Analysis Of Time-resolved Data Research Articles

Scaling and Merging Time-Resolved Laue Data with Variational Inference.

Time-resolved X-ray crystallography (TR-X) at synchrotrons and free electron lasers is a promising technique for recording dynamics of molecules at atomic resolution. While experimental methods for TR-X have proliferated and matured, data analysis is often difficult. Extracting small, time-dependent changes in signal is frequently a bottleneck for practitioners. Recent work demonstrated this challenge can be addressed when merging redundant observations by a statistical technique known as variational inference (VI). However, the variational approach to time-resolved data analysis requires identification of successful hyperparameters in order to optimally extract signal. In this case study, we present a successful application of VI to time-resolved changes in an enzyme, DJ-1, upon mixing with a substrate molecule, methylglyoxal. We present a strategy to extract high signal-to-noise changes in electron density from these data. Furthermore, we conduct an ablation study, in which we systematically remove one hyperparameter at a time to demonstrate the impact of each hyperparameter choice on the success of our model. We expect this case study will serve as a practical example for how others may deploy VI in order to analyze their time-resolved diffraction data.

Prospects of Genetically Encoded Flim Indicators for the Quantitative Assessment of Intracellular Parameters

A significant number of genetically encoded indicators based on fluorescent proteins that allow detecting changes in various parameters: membrane potential shift, pH, concentrations of hydrogen peroxide, lactate, pyruvate, NAD+/NADH, ATP, calcium cations, etc. have been created. Some of them (for example, indicators of calcium cations and hydrogen peroxide) are successfully used by numerous groups of researchers in experiments in vivo. The fundamental limitation of most fluorescent indicators is their ability to only qualitatively assess the change in the parameter of interest in the cell. The nature of this limitation is that it is difficult to compare the absolute value of the measured parameter and the detected fluorescent signal for various reasons. Quantitative measurements impose an additional requirement on the indicator signal: it should not depend on the technical features of the experiment (such as the level of protein expression, the type and power of the excitation source, a set of fluorescent filters, etc.). The fulfillment of this requirement may be associated with the detection of the indicator signal in the time domain, where the main characteristic of the signal is the fluorescence lifetime. The fluorescence lifetime is an absolute value, insensitive to changes in the intensity of the excitation source, detection settings, losses in the optical path or sample, changes in the concentration of the fluorophore in the sample, photobleaching. Thus, when calibrating an indicator in the time domain, a specific value of the measured parameter is associated with a specific value of the fluorescence lifetime. The time-resolved imaging mode imposes its own limitations on the properties of the indicator's fluorescent core. Thus, the lifetime of its fluorescence should change in proportion to the value of the measured parameter, which is not characteristic of any fluorophore. In this work, we make a brief review of the principles of detection of the fluorescent signal of genetically encoded indicators, focusing on current approaches related to the analysis of time-resolved data.

A Sweet Introduction to the Mathematical Analysis of Time-Resolved Spectra and Complex Kinetic Mechanisms: The Chameleon Reaction Revisited

We present a detailed yet easy-to-follow discussion of the mathematical treatment of time-resolved spectroscopic data in a model-based approach. This is accompanied and complemented by an example of a colorful and pedagogically rich chemical reaction: the permanganate oxidation of sugars in basic aqueous media (often known as the chameleon reaction). Our sweet approach allows both students and lecturers to tackle the problem of a model-based analysis of time-resolved data in a simple manner and one step at the time, while also exercising programming and data analysis skills─fundamental for present and future chemists of all levels.

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.

Tomographic phosphorescence lifetime multiplexing.

We present a tomographic reconstruction algorithm for recovering distributions of multiple phosphorescent dyes within turbid media from time-resolved measurements, using either point or spatially patterned sources and detectors. The algorithm employs a multi-exponential analysis of time-resolved data, followed by tomographic inversion of the decay amplitudes to recover independent yield distributions for each lifetime present in the medium. Using Monte Carlo simulations, we computationally demonstrate that this two-step inversion approach provides several-fold improvement in quantitative and localization accuracy compared to a direct inversion of the time domain phosphorescence. We also demonstrate the tomographic reconstruction of up to three phosphorescent lifetimes embedded in thick tissue. The proposed algorithm can allow quantitative multiplexed tomography of luminescent and phosphorescent dyes for a wide range of in vivo applications.

Measurements of DNA barcode label separations in nanochannels from time-series data.

We analyzed time-series data for fluctuations of intramolecular segments of barcoded E. coli genomic DNA molecules confined in nanochannels with sizes near the persistence length of DNA. These dynamic data allowed us to measure the probability distribution governing the distance between labels on the DNA backbone, which is a key input into the alignment methods used for genome mapping in nanochannels. Importantly, this dynamic method does not require alignment of the barcode to the reference genome, thereby removing a source of potential systematic error in a previous study of this type. The results thus obtained support previous evidence for a left-skewed probability density for the distance between labels, albeit at a lower magnitude of skewness. We further show that the majority of large fluctuations between labels are short-lived events, which sheds further light upon the success of the linearized DNA genome mapping technique. This time-resolved data analysis will improve existing genome map alignment algorithms, and the overall idea of using dynamic data could potentially improve the accuracy of genome mapping, especially for complex heterogeneous samples such as cancer cells.

Intrinsic carrier multiplication efficiency in bulk Si crystals evaluated by optical-pump/terahertz-probe spectroscopy

We estimated the carrier multiplication efficiency in the most common solar-cell material, Si, by using optical-pump/terahertz-probe spectroscopy. Through close analysis of time-resolved data, we extracted the exact number of photoexcited carriers from the sheet carrier density 10 ps after photoexcitation, excluding the influences of spatial diffusion and surface recombination in the time domain. For incident photon energies greater than 4.0 eV, we observed enhanced internal quantum efficiency due to carrier multiplication. The evaluated value of internal quantum efficiency agrees well with the results of photocurrent measurements. This optical method allows us to estimate the carrier multiplication and surface recombination of carriers quantitatively, which are crucial for the design of the solar cells.

MARTINI bead form factors for the analysis of time-resolved X-ray scattering of proteins.

Time-resolved small- and wide-angle X-ray scattering (SAXS and WAXS) methods probe the structural dynamics of proteins in solution. Although technologically advanced, these methods are in many cases limited by data interpretation. The calculation of X-ray scattering profiles is computationally demanding and poses a bottleneck for all SAXS/WAXS-assisted structural refinement and, in particular, for the analysis of time-resolved data. A way of speeding up these calculations is to represent biomolecules as collections of coarse-grained scatterers. Here, such coarse-graining schemes are presented and discussed and their accuracies examined. It is demonstrated that scattering factors coincident with the popular MARTINI coarse-graining scheme produce reliable difference scattering in the range 0 < q < 0.75 Å-1. The findings are promising for future attempts at X-ray scattering data analysis, and may help to bridge the gap between time-resolved experiments and their interpretation.

Decomposition of Neurological Multivariate Time Series by State Space Modelling

Decomposition of multivariate time series data into independent source components forms an important part of preprocessing and analysis of time-resolved data in neuroscience. We briefly review the available tools for this purpose, such as Factor Analysis (FA) and Independent Component Analysis (ICA), then we show how linear state space modelling, a methodology from statistical time series analysis, can be employed for the same purpose. State space modelling, a generalization of classical ARMA modelling, is well suited for exploiting the dynamical information encoded in the temporal ordering of time series data, while this information remains inaccessible to FA and most ICA algorithms. As a result, much more detailed decompositions become possible, and both components with sharp power spectrum, such as alpha components, sinusoidal artifacts, or sleep spindles, and with broad power spectrum, such as FMRI scanner artifacts or epileptic spiking components, can be separated, even in the absence of prior information. In addition, three generalizations are discussed, the first relaxing the independence assumption, the second introducing non-stationarity of the covariance of the noise driving the dynamics, and the third allowing for non-Gaussianity of the data through a non-linear observation function. Three application examples are presented, one electrocardigram time series and two electroencephalogram (EEG) time series. The two EEG examples, both from epilepsy patients, demonstrate the separation and removal of various artifacts, including hum noise and FMRI scanner artifacts, and the identification of sleep spindles, epileptic foci, and spiking components. Decompositions obtained by two ICA algorithms are shown for comparison.

Dynamics of male sexual arousal: distinct components of brain activation revealed by fMRI

The peripheral mechanisms of male sexual arousal are well known. Recently, neuroimaging techniques, such as PET or fMRI, allowed the investigation of the subjacent cerebral mechanisms. In ten healthy subjects, we have simultaneously recorded fMRI images of brain activation elicited by viewing erotic scenes, and the time course of penile tumescence by means of a custom-built MRI-compatible pneumatic cuff. We have compared activation elicited by video clips with a long duration, that led to sexual arousal and penile erection, and activation elicited by briefly presented still images, that did induce sexual arousal without erection. This comparison and the use of the time course of penile tumescence in video clips allowed to perform a time resolved data analysis and to correlate different patterns of brain activation with different phases of sexual response. The activation maps highlighted a complex neural circuit involved in sexual arousal. Of this circuit, only a few areas (anterior cingulate, insula, amygdala, hypothalamus, and secondary somatosensory cortices) were specifically correlated with penile erection. Finally, these areas showed distinct dynamic relationships with the time course of sexual response. These differences might correspond to different roles in the development and appraisal of the sexual response. These findings shed light on the psychophysiology of male sexuality and open new perspectives for the diagnosis, therapy, and possible rehabilitation of sexual dysfunction.

Global fluorescence lifetime distribution analyses of PSII energy dissipation mechanisms at low physiological temperatures

This study documents the spectral and kinetic resolution of the main energy dissipation processes that influence the PSII photochemical yield in vivo at low physiological temperatures. The primary experimental approach involves global statistical analysis of both fluorescence lifetime distribution data and steady state fluorescence data from pulse-amplitude-modulation instruments and 77K excitation-emission spectral maps. The materials of interest include marine prasinophyte algae, eucalyptus seedlings and a selection of Arabidopsis mutants exhibiting varying xanthophyll and PsbS protein concentrations. Global statistical analysis of the time-resolved data was augmented with independent data including the steady-state intensity, pH-estimates, PsbS protein levels and xanthophyll concentrations. At low temperatures, Mantoniella squamata cells exhibited dark-sustained nigericin-sensitive and antheraxanthin-dependent energy dissipation components independent of PSII photoinhibitory damage. Arabidopsis leaves also exhibited low temperature induced and sustained energy dissipation components that correlated with the PsbS titre and xanthophyll levels. Further, the PsbS deficient mutants facilitated definitive resolution of fluorescence lifetime distribution changes associated with PSII photochemistry, xanthophyll dependent photoprotection and photoinhibition. Sun and frost exposed snow gum seedlings exhibited complex fluorescence spectral-kinetic characteristics including components that correlated with deepoxidized xanthophylls and other components obviously associated with protein synthesis and or structural reorganization of the PSII core inner antenna. It is concluded that fluorescence lifetime distribution analysis provides quantifiable information regarding separate populations of PSII as they are influenced by reaction center photochemistry and both photoprotective and photoinhibitory energy dissipation mechanisms.

Effects of lateral diffusion on the fluorescence anisotropy in hexagonal lipid phases. I. Theory

It is shown that fluorescence anisotropy from lipidlike probes in the hexagonal HII phase gives information of (a) orientational order parameters, (b) the wobbling diffusion constant, and (c) the hopping diffusion constant of the probe, DH, equals DL/R2, the lateral diffusion constant over the square of the radius of the hexagonal tubes. Here we consider only lipidlike probes having the absorption transition movement and/or the emission transition moment along the long axis of the molecule. Three models are introduced for analysis of time-resolved data: the "WOBHOP," the "reduced WOBHOP," and the "P2P4HOP" model. The fluorescence anisotropy in response to a very short excitation pulse in each of the three models is a constant plus a number of exponentials. The WOBHOP and reduced WOBHOP models have 3 and 2 exponentials, respectively, and both contain four fitting parameters: r0 (the fundamental anisotropy), (P2) (the second rank orientational order parameter), DW (the wobbling diffusion constant), and DH (the hopping diffusion constant). The P2P4HOP model has eight exponentials and five fitting parameters: the four parameters listed above and (P4) (the fourth rank orientational order parameter). Analysis of fluorescence anisotropy data in the hexagonal HII phase using one of these models allows for obtaining the hopping diffusion constant, and, if the lateral diffusion constant is known, the radius of the hexagonal tubes. Substitution of DH = 0 in each of the three models yields an expression for the fluorescence anisotropy that is used in the literature for lamellar (L alpha or L beta) phases. The fluorescence anisotropy in coexisting L alpha/HII phases is discussed.

Determination of Spectral Parameters in Microwave Fouriertransform Spectroscopy by Analysis of Time-Domain Signals

Some disadvantages of using the Fouriertransform algorithm to obtain rotational spectra from microwave pulse induced transient signals are demonstrated. To overcome the difficulties, a fitting procedure is suggested which is based on the analysis of time-resolved data.

On the determination of kinetic rate and mass transport coefficients in laser pump-probe experiments

The solution to the radial diffusion equation for time-resolved data analysis is applied to laser pump-probe experiments. It is found that a collinear laser geometry is ideal for diffusion determinant experiments, whereas a perpendicular laser geometry is best for kinetic studies.