TABLE 4.

Electrostatic interaction energy between Glu³⁹⁴/Asp³⁹⁹ and Lys⁶⁰⁵

The electrostatic interaction energy (E_{electrostatic}) was calculated according to: E_{electrostatic} = (q₁q₂)/(4πϵ_rϵ₀D), with the distances (D) between the ϵ-amino nitrogen of Lys⁶⁰⁵ and the carboxyl carbons of Glu³⁹⁴ and Asp³⁹⁹, which were estimated in the structures E1Ca₂·AlF₄⁻·ADP (PDB 1T5T as E1PCa₂ analog) and E2·BeF₃₋ (PDB 2ZBE, E2P ground state analog). Here, q₁ and q₂ are the charges of the residues, and ϵ₀ and ϵ_r are the vacuum permittivity and the relative permittivity. ΔE_{electrostatic} is the difference in the electrostatic energy between the E1PCa₂ and E2P states, and reflects the stabilization of the product state E2P relative to the initial state E1PCa₂. Because it is not possible to evaluate the exact ϵ_r value of the solution or more precisely, that of the protein surface of our interest in solution, and because the value changes region by region on the protein surface, we assumed two extreme cases: first, each of the interacting free amino acids is completely surrounded by water molecules and thereby ϵ_r = 87.74 for water at 0 °C; in the other case the two residues are interacting in protein where typically ϵ_r = 2 (28). The ϵ_r value on a protein surface in solution is generally expected to be between these two extreme cases. Namely, in a real situation, residues on a protein surface are exposed to and surrounded by water molecules but not completely. Therefore the charged residues on a protein surface are able to produce electric fields over a wide surface region and form long-range electrostatic interactions (Figs. 6, 7C, 11, and 12). Consistently, we found that mutations over a wide surface region of the N and P domains (i.e. Glu³⁹⁴/Asp³⁹⁹ and Lys⁶⁰⁵ and the residues at the N-P domain hinge region) disrupt the N-P domain electric field and the acceleration of the EP transition.

	E1PCa2 (E1Ca2·AlF4−·ADP)			E2P (E2·BeF3−)			ΔEelectrostatic
	D	Eelectrostatic		D	Eelectrostatic
		ϵr = 87.74	ϵr = 2		ϵr = 87.74	ϵr = 2	ϵr = 87.74	ϵr = 2
	Å	kJ/mol	kJ/mol	Å	kJ/mol	kJ/mol	kJ/mol	kJ/mol
Glu394-Lys605	28.3	−0.56	−24.5	11.8	−1.34	−58.9	−0.78	−34.4
Asp399-Lys605	30.0	−0.53	−23.1	15.9	−1.00	−43.7	−0.47	−20.6
Suma		−1.09	−47.6		−2.34	−102.6	−1.25	−55.0

^a The sum of the two interactions Glu³⁹⁴-Lys⁶⁰⁵ and Asp³⁹⁹-Lys⁶⁰⁵ (Glu³⁹⁴/Asp³⁹⁹-Lys⁶⁰⁵).