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Single-molecule experiments revealed that the replication rate of T7 DNA polymerase has a peak value at tension of about 5.5 pN. However, the mechanism leading to this peak has only been partially investigated. Here, we present a two-state model to investigate the effect of mechanical tension on DNA polymerase activity. The model consists of polymerase and exonuclease. The polymerase's kinetic pathway has been simplified into Michaelis–Menten form with two steps. One is the conformational change from "open" to "close". The other is the base-stacking. The results are in good agreement with experimental observations. We also predict that the tension on template is beneficial to the fidelity of DNA replication.

The motion of molecular motor is essential to the biophysical functioning of living cells. This motion can be regarded as a multiple chemical state process. So, mathematically, the motion of molecular motor can be described by several coupled one-dimensional hopping processes or by several coupled Fokker–Planck equations. To know the basic properties of molecular motor, in this paper, we will give detailed analysis about the simplest case in which there are only two chemical states. Actually, many of the existing models, such as the flashing ratchet model, can be regarded as a two-state model. From the explicit expression of the mean velocity, one can see that the mean velocity of molecular motor might be non-zero even if the potential in each state is periodic, which means that there is no energy input to the molecular motor in each of the two states. At the same time, the mean velocity might be zero even if there is non-trivial energy input. Generally, the velocity of molecular motor depends not only on the potentials (or corresponding forward and backward transition rates) in the two chemical states, but also on the transition rates between them.

In living cells, molecular motors convert chemical energy into mechanical work. Its thermodynamic energy efficiency, i.e. the ratio of output mechanical work to input chemical energy, is usually high. However, using two-state models, we found the motion of molecular motors is loosely coupled to the chemical cycle. Only part of the input energy can be converted into mechanical work. Others are dissipated into environment during substeps without contributions to the unidirectional movement.

Six pyridyne isomers and their complexes with beryllium have been considered for the theoretical study of the third-order polarizability. The NLO properties are calculated by employing the DFT functionals BLYP, B3LYP, BHHLYP, B3PW91, BP86 and B2PLYP for the 6-311++G(d,p) basis set. The C-Be bond length in the complexes varies within 1.644 Å–1.771 Å indicating covalent interactions between the metal and pyridynes. The present investigation reveals that the magnitude of second-hyperpolarizability of pyridynes strongly enhances upon complex formation with beryllium. The maximum hyperpolarizability has been predicted for the 2,5-diberyllium pyridine complex. The lowest value of hyperpolarizability is obtained for the 2,3- and 3,4-diberyllium pyridine complexes. The chosen DFT methods predict almost identical pattern of variation of NLO property. The variation of second-hyperpolarizability has been satisfactorily explained by the excitation energy and transition dipole moment associated with the most dominant excited state.

Multimetallocene complexes (Cp–M_n–Cp) of Be, Mg and Ca have been considered for the theoretical study of static second hyperpolarizability using a number of DFT functionals. Owing to the cooperative effect in bonding, beryllium forms multiberyllocene complexes (Cp–Be_n–Cp) which have sufficient thermal stability with respect to dissociation into neutral fragments up to n = 10. On the other hand, multimetallocene complexes of Mg and Ca are found to be stable for n ≤ 5 which may be due to the weaker covalent bonding interaction between the larger metal atoms. The rather small variation of linear and cubic polarizabilities of Cp–Be_n–Cp complexes beyond n = 5 arises from the rather weaker charge transfer transitions. The difference in NLO property among the investigated metal complexes arises from the extent of charge transfer from the terminal metal atoms and the distance between them. The charge transfer at longer distances in the ground state of Mg and Ca complexes leads to more intense electronic transition — the spectroscopic parameters of which strongly favors the enhancement of second hyperpolarizability.

The conformation of five-membered furanose rings is a crucial issue for the structural analysis of many biologically-relevant molecules, including DNA and RNA. Oxolane can be treated as a prototypical furanose, composed only of saturated unsubstituted ring. In spite of its structural simplicity, providing the accurate quantitative description of the oxolane conformational features remains a great challenge for both the experimental and theoretical techniques. Here we show the method of recovering the free-energy profiles describing the conformational equilibrium in the oxolane ring (i.e. pseudorotation) based on the experimentally-inferred NMR data (${}^3{\text{J}}_{\text{H},\text{H}}$ coupling constants). The results remain in agreement with the quantum-mechanical-based molecular dynamics simulations and emphasize the large contributions of all ring conformers, even those located at the free-energy barriers. This includes the significant populations of limiting ³T₂/²T₃ and ^OE/E_O shapes. Our findings provide another example of a poor applicability of the two-state model, which is routinely applied to analyze the NMR data in terms of population of different ring conformers.