The formulation of chemical potentials and free energy changes in biochemical reactions.

In 1994, an IUBMB-IUPAC joint committee recommended a revised formulation for standard chemical potentials and reaction free energies motivated by the fact that, in biochemistry, the reactants and products often exist in multiple charge states depending on the pH and pMg of the solution environment. The recommendation involved both the use of (1) a mathematical transform with the intent to hold the pH constant, and (2) the formulation of reference chemical potentials of ionized isomeric species based on the log sum of the individual standard chemical potentials of each isomeric species. Recently, several reports including a 2020 IUPAC report have appeared that challenged the need for such summary formulations, arguing that the standard chemical potentials were sufficient with full accounting of each of the different charge state isomers involved in a biochemical reaction. This work critically evaluates both the use of thermodynamic transforms and the different chemical potential formulations. It is shown that (1) transforms are not necessary to hold the pH constant and (2) demonstrates that the two chemical potential formulations are not equivalent. Which formulation is appropriate depends on what species are measured experimentally or whether an assumption of equilibrium among the charge state isomers is reasonable and desirable.

Molecular dynamics investigation of the bimolecular reaction BeH + H(2) --> BeH(2) + H on an ab initio potential-energy surface obtained using neural network methods with both potential and gradient accuracy determination.

The classical reaction dynamics of a four-body, bimolecular reaction on a neural network (NN) potential-energy surface (PES) fitted to a database obtained solely from ab initio MP2/6-311G(d,p) calculations are reported. The present work represents the first reported application of ab initio NN methods to a four-body, bimolecular, gas-phase reaction where bond extensions reach 8.1 A for the BeH + H(2) --> BeH(2) + H reaction. A modified, iterative novelty sampling method is used to select data points based on classical trajectories computed on temporary NN surfaces. After seven iterations, the sampling process is found to converge after selecting 9604 configurations. Incorporation of symmetry increases this to 19 208 BeH(3) configurations. The analytic PES for the system is obtained from the ensemble average of a five-member (6-60-1) NN committee. The mean absolute error (MAE) for the committee is 0.0046 eV (0.44 kJ mol(-1)). The total energy range of the BeH(3) database is 147.0 kJ mol(-1). Therefore, this MAE represents a percent energy error of 0.30%. Since it is the gradient of the PES that constitutes the most important quantity in molecular dynamics simulations, the paper also reports mean absolute error for the gradient. This result is 0.026 eV A(-1) (2.51 kJ mol(-1) A(-1)). Since the gradient magnitudes span a range of 15.32 eV A(-1) over the configuration space tested, this mean absolute gradient error represents a percent error of 0.17%. The mean percent absolute relative gradient error is 4.67%. The classically computed reaction cross sections generally increase with total energy. They vary from 0.007 to 0.030 A(2) when H(2) is at ground state, and from 0.05 to 0.10 A(2) when H(2) is in the first excited state. Trajectory integration is very fast using the five-member NN PES. The average trajectory integration time is 1.07 s on a CPU with a clock speed of 2.4 GHz. Zero angular momentum collisions are also investigated and compared with previously reported quantum dynamics on the same system. The quantum reaction probabilities exhibit pronounced resonance effects that are absent in the classical calculations. The magnitudes of quantum and classical results are in fair accord with the classical results being about 30-40% higher due to the lack of quantum restrictions on the zero-point vibrational energy.

Molecular dissociation of hydrogen peroxide (HOOH) on a neural network ab initio potential surface with a new configuration sampling method involving gradient fitting.

The O-O bond dissociation of HOOH is investigated on an analytic ab initio potential-energy surface obtained by fitting the energies of 25,608 configurations using neural network (NN) methods. The electronic structure calculations are executed using MP2 calculations with the 6-31G* basis set. A new data-sampling technique is introduced to collect HOOH configurations in the six-dimensional hyperspace. This method is based on a comparison of the NN-computed gradients at configuration points currently in the database with the target gradients. By requiring that the NN gradients closely fit the MP2 target gradients, both the potential and the gradients are more accurately fitted. The selection criteria also ensure a more uniform distribution of configuration points throughout the important regions of configuration space. Molecular dynamics (MD) trajectories are not involved in the sampling. The final NN fitting yields average absolute and root-mean-squared testing set errors of 0.0060 eV (0.58 kJ mol(-1)) and 0.0099 eV (0.96 kJ mol(-1)), respectively. The effectiveness of the support vector machine (SVM) method in fitting large ab initio databases for MD calculations is investigated by using this method to fit the same HOOH database. The SVM fitting quality is tested by comparison to the NN fit. It is found that the average absolute and root-mean-squared testing set errors for the SVM fit are significantly larger than those obtained using NN methods. The total number of parameters in the SVM fit is more than a factor of 11 times the number of parameters in the NN fit. The trajectory computation time using a single NN averages about 1.8 s per picosecond of trajectory time. This increases to 9.0 s per picosecond of trajectory time if a five-NN committee is employed. The corresponding SVM computational time is almost 24 s per picosecond of trajectory time. Consequently, we conclude that a SVM is not as effective in fitting large databases for MD calculations as previously proposed methods, and thus is not employed to conduct MD studies. We employ the five-member NN committee to perform MD calculations at five different internal energies from 3.4 to 4.2 eV, including zero point energy. The rate coefficients are obtained directly from the first-order decay plots. They vary from 0.117 to 0.324 ps(-1). A Rice-Ramsperger-Kassel plot is found to exhibit good linearity.

Cis-->trans, trans-->cis isomerizations and N-O bond dissociation of nitrous acid (HONO) on an ab initio potential surface obtained by novelty sampling and feed-forward neural network fitting.

The isomerization and dissociation dynamics of HONO are investigated on an ab initio potential surface obtained by fitting the results of electronic structure calculations at 21 584 configurations by using previously described novelty sampling and feed-forward neural network (NN) methods. The electronic structure calculations are executed by using GAUSSIAN 98 with a 6-311G(d) basis set at the MP4(SDQ) level of accuracy. The average absolute error of the NN fits varies from 0.012 eV (1.22 kJ mol(-1)) to 0.017 eV (1.64 kJ mol(-1)). The average computation time for a HONO trajectory using a single NN surface is approximately 4.8 s. These computation times compare very favorably with those required by other methods primarily because the NN fitting needs to be executed only one time rather than at every integration point. If the average result obtained from a committee of NNs is employed at each point rather than a single NN, increased fitting accuracy can be achieved at the expense of increased computational requirements. In the present investigation, we find that a committee comprising five NN potentials reduces the average absolute interpolation error to 0.0111 eV (1.07 kJ mol(-1)). Cis-trans isomerization rates with total energy of 1.70 eV (including zero point energy) have been computed for a variety of different initial distributions of the internal energy. In contrast to results previously reported by using an empirical potential, where cis-->trans to trans-->cis rate coefficient ratios at 1.70 eV total energy were found to lie in the range of 2.0-12.9 depending on the vibration mode excited, these ratios on the ab initio NN potential lie in the range of 0.63-1.94. It is suggested that this result is a reflection of much larger intramode coupling terms present in the ab initio potential surface. A direct consequence of this increased coupling is a significant decrease in the mode specific rate enhancement when compared to results obtained by using empirical surfaces. All isomerizations are found to be first order in accordance with the results reported by using empirical potentials. The dissociation rate to NO+OH has been investigated at internal HONO energies of 3.10 and 3.30 eV for different distributions of this energy among the six vibrational modes of HONO. These dissociations are also found to be first order. The computed dissociation rate coefficients exhibit only modest mode specific rate enhancement that is significantly smaller than that obtained on an empirical surface because of the much larger mode couplings present on the ab initio surface.

Classification of atrial fibrillation episodes from sparse electrocardiogram data.

BACKGROUND: Atrial fibrillation (AF) is the most common form of cardiac arrhythmia. This paper presents the application of the Classification and Regression Tree (CART) technique for detecting spontaneous termination or sustenance of AF with sparse data. METHOD: Electrocardiogram (ECG) recordings were obtained from the PhysioNet (AF Termination Challenge Database 2004) Web site. Signal analysis, feature extraction, and classification were made to distinguish among 3 AF episodes, namely, Nonterminating (N), Soon (<1 minute) to be terminating (S), and Terminating immediately (<1 second) (T). RESULTS: A continuous wavelet transform whose basis functions match the EKG patterns was found to yield compact representation (approximately 2 orders of magnitude). This facilitates the development of efficient algorithms for beat detection, QRST subtraction, and multiple ECG quantifier extraction (eg, QRS width, QT interval). A compact feature set was extracted through principal component analysis of these quantifiers. Accuracies exceeding 90% for AF episode classification were achieved. CONCLUSIONS: A wavelet representation customized to the ECG signal pattern was found to yield 98% lower entropies compared with other representations that use standard library wavelets. The Classification and Regression Tree (CART) technique seems to distinguish the N vs T, and the S vs T classifications very accurately.

Molecular dynamics investigations of the dissociation of SiO2 on an ab initio potential energy surface obtained using neural network methods.

The neural network (NN) procedure to interpolate ab initio data for the purpose of molecular dynamics (MD) simulations has been tested on the SiO(2) system. Unlike other similar NN studies, here, we studied the dissociation of SiO(2) without the initial use of any empirical potential. During the dissociation of SiO(2) into Si+O or Si+O(2), the spin multiplicity of the system changes from singlet to triplet in the first reaction and from singlet to pentet in the second. This paper employs four potential surfaces. The first is a NN fit [NN(STP)] to a database comprising the lowest of the singlet, triplet, and pentet energies obtained from density functional calculations in 6673 nuclear configurations. The other three potential surfaces are obtained from NN fits to the singlet, triplet, and pentet-state energies. The dissociation dynamics on the singlet-state and NN(STP) surfaces are reported. The results obtained using the singlet surface correspond to those expected if the reaction were to occur adiabatically. The dynamics on the NN(STP) surface represent those expected if the reaction follows a minimum-energy pathway. This study on a small system demonstrates the application of NNs for MD studies using ab initio data when the spin multiplicity of the system changes during the dissociation process.

Prediction of molecular-dynamics simulation results using feedforward neural networks: reaction of a C2 dimer with an activated diamond (100) surface.

A new approach involving neural networks combined with molecular dynamics has been used for the determination of reaction probabilities as a function of various input parameters for the reactions associated with the chemical-vapor deposition of carbon dimers on a diamond (100) surface. The data generated by the simulations have been used to train and test neural networks. The probabilities of chemisorption, scattering, and desorption as a function of input parameters, such as rotational energy, translational energy, and direction of the incident velocity vector of the carbon dimer, have been considered. The very good agreement obtained between the predictions of neural networks and those provided by molecular dynamics and the fact that, after training the network, the determination of the interpolated probabilities as a function of various input parameters involves only the evaluation of simple analytical expressions rather than computationally intensive algorithms show that neural networks are extremely powerful tools for interpolating the probabilities and rates of chemical reactions. We also find that a neural network fits the underlying trends in the data rather than the statistical variations present in the molecular-dynamics results. Consequently, neural networks can also provide a computationally convenient means of averaging the statistical variations inherent in molecular-dynamics calculations. In the present case the application of this method is found to reduce the statistical uncertainty in the molecular-dynamics results by about a factor of 3.5.