Joint treatment of ab initio and experimental data in molecular force field calculations with Tikhonov’s method of regularization

Scaled in Cartesian Coordinates Ab Initio Molecular Force Fields of DNA Bases: Application to Canonical Pairs

The model of Regularized Quantum Mechanical Force Field (RQMFF) was applied to the joint treatment of ab initio and experimental vibrational data of the four primary nucleobases using a new algorithm based on the scaling procedure in Cartesian coordinates. The matrix of scaling factors in Cartesian coordinates for the considered molecules includes diagonal elements for all atoms of the molecule and off-diagonal elements for bonded atoms and for some non-bonded atoms (1–3 and some 1–4 interactions). The choice of the model is based on the results of the second-order perturbation analysis of the Fock matrix for uncoupled interactions using the Natural Bond Orbital (NBO) analysis. The scaling factors obtained within this model as a result of solving the inverse problem (regularized Cartesian scale factors) of adenine, cytosine, guanine, and thymine molecules were used to correct the Hessians of the canonical base pairs: adenine–thymine and cytosine–guanine. The proposed procedure is based on the block structure of the scaling matrix for molecular entities with non-covalent interactions, as in the case of DNA base pairs. It allows avoiding introducing internal coordinates (or coordinates of symmetry, local symmetry, etc.) when scaling the force field of a compound of a complex structure with non-covalent H-bonds.

Singular Value Decomposition Method To Determine Distance Distributions in Pulsed Dipolar Electron Spin Resonance: II. Estimating Uncertainty

This paper is a continuation of the method introduced by Srivastava and Freed (2017) that is a new method based on truncated singular value decomposition (TSVD) for obtaining physical results from experimental signals without any need for Tikhonov regularization or other similar methods that require a regularization parameter. We show here how to estimate the uncertainty in the SVD-generated solutions. The uncertainty in the solution may be obtained by finding the minimum and maximum values over which the solution remains converged. These are obtained from the optimum range of singular value contributions, where the width of this region depends on the solution point location (e.g., distance) and the signal-to-noise ratio (SNR) of the signal. The uncertainty levels typically found are very small with substantial SNR of the (denoised) signal, emphasizing the reliability of the method. With poorer SNR, the method is still satisfactory but with greater uncertainty, as expected. Pulsed dipolar electron spin resonance spectroscopy experiments are used as an example, but this TSVD approach is general and thus applicable to any similar experimental method wherein singular matrix inversion is needed to obtain the physically relevant result. We show that the Srivastava-Freed TSVD method along with the estimate of uncertainty can be effectively applied to pulsed dipolar electron spin resonance signals with SNR > 30, and even for a weak signal (e.g., SNR ≈ 3) reliable results are obtained by this method, provided the signal is first denoised using wavelet transforms (WavPDS).

Singular Value Decomposition Method to Determine Distance Distributions in Pulsed Dipolar Electron Spin Resonance

Regularization is often utilized to elicit the desired physical results from experimental data. The recent development of a denoising procedure yielding about 2 orders of magnitude in improvement in SNR obviates the need for regularization, which achieves a compromise between canceling effects of noise and obtaining an estimate of the desired physical results. We show how singular value decomposition (SVD) can be employed directly on the denoised data, using pulse dipolar electron spin resonance experiments as an example. Such experiments are useful in measuring distances and their distributions, P(r) between spin labels on proteins. In noise-free model cases exact results are obtained, but even a small amount of noise (e.g., SNR = 850 after denoising) corrupts the solution. We develop criteria that precisely determine an optimum approximate solution, which can readily be automated. This method is applicable to any signal that is currently processed with regularization of its SVD analysis.

Effect of a pH change on the conformational stability of the modified nucleotide queuosine monophosphate

The naturally occurring modified nucleotide queuosine 5'-monophosphate (QMP) related to biochemical regulatory pathways in the cell was investigated using quantum chemical approaches. The relative stability of biologically relevant conformations of QMP in solvent under a pH change was predicted at the BVP86/TZVP and MP2/TZVP levels of theory. Hydrogen bonding in QMP was studied using Bader's approach. The acidity constants of QMP were estimated using the COSMO-RS theory. It has been found that the neutral and anionic forms of QMP are the most stable in the physiological pH range. These forms correspond to the anti/north conformation and exist as zwitterionic tautomers having a negatively charged phosphate group (-1 for neutral and -2 for anionic) and a positively charged secondary amine group in the side chain. It was also found that QMP possesses the syn conformation in the cationic state at pH < 5.0 and undergoes syn to anti conformation transition when the pH increases, remaining in the anti conformation at the higher pH values. The marker IR bands specific for the anionic and neutral QMP forms in the 2300-2700 cm(-1) region were assigned to H-bonded NH groups of the QMP side chain. The bands between 800 and 1300 cm(-1) of the "fingerprint" (400-1500 cm(-1)) region were assigned to the vibrations of the ribose ring, the phosphate group and the side chain of QMP. The predicted IR spectra can be useful for the assignment of vibration bands in the experiential spectra of QMP or identification of the QMP forms. The revealed peculiarities of the QMP conformation sensitivity to a pH change as well as additional formed H-bonds could be responsible for specific nucleotide interactions with enzymes.

Potential energy functions

When energy is a critical quantity, accurate biomolecular simulations rest in substantial part on accurate potential energy functions (force fields). Improvements in methodology for determining parameters--particularly, in the systematic use of computational data obtained from quantum chemical calculations--and enhancements in functional form are leading to better potential energy functions. New calculations have been developed for water (including calculations that incorporate electronic polarizability to take account of the degree to which a molecule can be polarized), proteins, nucleic acids, carbohydrates, lipids, and general organic molecules. Most notably, two new biomolecular force fields have recently been derived and significant redeterminations of the parameters of two existing biomolecular force fields have been carried out. Some progress has also been made in incorporating polarizability into potential energy functions for molecules in general and in improving the treatment of metal-ligand interactions in systems of biomolecular interest.