Effects of monohydration on an adenine–thymine base pair

Abstract

We analyzed the monohydration effect on the hydrogen-bonded structure between the adenine–thymine base pair using path integral molecular dynamics simulations including the nuclear quantum and thermal effects. We focused on two monohydration models for an adenine–thymine base pair with a water molecule bound to each adenine and thymine site. The adenine–thymine base pair without a water molecule was also discussed to reveal the role of a water molecule in monohydrated models. We found that the monohydration effect varies depending on the location of the water molecule. The monohydration effect on the inter-molecular motions is also investigated using the principle component analysis. The monohydration alters the inter-molecular motions of adenine–thymine base pair. We found that the nuclear quantum effect on the motion depends on the positions of the bound water molecule. The nuclear quantum effect on the hydrogen-bonded structure of adenine, thymine and water molecules is rather small, but we found significantly large nuclear quantum effect on the inter-molecular motions of the monohydrated base pair systems.

Appendix

We analyzed the inter-molecular motions of buckle and propeller modes of adenine–thymine pair introducing a simple geometric model as shown in Fig. 4. The model is constructed with two plates $h_{1} h_{2} r_{1} r_{2}$ and $h_{1} h_{2} r_{3} r_{4}$ connected by two hinges $h_{1}$ and $h_{2}$. We assign 2a to both hydrogen-bond lengths and $z_{0}$ to the distance between two hydrogen bonds in this model. We fix the plate $h_{1} h_{2} r_{3} r_{4}$ on the z–x plane. The angles $\theta_{1}$ and $\theta_{2}$ are defined as angles between vector $\overrightarrow {{r_{1} h_{1} }}$ and the z–x plane and vector $\overrightarrow {{r_{2} h_{2} }}$ and the z–x plane, respectively. The angle between $\overrightarrow {{{\text{OM}}_{1} }}$ and $\overrightarrow {{{\text{M}}_{2} {\text{O}}}}$ is $\phi_{1}$, and the angle between $r_{1} - r_{2}$ and $r_{3} - r_{4}$ is $\phi_{2}$. The displacement of $\phi_{1}$ and $\phi_{2}$ corresponds to the buckle and propeller modes, respectively. These angles $\phi_{1}$ and $\phi_{2}$ are expressed as follows using $\theta_{1}$ and $\theta_{2}$.

$$\phi_{1} = \frac{{\cos \theta_{1} + \cos \theta_{2} }}{{\sqrt {2\cos \left( {\theta_{1} - \theta_{2} } \right) + 2} }},$$

(3)

and

$$\phi_{2} = \frac{{z_{0} }}{{\sqrt {2a^{2} \cos \left( {\theta_{1} - \theta_{2} } \right) + 2a^{2} + z_{0}^{2} } }}.$$

(4)

When $\theta_{1}$ and $\theta_{2}$ are small, Eqs. (3) and (4) can be approximated as

$$\phi_{1} = \frac{{\theta_{1} + \theta_{2} }}{2},$$

(5)

and

$$\phi_{2} = \frac{{a(\theta_{1} - \theta_{2} )}}{{z_{0} }}.$$

(6)

The displacement ratio of buckle and propeller modes corresponds to the ratio of $\phi_{1}$ and $\phi_{2}$. The relation can be written as

$$\frac{{\phi_{2} }}{{\phi_{1} }} = \frac{2a}{{z_{0} }} \times \frac{{1 - \theta_{2} /\theta_{1} }}{{1 + \theta_{2} /\theta_{1} }}.$$

(7)

Figure 5 shows the relation between $\phi_{2} /\phi_{1}$ and $\theta_{2} /\theta_{1}$ in Eq. (7). We set the parameter $a$ to be $a/z_{0} = 1$. Only the buckle mode exists when $\theta_{1} = \theta_{2}$ and $\phi_{2} /\phi_{1} = 0$, while only the propeller mode exists when $\theta_{1} = - \theta_{2}$ and $\phi_{2} /\phi_{1} = \infty$. In other areas, both buckle and propeller modes exist. The figure shows that the ratio of buckle and propeller modes may alter if the vibrational frequencies of the hydrogen-bond angle shift. The ratio depends on the difference between $\theta_{1}$ and $\theta_{2}$ and can rapidly change from buckle dominant motion (region around $\theta_{1} = \theta_{2}$) to propeller dominant motion (region around $\theta_{1} = - \theta_{2}$). Our finding indicates that the small difference in the hydrogen-bond structure may lead to large difference in molecular motion.

Fig. 4

A simple geometric model for the buckle and propeller modes of the adenine–thymine pair

Fig. 5

The relation between $\phi_{2} /\phi_{1}$ and $\theta_{2} /\theta_{1}$ in Eq. (7)