19 Analysis of Water Molecules in the Hras-GTP and GDP Complexes
359
Fig. 19.9 The categories of
the occurrence ratio of
duration time by the number
of water molecules
respect to the phosphorus atoms is larger in GDP than in GTP. Occurrence ratio of
duration time is proportional to t −1.4 when duration time is less than about 5 ps. PA
has a long tail in occurrence ratio of duration time. This suggests that the network
of water molecules is conserved in 5 ps. Here, for short-time behaviour, we will
explain three cases. (1) When we analyzed the occurrence ratio of duration time of
water molecules in the first hydration sphere around atoms in areas in which water
molecules rarely come in, we found that the occurrence ratio decay exponentially,
(data are not shown). (2) When we analyzed the occurrence ratio of duration time
around C α atoms near the protein surface, we found that the power is about −1.8,
and conserved time is about 10 ps or more, (data are not shown). (3) In our case
of Fig. 19.5, the occurrence ratio of duration time is proportional to t −1.4 when
duration time is less than about 5 ps, because the water molecules around GTP or
GDP are partially restricted, and the entering and the leaving the area around GTP
or GDP are not so rare.
We can categorize them into two: In one category ((1) above), the occurrence ratio of duration time of water molecules in the first hydration sphere is proportional
to exponential function, when the number of water molecules is very small. In the
other category ((2) and (3) above), the occurrence ratio of duration time is proportional to the power of t, when the number of water molecules is not very small.
In detail, the power index is small and conserved time is long when the number of
water molecules is large, while the power index is large and conserved time is short
when the number of water molecules is small, as is drawn schematically in Fig. 19.9.
The water molecules are distributed evenly around PG in GTP although not evenly
around PB in GDP. This suggests that the hydrolysis of GTP can be triggered by
the attack of water molecule to the γ -phosphate by an appropriate direction. The direction distribution of water molecules around PG in GTP is slightly different from
the distribution around PB in GDP. This slight difference in distribution of direction
possibly causes the difference in the density distribution of water molecules.
Acknowledgements This work was supported by JSPS KAKENHI Grant Number 24540442.
The computations were in part carried out at the Research Center for Computational Science,
Okazaki, Japan.
References
1. Alberts B, Johnson A, Lewis J, Raff M, Robertss K, Walter P (2002) Molecular biology of the
cell, 5th edn. Garland, New York
359
Fig. 19.9 The categories of
the occurrence ratio of
duration time by the number
of water molecules
respect to the phosphorus atoms is larger in GDP than in GTP. Occurrence ratio of
duration time is proportional to t −1.4 when duration time is less than about 5 ps. PA
has a long tail in occurrence ratio of duration time. This suggests that the network
of water molecules is conserved in 5 ps. Here, for short-time behaviour, we will
explain three cases. (1) When we analyzed the occurrence ratio of duration time of
water molecules in the first hydration sphere around atoms in areas in which water
molecules rarely come in, we found that the occurrence ratio decay exponentially,
(data are not shown). (2) When we analyzed the occurrence ratio of duration time
around C α atoms near the protein surface, we found that the power is about −1.8,
and conserved time is about 10 ps or more, (data are not shown). (3) In our case
of Fig. 19.5, the occurrence ratio of duration time is proportional to t −1.4 when
duration time is less than about 5 ps, because the water molecules around GTP or
GDP are partially restricted, and the entering and the leaving the area around GTP
or GDP are not so rare.
We can categorize them into two: In one category ((1) above), the occurrence ratio of duration time of water molecules in the first hydration sphere is proportional
to exponential function, when the number of water molecules is very small. In the
other category ((2) and (3) above), the occurrence ratio of duration time is proportional to the power of t, when the number of water molecules is not very small.
In detail, the power index is small and conserved time is long when the number of
water molecules is large, while the power index is large and conserved time is short
when the number of water molecules is small, as is drawn schematically in Fig. 19.9.
The water molecules are distributed evenly around PG in GTP although not evenly
around PB in GDP. This suggests that the hydrolysis of GTP can be triggered by
the attack of water molecule to the γ -phosphate by an appropriate direction. The direction distribution of water molecules around PG in GTP is slightly different from
the distribution around PB in GDP. This slight difference in distribution of direction
possibly causes the difference in the density distribution of water molecules.
Acknowledgements This work was supported by JSPS KAKENHI Grant Number 24540442.
The computations were in part carried out at the Research Center for Computational Science,
Okazaki, Japan.
References
1. Alberts B, Johnson A, Lewis J, Raff M, Robertss K, Walter P (2002) Molecular biology of the
cell, 5th edn. Garland, New York