物化生物學生物體系之電子與能量轉移

Applications of Electrochemistry

ATP SynthasePotential for a resting nerve cell

Membrane Equilibrium

ii

ni,ionZ+

Phase α Phase β

ii

ni,ionZ+

Phase α Phase β

ii

ni,ionZ+

Phase α Phase β In a closed electrochemical system, the phase equilibrium condition for two phases and

CC

nFRTEEE

EquationNerst

ln

ATP Synthase

Free-energy change during proton movement across a concentration gradient

The movement of protons from the cytoplasm into the matrix of the mitochondrion.

pHRTGpHpHRTRTG

RTRTEnFG

nFRTEEE

outin

inout

303.2)(303.2])Hlog[]H(log[303.2

]H[]H[log303.2

]H[]H[ln

]H[]H[ln

HH

outin

out

in

out

in

out

in

inout

Proton Pumping Proton pumping maintains a pH gradient of 1.4 u

nits, then pH = + 1.4G = -2.303RTΔpH =- 2.303 (8.315 × 10-3 kJ/mol)(298K)(1.4) = - 7.99 kJ/mol Proton concentration gradient

Free-energy change during solute movement across a voltage gradient

In mitochondria, electron transport drives proton pumping from the matrix into the intermembrane space.

There is no compensating movement of other charged ions, so pumping creates both a concentration gradient and a voltage gradient.

This voltage component makes the proton gradient an even more powerful energy source.

Membrane Potential m = in – out=0.14 V G =-nF m=-(1)(96485)(0.14 ) = - 13.5 kJ/mol

Proton-motive force

Proton-motive force (P) is a that combines the concentration and voltage effects of a proton gradient.

G=-nFP = - 2.303 RT pH + nFm

=(-7.99 kJ/mol)+( - 13.5 kJ/mol)

= -21.5 kJ/mol

ATP synthesis Mitochondrial proton gradient as a source of

energy for ATP synthesis Estimated consumption of the proton gradient

by ATP synthesis is about 3 moles protons per mole ATP.

G = 50 kJ/mol for ATP synthesis G = 50 + 3(- 21.5) = - 3.4 kJ/mol The synthesis of ATP is spontaneous under

mitochondrial conditions.

Potential for a resting nerve cell Goldman-Hodgkin-Katz equation

membrane of thicness:τtcoefficiendiffusion :D

typermeabili:P

DP

])[ClP(Cl])[NaP(Na])[KP(K])[ClP(Cl])[NaP(Na])[KP(Kln

FRT

potential anetransmembr

extintint

intextext

extint

E

Resting Nerve Cell of a Squid P(K+)/P(Cl-)=2 P(K+)/P(Na+)=25△(K+)=-95 mV△(Na+)=+57 mV△(Cl-)=-67 mV

(mmol/dm3) K+ Na+ Cl-

int 410 49 40

ext 10 460 540

The observed potential for a resting squid nerve cell is about -70 mV at 25oC.

Resting Nerve Cell of a Squid The observed potential for a resting squid nerv

e cell is about -70 mV at 25oC. Hence Cl- is in electrochemical equilibrium, bu

t K+ and Na+ are not. Na+ continuously flows spontaneously into the

cell and K+ flows spontaneously out. Na+-K+ pump