Multidimensional Separation Research Articles

The rCOS framework for multi-dimensional separation of concerns in model-driven engineering

The software industry increasingly turns to Model-Driven Engineering (MDE) to mitigate complexity by automating model creation and transformation. Many organisations are pursuing Integrated Development Platforms (IDPs) to enhance automation in their software development processes within MDE. However, the adoption of MDE and engagement with IDPs remain limited due to concerns over their efficacy. We address these challenges in this review paper by introducing a framework for the formal refinement of component and object systems (rCOS). It provides: (1) a formal theory that consists of a modelling language (named OPL) with a calculus of refinement for object-oriented models and component models; (2) a suite of analysis and design techniques that facilitate abstractions and decompositions, leading to a multidimensional separation of concerns; and (3) an IDP (named rCOS Modeller) that supports modelling, design and verification from requirements elicitation through to coding. By advocating for an rCOS-enabled multidimensional approach to separating concerns, this paper offers a comprehensive solution to the challenges facing MDE and IDPs, paving the way for their successful implementation in practice. By delineating the emerging challenges and prospects associated with integrating formal methods for modelling and designing human-cyber–physical systems (HCPS), we show the potential of extending rCOS for MDE in HCPS.

Super-resolution electromagnetic imaging with an optical frequency comb sampling via multi-dimensional signal separation

Electromagnetic sources show wide distribution, broad frequency coverage, and numerous quantities, posing challenges for traditional sensing techniques to achieve ultra-wideband, large-scale detection and localization. The “electromagnetic eye” imaging technique, inspired by the human eye, utilizes a Luneberg lens and a wideband optoelectronic sensing array as the electromagnetic “lens” and “retina,” respectively. This technique utilizes femtosecond optical pulse sampling reception to down-convert wideband signals, facilitating rapid, large range, and wideband sensing of multiple targets in complex electromagnetic environments. However, the limited aperture of the Luneberg lens results in diffraction-limited blurring, and optical down-conversion may lead to spectral aliasing, causing time-frequency-space overlap and reduced system resolution. In this paper, the frequency variation of the point spread function (PSF) in the wideband degraded images is analyzed, and a multi-dimensional joint super-resolution algorithm is proposed, which involves joint time-frequency-space diagonalization of eigenmatrices based on convolutional mixing array model. The concept is demonstrated through a four-sources imaging simulation achieving 2° resolution, breaking the Rayleigh limit 7.25 times. Furthermore, experimental results show 4-10 GHz imaging breaks the Rayleigh limit 4.5 times.

Multidimensional Characterization and Separation of Ultrafine Particles: Insights and Advances by Means of Froth Flotation

Particle systems and their efficient and precise separation are becoming increasingly complex. Therefore, instead of focusing on a single separation feature, a multidimensional approach is needed where more than one particle property is considered. This, however, requires the precise characterization of the particle system, which is especially challenging for fine particles with sizes below 10 µm. This paper discusses the benefits and limitations of different characterization techniques, including optical contour analysis, inverse gas chromatography, flow cytometry, and SEM-based image analysis. The separation of ultrafine particles was investigated for a binary system using froth flotation, where a novel developed flotation apparatus is used. A special focus was placed on the multidimensional evaluation of the separation according to the particle properties of size, shape, and wettability, which was addressed via multivariate Tromp and entropy functions. The results emphasize the intricacy of the flotation process and the complex interaction of the individual particle properties and process parameters. The investigations contribute to the understanding of the characterization of particulate properties as well as the separation behavior of ultrafine particles via froth flotation, especially in the case of a multidimensional approach.

A water-resistant, ultrathin, conformable organic photodetector for vital sign monitoring.

Ultrathin flexible photodetectors can be conformably integrated with the human body, offering promising advancements for emerging skin-interfaced sensors. However, the susceptibility to degradation in ambient and particularly in aqueous environments hinders their practical application. Here, we report a 3.2-micrometer-thick water-resistant organic photodetector capable of reliably monitoring vital sign while submerged underwater. Embedding the organic photoactive layer in an adhesive elastomer matrix induces multidimensional hybrid phase separation, enabling high adhesiveness of the photoactive layer on both the top and bottom surfaces with maintained charge transport. This improves the water-immersion stability of the photoactive layer and ensures the robust sealing of interfaces within the device, notably suppressing fluid ingression in aqueous environments. Consequently, our fabricated ultrathin organic photodetector demonstrates stability in deionized water or cell nutrient media over extended periods, high detectivity, and resilience to cyclic mechanical deformation. We also showcase its potential for vital sign monitoring while submerged underwater.

Chromatographic parameters: Transport efficiency—A meaningful alternative to the plate number parameter

The plate number parameter officially defined in GC and LC as N = (tR/σ)2 (tR and σ are peak retention time and standard deviation, respectively, under no-programming conditions) can be substantially smaller than the actual number of plates. Therefore, N does not always represent what its name implies it does, and its interpretation is not clear. This is even more so for the extensions of N to multidimensional separations. N has other shortcomings. Metrics of separation performance of chromatographic analyses (peak resolution, Rs, peak capacity, nc, and others) are not proportional to N.A column transport efficiency, Q = tR/σ, is free of the shortcomings of N. Metrics Rs and nc are proportional to Q. Q also has a transparent interpretation – it is the number of σ-wide segments in the time-intervals of certain significance in static and programmable GC and LC analyses. Q also has meaningful extensions to multi-dimensional separations.

Hyphenation of supercritical fluid chromatography and trapped ion mobility-mass spectrometry for quantitative lipidomics

BackgroundLipidomics studies require rapid separations with accurate and reliable quantification results to further elucidate the role of lipids in biological processes and their biological functions. Supercritical fluid chromatography (SFC), in particular, can provide this rapid and high-resolution separation. The combination with trapped ion mobility spectrometry (TIMS) has not yet been applied, although the post-ionization separation method in combination with liquid chromatography or imaging techniques has already proven itself in resolving isomeric and isobaric lipids and preventing false identifications. However, a multidimensional separation method should not only allow confident identification but also provide quantitative results to substantiate studies with absolute concentrations. ResultsA SFC method was developed and the hyphenation of SFC and TIMS was further explored towards the separation of different isobaric overlaps. Furthermore, lipid identification was performed using mass spectrometry (MS) and parallel accumulation serial fragmentation (PASEF) MS/MS experiments in addition to retention time and collision cross section (CCS). Quantification was further investigated with short TIMS ramps and performed based on the ion mobility signal of lipids, since TIMS increases the sensitivity by noise filtering. The final method was, as an exemplary study, applied to investigate the function of different ceramide synthases (CerS) in the nematode and model organism Caenorhabditis elegans (C. elegans). Loss of three known CerS hyl-1, hyl-2 and lagr-1 demonstrated different influences on and alterations in the sphingolipidome. SignificanceThis method describes for the first time the combination of SFC and TIMS-MS/MS, which enables a fast and sensitive quantification of lipids. The results of the application to C. elegans samples prove the functionality of the method and support research on the metabolism of sphingolipids in nematodes.

Multidimensional Separation by Magnetic Seeded Filtration: Theoretical Study

Magnetic seeded filtration (MSF) is a multidimensional solid–liquid separation process capable of fractionating a multimaterial suspension based on particle size and surface properties. It relies on the selective hetero-agglomeration between nonmagnetic target and magnetic seed particles followed by a magnetic separation. Experimental investigations of multimaterial suspensions are challenging and limited. Therefore, a Monte Carlo model for the simulation of hetero-agglomeration processes is developed, validated, and compared to a discrete population balance model. The numerical investigation of both charge-based and hydrophobicity-based separation in an 11-material system, using synthetic agglomeration kernels based on real-world observations, yields results consistent with prior experimental studies and expectations: Although a multidimensional separation is indeed possible, unwanted hetero-agglomeration between target particles results in a reduced selectivity. This effect is more pronounced when separation is based on a dissimilarity rather than a similarity in the separation criterion and emphasizes the advantages of hydrophobicity-based systems. For the first time, 2D grade efficiency functions T(φ,d) are presented for MSF. However, it is shown that these functions strongly depend on the initial state of the suspension, which casts doubt on their general definition for agglomeration-based processes and underlines the importance of a simulation tool like the developed MC model.

Human arm redundancy: a new approach for the inverse kinematics problem.

The inverse kinematics (IK) problem addresses how both humans and robotic systems coordinate movement to resolve redundancy, as in the case of arm reaching where more degrees of freedom are available at the joint versus hand level. This work focuses on which coordinate frames best represent human movements, enabling the motor system to solve the IK problem in the presence of kinematic redundancies. We used a multi-dimensional sparse source separation method to derive sets of basis (or source) functions for both the task and joint spaces, with joint space represented by either absolute or anatomical joint angles. We assessed the similarities between joint and task sources in each of these joint representations, finding that the time-dependent profiles of the absolute reference frame's sources show greater similarity to corresponding sources in the task space. This result was found to be statistically significant. Our analysis suggests that the nervous system represents multi-joint arm movements using a limited number of basis functions, allowing for simple transformations between task and joint spaces. Additionally, joint space seems to be represented in an absolute reference frame to simplify the IK transformations, given redundancies. Further studies will assess this finding's generalizability and implications for neural control of movement.

Capillary zone electrophoresis-high field asymmetric ion mobility spectrometry-tandem mass spectrometry for top-down characterization of histone proteoforms.

Characterization of histone proteoforms with various post-translational modifications (PTMs) is critical for a better understanding of functions of histone proteoforms in epigenetic control of gene expression. Mass spectrometry (MS)-based top-down proteomics (TDP) is a valuable approach for delineating histone proteoforms because it can provide us with a bird's-eye view of histone proteoforms carrying diverse combinations of PTMs. Here, we present the first example of coupling capillary zone electrophoresis (CZE), ion mobility spectrometry (IMS), and MS for online multi-dimensional separations of histone proteoforms. Our CZE-high-field asymmetric waveform IMS (FAIMS)-MS/MS platform identified 366 (ProSight PD) and 602 (TopPIC) histone proteoforms from a commercial calf histone sample using a low microgram amount of histone sample as the starting material. CZE-FAIMS-MS/MS improved the number of histone proteoform identifications by about 3 folds compared to CZE-MS/MS alone (without FAIMS). The results indicate that CZE-FAIMS-MS/MS could be a useful tool for comprehensive characterization of histone proteoforms with high sensitivity.

Using Multidimensional Separations to Distinguish Isomeric Amino Acid-Bile Acid Conjugates and Assess Their Presence and Perturbations in Model Systems.

Bile acids play key roles in nutrient uptake, inflammation, signaling, and microbiome composition. While previous bile acid analyses have primarily focused on profiling 5 canonical primary and secondary bile acids and their glycine and taurine amino acid-bile acid (AA-BA) conjugates, recent studies suggest that many other microbial conjugated bile acids (or MCBAs) exist. MCBAs are produced by the gut microbiota and serve as biomarkers, providing information about early disease onset and gut health. Here we analyzed 8 core bile acids synthetically conjugated with 22 proteinogenic and nonproteogenic amino acids totaling 176 MCBAs. Since many of the conjugates were isomeric and only 42 different m/z values resulted from the 176 MCBAs, a platform coupling liquid chromatography, ion mobility spectrometry, and mass spectrometry (LC-IMS-MS) was used for their separation. Their molecular characteristics were then used to create an in-house extended bile acid library for a combined total of 182 unique compounds. Additionally, ∼250 rare bile acid extracts were also assessed to provide additional resources for bile acid profiling and identification. This library was then applied to healthy mice dosed with antibiotics and humans having fecal microbiota transplantation (FMT) to assess the MCBA presence and changes in the gut before and after each perturbation.

GeLC-FAIMS-MS workflow for in-depth middle-down proteomics.

Middle-down proteomics (MDP) is an analytical approach in which protein samples are digested with proteases such as Glu-C to generate large peptides (>3kDa) that are analyzed by mass spectrometry (MS). This method is useful for characterizing high-molecular-weight proteins that are difficult to detect by top-down proteomics (TDP), in which intact proteins are analyzed by MS. In this study, we applied GeLC-FAIMS-MS, a multidimensional separation workflow that combines gel-based prefractionation with LC-FAIMS MS, for deep MDP. Middle-down peptides generated by optimized limited Glu-C digestion conditions were first size-fractionated by polyacrylamide gel electrophoresis, followed by C4 reversed-phase liquid chromatography separation and additional ion mobility fractionation, resulting in a significant increase in peptide length detectable by MS. In addition to global analysis, the GeLC-FAIMS-MS concept can also be applied to targeted MDP, where only proteins in the desired molecular weight range are gel-fractionated and their Glu-C digestion products are analyzed, as demonstrated by targeted analysis of integrins in exosomes. In-depth MDP achieved by global and targeted GeLC-FAIMS-MS supports the exploration of proteoform information not covered by conventional TDP by increasing the number of detectable protein groups or post-translational modifications (PTMs) and improving the sequence coverage.

Right in two: capabilities of ion mobility spectrometry for untargeted metabolomics.

This mini review focuses on the opportunities provided by current and emerging separation techniques for mass spectrometry metabolomics. The purpose of separation technologies in metabolomics is primarily to reduce complexity of the heterogeneous systems studied, and to provide concentration enrichment by increasing sensitivity towards the quantification of low abundance metabolites. For this reason, a wide variety of separation systems, from column chemistries to solvent compositions and multidimensional separations, have been applied in the field. Multidimensional separations are a common method in both proteomics applications and gas chromatography mass spectrometry, allowing orthogonal separations to further reduce analytical complexity and expand peak capacity. These applications contribute to exponential increases in run times concomitant with first dimension fractionation followed by second dimension separations. Multidimensional liquid chromatography to increase peak capacity in metabolomics, when compared to the potential of running additional samples or replicates and increasing statistical confidence, mean that uptake of these methods has been minimal. In contrast, in the last 15years there have been significant advances in the resolution and sensitivity of ion mobility spectrometry, to the point where high-resolution separation of analytes based on their collision cross section approaches chromatographic separation, with minimal loss in sensitivity. Additionally, ion mobility separations can be performed on a chromatographic timescale with little reduction in instrument duty cycle. In this review, we compare ion mobility separation to liquid chromatographic separation, highlight the history of the use of ion mobility separations in metabolomics, outline the current state-of-the-art in the field, and discuss the future outlook of the technology. "Where there is one, you're bound to divide it. Right in two", James Maynard Keenan.

Multidimensional Separation by Magnetic Seeded Filtration: Experimental Studies

The current state of separation technology often neglects the multidimensional nature of real particle systems, which are distributed not only in terms of size, but also in terms of other properties, such as surface charge. Therefore, the aim of this study is to experimentally investigate the applicability of magnetic seeded filtration as a multidimensional separation process. Magnetic seed particles are added to a multisubstance suspension, and a selective heteroagglomeration with the nonmagnetic target particles is induced, allowing for an easy subsequent magnetic separation. The results show that high separation efficiencies can be achieved and that the parameters pH and ionic strength govern the agglomeration process. Selective separation based on surface charge was observed, but undesirable heteroagglomeration processes between the target particles lead to a loss of selectivity. Particle size was clearly identified as a second relevant separation feature, and its partially opposite influence on collision frequency and collision efficiency was discussed. Finally, experimental data of multidimensional separation are presented, in which a size-distributed two-substance suspension is separated into defined size and material fractions in a single process step. This study highlights the need for multidimensional evaluation in general and the potential of magnetic seeded filtration as a promising separation technique.

Evaluating orthogonality between ion-pair reversed phase, anion exchange, and hydrophilic interaction liquid chromatography for the separation of synthetic oligonucleotides

The orthogonality of separation between ion-pair reversed phase (IP-RP), anion exchange (AEX), and hydrophilic interaction liquid chromatography (HILIC) was evaluated for oligonucleotides. A polythymidine standard ladder was first used to evaluate the three methods and showed zero orthogonality, where retention and selectivity were based on oligonucleotide charge/size under all three conditions. Next, a model 23-mer synthetic oligonucleotide containing 4 phosphorothioate bonds with 2′ fluoro and 2′-O-methyl ribose modifications typical of small interfering RNA was used for evaluating orthogonality. The resolution and orthogonality were evaluated between the three modes of chromatography in terms of selectivity differences for nine common impurities, including truncations (n-1, n-2), addition (n + 1), oxidation, and de-fluorination. We first evaluated different ion-pairing reagents that provided the best separation of the key impurities while suppressing diastereomer separation due to phosphorothioate linkages. Although different ion-pairing reagents affected resolution, very little orthogonality was observed. We then compared the retention times between IP-RP, HILIC, and AEX for each impurity of the model oligonucleotide and observed various selectivity changes. The results suggest that coupling HILIC with either AEX or IP-RP provide the highest degree of orthogonality due to the differences in retention for hydrophilic nucleobases and modifications under HILIC conditions. IP-RP provided the highest overall resolution for the impurity mixture, whereas more co-elution was observed with HILIC and AEX. The unique selectivity patterns offered by HILIC provides an interesting alternative to IP-RP or AEX, in addition to the potential for coupling with multidimensional separations. Future work should explore orthogonality for oligonucleotides with subtle sequence differences such as nucleobase modifications and base flip isomers, longer strands such as guide RNA and messenger RNA, and other biotherapeutic modalities such as peptides, antibodies, and antibody-drug-conjugates.

Past to Future: Application of Gel Permeation Chromatography from Petroleomics and Metallopetroleomics to New Energies Applications: A Minireview

In the field of petroleomics and metallopetroleomics, the gel permeation chromatography (GPC) technique coupled with high-resolution detection technologies has made significant contributions as an analytical and preparative tool for over five decades. This bibliographic minireview highlights the study of the supramolecular and structural behavior of heavy crude oil and its fractions, as well as their reactivity to various processes by use of GPC. The preferred mobile phase is tetrahydrofuran (THF), whereas the stationary phase is polystyrene–divinylbenzene copolymer to avoid compound retention in the column. Other techniques such as HPTLC, RPLC, and NPHPLC have been used to provide multidimensional separations complementary to GPC. The high molecular weight (HMW) fraction, due to its greater polarity, reactivity to polymerization, and resistance to hydrodemetallization processes, has been the focus of interest for years. GPC coupled with high-resolution techniques has proven to be reliable for the detection of organic and inorganic species in bio-oils, making it a valuable tool for researchers and industry professionals in the context of feedstocks changes and new energy production.

Multidimensional separation methods can improveseparation performance forextremely complicated proteomics samples and provide a powerful tool for comprehensive proteome profiling of low-microgram samples.

Tweetable abstract Multidimensional separation methods with improved sensitivity andpeak capacity and throughput allow in-depth proteome profiling of low-microgram samples.

Multidimensional Separations in Top-Down Proteomics.

Top-down proteomics (TDP) identifies, quantifies, and characterizes proteins at the intact proteoform level in complex biological samples to understand proteoform function and cellular mechanisms. However, analyzing complex biological samples using TDP is still challenging due to high sample complexity and wide dynamic range. High-resolution separation methods are often applied prior to mass spectrometry (MS) analysis to decrease sample complexity and increase proteomics throughput. These separation methods, however, may not be efficient enough to characterize low abundance intact proteins in complex samples. As such, multidimensional separation techniques (combination of two or more separation methods with high orthogonality) have been developed and applied that demonstrate improved separation resolution and more comprehensive identification in TDP. A suite of multidimensional separation methods that couple various types of liquid chromatography (LC), capillary electrophoresis (CE), and/or gel electrophoresis-based separation approaches have been developed and applied in TDP to analyze complex biological samples. Here, we reviewed multidimensional separation strategies employed for TDP, summarized current applications, and discussed the gaps that may be addressed in the future.

Parametric Stochastic Modeling of Particle Descriptor Vectors for Studying the Influence of Ultrafine Particle Wettability and Morphology on Flotation-Based Separation Behavior

Practically all particle separation processes depend on more than one particulate property. In the case of the industrially important froth flotation separation, these properties concern wettability, composition, size and shape. Therefore, it is useful to analyze different particle descriptors when studying the influence of particle wettability and morphology on the separation behavior of particle systems. A common tool for classifying particle separation processes are Tromp functions. Recently, multivariate Tromp functions, computed by means of non-parametric kernel density estimation, have emerged which characterize the separation behavior with respect to multidimensional vectors of particle descriptors. In the present paper, an alternative parametric approach based on copulas is proposed in order to compute multivariate Tromp functions and, in this way, to characterize the separation behavior of particle systems. In particular, bivariate Tromp functions for the area-equivalent diameter and aspect ratio of glass particles with different morphologies and surface modification have been computed, based on image characterization by means of mineral liberation analysis (MLA). Comparing the obtained Tromp functions with one another reveals the combined influence of multiple factors, in this case particle wettability, morphology and size, on the separation behavior and introduces an innovative approach for evaluating multidimensional separation. In addition, we extend the parametric copula-based method for the computation of multivariate Tromp functions, in order to characterize separation processes, also in the case when image measurements are not available for all separated fractions.

Multidimensional Fractionation of Particles

The increasing complexity in particle science and technology requires the ability to deal with multidimensional property distributions. We present the theoretical background for multidimensional fractionations by transferring the concepts known from one dimensional to higher dimensional separations. Particles in fluids are separated by acting forces or velocities, which are commonly induces by external fields, e.g., gravitational, centrifugal or electro-magnetic fields. In addition, short-range force fields induced by particle interactions can be employed for fractionation. In this special case, nanoparticle chromatography is a recent example. The framework for handling and characterizing multidimensional separation processes acting on multidimensional particle size distributions is presented. Illustrative examples for technical realizations are given for shape-selective separation in a hydrocyclone and for density-selective separation in a disc separator.

A mass spectrum-oriented computational method for ion mobility-resolved untargeted metabolomics

Ion mobility (IM) adds a new dimension to liquid chromatography-mass spectrometry-based untargeted metabolomics which significantly enhances coverage, sensitivity, and resolving power for analyzing the metabolome, particularly metabolite isomers. However, the high dimensionality of IM-resolved metabolomics data presents a great challenge to data processing, restricting its widespread applications. Here, we develop a mass spectrum-oriented bottom-up assembly algorithm for IM-resolved metabolomics that utilizes mass spectra to assemble four-dimensional peaks in a reverse order of multidimensional separation. We further develop the end-to-end computational framework Met4DX for peak detection, quantification and identification of metabolites in IM-resolved metabolomics. Benchmarking and validation of Met4DX demonstrates superior performance compared to existing tools with regard to coverage, sensitivity, peak fidelity and quantification precision. Importantly, Met4DX successfully detects and differentiates co-eluted metabolite isomers with small differences in the chromatographic and IM dimensions. Together, Met4DX advances metabolite discovery in biological organisms by deciphering the complex 4D metabolomics data.