46 12 3 1

ATP ( ) ATP ~P 1~P hyd Gº 1 1 1950 ~P hyd Gº Hansia et al. Biophys Chem 119: 127, 2006 ~P hyd Gº 1? ATP hyd Gº ATP ATP ATP ~P ε ~P George [BBA 223: 1, 1970] ~P 2) hyd Gº 1. ph Mg 2+ 2. 1 2 2 1

2 3 AB A desol B rxn B sol rxn G rxn G sol G sol G AB 3) ATP 3 ATPADPPi ATP ATP ATP Pi ADP ATPPiADP - + ATP/ADP+Pi + ATP 3. ε = 80 rxn Gε = 80 rxn G Fig. 3 sol GA sol GB 3

ATP PCM(polarizable continuum model) (Hoshi et al., J. Chem. Phys., 87, 1107 (1987)) ATP G total 1 E gas 2 E thermo 3 E elec 4 E non-elec E thermo E elec 80 E gas G non-elec ATP kcal/mol MNDO E elec E gas G total -5-8 kcal/mol ATP E gas 4

5

(Mehta et al., Nature, 1999) 6

ATP, ADP, Pi 7

ATP 3- + H 2 O ADP 2- + H + 8

Hofmeister S. R. Kabir, K. Yokoyama, K. Mihashi, T. Kodama, and M. Suzuki, (2003) MD SPC/E KI ( PDB1b7t) H18-19 9

T. Takahashi, M. Yamashita and M. Suzuki, (2008) Takahashi, Y. Miya, Yu. Takagi, and Kenri. Konno, (2006). MD MD ATP 10

11 ATP ATP G [1] [2] (A)

(B) [3] ATP F G = H TS P = (E P +PV p ) TS P ( ) F = E V TS V GF H=E V 12

E P E V E P /(k B T)= E V /(k B T) + ( * / * 3 T )V p /d s PV H=E V S P =S V [4] T = * T d 3 s /(k B T) = * /T V p ( * / * T ) 298K 0.84 V p ATP [5] ADP ATP G= 30H = 20 TS P = 10 [kj/mol] d 3 s =15cm 3 /mol V p = 142 cm 3 /mol F= 30E V = 0 TS V = 30 [kj/mol] [6] F * T * [1] 46(4) 214(2006). Ref. [2] D. Chandler et al., Science 220 787(1983) WCA [3] PdV S. Asakura and F. Oosawa, J. Chem. Phys. 22 1255(1954) [4] M. Kinoshita et al., J. Chem. Phys. 125 244504(2006). [5] T. Kodama, Physiological Reviews, 65 467(1985) [6] M. Yamanaka et al., Coll. and Surf. B 22 23(2001) 13

14

1) Theory of solutions in the energetic representation. I. Formulation, N. Matubayasi and M. Nakahara, J. Chem. Phys. 113, 6070 (2000). 2) Theory of solutions in the energy representation. II. Functional for the chemical potential, N. Matubayasi and M. Nakahara, J. Chem. Phys. 117, 3605 (2002); 118, 2446 (2003). 3) Free-energy analysis of the molecular binding into lipid membrane with the method of energy representation, N. Matubayasi, W. Shinoda, and M. Nakahara, J. Chem. Phys. 128, 195107 (2008). 15

1-3) 4) 4) 5) Z 4 V, A, X, Y Z=C 1 V+C 2 A+C 3 X+C 4 Y. V= A= X Y 4 C 1, C 2, C 3, C 4 (Z, V, A, X, Y) Z 4 3 1,5) ±2% 1 1 6) 7) 8) 3 16

9) 1) ATP ADP ADP 1) M. Kinoshita, J. Chem. Phys. 116, 3493-3501 (2002). 2) 89, 317-371 (2007). 3) M. Kinoshita, Roles of translational motion of water molecules in sustaining life, Encyclopedia of Bioscience, Frontiers in Bioscience, Special issue entitled Theoretical studies on roles of water in biological systems, edited by M. Kinoshita. 4) M. Kinoshita, J. Chem. Phys. 128, 024507 (1-14) (2008). 5) R. Roth, Y. Harano, and M. Kinoshita, Phys. Rev. Lett. 97, 078101(1-4) (2006). 6) T. Yoshidome, M. Kinoshita, S. Hirota, N. Baden, and M. Terazima, J. Chem. Phys. 128, 225104(1-9) (2008). 7) Y. Harano, T. Yoshidome, and M. Kinoshita, J. Chem. Phys., 129, 145103(1-9) (2008). 8) Y. Harano, R. Roth, Y. Sugita, M. Ikeguchi, and M. Kinoshita, Chem. Phys. Lett. 437, 112-116 (2007). 9) 10, 18-26 (2008). 17

200K 180K 300K 300K 180K Vitkup et al. Nat. Str. Biol. 7: 34, 2000 Shibata & Kandori, Biochem. 44: 7406, 2005 Photoactive Yellow Protein b 18

pca(chromophore) Kamiya et al. J. Phys. Chem. B111: 2948, 2007 Itoh & Sasai, PNAS 101: 14736, 2004 PYP ATP / 19