Studies on Chromophore Coupling in Isolated Phycobiliproteins: II. Picosecond Energy Transfer Kinetics and Time-Resolved Fluorescence Spectra of C-Phycocyanin from Synechococcus 6301 as a Function of the Aggregation State

The fluorescence kinetics of C-Phycocyanin in the monomeric, trimeric, and hexameric aggregation states has been measured as a function of the emission wavelength with picosecond resolution using the single-photon timing technique. All the decay curves measured at the various emission wavelengths were analyzed simultaneously by a global data analysis procedure. A sum of four exponentials was required to fit the data for the monomers and trimers. Only in the case of the hexamers, a three-exponential model function proved to be nearly sufficient to describe the experimental decays. The lifetime of those fluorescence components reflecting energy transfer decreased with increasing aggregation. This is due to the increased number of efficient acceptor molecules next to a donor in the higher aggregates. In all aggregates the shortest-lived component, ranging from 50 ps for monomer to 10 ps for hexamers, is observed as a decay term (positive amplitude) at short emission wavelength. At long emission wavelength it turns into a rise term (negative amplitude). The lifetime of a second ps-component ranges from 200 ps for monomers to 50 ps for hexamers. The long-lived (ns) fluorescence is inhomogeneous in monomers and trimers, showing two lifetimes of ~0.6 and 1.3 ns. The latter one carries the larger amplitude. The amplitudes of the kinetic components in the fluorescence decays are presented as time-resolved component spectra. A theoretical model has been derived to rationalize the observed fluorescence kinetics. Using symmetry arguments, it is shown that the fluorescence kinetics of C-Phycocyanin is expected to be characterized by three exponential kinetic components, independent of the aggregation state. An analytical expression is derived, which allows us to gain a detailed understanding of the origin of the different kinetic components and their associated time-resolved spectra. Numerical calculations of time-resolved spectra are compared with the experimental data.     

Assessing Mathematical Models of Influenza Infections Using Features of the Immune Response

The role of the host immune response in determining the severity and duration of an influenza infection is still unclear. In order to identify severity factors and more accurately predict the course of an influenza infection within a human host, an understanding of the impact of host factors on the infection process is required. Despite the lack of sufficiently diverse experimental data describing the time course of the various immune response components, published mathematical models were constructed from limited human or animal data using various strategies and simplifying assumptions. To assess the validity of these models, we assemble previously published experimental data of the dynamics and role of cytotoxic T lymphocytes, antibodies, and interferon and determined qualitative key features of their effect that should be captured by mathematical models. We test these existing models by confronting them with experimental data and find that no single model agrees completely with the variety of influenza viral kinetics responses observed experimentally when various immune response components are suppressed. Our analysis highlights the strong and weak points of each mathematical model and highlights areas where additional experimental data could elucidate specific mechanisms, constrain model design, and complete our understanding of the immune response to influenza.     

Energy transfer processes in Gloeobacter violaceus PCC 7421 that possesses phycobilisomes with a unique morphology

We examined energy transfer dynamics in phycobilisomes (PBSs) of cyanobacteria in relation to the morphology and pigment compositions of PBSs. We used Gloeobacter violaceus PCC 7421 and measured time-resolved fluorescence spectra in three types of samples, i.e., intact cells, PBSs, and rod assemblies separated from cores. Fremyella diplosiphon, a cyanobacterial species well known for its complementary chromatic adaptation, was used for comparison after growing under red or green light. Spectral data were analyzed by the fluorescence decay-associated spectra with components common in lifetimes with a time resolution of 3 ps/channel and a spectral resolution of 2 nm/channel. This ensured a higher resolution of the energy transfer kinetics than those obtained by global analysis with fewer sampling intervals. We resolved four spectral components in phycoerythrin (PE), three in phycocyanin (PC), two in allophycocyanin, and two in photosystem II. The bundle-like PBSs of G. violaceus showed multiple energy transfer pathways; fast ( approximately 10 ps) and slow ( approximately 100 ps and approximately 500 ps) pathways were found in rods consisting of PE and PC. Energy transfer time from PE to PC was two times slower in G. violaceus than in F. diplosiphon grown under green light.     

Time-resolved fluorescence spectroscopy of spinach chloroplast

Picosecond fluorescent kinetics and time-resolved spectra of spinach chloroplast were measured at room temperature and low temperatures. The measurement is conducted with 530 nm excitation at an average intensity of 2 · 10¹⁴ photons/cm², pulse and at a pulse separation of 6 ns for the 100 pulses used. The 685 nm fluorescent kinetics was found to decay with two components, a fast component with a 56 ps lifetime, and a slow component with a 220 ps lifetime. The 730 nm fluorescent kinetics at room temperature is a single exponential decay with a 100 ps lifetime. The 730 nm fluorescence lifetime was found to increase by a factor of 6 when the temperature was lowered from room temperature to 90 K, while the 685 and 695 nm fluorescent kinetics were unchanged. The time-resolved spectra data obtained within 10 ps after excitation is consistent with the kinetic data reported here. A two-level fluorescence scheme is proposed to explain the kinetics. The effect of excitation with high light intensity and multiple pulses is discussed.     

Excitation Dynamics in Phycoerythrin 545: Modeling of Steady-State Spectra and Transient Absorption with Modified Redfield Theory

We model the spectra and excitation dynamics in the phycobiliprotein antenna complex PE545 isolated from the unicellular photosynthetic cryptophyte algae Rhodomonas CS24. The excitonic couplings between the eight bilins are calculated using the CIS/6-31G method. The site energies are extracted from a simultaneous fit of the absorption, circular dichroism, fluorescence, and excitation anisotropy spectra together with the transient absorption kinetics using the modified Redfield approach. Quantitative fit of the data enables us to assign the eight exciton components of the spectra and build up the energy transfer picture including pathways and timescales of energy relaxation, thus allowing a visualization of excitation dynamics within the complex.     

Kinetic multichannel spectroscopy of biological molecules: decomposition of the spectral matrix

The time-resolved difference spectra after flash excitation of various biological molecules are measured on a gated optical multichannel analyzer. Electron transfer between the photoactive covalent label thiouredopyrene-trisulfonate and the heme of cytochrome c and the photocycle of the E204Q mutant bacteriorhodopsin are studied. The spectral matrices containing consecutive difference spectra are analyzed to reveal the reaction kinetics and individual component spectra. Singular value decomposition combined with stoichiometric analysis and self-modeling is demonstrated as a tool for successful dissection of the matrix, despite the difficulties arising from broad, featureless, overlapping spectra and the overlapping kinetics of the components.     

Structure-based kinetic modeling of excited-state transfer and trapping in histidine-tagged photosystem II core complexes from synechocystis

Chlorophyll fluorescence decay kinetics in photosynthesis are dependent on processes of excitation energy transfer, charge separation, and electron transfer in photosystem II (PSII). The interpretation of fluorescence decay kinetics and their accurate simulation by an appropriate kinetic model is highly dependent upon assumptions made concerning the homogeneity and activity of PSII preparations. While relatively simple kinetic models assuming sample heterogeneity have been used to model fluorescence decay in oxygen-evolving PSII core complexes, more complex models have been applied to the electron transport impaired but more highly purified D1-D2-cyt b(559) preparations. To gain more insight into the excited-state dynamics of PSII and to characterize the origins of multicomponent fluorescence decay, we modeled the emission kinetics of purified highly active His-tagged PSII core complexes with structure-based kinetic models. The fluorescence decay kinetics of PSII complexes contained a minimum of three exponential decay components at F(0) and four components at F(m). These kinetics were not described well with the single radical pair energy level model, and the introduction of either static disorder or a dynamic relaxation of the radical pair energy level was required to simulate the fluorescence decay adequately. An unreasonably low yield of charge stabilization and wide distribution of energy levels was required for the static disorder model, and we found the assumption of dynamic relaxation of the primary radical pair to be more suitable. Comparison modeling of the fluorescence decay kinetics from PSII core complexes and D1-D2-cyt b(559) reaction centers indicated that the rates of charge separation and relaxation of the radical pair are likely altered in isolated reaction centers.     

Top-down elasticity analysis and its application to energy metabolism in isolated mitochondria and intact cells

This paper reviews top-down elasticity analysis, which is a subset of metabolic control analysis. Top-down elasticity analysis provides a systematic yet simple experimental method to identify all the primary sites of action of an effector in complex systems and to distinguish them from all the secondary, indirect, sites of action. In the top-down approach, the complex system (for example, a mitochondrion, cell, organ or organism) is first conceptually divided into a small number of blocks of reactions interconnected by one or more metabolic intermediates. By changing the concentration of one intermediate when all others are held constant and measuring the fluxes through each block of reactions, the overall kinetic response of each block to each intermediate can be established. The concentrations of intermediates can be changed by adding new branches to the system or by manipulating the activities of blocks of reactions whose kinetics are not under investigation. To determine how much an effector alters the overall kinetics of a block of reactions, the overall kinetic response of the block to the intermediate is remeasured in the presence of the effector. Blocks that contain significant primary sites of action will display altered kinetics; blocks that change rate only because of secondary alterations in the concentrations of other metabolites will not. If desired, this elasticity analysis can be repeated with the primary target blocks subdivided into simpler blocks so that the primary sites of action can be defined with more and more precision until, with sufficient subdivision, they are mapped onto individual kinetic steps. Top-down elasticity analysis has been used to identify the targets of effectors of oxygen consumption in mitochondria, hepatocytes and thymocytes. Effectors include poisons such as cadmium and hormones such as tri-iodothyronine. However, the method is more general than this; in principle it can be applied to any metabolic or other steady-state system.     

Measurement of rotational dynamics by the simultaneous nonlinear analysis of optical and EPR data.

In the preceding companion article in this issue, an optical dye and a nitroxide radical were combined in a new dual function probe, 5-SLE. In this report, it is demonstrated that time-resolved optical anisotropy and electron paramagnetic resonance (EPR) data can be combined in a single analysis to measure rotational dynamics. Rigid-limit and rotational diffusion models for simulating nitroxide EPR data have been incorporated into a general non-linear least-squares procedure based on the Marquardt-Levenberg algorithm. Simultaneous fits to simulated time-resolved fluorescence anisotropy and linear EPR data, together with simultaneous fits to experimental time-resolved phosphorescence anisotropy decays and saturation transfer EPR (ST-EPR) spectra of 5-SLE noncovalently bound to bovine serum albumin (BSA) have been performed. These results demonstrate that data from optical and EPR experiments can be combined and globally fit to a single dynamic model.     

Macro-level modeling of the response of C. elegans reproduction to chronic heat stress

A major goal of systems biology is to understand how organism-level behavior arises from a myriad of molecular interactions. Often this involves complex sets of rules describing interactions among a large number of components. As an alternative, we have developed a simple, macro-level model to describe how chronic temperature stress affects reproduction in C. elegans. Our approach uses fundamental engineering principles, together with a limited set of experimentally derived facts, and provides quantitatively accurate predictions of performance under a range of physiologically relevant conditions. We generated detailed time-resolved experimental data to evaluate the ability of our model to describe the dynamics of C. elegans reproduction. We find considerable heterogeneity in responses of individual animals to heat stress, which can be understood as modulation of a few processes and may represent a strategy for coping with the ever-changing environment. Our experimental results and model provide quantitative insight into the breakdown of a robust biological system under stress and suggest, surprisingly, that the behavior of complex biological systems may be determined by a small number of key components.     

Energy dissipation efficiency in the CP43 assembly intermediate complex of photosystem II

Photosystem II in oxygenic organisms is a large membrane bound rapidly turning over pigment protein complex. During its biogenesis, multiple assembly intermediates are formed, including the CP43-preassembly complex (pCP43). To understand the energy transfer dynamics in pCP43, we first engineered a His-tagged version of the CP43 in a CP47-less strain of the cyanobacterium Synechocystis 6803. Isolated pCP43 from this engineered strain was subjected to advanced spectroscopic analysis to evaluate its excitation energy dissipation characteristics. These included measurements of steady-state absorption and fluorescence emission spectra for which correlation was tested with Stepanov relation. Comparison of fluorescence excitation and absorptance spectra determined that efficiency of energy transfer from β-carotene to chlorophyll a is 39 %. Time-resolved fluorescence images of pCP43-bound Chl a were recorded on streak camera, and fluorescence decay dynamics were evaluated with global fitting. These demonstrated that the decay kinetics strongly depends on temperature and buffer used to disperse the protein sample and fluorescence decay lifetime was estimated in 3.2–5.7 ns time range, depending on conditions. The pCP43 complex was also investigated with femtosecond and nanosecond time-resolved absorption spectroscopy upon excitation of Chl a and β-carotene to reveal pathways of singlet excitation relaxation/decay, Chl a triplet dynamics and Chl a → β-carotene triplet state sensitization process. The latter demonstrated that Chl a triplet in the pCP43 complex is not efficiently quenched by carotenoids. Finally, detailed kinetic analysis of the rise of the population of β-carotene triplets determined that the time constant of the carotenoid triplet sensitization is 40 ns.     

Rapid Global Fitting of Large Fluorescence Lifetime Imaging Microscopy Datasets

Fluorescence lifetime imaging (FLIM) is widely applied to obtain quantitative information from fluorescence signals, particularly using Förster Resonant Energy Transfer (FRET) measurements to map, for example, protein-protein interactions. Extracting FRET efficiencies or population fractions typically entails fitting data to complex fluorescence decay models but such experiments are frequently photon constrained, particularly for live cell or in vivo imaging, and this leads to unacceptable errors when analysing data on a pixel-wise basis. Lifetimes and population fractions may, however, be more robustly extracted using global analysis to simultaneously fit the fluorescence decay data of all pixels in an image or dataset to a multi-exponential model under the assumption that the lifetime components are invariant across the image (dataset). This approach is often considered to be prohibitively slow and/or computationally expensive but we present here a computationally efficient global analysis algorithm for the analysis of time-correlated single photon counting (TCSPC) or time-gated FLIM data based on variable projection. It makes efficient use of both computer processor and memory resources, requiring less than a minute to analyse time series and multiwell plate datasets with hundreds of FLIM images on standard personal computers. This lifetime analysis takes account of repetitive excitation, including fluorescence photons excited by earlier pulses contributing to the fit, and is able to accommodate time-varying backgrounds and instrument response functions. We demonstrate that this global approach allows us to readily fit time-resolved fluorescence data to complex models including a four-exponential model of a FRET system, for which the FRET efficiencies of the two species of a bi-exponential donor are linked, and polarisation-resolved lifetime data, where a fluorescence intensity and bi-exponential anisotropy decay model is applied to the analysis of live cell homo-FRET data. A software package implementing this algorithm, FLIMfit, is available under an open source licence through the Open Microscopy Environment.     

Nanosecond temperature jump relaxation dynamics of cyclic beta-hairpin peptides

The thermal unfolding of a series of 6-, 10-, and 14-mer cyclic beta-hairpin peptides was studied to gain insight into the mechanism of formation of this important secondary structure. The thermodynamics of the transition were characterized using temperature dependent Fourier transform infrared spectroscopy. Thermodynamic data were analyzed using a two-state model which indicates increasing cooperativity along the series. The relaxation kinetics of the peptides in response to a laser induced temperature jump were probed using time-resolved infrared spectroscopy. Single exponential relaxation kinetics were observed and fit with a two-state model. The folding rate determined for these cyclic peptides is accelerated by some two orders of magnitude over the rate of a linear peptide that forms a beta-hairpin. This observation supports the argument that the rate limiting step in the linear system is either stabilization of compact collapsed structures or rearrangement of collapsed structures over a barrier to achieve the native interstrand registry. Small activation energies for folding of these peptides obtained from an Arrhenius analysis of the rates imply a primarily entropic barrier, hence an organized transition state having specific stabilizing interactions.     

Profiling of dynamics in protein–lipid–water systems: a time-resolved fluorescence study of a model membrane protein with the label BADAN at specific membrane depths

Profiles of lipid-water bilayer dynamics were determined from picosecond time-resolved fluorescence spectra of membrane-embedded BADAN-labeled M13 coat protein. For this purpose, the protein was labeled at seven key positions. This places the label at well-defined locations from the water phase to the center of the hydrophobic acyl chain region of a phospholipid model membrane, providing us with a nanoscale ruler to map membranes. Analysis of the time-resolved fluorescence spectroscopic data provides the characteristic time constant for the twisting motion of the BADAN label, which is sensitive to the local flexibility of the protein–lipid environment. In addition, we obtain information about the mobility of water molecules at the membrane–water interface. The results provide an unprecedented nanoscale profiling of the dynamics and distribution of water in membrane systems. This information gives clear evidence that the actual barrier of membranes for ions and aqueous solvents is located at the region of carbonyl groups of the acyl chains.     

Flexible components of functional responses

1. The functional response of predators describes the rate at which a predator consumes prey and is an important determinant of community dynamics. Despite the importance, most empirical studies have considered a limited number of models of functional response. In addition, the models often make strong assumptions about the pattern of predation processes, even though functional responses can potentially exhibit a wide variety of patterns. 2. In addition to the limited model consideration, model selections of functional response models cannot tease apart the components of predation (i.e. capture rate and handling time) when flexible traits are considered because it is always possible that many different combinations of the capture rate and handling time can lead to the same predation rate. 3. This study directly examined the capture rate and handling time of functional response in a mite community. To avoid the model selection problem, the searching and handling behaviour data were collected. The model selection was applied directly to these two components of predation data. Commonly used functional response models and models that allow for more flexible patterns were compared. 4. The results indicated that assumptions of the commonly used models were not supported by the data, and a flexible model was selected as the best model. These results suggest the need to consider a wider variety of predation patterns when characterizing a functional response. Without making a strong assumption (e.g. static handling time), model selections on functional response models cannot be used to make reliable inferences on the predation mechanisms.