Generic approach to the method development of intact protein separations using hydrophobic interaction chromatography

We describe a liquid chromatography method development approach for the separation of intact proteins using hydrophobic interaction chromatography. First, protein retention was determined as function of the salt concentration by isocratic measurements and modeled using linear regression. The error between measured and predicted retention factors was studied while varying gradient time (between 15 and 120 min) and gradient starting conditions, and ranged between 2 and 15%. To reduce the time needed to develop optimized gradient methods for hydrophobic interaction chromatography separations, retention‐time estimations were also assessed based on two gradient scouting runs, resulting in significantly improved retention‐time predictions (average error < 2.5%) when varying gradient time. When starting the scouting gradient at lower salt concentrations (stronger eluent), retention time prediction became inaccurate in contrast to predictions based on isocratic runs. Application of three scouting runs and a nonlinear model, incorporating the effects of gradient duration and mobile‐phase composition at the start of the gradient, provides accurate results (improved fitting compared to the linear solvent‐strength model) with an average error of 1.0% and maximum deviation of –8.3%. Finally, gradient scouting runs and retention‐time modeling have been applied for the optimization of a critical‐pair protein isoform separation encountered in a biotechnological sample.     

Computer-assisted method development in liquid chromatography-mass spectrometry: new proposals

A new approach is proposed for computer-assisted method development in LC-MS. The procedure consists of three stages. Firstly, an accurate retention model is developed for the peaks in the mixture to be separated by use of an iterative approach with isocratic priming data, which is calibrated and validated by means of a few gradient runs. Secondly, a specially developed LC-MS objective function, based on selectivity targets (the selectivity matrix), is calculated and used to evaluate the simulated chromatograms and drive the optimization process. Thirdly, the retention model and the selectivity matrix objective function are used with an evolutionary algorithm in which the concepts of constrained Pareto optimality are applied, to carry out the unattended optimization process. The system was applied to real data for a complex separation and compared with the results provided by a commercial tool for computer-assisted method development.     

Optimization of Artificial Neural Networks for Modeling of Atorvastatin and Its Impurities Retention in Micellar Liquid Chromatography

Artificial Neural Networks (ANNs) present a powerful tool for the modeling of chromatographic retention. In this paper, the main objective was to use ANNs as a tool in modeling of atorvastatin and its impurities?? retention in a micellar liquid chromatography (MLC) protocol. Factors referred to MLC were evaluated through 30 experiments defined by the Central Composite Design. In this manner, 5?Cx?C3 topology as a starting point for ANNs?? optimization was defined too. In the next step, in order to set the network with the best performance, network optimization was done. In the first part, the number of nodes in the hidden layer and the number of experimental data points in training set were simultaneously varied, and their importance was estimated with suitable statistical parameters. Furthermore, a series of training algorithms was applied to the current network. The Back Propagation, Conjugate Gradient-descent, Quick Propagation, Quasi-Newton, and Delta-bar-Delta algorithms were used to obtain the optimal network. Finally, the predictive ability of the optimized neural network was confirmed through several statistical tests. The obtained network showed high ability to predict chromatographic retention of atorvastatin and its impurities in MLC.     

Quantitative prediction of liquid chromatography retention of N-benzylideneanilines based on quantum chemical parameters and radial basis function neural network

Based on quantum chemical parameters and a simple numerical coding, the liquid chromatography retention of bifunctionally substituted N-benzylideneaniles (NBA) has been predicted using a radial basis function neural network (RBFNN) model. The quantum chemical parameters involved in the model are dipole moment (m), energies of the highest occupied and lowest unoccupied molecular orbitals (E(homo,) E(lumo)), net charge of the most negative atom (Q(min)), sum of absolute values of the charges of all atoms in two given functional groups (Delta), total energy of the molecule (E(T)), weight of the molecule (W), and numerical coding (N). N was used to indicate the different positions of two substituents. The predictive values are consistent with the experimental results. The mean relative error of the testing set is 1.6%, and the maximum relative error is less than 5.0%. In this work the success of the whole modeling process only depends on the optimization of the spread parameter in network.     

Neural networks convergence using physicochemical data

An investigation of the neural network convergence and prediction based on three optimization algorithms, namely, Levenberg-Marquardt, conjugate gradient, and delta rule, is described. Several simulated neural networks built using the above three algorithms indicated that the Levenberg-Marquardt optimizer implemented as a back-propagation neural network converged faster than the other two algorithms and provides in most of the cases better prediction. These conclusions are based on eight physicochemical data sets, each with a significant number of compounds comparable to that usually used in the QSAR/QSPR modeling. The superiority of the Levenberg-Marquardt algorithm is revealed in terms of functional dependence of the change of the neural network weights with respect to the gradient of the error propagation as well as distribution of the weight values. The prediction of the models is assessed by the error of the validation sets not used in the training process.     

Application of Artificial Neural Network and Multiple Linear Regression Retention Models for Optimization of Separation in Ion Chromatography by Using Several Criteria Functions

This work focuses on problems regarding empirical retention modelling and optimization of separation in ion chromatography. Influences of eluent flow rate and concentration of eluent competing ion (OH^–) on separation of seven inorganic anions (fluoride, chloride, nitrite, sulphate, bromide, nitrate, and phosphate) were investigated. Artificial neural networks and multiple linear regression retention models in combination with several criteria functions were used and compared in global optimization process. It can be seen that general recommendations for optimization of separation in ion chromatography is application of chromatography exponential function criterion in combination with artificial neural networks retention model.     

Development of an inorganic cations retention model in ion chromatography by means of artificial neural networks with different two-phase training algorithms

This paper describes development of artificial neural network (ANN) retention model, which can be used for method development in variety of ion chromatographic applications. By using developed retention model it is possible both to improve performance characteristic of developed method and to speed up new method development by reducing unnecessary experimentation. Multilayered feed forward neural network has been used to model retention behaviour of void peak, lithium, sodium, ammonium, potassium, magnesium, calcium, strontium and barium in relation with the eluent flow rate and concentration of methasulphonic acid (MSA) in eluent. The probability of finding the global minimum and fast convergence at the same time were enhanced by applying a two-phase training procedure. The developed two-phase training procedure consists of both first and second order training. Several training algorithms were applied and compared, namely: back propagation (BP), delta-bar-delta, quick propagation, conjugate gradient, quasi Newton and Levenberg-Marquardt. It is shown that the optimized two-phase training procedure enables fast convergence and avoids problems arisen from the fact that every new weight initialization can be regarded as a new starting position and yield irreproducible neural network if only second order training is applied. Activation function, number of hidden layer neurons and number of experimental data points used for training set were optimized in order to insure good predictive ability with respect to speeding up retention modelling procedure by reducing unnecessary experimental work. The predictive ability of optimized neural networks retention model was tested by using several statistical tests. This study shows that developed artificial neural network are very accurate and fast retention modelling tool applied to model varied inherent non-linear relationship of retention behaviour with respect to mobile phase parameters.     

Retention modeling and simultaneous optimization of pH value and gradient steepness in RP‐HPLC using feed‐forward neural networks

A novel approach is proposed for the simultaneous optimization of mobile phase pH and gradient steepness in RP‐HPLC using artificial neural networks. By presetting the initial and final concentration of the organic solvent, a limited number of experiments with different gradient time and pH value of mobile phase are arranged in the two‐dimensional space of mobile phase parameters. The retention behavior of each solute is modeled using an individual artificial neural network. An “early stopping” strategy is adopted to ensure the predicting capability of neural networks. The trained neural networks can be used to predict the retention time of solutes under arbitrary mobile phase conditions in the optimization region. Finally, the optimal separation conditions can be found according to a global resolution function. The effectiveness of this method is validated by optimization of separation conditions for amino acids derivatised by a new fluorescent reagent.     

Development of Gradient Retention Model in Ion Chromatography. Part III: Fuzzy Logic QSRR Approach

In this paper, the authors tested methodology that overcame the most common limitation of quantitative structure-retention relationship (QSRR) models: their limited applicability at the specific conditions for which models were developed. The modeling was performed on ion chromatographic analysis of “wood sugars”. Adaptive neuro-fuzzy interference system, an advanced artificial intelligence regression tool, was applied in combination with genetic algorithm scanning to obtain good and reliable QSRR models. The obtained QSRR models were applied for predicting data that were required for further development of general isocratic and gradient retention models. All three developed models (QSRR, isocratic, and gradient) indicated good prediction ability with root mean square error of prediction ≤0.1557. The performances of the methodology were compared with those presented in previous research—namely genetic algorithm in combinations with—stepwise multiple linear regression, partial least squares, uninformative variable elimination–partial least squares, and artificial neural network regression.

     

From Isocratic Data to a Gradient Elution Retention Model in IC: An Artificial Neural Network Approach

Gradient elution is used in ion chromatography to achieve rapid analysis with reasonable separation. Optimization and prediction of the gradient is clearly a multidimensional problem, however. One approach to prediction of gradient retention behavior is based on isocratic experimentation. In this work, a gradient model for simultaneous prediction of the retention behavior of fluoride, chlorite, chloride, chlorate, nitrate, and sulfate ions, on the basis of isocratic experimental data, is proposed. An artificial neural network was used to predict isocratic results; the network was optimized with regard to the number of data in the training set (25) and number of neurons in the hidden layer (6). A slight systematic error was observed in the isocratic prediction, but this did not effect gradient prediction. Good predictions were achieved for all the anions investigated (average error 1.79%). Deviations were somewhat higher for prediction of sulfate retention than for the other anions, probably because of the higher charge and larger size of sulfate in comparison with the other ions examined.     

Applicability of linear and nonlinear retention‐time models for reversed‐phase liquid chromatography separations of small molecules,peptides, and intact proteins

The applicability and predictive properties of the linear solvent strength model and two nonlinear retention‐time models, i.e., the quadratic model and the Neue model, were assessed for the separation of small molecules (phenol derivatives), peptides, and intact proteins. Retention‐time measurements were conducted in isocratic mode and gradient mode applying different gradient times and elution‐strength combinations. The quadratic model provided the most accurate retention‐factor predictions for small molecules (average absolute prediction error of 1.5%) and peptides separations (with a prediction error of 2.3%). An advantage of the Neue model is that it can provide accurate predictions based on only three gradient scouting runs, making tedious isocratic retention‐time measurements obsolete. For peptides, the use of gradient scouting runs in combination with the Neue model resulted in better prediction errors (<2.2%) compared to the use of isocratic runs. The applicability of the quadratic model is limited due to a complex combination of error and exponential functions. For protein separations, only a small elution window could be applied, which is due to the strong effect of the content of organic modifier on retention. Hence, the linear retention‐time behavior of intact proteins is well described by the linear solvent strength model. Prediction errors using gradient scouting runs were significantly lower (2.2%) than when using isocratic scouting runs (3.2%).     

Determination of Inorganic Ions in Fertilizer Industry Wastewater by Ion Chromatography

The aim of this work is development of methodology for analysis of inorganic cations (sodium, ammonium, potassium, magnesium and calcium) in fertilizer industry wastewater. Method development includes optimization of eluent flow rate and concentration of eluent competing ion in order to obtain optimal separation within reasonable analysis time. For that purpose artificial neural network retention model was developed and used in combination with normalized resolution product criteria function. Developed artificial neural network retention model shows good predictive ability R² ≥ 0.9983. The determined ion chromatographic parameters enable baseline separation of all components of interest. By performing validation procedure and number of statistical tests it is shown that developed ion chromatographic method has superior performance characteristic: linearity R² ≥ 0.9984, recovery = 99.81% − 99.44%, repeatability RSD ≤ 0.52%. That result proves that proposed method can be used for routine monitoring analysis in fertilizer industry.