We apply moving root-mean-square deviation (mRMSD), which does not require a reference structure, as a method for analyzing protein dynamics. This method can be used to calculate the root-mean-square deviation (RMSD) of structure between two specified time points and to analyze protein dynamics behavior through time series analysis. We applied this method to the Trp-cage trajectory calculated by the Anton supercomputer and found that it shows regions of stable states as well as the conventional RMSD. In addition, we extracted a characteristic structure in which the side chains of Asp1 and Arg16 form hydrogen bonds near the most stable structure of the Trp-cage. We also determined that ≥20 ns is an appropriate time interval to investigate protein dynamics using mRMSD. Applying this method to NuG2 protein, we found that mRMSD can be used to detect regions of metastable states in addition to the stable state. This method can be applied to molecular dynamics simulations of proteins whose stable structures are unknown.

We compared shoot and needle morphology and photosynthesis in Picea glehnii (Friedr. Schmidt) M.T. Mast. and Picea jezoensis (Sieb. et Zucc.) Carr. trees planted on immature volcanic ash and well-developed brown forest soils to investigate whether species differences in morphological and physiological plasticity affected tree growth on different soil types. Height growth of P. glehnii was reduced by about 10% on volcanic ash compared with forest soil, whereas that of P. jezoensis was reduced by more than 60%. Needle morphology of P. glehnii was unaffected by soil type. In contrast, needles of P. jezoensis trees growing on volcanic ash were shorter, narrower and thicker, with less dry mass and area, than those of trees growing on forest soil, and specific needle area was lower, indicating lower foliar light-interception efficiency. In both species, changes in needle morphology with increasing irradiance were similar in trees growing on both soil types, indicating that plasticity of needle morphology was unaffected by soil type. In both species, shoot mass and shoot silhouette area were lower and needle mass per unit shoot mass was higher in trees growing on volcanic ash than in trees growing on forest soil. Trees of both species had more needles per unit shoot length, lower shoot silhouette to projected needle area ratios and lower shoot silhouette areas per unit shoot mass (SAM) on volcanic ash than on forest soil, indicating lower shoot-level light-interception efficiency. For P. glehnii, the response of shoot morphology to increasing irradiance was similar on both soil types, with the exception of SAM, which showed lower plasticity in trees growing on volcanic ash. In contrast, shoot-level morphological plasticity of P. jezoensis was reduced in trees growing on volcanic ash. Light-saturated maximum photosynthetic rate (P_max) of P. glehnii was unaffected by soil type, whereas mass-based P_max of P. jezoensis was lower in trees growing on volcanic ash than in trees growing on forest soil. In P. jezoensis trees growing on forest soil, area-based P_max increased with increasing irradiance, but this response was not observed in trees growing on volcanic ash. As a result, area-based P_max at the top of the canopy was 39 to 54% lower in trees growing on volcanic ash than in trees growing on forest soil. Our results indicate that constraints on morphological acclimation to high irradiances may contribute to reduced height growth of P. jezoensis on volcanic ash.

In the conventional classical density functional theory (DFT) for simple fluids, an ideal gas is usually chosen as the reference system because there is a one-to-one correspondence between the external field and the density distribution function, and the exact intrinsic free-energy functional is available for the ideal gas. In this case, the second-order density functional Taylor series expansion of the excess intrinsic free-energy functional provides the hypernetted-chain (HNC) approximation. Recently, it has been shown that the HNC approximation significantly overestimates the solvation free energy (SFE) for an infinitely dilute Lennard-Jones (LJ) solution, especially when the solute particles are several times larger than the solvent particles [T. Miyata and J. Thapa, Chem. Phys. Lett. 604, 122 (2014)]. In the present study, we propose a reference-modified density functional theory as a systematic approach to improve the SFE functional as well as the pair distribution functions. The second-order density functional Taylor series expansion for the excess part of the intrinsic free-energy functional in which a hard-sphere fluid is introduced as the reference system instead of an ideal gas is applied to the LJ pure and infinitely dilute solution systems and is proved to remarkably improve the drawbacks of the HNC approximation. Furthermore, the third-order density functional expansion approximation in which a factorization approximation is applied to the triplet direct correlation function is examined for the LJ systems. We also show that the third-order contribution can yield further refinements for both the pair distribution function and the excess chemical potential for the pure LJ liquids.