Module 101: Molecular Biology and Biochemistry of the Cell Lecture 6

The Principles of Free Energy Dale Sanders 27 January 2010

Aims of the lecture By the end of this lecture you should understand… • How Gibbs Free Energy can be used to determine the direction of a reaction • The meaning and significance of the “mass action ratio” • The meaning of the term “equilibrium constant” • How Redox Potentials are used to determine the direction of redox reactions • How Gibbs Free Energy is related to Redox Potential

Reading Any of the big Biochemistry textbooks More detailed discussion in Nicholls, DG & Ferguson, SJ (2002) Bioenergetics 3, Chapter 3, Academic Press

Why study energetics in Biology? Growth & maintenance of order (homeostasis) depend on energy as well as more obvious functions:– Generation of heat; – Movement; – Transmission of information. • Energetics underpins the existence of life

What energetics (thermodynamics) tells us:“the limits of the possible”. What thermodynamics cannot tell us:1. Whether a given reaction actually occurs. 2. How a reaction occurs (mechanism). 3. Rate at which a reaction occurs.

Predicting the Spontaneity of Reactions: Gibbs Free Energy The 2nd Law of Thermodynamics (Clausius, 1850): For all changes in a system, the total entropy of the system and its surroundings will increase. SSys + SSurr > 0 This is the criterion for reaction spontaneity

(1)

J W Gibbs (late 19th Century) combined 1st and 2nd Laws to express spontaneity of reactions in terms of measurable system parameters. G = H – TS

(2)

H: change in enthalpy (heat content) T: absolute temp. G: change in (Gibbs) Free Energy. Units: J/mol : a measure of the useful work system can perform : must be – ve for spontaneous reaction If G is –ve; reaction exergonic; i.e. thermodynamically downhill. If G is +ve, reaction endergonic; proceeds in reverse direction. If G is 0: equilibrium; no change

Properties of G: 1. Every reaction has a specific standard free energy (Go)

e.g. the reaction catalysed by hexokinase: Glucose + ATP

Glu-6-P + ADP Go = - 16.7 kJ/mol

(3)

2. Values of Go are additive What the cell “wants” to do: Glu +Pi

Glu-6-P + H2O

Go = + 13.8 kJ/mol (4)

 but if Pi from ATP: ATP + H2O

ADP + Pi

Go = - 30.5 kJ/mol (5)

Adding the reactions and the Gos Glu + ATP

Glu-6-P + ADP

Go = - 16.7 kJ/mol

(6)

3. ΔGo is a function of state ΔGo associated with conversion of specific substrate to specific product is independent of pathway: e.g.: A B C D Path A Path B Thus ΔGoAB + ΔGoBC + ΔGoCD = ΔGoAD Note that reaction A D can occur spontaneously even if ΔGoAB is positive, so long as ΔGoAB + ΔGoBC + ΔGoCD < 0

Standard free energy (Go) (J/mol)

Reaction will proceed spontaneously from A to D, even though ΔGoAB is positive

A

B C Compound

D

Hydraulic Analogue: The Siphon

Effect of Concentration on Free Energy Change ΔGo values are derived for standard conditions. Reactants and products all present at 1 M Modification of standard Gibbs Free Energy change to non-standard concentration for the reaction aA + bB pP + qQ (6) results in ** ΔG = ΔGo + RT ln { [P]p [Q]q } (7) { [A]a [B]b } mass action ratio [R is the gas constant = 8.31 J.mol –1 K-1 ]

Other non-standard conditions ΔGo is also derived at pH 0, 25oC. For other conditions (eg pH 7, 37oC) symbolize with prime (‘):

ΔG’ , ΔGo’

Reactant and Product Concentrations at Equilibrium The equilibrium constant (Keq) At equilibrium, G’ = 0, so Eq. 7 can be rewritten ΔGo’ = - RT In [P]p [Q]q (8) [A]a [B]b where the [ ] terms are specified for the equilibrium conditions. For this special condition, the mass action ratio is known as the equilibrium constant (Keq), so ΔG°’ = -RT In Keq (9)

Oxido-reduction (Redox) Potentials e.g. NAD+ + H+ + 2eNADH Oxidant/reductant together = redox couple What is capacity of redox couple to donate/accept e-? Measure Electromotive force (emf): Volts V KCI bridge

Pt electrode

A

eRed1

Ox1

pH = O

“Half cell”

Pt electrode

B Ox2

Red2

Measurement of Standard Redox Potential (EO) Half Cell A: Standard hydrogen electrode: Pt electrode, pH = O, H2 bubbled 2H+ + 2eH2 Half Cell B: Any redox couple: oxidant and reductant concs =1 Molar. Strongly REDUCING couples donate e-: Eo very – ve Strongly OXIDIZING couples accept e-: Eo very + ve.

As with ΔGº, Eo values can be added and subtracted to yield ΔEo for reaction sequence ΔEo = Eo (oxidizing couple) - Eo (reducing couple) eg Reaction: a + bn+ an+ + b Comprises 2 redox couples: Std. Redox potential Oxidizing bn+ + neb (Eo)b Reducing an+ + nea (Eo)a Subtracting generates original reaction, with ΔEo = (Eo)b – (Eo) a

Relationship of ΔGo to ΔEo Recall (Slide 7): ΔGo defines capacity for useful work (w) w = - ΔGo (11) Electrical work done by redox couple: w = force (Volts) x charge (Coulombs)

(12)

Charge carried by 1 “mol” e- in 1 s is the Faraday Constant (F) F = 96 500 Coulombs/mol Thus, for reaction in which n electrons participate w = Eo x nF

(13)

Combining Equations 11 and 13 yields

-ΔG° = nFEo

(14)

Thus there are 2 ways to describe Free Energy Change in a Redox System: 1. Difference in Redox potential, ΔE (units, V) 2. Difference in Gibbs free energy, ΔG (units, J/mol) Whichever we choose is simply a matter of convenience

Modification of Eo for Non-Standard Conditions A.

Concentration: G0 = - nFEo (14) G = - nFE : non standard states (15) Recall: G = Go + RT ln [products] (7) [reactants] Substituting Eqs 14 and 15 into Eq 7, for generalised reaction (oxidized states)n+ +ne- (reduced states) we can write nFE = nFEo - RT ln [reduced states] (16) [oxidized states]

Dividing Eq 16 by nF yields

or

E = Eo – RT ln _[red]_ nF [ox] E = Eo + RT ln _[ox]_ nF [red]

b. other conditions (e.g. pH  0): signify with ‘ : E’ = E’o + RT ln [ox] nF [red] “mid point potential”

(17)

(18)

Summary • Gibbs Free Energy can be used to determine the direction of a reaction • The “mass action ratio” modifies Gibbs free energies to take account of concentration • The Equilibrium Constant defines the ratio of product and reactant concentrations for a reaction at equilibrium • Redox potentials are used to determine the direction of redox reactions • Redox potentials can be related to Gibbs free energies by using the Faraday constant to interconvert Volts to J/mol