SVD-aided pseudo principal-component analysis: A new method to speed up and improve determination of the optimum kinetic model from time-resolved data

Tracking the structural dynamics of proteins with time-resolved X-ray solution scattering

Relevant events during protein function such as ligand binding/release and interaction with substrates or with light are often accompanied by out-of-equilibrium structural dynamics. Time-resolved experimental techniques have been developed to follow protein structural changes as they happen in real time after a given reaction-triggering event. Time-resolved X-ray solution scattering is a promising approach that bears structural sensitivity with temporal resolution in the femto-to-millisecond time range, depending on the X-ray source characteristics and the triggering method. Here we present the basic principles of the technique together with a description of the most relevant results recently published and a discussion on the computational methods currently developed to achieve a structural interpretation of the time-resolved X-ray solution scattering experimental data.

Projection to extract the perpendicular component (PEPC) method for extracting kinetics from time-resolved data

Time-resolved x-ray liquidography (TRXL) is a potent method for investigating the structural dynamics of chemical and biological reactions in the liquid phase. It has enabled the extraction of detailed structural aspects of various dynamic processes, the molecular structures of intermediates, and kinetics of reactions across a wide range of systems, from small molecules to proteins and nanoparticles. Proper data analysis is key to extracting the information of the kinetics and structural dynamics of the studied system encrypted in the TRXL data. In typical TRXL data, the signals from solute scattering, solvent scattering, and solute-solvent cross scattering are mixed in the q-space, and the solute kinetics and solvent hydrodynamics are mixed in the time domain, thus complicating the data analysis. Various methods developed so far generally require prior knowledge of the molecular structures of candidate species involved in the reaction. Because such information is often unavailable, a typical data analysis often involves tedious trial and error. To remedy this situation, we have developed a method named projection to extract the perpendicular component (PEPC), capable of removing the contribution of solvent kinetics from TRXL data. The resulting data then contain only the solute kinetics, and, thus, the solute kinetics can be easily determined. Once the solute kinetics is determined, the subsequent data analysis to extract the structural information can be performed with drastically improved convenience. The application of the PEPC method is demonstrated with TRXL data from the photochemistry of two molecular systems: [Au(CN)₂^-]₃ in water and CHI₃ in cyclohexane.

Extracting Kinetics and Thermodynamics of Molecules without Heavy Atoms via Time-Resolved Solvent Scattering Signals

Time-resolved X-ray liquidography (TRXL) has emerged as a powerful technique for studying the structural dynamics of small molecules and macromolecules in liquid solutions. However, TRXL has limited sensitivity for small molecules containing light atoms only, whose signal has lower contrast compared with the signal from solvent molecules. Here, we present an alternative approach to bypass this limitation by detecting the change in solvent temperature resulting from a photoinduced reaction. Specifically, we analyzed the heat dynamics of TRXL data obtained from p-hydroxyphenacyl diethyl phosphate (HPDP). This analysis enabled us to experimentally determine the number of intermediates and their respective enthalpy changes, which can be compared to theoretical enthalpies to identify the intermediates. This work demonstrates that TRXL can be used to uncover the kinetics and reaction pathways for small molecules without heavy atoms even if the scattering signal from the solute molecules is buried under the strong solvent scattering signal.

KiMoPack: A python Package for Kinetic Modeling of the Chemical Mechanism

Herein, we present KiMoPack, an analysis tool for the kinetic modeling of transient spectroscopic data. KiMoPack enables a state-of-the-art analysis routine including data preprocessing and standard fitting (global analysis), as well as fitting of complex (target) kinetic models, interactive viewing of (fit) results, and multiexperiment analysis via user accessible functions and a graphical user interface (GUI) enhanced interface. To facilitate its use, this paper guides the user through typical operations covering a wide range of analysis tasks, establishes a typical workflow and is bridging the gap between ease of use for less experienced users and introducing the advanced interfaces for experienced users. KiMoPack is open source and provides a comprehensive front-end for preprocessing, fitting and plotting of 2-dimensional data that simplifies the access to a powerful python-based data-processing system and forms the foundation for a well documented, reliable, and reproducible data analysis.

Optical Kerr Effect of Liquid Acetonitrile Probed by Femtosecond Time-Resolved X-ray Liquidography

Optical Kerr effect (OKE) spectroscopy is a method that measures the time-dependent change of the birefringence induced by an optical laser pulse using another optical laser pulse and has been used often to study the ultrafast dynamics of molecular liquids. Here we demonstrate an alternative method, femtosecond time-resolved X-ray liquidography (fs-TRXL), where the microscopic structural motions related to the OKE response can be monitored using a different type of probe, i.e., X-ray solution scattering. By applying fs-TRXL to acetonitrile and a dye solution in acetonitrile, we demonstrate that different types of molecular motions around photoaligned molecules can be resolved selectively, even without any theoretical modeling, based on the anisotropy of two-dimensional scattering patterns and extra structural information contained in the q-space scattering data. Specifically, the dynamics of reorientational (libration and orientational diffusion) and translational (interaction-induced motion) motions are captured separately by anisotropic and isotropic scattering signals, respectively. Furthermore, the two different types of reorientational motions are distinguished from each other by their own characteristic scattering patterns and time scales. The measured time-resolved scattering signals are in excellent agreement with the simulated scattering signals based on a molecular dynamics simulation for plausible molecular configurations, providing the detailed structural description of the OKE response in liquid acetonitrile.

Effect of the abolition of intersubunit salt bridges on allosteric protein structural dynamics

A salt bridge, one of the representative structural factors established by non-covalent interactions, plays a crucial role in stabilizing the structure and regulating the protein function, but its role in dynamic processes has been elusive. Here, to scrutinize the structural and functional roles of the salt bridge in the process of performing the protein function, we investigated the effects of salt bridges on the allosteric structural transition of homodimeric hemoglobin (HbI) by applying time-resolved X-ray solution scattering (TRXSS) to the K30D mutant, in which the interfacial salt bridges of the wild type (WT) are abolished. The TRXSS data of K30D are consistent with the kinetic model that requires one monomer intermediate in addition to three structurally distinct dimer intermediates (I1, I2, and I3) observed in WT and other mutants. The kinetic and structural analyses show that K30D has an accelerated biphasic transition from I2 to I3 by more than nine times compared to WT and lacks significant structural changes in the transition from R-like I2 to T-like I3 observed in WT, unveiling that the loss of the salt bridges interrupts the R-T allosteric transition of HbI. Besides, the correlation between the bimolecular CO recombination rates in K30D, WT, and other mutants reveals that the bimolecular CO recombination is abnormally decelerated in K30D, indicating that the salt bridges also affect the cooperative ligand binding in HbI. These comparisons of the structural dynamics and kinetics of K30D and WT show that the interfacial salt bridges not only assist the physical connection of two subunits but also play a critical role in the global structural signal transduction of one subunit to the other subunit via a series of well-organized structural transitions.

Protein folding from heterogeneous unfolded state revealed by time-resolved X-ray solution scattering

One of the most challenging tasks in biological science is to understand how a protein folds. In theoretical studies, the hypothesis adopting a funnel-like free-energy landscape has been recognized as a prominent scheme for explaining protein folding in views of both internal energy and conformational heterogeneity of a protein. Despite numerous experimental efforts, however, comprehensively studying protein folding with respect to its global conformational changes in conjunction with the heterogeneity has been elusive. Here we investigate the redox-coupled folding dynamics of equine heart cytochrome c (cyt-c) induced by external electron injection by using time-resolved X-ray solution scattering. A systematic kinetic analysis unveils a kinetic model for its folding with a stretched exponential behavior during the transition toward the folded state. With the aid of the ensemble optimization method combined with molecular dynamics simulations, we found that during the folding the heterogeneously populated ensemble of the unfolded state is converted to a narrowly populated ensemble of folded conformations. These observations obtained from the kinetic and the structural analyses of X-ray scattering data reveal that the folding dynamics of cyt-c accompanies many parallel pathways associated with the heterogeneously populated ensemble of unfolded conformations, resulting in the stretched exponential kinetics at room temperature. This finding provides direct evidence with a view to microscopic protein conformations that the cyt-c folding initiates from a highly heterogeneous unfolded state, passes through still diverse intermediate structures, and reaches structural homogeneity by arriving at the folded state.

A new visible light triggered Arrhenius photobase and its photo-induced reactions

Visible light triggered Arrhenius photobases are of potential use for excited state hydroxide ion dissociation (ESHID), photo-induced pOH jump experiments, and base-catalyzed reactions.

SVD-aided non-orthogonal decomposition (SANOD) method to exploit prior knowledge of spectral components in the analysis of time-resolved data

Analysis of time-resolved data typically involves discriminating noise against the signal and extracting time-independent components and their time-dependent contributions. Singular value decomposition (SVD) serves this purpose well, but the extracted time-independent components are not necessarily the physically meaningful spectra directly representing the actual dynamic or kinetic processes but rather a mathematically orthogonal set necessary for constituting the physically meaningful spectra. Converting the orthogonal components into physically meaningful spectra requires subsequent posterior analyses such as linear combination fitting (LCF) and global fitting (GF), which takes advantage of prior knowledge about the data but requires that all components are known or satisfactory components are guessed. Since in general not all components are known, they have to be guessed and tested via trial and error. In this work, we introduce a method, which is termed SVD-aided Non-Orthogonal Decomposition (SANOD), to circumvent trial and error. The key concept of SANOD is to combine the orthogonal components from SVD with the known prior knowledge to fill in the gap of the unknown signal components and to use them for LCF. We demonstrate the usefulness of SANOD via applications to a variety of cases.

Protein Structural Dynamics of Wild-Type and Mutant Homodimeric Hemoglobin Studied by Time-Resolved X-Ray Solution Scattering

The quaternary transition between the relaxed (R) and tense (T) states of heme-binding proteins is a textbook example for the allosteric structural transition. Homodimeric hemoglobin (HbI) from Scapharca inaequivalvis is a useful model system for investigating the allosteric behavior because of the relatively simple quaternary structure. To understand the cooperative transition of HbI, wild-type and mutants of HbI have been studied by using time-resolved X-ray solution scattering (TRXSS), which is sensitive to the conformational changes. Herein, we review the structural dynamics of HbI investigated by TRXSS and compare the results of TRXSS with those of other techniques.

Shedding Light on the Nature of Photoinduced States Formed in a Hydrogen-Generating Supramolecular RuPt Photocatalyst by Ultrafast Spectroscopy

Photoinduced electronic and structural changes of a hydrogen-generating supramolecular RuPt photocatalyst are studied by a combination of time-resolved photoluminescence, optical transient absorption, and X-ray absorption spectroscopy. This work uses the element specificity of X-ray techniques to focus on the interplay between the photophysical and -chemical processes and the associated time scales at the catalytic Pt moiety. We observe very fast (<30 ps) photoreduction of the Pt catalytic site, followed by an ∼600 ps step into a strongly oxidized Pt center. The latter process is likely induced by oxidative addition of reactive iodine species. The oxidized Pt species is long-lived and fully recovers to the original ground state complex on a >10 μs time scale. However, the photosensitizing Ru moiety is fully restored on a much shorter ∼300 ns time scale. This reaction scheme implies that we may withdraw two electrons from a catalyst that is activated by a single photon.

Insulin hexamer dissociation dynamics revealed by photoinduced T-jumps and time-resolved X-ray solution scattering

The structural dynamics of insulin hexamer dissociation were studied by the photoinduced temperature jump technique and monitored by time-resolved X-ray scattering. The process of hexamer dissociation was found to involve several transient intermediates, including an expanded hexamer and an unstable tetramer. Our findings provide insights into the mechanisms of protien-protein association.

Probing Cytochrome c Folding Transitions upon Phototriggered Environmental Perturbations Using Time-Resolved X-ray Scattering

Direct tracking of protein structural dynamics during folding-unfolding processes is important for understanding the roles of hierarchic structural factors in the formation of functional proteins. Using cytochrome c (cyt c) as a platform, we investigated its structural dynamics during folding processes triggered by local environmental changes (i.e., pH or heme iron center oxidation/spin/ligation states) with time-resolved X-ray solution scattering measurements. Starting from partially unfolded cyt c, a sudden pH drop initiated by light excitation of a photoacid caused a structural contraction in microseconds, followed by active site restructuring and unfolding in milliseconds. In contrast, the reduction of iron in the heme via photoinduced electron transfer did not affect conformational stability at short timescales (<1 ms), despite active site coordination geometry changes. These results demonstrate how different environmental perturbations can change the nature of interaction between the active site and protein conformation, even within the same metalloprotein, which will subsequently affect the folding structural dynamics.

Direct Observation of Insulin Association Dynamics with Time-Resolved X-ray Scattering

Biological functions frequently require protein-protein interactions that involve secondary and tertiary structural perturbation. Here we study protein-protein dissociation and reassociation dynamics in insulin, a model system for protein oligomerization. Insulin dimer dissociation into monomers was induced by a nanosecond temperature-jump (T-jump) of ∼8 °C in aqueous solution, and the resulting protein and solvent dynamics were tracked by time-resolved X-ray solution scattering (TRXSS) on time scales of 10 ns to 100 ms. The protein scattering signals revealed the formation of five distinguishable transient species during the association process that deviate from simple two-state kinetics. Our results show that the combination of T-jump pump coupled to TRXSS probe allows for direct tracking of structural dynamics in nonphotoactive proteins.