmodulin. Thus, as a rule, the pattern of correlated motions in dynamic domains, which determines their stability, is insensitive to ligand binding. This rule may be the general feature for a vast majority of proteins.

Dynamic protein domains: identification, interdependence, and stability.

Existing methods of domain identification in proteins usually provide no information about the degree of domain independence and stability. However, this information is vital for many areas of protein research. The recently developed hierarchical clustering of correlation patterns (HCCP) technique provides machine-based domain identification in a computationally simple and physically consistent way. Here we present the modification of this technique, which not only allows determination of the most plausible number of dynamic domains but also makes it possible to estimate the degree of their independence (the extent of correlated motion) and stability (the range of environmental conditions, where domains remain intact). With this technique we provided domain assignments and calculated intra- and interdomain correlations and interdomain energies for >2500 test proteins. It is shown that mean intradomain correlation of motions can serve as a quantitative criterion of domain independence, and the HCCP stability gap is a measure of their stability. Our data show that the motions of domains with high stability are usually independent. In contrast, the domains with moderate stability usually exhibit a substantial degree of correlated motions. It is shown that in multidomain proteins the domains are most stable if they are of similar size, and this correlates with the observed abundance of such proteins.

Self-regulation phenomena applied to bacterial reaction centers: 2. Nonequilibrium adiabatic potential: dark and light conformations revisited.

Experimental and theoretical results in support of nonlinear dynamic behavior of photosynthetic reaction centers under light-activated conditions are presented. Different conditions of light adaptation allow for preparation of reaction centers in either of two different conformational states. These states were detected both by short actinic flashes and by the switching of the actinic illumination level between different stationary state values. In the second method, the equilibration kinetics of reaction centers isolated from Rhodobacter sphaeroides were shown to be inherently biphasic. The fast and slow equilibration kinetics are shown to correspond to electron transfer (charge separation) at a fixed structure and to combined electron-conformational transitions governed by the bounded diffusion along the potential surface, respectively. The primary donor recovery kinetics after an actinic flash revealed a pronounced dependence on the time interval (deltat) between cessation of a lengthy preillumination of a sample and the actinic flash. A pronounced slow relaxation component with a decay half time of more than 50 s was measured for deltat > 10 s. This component corresponds to charge recombination in reaction centers for which light-induced structural changes have not relaxed completely before the flash. The amplitude of this component depended on the conditions of the sample preparation, specifically on the type of detergent used in the preparation. The redox potential parameters as well as the structural diffusion constants were estimated for samples prepared in different ways.