Identifying reliable ions for the statistical differentiation of structurally similar fentanyl analogs

Definitive identification of fentanyl analogs based on mass spectral comparison is challenging given the high degree of structural and, hence, spectral similarity. To address this, a statistical method was previously developed in which two electron-ionization (EI) mass spectra are compared using the unequal variance t-test. Normalized intensities of corresponding ions are compared, testing the null hypothesis (H0 ) that the difference in intensity is equal to zero. If H0 is accepted at all m/z values, the two spectra are statistically equivalent at the specified confidence level. If H0 is not accepted at any m/z value, then there is a significant difference in intensity at that m/z value between the two spectra. In this work, the statistical comparison method is applied to distinguish EI spectra of valeryl fentanyl, isovaleryl fentanyl, and pivaloyl fentanyl. Spectra of the three analogs were collected over a 9-month period and at different concentrations. At the 99.9% confidence level, the spectra of corresponding isomers were statistically associated. Spectra of different isomers were statistically distinct, and ions responsible for discrimination were identified in each comparison. To account for inherent instrument variations, discriminating ions for each pairwise comparison were ranked based on the magnitude of the calculated t-statistic (tcalc ) value. For a given comparison, ions with higher tcalc values are those with the greatest difference in intensity between the two spectra and, therefore, are considered more reliable for discrimination. Using these methods, objective discrimination among the spectra was achieved and ions considered most reliable for discrimination of these isomers were identified.

Measuring evaporation rate constants of highly volatile compounds for use in predictive kinetic models

A kinetic model was previously developed in our laboratory to predict evaporation of compounds as a function of gas chromatographic retention index (I^T). To define the initial model, evaporation rate constants were experimentally determined for compounds in the range I^T = 800-1400 at temperatures from 5 to 35 °C. While the predictive accuracy was demonstrated, broader application of the model requires extension of the I^T range to include more volatile compounds. However, such extension requires experimental determination of rate constants, which is challenging due to the explosive hazard and rapid evaporation of volatile compounds. In this work, rate constants of highly volatile compounds were experimentally determined and used to extend the kinetic model to predict evaporation. Prior to experimental evaporations, theoretical calculations were performed to optimize experimental parameters and to ensure that the vapor generated remained below the lower flammability limit for each compound. Compounds were then experimentally evaporated at three different temperatures (10, 20, and 30 °C) and analyzed by gas chromatography-mass spectrometry. The evaporation rate constants for each compound, corrected for condensation, were determined by regression to a first-order rate equation. These rate constants were combined with previously collected data to extend the kinetic model at each temperature. Comparison of predicted and experimentally determined chromatograms of an evaporated validation mixture indicated good model performance, with correlation coefficients ranging from 0.955 to 0.997 and mean absolute percent errors in predicting abundance ranging from 3 to 26%.

Statistical comparison of mass spectra for identification of amphetamine-type stimulants

A method for the statistical comparison of mass spectral data is demonstrated for applications in controlled substance analysis. The method uses an unequal variance t-test at each mass-to-charge ratio in the scan range to determine if two spectra are statistically associated or discriminated. If the two spectra are associated, a random-match probability is calculated to estimate the likelihood that the mass spectral fragmentation pattern in question occurs by random chance alone. If the two spectra are discriminated, the fragment ions responsible for the discrimination are determined. In this work, mass spectral data from case samples containing amphetamine, methamphetamine, 3,4-methylenedioxyamphetamine (MDA), 3,4-methylenedioxymethamphetamine (MDMA), phentermine, and psilocin were investigated. All spectra were collected in an accredited forensic laboratory using routine methods for controlled substance analysis. Using the statistical method, spectra of case samples were statistically associated to the corresponding reference standard at the 99.9% confidence level. In these instances, random-match probabilities ranged from 10^-39 to 10^-29, indicating the probability that the characteristic fragmentation pattern occurred by random chance is extremely small. Further, spectra of case samples were discriminated from other reference standards at the 99.9% or 99.0% confidence level, with 1-26 ions responsible for discrimination in each comparison.

Statistical approach to establish equivalence of unabbreviated mass spectra

RATIONALE

In many legal and regulatory applications, mass spectral comparison of an unknown or questioned sample to a reference standard or database is used for identification; however, no statistical confidence level or error rate is determined. Therefore, a simple and rapid method to establish the statistical equivalence of mass spectra is needed.

METHODS

The standard deviation of the abundance at each m/z ratio was determined from replicate measurements or from a statistical model. These standard deviations were used in an unequal variance t-test to compare two spectra at every m/z ratio over the entire scan range. If determined to be statistically indistinguishable at every m/z ratio, the random-match probability (RMP) that the specific mass spectral fragmentation pattern occurred by chance was calculated.

RESULTS

n-Alkane and alkylbenzene standards of varying concentrations were analyzed on the same instrument at different ionization voltages. Using the proposed method, replicate spectra were successfully associated at the 99.9% confidence level, with RMP values less than 10(-29). Despite the similarity in fragmentation patterns, spectra were distinguished from others in the homologous series. Moreover, the n-alkane spectra were appropriately associated to and discriminated from those in a standard reference database at the 99.9% confidence level.

CONCLUSIONS

A simple and rapid method to assign statistical significance to the comparison of mass spectra was developed and validated. This method may be useful for legal and regulatory applications, such as the identification of controlled substances, environmental pollutants, and food and drug contaminants.

Capillary electrophoresis for thermodynamic and kinetic studies of peptidyl-proline isomerization by the theoretical plate height model

The theoretical plate height model, extended to include reactive CE, is used to calculate equilibrium constants and rate constants for the reversible, first-order isomerization of proline dipeptides. This model is consistent with chromatographic theory and enables calculation of equilibrium constants from velocity and calculation of rate constants from plate height. Thermodynamic and kinetic parameters for isomerization of Ala-Pro and Phe-Pro are calculated by using the plate height model, and are shown to be in good agreement with literature values. Additionally, the efficacy of the plate height model is compared to ChromWin, an existing simulation method for calculating rate constants from zone profiles. It is shown that ChromWin and the plate height model are complementary methods. ChromWin is best used for calculating rate constants for reactions that are far from steady state, where the zone profiles exhibit plateau formation. On the other hand, the plate height model is best used for calculating rate constants for reactions that are at or near steady state, where the zone profiles exhibit a single zone containing both reacting species.

Effects of nonequilibrium on velocity and plate height in reactive capillary electrophoresis

Models for velocity and plate height for reactive CE are developed under the formalism of generalized nonequilibrium theory, as described by Giddings. The resultant equations are consistent with chromatographic theory and validated with an independent stochastic simulation. Moreover, unlike prior methods for CE, this model allows calculation of thermodynamic equilibrium constants and kinetic rate constants from a single, undistorted peak. The theoretical development shows that velocity is directly dependent on the equilibrium constant and is independent of the rate constant. On the other hand, plate height varies little with equilibrium constant and is inversely proportional to rate constant. The ability to evaluate equilibrium constants from velocity and rate constants from plate height is most greatly influenced by electric field strength and mobility difference. The accuracy in calculated equilibrium constants is limited by mobility difference; however, the accuracy in rate constants is limited by plate height and equilibrium constant.

Thermodynamic and kinetic characterization of nitrogen-containing polycyclic aromatic hydrocarbons in reversed-phase liquid chromatography

A series of five nitrogen-containing polycyclic aromatic hydrocarbons (NPAHs) was studied on polymeric octadecylsilica using methanol and acetonitrile as the mobile phase. The thermodynamic and kinetic behavior was examined as a function of ring number, annelation structure, and position of the nitrogen atom. The retention factors for the NPAHs are smaller than those for the parent PAHs in methanol, while the converse is true in acetonitrile. The changes in molar enthalpy are relatively comparable in both mobile phases with 1-aminopyrene having values of -5.0 +/- 0.2 kcal/mol in methanol and -6.3 +/- 0.7 kcal/mol in acetonitrile (1 cal = 4.184 J). However, the rate constants from mobile to stationary phase (k(sm)) and from stationary to mobile phase (k(ms)) demonstrate large differences as a function of mobile phase. For example, the rate constants k(ms) for 1-aminopyrene and 4-azapyrene are 675 and 62 s(-1), respectively, in methanol at 303 K. In contrast, the same solutes demonstrate rate constants of 3.47 and 3.9 x 10(-3) s(-1), respectively, in acetonitrile. The activation energies for transfer from mobile phase to transition state (deltaE(double dagger(m)) and from stationary phase to transition state (deltaE(double dagger(s)) also differ as a function of mobile phase. For example, the activation energies deltaE(double dagger(s)), for 1-aminopyrene are 21 and approximately 0 kcal/mol, whereas those for 4-azapyrene are 19 and 23 kcal/mol, in methanol and acetonitrile, respectively. Based on these thermodynamic and kinetic results, the relative contributions from the partition and adsorption mechanisms are discussed.

Stochastic simulation of reactive separations in capillary electrophoresis

A stochastic (Monte Carlo) simulation is used to investigate thermodynamic and kinetic contributions from the reversible A <--> B reaction in capillary electrophoresis (CE). The effects of equilibrium constant, rate constant, and electrophoretic mobility on the molecular zone profiles and the corresponding statistical moments are evaluated. As the reaction approaches steady state, the velocity of the zone is governed by the equilibrium constant and the electrophoretic mobilities of the reacting molecules. When the equilibrium constant is less than unity, the mean zone velocity is more similar to that of the reactant A. Conversely, when the equilibrium constant is greater than unity, the velocity is more similar to that of the product B. The extent of zone-broadening and asymmetry at steady state is dependent upon the equilibrium constant, the characteristic reaction lifetime, and the electrophoretic mobility difference between reacting molecules. If all other parameters are held constant, the plate height is greatest and skew is least when the equilibrium constant is unity. The plate height increases linearly with the characteristic reaction lifetime and electrophoretic mobility difference, whereas the skew is independent of these parameters. These conclusions have important implications for the elucidation of thermodynamic and kinetic information from experimental data.

Thermodynamics and kinetics of solute transfer in reversed-phase liquid chromatography

A series of four-ring polycyclic aromatic hydrocarbons (PAHs) with varying annelation structure was studied by reversed-phase liquid chromatography. Using a polymeric octadecylsilica stationary phase over a temperature range from 273 to 303 K and an average pressure range from 585 to 3585 psi (1 psi = 6894.76 Pa), the thermodynamic and kinetic aspects of the retention mechanism were examined. Thermodynamic behavior was characterized by the retention factor, together with the associated changes in molar enthalpy and molar volume, whereas kinetic behavior was characterized by the rate constants, together with the associated activation enthalpies and activation volumes. The data indicate that pyrene, with a more condensed annelation structure, exhibits smaller changes in molar enthalpy and molar volume (delta Hsm = -4.4 kcal/mol, delta Vsm = -1.9 ml/mol; 1 cal = 4.184J) than PAHs with a more linear structure such as chrysene (delta Hsm = -8.2 kcal/mol, delta Vsm = - 11.7 ml/mol). The kinetic data indicate that pyrene undergoes faster rates of transport than chrysene (k(ms) = 313 and 14 s(-1), respectively), but the non-planar benzo[c]phenanthrene undergoes the fastest transport (k(ms) = 330 s(-1)). The activation enthalpies and activation volumes are similarly affected by the annelation structure. It is noteworthy that deviations from the exponentially modified Gaussian (EMG) model are observed for some PAH zone profiles at the lowest temperature, which suggests a possible change in retention mechanism. In order to characterize these deviations, the non-linear chromatography (NLC) model and a new bi-exponentially modified Gaussian (E2MG) model were examined. The regression results indicate that neither the NLC nor E2MG model offer significant improvements in the statistical quality of fit or provide a better description of the observed retention behavior.

Thermodynamic and Kinetic Characterization of Polycyclic Aromatic Hydrocarbons in Reversed-Phase Liquid Chromatography

The retention of six polycyclic aromatic hydrocarbons (PAHs) was characterized by reversed-phase liquid chromatography. The PAHs were detected by laser-induced fluorescence at four points along an optically transparent capillary column. The profiles were characterized in space and time using an exponentially modified Gaussian equation. The resulting parameters were used to calculate the retention factors, as well as the concomitant changes in molar enthalpy and molar volume, for each PAH on monomeric (2.7 micromol/m2) and polymeric (5.4 micromol/m2) octadecylsilica. The changes in molar enthalpy become more exothermic as ring number increases and as annelation structure becomes less condensed. The changes in molar volume become more negative as ring number increases for the planar PAHs, but are positive for the nonplanar solutes. In addition, the rate constants, as well as the concomitant activation enthalpy and activation volume, are calculated for the first time. The kinetic data demonstrate that many of the PAHs exhibit very fast transitions between the mobile and stationary phases. The transition state is very high in energy, and the activation enthalpies and volumes become greater as ring number increases and as annelation structure becomes less condensed. The changes in thermodynamic and kinetic behavior are much more pronounced for the polymeric phase than for the monomeric phase.

Thermodynamics and kinetics of solute transfer in reversed-phase liquid chromatography

In this study, the thermodynamic and kinetic behavior of a homologous series of fatty acids is examined using a polymeric octadecylsilica stationary phase and a methanol mobile phase. The zone profiles are evaluated as the temperature is varied from 20 to 60 degrees C and the average pressure from 400 to 4570 p.s.i. (1 p.s.i.=6894.76 Pa). The rate constant for solute transfer from mobile to stationary phase (k(ms)) appears to be relatively constant with carbon number. In contrast, the rate constant from stationary to mobile phase (k(sm)) decreases logarithmically with increasing carbon number. This suggests that the mass transport processes become progressively slower, owing to the smaller diffusion coefficients of the larger solutes in the stationary phase. The activation energy decreases slightly in the mobile phase and increases slightly in the stationary phase with increasing carbon number. The activation energy in the stationary phase ranges from 41.6 to 55.9 kcal/mol, while the thermodynamic change in internal energy ranges from -9.8 to -29.0 kcal/mol for C10 to C22, respectively (1 cal=4.184 J). The activation volume increases with increasing carbon number in both the mobile and stationary phase. The activation volume in the stationary phase ranges from 31.7 to 211 cm3/mol, while the thermodynamic change in molar volume ranges from -27.1 to -104 cm3/mol for C10 to C22, respectively. These large changes in activation energy and volume suggest that the solutes do not enter and leave the stationary phase in a single step, but in a stepwise or progressive manner.

Stochastic simulation of the partition mechanism with a heterogeneous surface phase

A three-dimensional stochastic model of chromatography has been used to determine the effect of multiple sites on the partition mechanism. The effect of additional sites on mass transfer rates, zone profiles, and their statistical moments are investigated as a function of the partition coefficient, diffusion coefficient, and interfacial barrier to mass transfer. These studies have demonstrated that changes in the partition coefficient alone are not sufficient to alter the system response from that of a single site. Changes in the diffusion coefficient and the barrier to mass transfer do cause changes in the response compared to that of a single site. The zone profiles produced by the systems become more asymmetric as the difference between the diffusion coefficients or the barriers to mass transfer increases. The site with the slower mass transfer rate plays the dominant role in the total system response.

Fluorescence Quenching as an Indirect Detection Method for Nitrated Explosives

A novel approach based on fluorescence quenching is presented for the analysis of nitrated explosives. Seventeen common explosives and their degradation products are shown to be potent quenchers of pyrene, having Stern-Volmer constants that generally increase with the degree of nitration. Aromatic explosives such as 2,4,6-trinitrotoluene (2,4,6-TNT) are more effective quenchers than aliphatic or nitramine explosives. In addition, nitroaromatic explosives are found to have unique interactions with pyrene that lead to a wavelength dependence of their Stern-Volmer constants. This phenomenon allows for their differentiation from other nitrated explosives. The fluorescence quenching method is then applied to the determination of hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazine(HMX), 2,4,6-TNT, nitromethane, and ammonium nitrate in various commercial explosive samples. The samples are separated by capillary liquid chromatography with post-column addition of the pyrene solution and detection by laser-induced fluorescence. The indirect fluorescence quenching method shows increased sensitivity and selectivity over traditional UV-visible absorbance as well as the ability to detect a wider range of organic and inorganic nitrated compounds.