Prediction of pair interactions in mixtures by matrix completion.

Molecular simulations enable the prediction of physicochemical properties of mixtures based on pair-interaction models of the pure components and combining rules to describe the unlike interactions. However, if no adjustment to experimental data is made, the existing combining rules often do not yield sufficiently accurate predictions of mixture data. To address this problem, adjustable binary parameters ξij describing the pair interactions in mixtures (i + j) are used. In this work, we present the first method for predicting ξij for unstudied mixtures based on a matrix completion method (MCM) from machine learning (ML). Considering molecular simulations of Henry's law constants as an example, we demonstrate that ξij for unstudied mixtures can be predicted with high accuracy. Using the predicted ξij significantly increases the accuracy of the Henry's law constant predictions compared to using the default ξij = 1. Our approach is generic and can be transferred to molecular simulations of other mixture properties and even to combining rules in equations of state, granting predictive access to the description of unlike intermolecular interactions.

Automated nuclear magnetic resonance fingerprinting of mixtures.

Nuclear magnetic resonance (NMR) spectroscopy is a powerful tool for qualitative and quantitative analysis. However, for complex mixtures, determining the speciation from NMR spectra can be tedious and sometimes even unfeasible. On the other hand, identifying and quantifying structural groups in a mixture from NMR spectra is much easier than doing the same for components. We call this group-based approach "NMR fingerprinting." In this work, we show that NMR fingerprinting can even be performed in an automated way, without expert knowledge, based only on standard NMR spectra, namely, 13C, 1H, and 13C DEPT NMR spectra. Our approach is based on the machine-learning method of support vector classification (SVC), which was trained here on thousands of labeled pure-component NMR spectra from open-source data banks. We demonstrate the applicability of the automated NMR fingerprinting using test mixtures, of which spectra were taken using a simple benchtop NMR spectrometer. The results from the NMR fingerprinting agree remarkably well with the ground truth, which was known from the gravimetric preparation of the samples. To facilitate the application of the method, we provide an interactive website (https://nmr-fingerprinting.de), where spectral information can be uploaded and which returns the NMR fingerprint. The NMR fingerprinting can be used in many ways, for example, for process monitoring or thermodynamic modeling using group-contribution methods-or simply as a first step in species analysis.

Rational method for defining and quantifying pseudo-components based on NMR spectroscopy.

Poorly specified mixtures, whose composition is unknown, are ubiquitous in chemical and biochemical engineering. In the present work, we propose a rational method for defining and quantifying pseudo-components in such mixtures that is free of ad hoc assumptions. The new method requires only standard nuclear magnetic resonance (NMR) experiments and can be fully automated. In the first step, the method analyzes the composition of the poorly specified mixture in terms of structural groups, which is much easier than obtaining the component speciation. The structural groups are then clustered into pseudo-components based on information on the self-diffusion coefficients measured by pulsed-field gradient (PFG) NMR spectroscopy. We demonstrate the performance of the new method on several aqueous mixtures. The method is broadly applicable and provides a sound basis for modeling and simulation of processes with poorly specified mixtures, without the need for tedious and expensive structure elucidation. It is also attractive for process monitoring.

Prediction of parameters of group contribution models of mixtures by matrix completion.

Group contribution (GC) methods are widely used for predicting the thermodynamic properties of mixtures by dividing components into structural groups. These structural groups can be combined freely so that the applicability of a GC method is only limited by the availability of its parameters for the groups of interest. For describing mixtures, pairwise interaction parameters between the groups are of prime importance. Finding suitable numbers for these parameters is often impeded by a lack of suitable experimental data. Here, we address this problem by using matrix completion methods (MCMs) from machine learning to predict missing group-interaction parameters. This new approach is applied to UNIFAC, an established group contribution method for predicting activity coefficients in mixtures. The developed MCM yields a complete set of parameters for the first 50 main groups of UNIFAC, which substantially extends the scope and applicability of UNIFAC. The quality of the predicted parameter set is evaluated using vapor-liquid equilibrium data of binary mixtures from the Dortmund Data Bank. This evaluation reveals that our approach gives prediction accuracies comparable with UNIFAC for data sets to which UNIFAC was fitted, and only slightly lower accuracies for data sets to which UNIFAC is not applicable.

Automated Methods for Identification and Quantification of Structural Groups from Nuclear Magnetic Resonance Spectra Using Support Vector Classification.

Nuclear magnetic resonance (NMR) spectroscopy is a powerful tool for elucidating the structure of unknown components and the composition of liquid mixtures. However, these tasks are often tedious and challenging, especially if complex samples are considered. In this work, we introduce automated methods for the identification and quantification of structural groups in pure components and mixtures from NMR spectra using support vector classification. As input, a 1H NMR spectrum and a 13C NMR spectrum of the liquid sample (pure component or mixture) that is to be analyzed is needed. The first method, called group-identification method, yields qualitative information on the structural groups in the sample. The second method, called group-assignment method, provides the basis for a quantitative analysis of the sample by identifying the structural groups and assigning them to signals in the 13C NMR spectrum of the sample; quantitative information can then be obtained with readily available tools by simple integration. We demonstrate that both methods, after being trained to NMR spectra of nearly 1000 pure components, yield excellent predictions for pure components that were not part of the training set as well as mixtures. The structural group-specific information obtained with the presented methods can, e.g., be used in combination with thermodynamic group-contribution methods to predict fluid properties of unknown samples.

Combining Machine Learning with Physical Knowledge in Thermodynamic Modeling of Fluid Mixtures.

Thermophysical properties of fluid mixtures are important in many fields of science and engineering. However, experimental data are scarce in this field, so prediction methods are vital. Different types of physical prediction methods are available, ranging from molecular models over equations of state to models of excess properties. These well-established methods are currently being complemented by new methods from the field of machine learning (ML). This review focuses on the rapidly developing interface between these two approaches and gives a structured overview of how physical modeling and ML can be combined to yield hybrid models. We illustrate the different options with examples from recent research and give an outlook on future developments.

Adsorption of conjugates of lysozyme and fluorescein isothiocyanate in hydrophobic interaction chromatography.

Bioconjugates, such as antibody-drug conjugates or fluorescent-labeled proteins, are highly interesting for various applications in medicine and biology. In their production, not only the synthesis is challenging but also the downstream processing, for which hydrophobic interaction chromatography (HIC) is often used. However, in-depth studies of the adsorption of bioconjugates in HIC are still rare. Therefore, in the present work, three different conjugates of lysozyme and fluorescein isothiocyanate (FITC) were synthesized and isolated, and their adsorption on the hydrophobic resin Toyopearl PPG-600 M was systematically studied in batch experiments. The influence of sodium chloride and ammonium sulfate with ionic strengths up to 2000 mM on the adsorption isotherms was investigated at pH 7.0 and 25 °C, and the results were compared to those for pure lysozyme. The conjugation leads to an increase of the adsorption in all studied cases. All studied conjugates contain only a single FITC and differ only in the position of the conjugation on the lysozyme. Despite this, strong differences in the adsorption behavior were observed. Moreover, a mathematical model was developed, which enables the prediction of the adsorption isotherms in the studied systems for varying ionic strengths.

Attribute-based Explanation of Non-Linear Embeddings of High-Dimensional Data.

Embeddings of high-dimensional data are widely used to explore data, to verify analysis results, and to communicate information. Their explanation, in particular with respect to the input attributes, is often difficult. With linear projects like PCA the axes can still be annotated meaningfully. With non-linear projections this is no longer possible and alternative strategies such as attribute-based color coding are required. In this paper, we review existing augmentation techniques and discuss their limitations. We present the Non-Linear Embeddings Surveyor (NoLiES) that combines a novel augmentation strategy for projected data (rangesets) with interactive analysis in a small multiples setting. Rangesets use a set-based visualization approach for binned attribute values that enable the user to quickly observe structure and detect outliers. We detail the link between algebraic topology and rangesets and demonstrate the utility of NoLiES in case studies with various challenges (complex attribute value distribution, many attributes, many data points) and a real-world application to understand latent features of matrix completion in thermodynamics.

Making thermodynamic models of mixtures predictive by machine learning: matrix completion of pair interactions.

Predictive models of thermodynamic properties of mixtures are paramount in chemical engineering and chemistry. Classical thermodynamic models are successful in generalizing over (continuous) conditions like temperature and concentration. On the other hand, matrix completion methods (MCMs) from machine learning successfully generalize over (discrete) binary systems; these MCMs can make predictions without any data for a given binary system by implicitly learning commonalities across systems. In the present work, we combine the strengths from both worlds in a hybrid approach. The underlying idea is to predict the pair-interaction energies, as they are used in basically all physical models of liquid mixtures, by an MCM. As an example, we embed an MCM into UNIQUAC, a widely-used physical model for the Gibbs excess energy. We train the resulting hybrid model in a Bayesian machine-learning framework on experimental data for activity coefficients in binary systems of 1146 components from the Dortmund Data Bank. We thereby obtain, for the first time, a complete set of UNIQUAC parameters for all binary systems of these components, which allows us to predict, in principle, activity coefficients at arbitrary temperature and composition for any combination of these components, not only for binary but also for multicomponent systems. The hybrid model even outperforms the best available physical model for predicting activity coefficients, the modified UNIFAC (Dortmund) model.

Influence of pH value and salts on the adsorption of lysozyme in mixed-mode chromatography.

Mixed-mode chromatography (MMC) is an interesting technique for challenging protein separation processes which typically combines adsorption mechanisms of ion exchange (IEC) and hydrophobic interaction chromatography (HIC). Adsorption equilibria in MMC depend on multiple parameters but systematic studies on their influence are scarce. In the present work, the influence of the pH value and ionic strengths up to 3000 mM of four technically relevant salts (sodium chloride, sodium sulfate, ammonium chloride, and ammonium sulfate) on the lysozyme adsorption on the mixed-mode resin Toyopearl MX-Trp-650M was studied systematically at 25℃. Equilibrium adsorption isotherms at pH 5.0 and 6.0 were measured and compared to experimental data at pH 7.0 from previous work. For all pH values, an exponential decay of the lysozyme loading with increasing ionic strength was observed. The influence of the pH value was found to depend significantly on the ionic strength with the strongest influence at low ionic strengths where increasing pH values lead to decreasing lysozyme loadings. Furthermore, a mathematical model that describes the influence of salts and the pH value on the adsorption of lysozyme in MMC is presented. The model enables predicting adsorption isotherms of lysozyme on Toyopearl MX-Trp-650M for a broad range of technically relevant conditions.

Hybridizing physical and data-driven prediction methods for physicochemical properties.

We present a generic way to hybridize physical and data-driven methods for predicting physicochemical properties. The approach 'distills' the physical method's predictions into a prior model and combines it with sparse experimental data using Bayesian inference. We apply the new approach to predict activity coefficients at infinite dilution and obtain significant improvements compared to the physical and data-driven baselines and established ensemble methods from the machine learning literature.

Machine Learning in Thermodynamics: Prediction of Activity Coefficients by Matrix Completion.

Activity coefficients, which are a measure of the nonideality of liquid mixtures, are a key property in chemical engineering with relevance to modeling chemical and phase equilibria as well as transport processes. Although experimental data on thousands of binary mixtures are available, prediction methods are needed to calculate the activity coefficients in many relevant mixtures that have not been explored to date. In this report, we propose a probabilistic matrix factorization model for predicting the activity coefficients in arbitrary binary mixtures. Although no physical descriptors for the considered components were used, our method outperforms the state-of-the-art method that has been refined over three decades while requiring much less training effort. This opens perspectives to novel methods for predicting physicochemical properties of binary mixtures with the potential to revolutionize modeling and simulation in chemical engineering.

Solid-Liquid Equilibrium in the System 2-Keto-L-Gulonic Acid + L-Ascorbic Acid + Water.

The solid-liquid equilibrium (SLE) in the ternary system 2-keto-L-gulonic acid (HKGA) + L-ascorbic acid (vitamin C) + water was investigated experimentally at temperatures between 276 K and 308 K at ambient pressure, i.e., under conditions that are of particular interest for industrial applications. Phase diagrams with one eutonic point were obtained for all temperatures. The dissociation constant and the solubility constant of vitamin C were determined as a function of temperature. Based on an extended version of the Debye-Hückel theory, a physicochemical model was developed that describes the SLE in the ternary system. The agreement between experimental data and results from the model is excellent.

Recovery of Furfural and Acetic Acid from Wood Hydrolysates in Biotechnological Downstream Processing.

Wood hydrolysates contain sugars that can be used as feedstock in fermentation processes. For that purpose, the hydrolysate must be concentrated and inhibitors that harm fermentation must be removed. Herein, the integration of these tasks with the recovery of inhibitors is studied. The wood hydrolysate is represented as a mixture of water, xylose, acetic acid, and furfural. Acetic acid and furfural are two frequently occurring inhibitors and valuable chemicals, and thus, their recovery is studied. Furfural is recovered from the vapors by heteroazeotropic distillation. It is shown that this can be achieved without additional energy. The recovery of acetic acid by distillation is also possible, but not attractive. The new process is simulated by using a thermodynamic model based on experimental data.

Influence of pH and Salts on Partial Molar Volume of Lysozyme and Bovine Serum Albumin in Aqueous Solutions.

The partial molar volume of lysozyme and bovine serum albumin in aqueous solutions at different pH values and in aqueous solutions containing sodium chloride, ammonium chloride, sodium sulfate, or ammonium sulfate at different concentrations at pH 7.0 was investigated experimentally at 298.15 K and 1 bar. It was found that the influence of the pH value and the salts on the partial molar volume of the proteins is small, but trends were measurable. Furthermore, the partial molar volume of lysozyme in pure water at different pH values and in aqueous solutions with different sodium chloride concentrations at pH 7.0 was predicted by molecular simulations. The predictions are in good agreement with the experimental data.