Tautomeric equilibrium, stability, and hydrogen bonding in 2'-deoxyguanosine monophosphate complexed with Mg2+

The tautomeric equilibrium and hydrogen bonding in nucleotide 2'-deoxyguanosine monophosphate that interacts with hydrated Mg2+ cation (4H2O.Mg[dGMP]) were studied at the MP2/cc-pVDZ//B3LYP/cc-pVDZ and B3LYP/aug-cc-pVTZ//B3LYP/cc-pVDZ levels of theory. The Mg2+ ion forms two inner-shell contacts with the nucleotide, similar to small phosphorylated molecules under physiological conditions. The presence of the phosphate group and the hydrated magnesium cation leads to a change in guanine tautomeric equilibrium of 4H2O.Mg[dGMP] in comparison to free guanine. The influence of the phosphate group and the magnesium cation on tautomeric equilibrium is larger in the anti conformation where the P=O-->Mg and Mg<--N7 coordinate bonds are formed. The canonical oxo form of guanine is more stable (by 6-8 kcal/mol) than the O6-hydroxo form in anti conformation. Thus, the interaction with Mg2+ ion is capable of further suppressing the likelihood of a spontaneous transient formation of the rare tautomer. In the syn conformation of 4H2O.Mg[dGMP], the interaction of the guanine nucleobase with the phosphate group and the magnesium cation is not as strong as in the anti conformation, and the relative stability of guanine tautomers is close to those in free guanine.     

Evolution of a heavy rigid body rotation under the action of unsteady restoring and perturbation torques

The paper develops an approximate solution to the system of Euler’s equations with additional perturbation term for dynamically symmetric rotating rigid body. The perturbed motions of a rigid body, close to Lagrange’s case, under the action of restoring and perturbation torques that are slowly varying in time are investigated. We describe an averaging procedure for slow variables of a rigid body perturbed motion, similar to Lagrange top. Conditions for the possibility of averaging the equations of motion with respect to the nutation phase angle are presented. The averaging technique reduces the system order from 6 to 3 and does not contain fast oscillations. An example of motion of the body using linearly dissipative torques is worked out to demonstrate the use of general equations. The numerical integration of the averaged system of equations is conducted of the body motion. The graphical presentations of the solutions are represented and discussed. A new class of rotations of a dynamically symmetric rigid body about a fixed point with account for a nonstationary perturbation torque, as well as for a restoring torque that slowly varies with time, is studied. The main objective of this paper is to extend the previous results for problem of the dynamic motion of a symmetric rigid body subjected to perturbation and restoring torques. The proposed averaging method is implemented to receive the averaging system of equations of motion. The graphical representations of the solutions are presented and discussed. The attained results are a generalization of our former works where µ and M_i are independent of the slow time τ and M_i depend on the slow time only.