Laser-induced Fluorescence Detection Research Articles

The wavelet transform assisted laser-induced fluorescence detector with high sensitivity

A wavelet transform assisted laser-induced fluorescence detector with high sensitivity was developed and evaluated. An unconventional microscope objective with a numerical aperture (NA) of 0.5 and a working distance (WD) of 4.0 mm was employed, which improved fluorescence collection efficiency, increasing SNR to about 5 times. An aspherical lens was used in the collection optical path to reduce the diameter of the fluorescence imaging size, increasing the SNR to about 1.3 times. The “inverted suction injection” method of flow injection analysis (FIA) was used for the first time in LIF evaluation to reduce contamination errors and improve the accuracy of ultra-trace analysis. The wavelet transform method was proposed for data processing of LIF signals, which can reduce noise from 0.009 mV to 0.002 mV without changing the peak height and peak width. The limit of detection (LOD, 3σ method) for sodium fluorescein was 9.7 × 10−14 M or 3.9 fluorescein molecules in 68 pL detection volume, which was the lowest level of LIFs evaluated by FIA mode. The LIF combined with capillary electrophoresis (CE) achieved an LOD of 4.9 × 10−15 M for fluorescein sodium, which is the best level that has been reported.

Hyperfine structure odd-parity configurations of the terbium atom, Part I: Levels with small [formula omitted]

The paper presents the results of measurements of the hyperfine structure for electronic levels belonging to odd configurations in the terbium atom with a small quantum number J. Laser spectroscopy with laser-induced fluorescence detection was used in the measurements. The hyperfine structure of 32 terbium lines was measured in three spectral regions. The hyperfine structure constants were determined for 20 levels with quantum number J values between 1/2 and 7/2, of which 13 levels have not been studied so far. For the remaining 7 levels, the precision of the constants was improved.

In-capillary magnetic separation and enrichment coupled with laser-induced fluorescence for rapid determination of biomolecules

Biomolecules are indispensable in the life activities and metabolism of various organisms, and their highly sensitive detection is of great significance for disease diagnosis and food safety. Due to the complexity of the matrix and the low concentration of the target, separation and enrichment of biomolecules prior to detection are necessary and time-consuming. Herein, a novel approach combining in-capillary magnetic separation and enrichment with laser-induced fluorescence detection method was proposed for qualitative and quantitative analysis of biomolecules. Two different sequence aptamers modified with magnetic nanoparticles and labeled with fluorescence were used as capture probes and signal probes to form sandwich structures with target molecules for detection. Under the combined influence of magnetic field force and fluid drag force, the integration of separation, enrichment and on-line detection were finished within 5 min. Under optimal conditions, the developed method provided a low limit of detection as 2.7 fmol/L, 0.57 nmol/L, 3 CFU/mL for DNA, thrombin and Staphylococcus aureus, respectively. This proposed method offers a promising platform for the sensitive and rapid determination of biomolecules. It holds significant potential for future applications in fields of environmental and biochemical analysis.

Multimass Analysis of Adeno-Associated Virus Vectors by Orbitrap-Based Charge Detection Mass Spectrometry.

Adeno-associated virus (AAV) vectors have attracted significant attention as the main platform for gene therapy. To ensure the safety and efficacy of AAV vectors when used as gene therapy drugs, it is essential to assess their critical quality attributes (CQAs). These CQAs include the genome packaging status, the size of the genome encapsidated within the AAV capsid, and the stoichiometry of viral proteins (VPs) that constitute the AAV capsids. Analytical methods have been established for evaluating CQAs, such as analytical ultracentrifugation, capillary gel electrophoresis with laser-induced fluorescence detection, and capillary gel electrophoresis using sodium dodecyl sulfate with UV detection. Here, we present a multimass analysis of AAV vectors using orbitrap-based charge detection mass spectrometry (CDMS), a single-ion mass spectrometry. Orbitrap-based CDMS facilitates the quantitative evaluation of the genome packaging status based on the mass distribution of empty and full particles. Additionally, we established a novel method to analyze the encapsidated genome directly without pretreatment, such as protein digestion or heat treatment, and to estimate the stoichiometric variation of VP for the capsid based on the mass distribution constituted by the single peak corresponding to AAV particles. Orbitrap-based CDMS is a distinctive method that allows multiple mass characterizations of AAV vectors with a small sample volume of 20 μL for 1013 cp/mL in a short time (30 min), and it holds the potential to become a new standard method in the assessment of CQAs for AAV vectors.

Compact Laser-Induced Fluorescence Detector with Adjustable Laser Focal Spot for Multiple Purposes.

In many research fields, the demand for miniaturized laser-induced fluorescence (LIF) detection systems has been increasing. This work has developed a compact LIF detector, employing a laser diode as the excitation source and a photodiode as the photodetector with an adjustable laser focal spot, to meet the diverse requirements of various observation targets, such as capillaries, PCR tubes, and microfluidic chips. It features the functionalities of background fluorescence correction, the adaptive adjustment of the dynamic range, and constant power control for the laser. The influence of the excitation power on the detection limit was studied through experiments, and the configuration results for LED/LD as light sources and 487/450 nm wavelengths were compared and optimized. A fully integrated, compact, modular epifluorescence LIF detector was subsequently constructed, measuring 40 × 22 × 38 mm3 in total size, with a cost of USD 320, and achieving a detection limit of 0.4 nM for fluorescein sodium. Finally, the detector was integrated into a nucleic acid detection system with a microfluidic chip on the Chinese Space Station (CSS) and was also tested with PCR tubes and capillaries, proving its broad practicality and adaptability to various analytical systems.

Cross-Species Applications of Peptide Substrate Reporters to Quantitative Measurements of Kinase Activity.

Peptide substrate reporters are short chains of amino acids designed to act as substrates for enzymes of interest. Combined with capillary electrophoresis and laser-induced fluorescence detection (CE-LIF), they are powerful molecular tools for quantitative measurements of enzyme activity even at the level of single cells. Although most peptide substrate reporters have been optimized for human or murine cells in health-related applications, their performance in nonmammalian organisms remains largely unexplored. In this study, we evaluated three peptide substrate reporters for protein kinase B (PKB) in two eukaryotic microbes, Dictyostelium discoideum and Tetrahymena thermophila, which are evolutionarily distant from mammals and from each other yet express PKB homologues. All three peptide substrate reporters were phosphorylated in lysates from both organisms but with varying phosphorylation kinetics and stability. To demonstrate reporter utility, we used one to screen for and identify the previously unknown stimulus needed to activate PHK5, the PKB homologue in T. thermophila. In D. discoideum, we employed the highly quantitative nature of these assays using CE-LIF to make precise measurements of PKB activity in response to transient stimulation, drug treatment, and genetic mutation. These results underscore the broad applicability of peptide substrate reporters across diverse species while highlighting the need for further research to determine effective peptide stabilization strategies across different biological contexts.

Development of a capillary electrophoresis method with laser-induced fluorescence detection for the characterization of oligosaccharides in human milk

Breast milk is the most appropriate food for an infant in the first months of life - it provides the essential nutrients required for proper growth, with breast milk oligosaccharides (HMOs) being the third most abundant component. HMO concentrations vary based on factors like lactation stage and maternal health. They play crucial roles in infant health, acting as prebiotics, antimicrobials, and immune modulators. Analytical methods like capillary electrophoresis and liquid chromatography are the most often used in HMOs qualitative and quantitative analysis. Continuing research aims to enhance analytical techniques for comprehensive HMOs analysis, this work presents the development of a capillary electrophoresis method with laser-induced fluorescence detection along with derivatization and solid-phase extraction steps for the characterisation of major oligosaccharides in colostrum samples. Validation parameters, such as linearity (0.9949–0.9989), limits of detection (5.49–16.40 ng cm−3) and quantification (18.30–54.67 ng cm−3), intra- and inter-day precision (2.41–9.78% and 1.27—14.5%, respectively), trueness (− 8.4 to − 2.0%), and recovery (70.02–113.5%) and repeatability (2.22–10.58%) for solid-phase extraction stage were assessed. The method was evaluated using RGB additive colour model regarding the analytical and practical effectiveness and greenness of the method (achieving a brilliance score of 67.1%). Moreover, the developed method was successfully applied to determine three oligosaccharides (DSLNT, 3’SL, and 6’SL) in colostrum samples. Considering its effectiveness, the method has promise for this type of application.Graphical abstract

Indirect and sensitive determination of microRNAs by magnetic field-assisted capillary sieving electrophoresis combined with catalytic hairpin assembly.

To determine multiple microRNAs (miRNAs) from cells simultaneously is essential for understanding biological functions. Capillary electrophoresis (CE) can simultaneously determine multiple miRNAs by separation. Nevertheless, similar lengths and low concentrations in cells make miRNAs hard to separate and detect. In this study, CE with laser-induced fluorescence detection was combined with catalytic hairpin assembly (CHA) to determine three miRNAs, miR-21, miR-31, and miR-122. The amplification products of CHA, which were DNA duplexes, were designed to have different lengths for different miRNAs. This allowed for easy separation of the duplexes of different miRNAs by CE. The indirect determination of miRNAs was then achieved by separating and detecting these duplexes. A magnetic field was first applied on the capillary sieving electrophoresis to assist in the separation of the duplexes. Under the optimal conditions, the three duplexes could be completely separated within 2.5min with the detection limits of miRNAs in the range 1.12-4.05 × 10-15M. MiR-21 and miR-31 were successfully determined from Hela cells, while miR-122 was determined from chicken livers by this method. The recoveries ranged from 97.5% to 118%. The developed method was sensitive and reliable for miRNA determination.

Characterization of Product Related Variants in Therapeutic Monoclonal Antibodies

The characterization of product-related variants in monoclonal antibodies involves identifying and quantifying the size and charge of variants that can impact the activity, efficacy, and safety of the antibodies. These variants represent distinct molecular forms that may arise from processes such as fragmentation, dimerization, aggregation, or post-translational modifications. The characterization of variants typically involves isolating the relevant species using a semi-preparative scale HPLC and analyzing them using various analytical techniques and biological assays. The commonly used analytical techniques include size-exclusion and ion-exchange chromatography, light scattering, mass spectrometry, capillary isoelectric focusing, and capillary electrophoresis-sodium dodecyl sulfate with ultraviolet or laser-induced fluorescence detection, among others. Additionally, functional assessments are performed using cell-based assays and binding assays to assess the biological activities of the variants. Identifying product-related variants through characterization enables the recognition of impurities that compromise the quality and safety of the drug.

Infrared spectroscopy of the syn-methyl-substituted Criegee intermediate: A combined experimental and theoretical study.

An IR-vacuum ultraviolet (VUV) ion-dip spectroscopy method is utilized to examine the IR spectrum of acetaldehyde oxide (CH3CHOO) in the overtone CH stretch (2νCH) spectral region. IR activation creates a depletion of the ground state population that reduces the VUV photoionization signal on the parent mass channel. IR activation of the more stable and populated syn-CH3CHOO conformer results in rapid unimolecular decay to OH + vinoxy products and makes the most significant contribution to the observed spectrum. The resultant IR-VUV ion-dip spectrum of CH3CHOO is similar to that obtained previously for syn-CH3CHOO using IR action spectroscopy with UV laser-induced fluorescence detection of OH products. The prominent IR features at 5984 and 6081cm-1 are also observed using UV + VUV photoionization of OH products. Complementary theoretical calculations utilizing a general implementation of second-order vibrational perturbation theory provide new insights on the vibrational transitions that give rise to the experimental spectrum in the overtone CH stretch region. The introduction of physically motivated small shifts of the harmonic frequencies yields remarkably improved agreement between experiment and theory in the overtone CH stretch region. The prominent features are assigned as highly mixed states with contributions from two quanta of CH stretch and/or a combination of CH stretch with an overtone in mode 4. The generality of this approach is demonstrated by applying it to three different levels of electronic structure theory/basis sets, all of which provide spectra that are virtually indistinguishable despite showing large deviations prior to introducing the shifts to the harmonic frequencies.

Laser spectroscopy of triply charged 229Th isomer for a nuclear clock.

Thorium-229 (229Th) possesses an optical nuclear transition between the ground state (229gTh) and low-lying isomer (229mTh). A nuclear clock based on this nuclear-transition frequency is expected to surpass existing atomic clocks owing to its insusceptibility to surrounding fields1-5. In contrast to other charge states, triply charged 229Th (229Th3+) is the most suitable for highly accurate nuclear clocks because it has closed electronic transitions that enable laser cooling, laser-induced fluorescence detection and state preparation of ions1,6-8. Although laser spectroscopic studies of 229Th3+ in the nuclear ground state have been performed8, properties of 229mTh3+, including its nuclear decay lifetime that is essential to specify the intrinsic linewidth of the nuclear-clock transition, remain unknown. Here we report the trapping of 229mTh3+ continuously supplied by a 233U source and the determination of nuclear decay half-life of the isolated 229mTh3+ to be through nuclear-state-selective laser spectroscopy. Furthermore, by determining the hyperfine constants of 229mTh3+, we reduced the uncertainty of the sensitivity of the 229Th nuclear clock to variations in the fine-structure constant by a factor of four. These results offer key parameters for the 229Th3+ nuclear clock and its applications in the search for new physics.

Spatially resolved TALIF investigation of atomic oxygen in the effluent of a CO2 microwave discharge

A diagnostic setup for one-dimensionally spatially resolved two-photon absorption laser-induced fluorescence (TALIF) detection of ground state oxygen atoms ( 2p43P2,1,0 ) is developed. The goal of this study is to investigate the evolution of temperatures and absolute number densities of oxygen atoms along the effluent of a low-pressure CO2 microwave discharge in order to gain insights into some of the mechanisms governing the post-discharge regime. The plasma source is operated at conditions of 600 W– 1200 W of absorbed power with flow rates of 74 sccm and 370 sccm pure CO2 at pressures between 1.2 mbar and 5 mbar with specific energy inputs up to 111.9 eV/molecule. These operating conditions exhibit high CO2 conversions (up to 90%) at low energy efficiencies (2%–7.4%), due to direct electron impact dissociation driving the conversion process resulting in splitting of CO2 into CO and metastable oxygen atoms. The TALIF measurements yield spatially resolved translational temperatures between 1000 K– 1600 K for most operating conditions and axial positions along the effluent. Reference measurements with xenon 6p′[3/2]2 are used for absolute number density calibration. The resulting axially resolved number density profiles of ground state atomic oxygen increase along the effluent, even at considerable distances of several centimeters from the active discharge, before they reach a maximum between 5×1020 m−3 and 2.2×1021 m−3 depending on the condition, and decrease after that. This behavior indicates the potential significance of quenching of metastable oxygen atoms within the post-discharge regime of the investigated CO2 discharges. The measured spatially resolved number density evolutions are qualitatively consistent with quenching via wall collisions being the dominant deactivation mechanism, underlining the importance of particle-wall interactions.

Comparison of Optogalvanic and Laser-Induced Fluorescence Spectroscopy

When investigating complex atomic spectra, it may happen accidentally that two or even several transitions between different pairs of combining energy levels have nearly the same wavenumber, and the observed spectral lines are overlapping (blend situations). In such cases, investigations of hyperfine structures can be very helpful in the identification of the involved transitions. In this paper, two complicated blend situations within the spectra of lanthanide atoms (Praseodymium and Lanthanum) are discussed as examples. The experimental methods applied are optogalvanic and laser-induced fluorescence spectroscopy, combined with emission spectra gained via Fourier transform spectroscopy. It is shown that, in such cases, a combination of optogalvanic and laser-induced fluorescence detection is necessary to find all transitions contributing to the observed spectral signatures.

Laser-induced fluorescence detection of nitroxyl (HNO) formed from the thermal decomposition of hydroxylammonium nitrate vapor

The decomposition of the ionic liquid hydroxylammonium nitrate (HAN) produces gas phase products which have utility in spacecraft propulsion systems. Among the various gas phase species generated from HAN decomposition is the nitroxyl (HNO) radical, a highly reactive molecule with implications in both chemical and electric propulsion applications. The work described here used a laser-induced fluorescence platform to directly detect the relative density of the HNO radical formed by passing HAN vapor through heated porous disks of varying composition. The use of heated porous 316-stainless steel and aluminum disks showed significant HNO density production and is attributed to a surface hydrogen abstraction mechanism. There was also evidence of surface modification to the metal disks which resulted in a shift in the HNO density temperature profiles. The results reported demonstrate that use of a heated porous material can easily generate a molecular vapor at moderate temperatures for combustion and electric propulsion applications.

A171 A MISSENSE MUTATION IN FCGBP, A STRUCTURAL COMPONENT OF MUC2 MUCUS, ALTERS THE GLYCOMICS PROFILE AND FUNCTION OF COLONIC MUCUS

Abstract Background MUC2 mucin produced by colonic goblet cells, form a mucus bilayer that provides a physical barrier between potential pathogens in the lumen and the underlying epithelial cells. Mucus is thus the first line of innate host defense in the gastrointestinal (GI) tract. Many GI diseases including inflammatory bowel disease and colon cancer affect the glycosylation of mucus. Goblet cells produce a variety of proteins that are associated with the mucus layer. Of these proteins, FCGBP is of significant interest due to its structural similarities to MUC2 mucin with unknown functions. In this study, we investigated if a missense mutation in FCGBP altered the glycosylation of goblet cell MUC2 and affected its barrier functions. Aims Aims: 1) To determine mechanistically how FCGBP impeded the structural integrity of the mucus layer 2) To quantify MUC2 glycoprotein modifications in the altered mucus layer Methods To investigate whether FCGBP impaired mucus barrier functions, two cell types were investigated: wildtype LS174T (WT) MUC2 mucus-producing goblet cells and LS174T cells with a missense mutation in FCGBP (FCGBP-Mut). To determine if FCGBP-Mut led to loss in barrier function in the mucus layer, the penetration of 0.2, 1, and 2 μm fluorescent beads (to mimic bacteria) through the mucus layer were quantified. To determine if the differences in penetrability were caused by differences in MUC2 glycosylation in the goblet cell lines, sensitive glycomic analyses were performed by high-performance liquid chromatography-mass spectrometry (HPLC-MS) and capillary electrophoresis with laser-induced fluorescence detection (CE-LIF). Both cells and purified MUC2 mucin granules were analyzed and confirmed by lectin binding assays. To enumerate differences in the glycomics profiles, RT-PCR was performed on over 30 human glycosyltransferases. Results FCGBP-Mut cells exhibited an altered glycomics profile with a significant increase in sialylated/fucosylated glycans as quantified by HPLC-MS and an increase in sialyl- and fructosyltransferase mRNA expression. In contrast to WT goblet cells, FCGBP-Mut cells exhibited significant loss in MUC2 mucus barrier function as quantified by fluorescent beads penetration through the mucus layer temporally. The altered glycosylation in FCGBP-Mut cells triggered increased metabolic stress and ROS production that enhanced susceptibility to Salmonella enterica binding, invasion and cell death. Conclusions This study demonstrates that a single missense mutation in FCGBP altered the penetrability of the mucus layer associated with an increase in sialylated/fucosylated glycans, a signature hallmark of numerous colonic diseases. These findings underscore the importance of FCGBP in providing structural integrity of the mucus layer and homeostatic maintenance of goblet cell glycosylation profiles. Funding Agencies CIHR

Targeting the glycan epitope type I N-acetyllactosamine enables immunodepletion of human pluripotent stem cells from early differentiated cells.

Cell surface biomarkers are fundamental for specific characterization of human pluripotent stem cells (hPSCs). Importantly, they can be applied for hPSC enrichment and/or purification but also to remove potentially teratoma-forming hPSCs from differentiated populations before clinical application. Several specific markers for hPSCs are glycoconjugates comprising the glycosphingolipid (GSL)-based glycans SSEA-3 and SSEA-4. We applied an analytical approach based on multiplexed capillary gel electrophoresis coupled to laser-induced fluorescence detection to quantitatively assess the GSL glycome of human embryonic stem cells and human induced pluripotent stem cells as well as during early stages of differentiation into mesoderm, endoderm, and ectoderm. Thereby, we identified the GSL lacto-N-tetraosylceramide (Lc4-Cer, Galβ1-3GlcNAcβ1-3Galβ1-4Glc-Cer), which comprises a terminal type 1 LacNAc (T1LN) structure (Galβ1-3GlcNAc), to be rapidly decreased upon onset of differentiation. Using a specific antibody, we could confirm a decline of T1LN-terminating glycans during the first four days of differentiation by live-cell staining and subsequent flow cytometry. We could further separate T1LN-positive and T1LN-negative cells out of a mixed population of pluripotent and differentiated cells by magnetic activated cell sorting. Notably, not only the T1LN-positive but also the T1LN-negative population was positive for SSEA-3, SSEA-4, and SSEA-5 while expression of nuclear pluripotency markers OCT4 and NANOG was highly reduced in the T1LN-negative population, exclusively. Our findings suggest T1LN as a pluripotent stem cell-specific glycan epitope that is more rapidly down-regulated upon differentiation than SSEA-3, SSEA-4, and SSEA-5.

Abstract TP162: Polyamine Levels Are Elevated After Intracerebral Hemorrhage

Introduction: Intracerebral hemorrhage (ICH) has high morbidity and mortality without available targets for intervention. Polyamines are metabolites implicated in neurological diseases such as traumatic brain injury, Alzheimer’s Disease, and ischemic stroke. No studies have evaluated polyamines as they relate to ICH occurrence or outcomes. In this pilot study, we sought preliminary data on whether polyamines could be potential novel targets to improve outcomes after ICH. Methods: We analyzed plasma samples from 7 ICH cases and 10 control participants from the Genetics and Environmental Risk Factors for Stroke (GERFHS) IV study for polyamine measurements using Capillary Electrophoresis with Laser Induced Fluorescence Detection with the modality of Micellar Electrokinetic Chromatography. Plasma samples were deproteinized and derivatized with Fluorescein Isothiocyanate. Samples were spiked with standard solutions and compared with standard curves developed per each polyamine. We report median age and sex of the cohort. Peak spermine, spermidine and putrescine levels were compared using a student’s t-test. Results: In this pilot study of participants enrolled into GERFHS IV (median age 67 vs 61, cases vs controls respectively, 50% female) all three unacetylated polyamine levels were higher in cases. Although sample size is modest, there was a trend towards increased spermidine levels with higher mRS at 90 days (r 2 = 0.3342) (Figure 1). Conclusions: For the first time, we have shown that polyamines are elevated after ICH, and that higher polyamine levels may be associated with worse outcomes. This preliminary data supports further evaluation of polyamines as potential targets to improve outcomes after ICH in a larger cohort.

Droplet Microfluidics with Capillary Electrophoresis for Glycan Biomarker Analysis.

Several glycoproteins are validated biomarkers of various diseases such as cancer, cardiovascular diseases, chronic alcohol abuse, or congenital disorders of glycosylation (CDG). In particular, CDG represent a group of more than 150 inherited diseases with varied symptoms affecting multiple organs. The distribution of glycans from target glycoprotein(s) can be used to extract information to help the diagnosis and possibly differentiate subtypes of CDG. Indeed, depending on the glycans and the proteins to which they are attached, glycans can play a very broad range of roles in both physical and biological properties of glycoproteins. For glycans in general, capillary electrophoresis with laser-induced fluorescence detection (CE-LIF) has become a staple. Analysis of glycans with CE-LIF requires several sample preparation steps, including release of glycans from the target glycoprotein, fluorescent labeling of glycans, and purification of labeled glycans. Here, we describe the protocol for glycan sample treatment in a microfluidic droplet system prior to CE-LIF of labeled glycans. The microfluidic droplet approach offers full automation, sample, and reagent volume reduction and elimination of contamination from external environment.

Research progress of hydroxy-plane laser induced fluorescence detection based on ultraviolet laser

Research progress of hydroxy-plane laser induced fluorescence detection based on ultraviolet laser

Vibrational spectroscopy and dissociation dynamics of cyclohexyl hydroperoxide.

Organic hydroperoxides (ROOH) are ubiquitous in the atmospheric oxidation of volatile organic compounds (VOCs) as well as in low-temperature oxidation of hydrocarbon fuels. The present work focuses on a prototypical cyclic hydroperoxide, cyclohexyl hydroperoxide (CHHP). The overtone OH stretch (2νOH) spectrum of jet-cooled CHHP is recorded by IR multiphoton excitation with UV laser-induced fluorescence detection of the resulting OH products. A distinctive IR feature is observed at 7012.5 cm-1. Two conformers of CHHP are predicted to have similar stabilities (within 0.2 kcal mol-1) and overtone OH stretch transitions (2νOH), yet are separated by a significant interconversion barrier. The IR power dependence indicates that absorption of three or more IR photons is required for dissociation of CHHP to cyclohexoxy (RO) and OH radical products. Accompanying high-level single- and multi-reference electronic structure calculations quantitatively support the experimental results. Calculations are extended to a range of organic hydroperoxides to examine trends in bond dissociation energies associated with RO + OH formation and compared with prior theoretical results.