Lecture 24

Thermodynamics in Biology

A Simple Thought Experiment

1 E. coli cell (10-11 mL)

1 mL H2O

5 mg glucose

1 mg (NH4)SO4

Mg++, PO4=, Fe3+, etc...

48 hours

109 cells

1 mL H2O

0 mg glucose

<1 mg (NH4)SO4

CO2

Glucose + (NH4)SO4 Cells + CO2

Driving Forces for Natural Processes

• Enthalpy– Tendency toward lowest energy state

• Form stablest bonds

• Entropy– Tendency to maximize randomness

Enthalpy and Bond Strength• Enthalpy = ∆H = heat change at constant pressure

• Units– cal/mole or joule/mole

• 1 cal = 4.18 joule

• Sign– ∆H is negative for a reaction that liberates heat

Entropy and Randomness

153 freeamino acids

Decreasedrandomness

Myoglobin

Entropy and Randomness

• Entropy = S = measure of randomness– cal/deg·mole

• T∆S = change of randomness

• For increased randomness, sign is “+”

“System” Definition

System

Surroundings

Closed system:No exchange ofmass or energy

“System” Definition

Isolated system:Energy is exchanged

E

E

“System” Definition

E

EM

M

Open System:Mass and energyare exchanged

Cells and Organisms: Open Systems

• Material exchange with surroundings– Fuels and nutrients in (glucose)– By-products out (CO2)

• Energy exchange– Heat release (fermentation)– Light release (fireflies)– Light absorption (plants)

1st Law of Thermodynamics

• Energy is conserved, but transduction is allowed

• TransductionOne form

of EAnother form

of E

Light Plants Chemicalbonds

Mayer: 1842

2nd Law of Thermodynamics

• In all spontaneous processes, total entropy of the universe increases

2nd Law of Thermodynamics

• ∆Ssystem + ∆Ssurroundings = ∆Suniverse > 0

• A cell (system) can decrease in entropy only if a greater increase in entropy occurs in surroundings

• C6H12O6 + 6O2 6CO2 + 6H2O complex simple

Entropy: A More Rigorous Definition

• From statistical mechanics:– S = k lnW

• k = Boltzmann constant = 1.3810–23 J/K

• W = number of ways to arrange the system

• S = 0 at absolute zero (-273ºC)

Gibbs Free Energy• Unifies 1st and 2nd laws• ∆G

– Gibbs free energy– Useful work available in a process

• ∆G = ∆H – T∆S– ∆H from 1st law

• Kind and number of bonds

– T∆S from 2nd law• Order of the system

∆G• Driving force on a reaction• Work available distance from equilibrium• ∆G = ∆H – T∆S

– State functions• Particular reaction• T• P• Concentration (activity) of reactants and products

Equilibrium• ∆G = ∆H – T∆S = 0

• So ∆H = T∆S– ∆H is measurement of enthalpy– T∆S is measurement of entropy

• Enthalpy and entropy are exactly balanced at equilibrium

Effects of ∆H and ∆S on ∆G

Voet, Voet, and Pratt. Fundamentals of Biochemistry. 1999.

Standard State and ∆Gº

• Arbitrary definition, like sea level

• [Reactants] and [Products]– 1 M or 1 atmos (activity)

• T = 25ºC = 298K

• P = 1 atmosphere

• Standard free energy change = ∆Gº

Biochemical Conventions: ∆Gº

• Most reactions at pH 7 in H2O

• Simplify ∆Gº and Keq by defining [H+] = 10–7 M

• [H2O] = unity

• Biochemists use ∆Gº and Keq

Relationship of ∆G to ∆Gº

• ∆G is real and ∆Gº is standard• For A in solution

– GA = GA + RT ln[A]

• For reaction aA + bB cC + dD

– ∆G = ∆Gº + RT ln

– Constant Variable (from table)

º

[C]c [D]d

[A]a [B]b

}

Relationship Between ∆Gº and Keq

• ∆G = ∆Gº + RT ln

• At equilibrium, ∆G = 0, so

– ∆Gº = –RT ln

– ∆Gº = –RT ln Keq

[C]c [D]d

[A]a [B]b

[C]c [D]d

[A]a [B]b

Relationship Between Keq and ∆Gº

Keq ∆Gº (k /J mol)10-6 34.310-5 28.510-4 21.410-3 17.210-2 11.310-1 5.91 0.0101 -5.9102 -11.3103 -17.2

Will Reaction Occur Spontaneously?

• When:– ∆G is negative, forward reaction tends to occur– ∆G is positive, back reaction tends to occur– ∆G is zero, system is at equilibrium

∆G = ∆Gº + RT ln [C]c [D]d

[A]a [B]b

A + B C + D

A Caution About ∆Gº

• Even when a reaction has a large, negative ∆Gº, it may not occur at a measurable rate

• Thermodynamics– Where is the equilibrium point?

• Kinetics– How fast is equilibrium approached?

• Enzymes change rate of reactions, but do not change Keq

∆Gº is Additive (State Function)

Reaction

A B

B C

Sum: A C

Also: B A

Free energy change

∆G1º

∆G2º

∆G1º + ∆G2º

– ∆G1º

Coupling Reactions

Glucose + HPO42– Glucose-6-P

ATP ADP + HPO42–

ATP + Glucose ADP + Glucose-6-P

∆Gºkcal/mol kJ/mol +3.3

+13.8 –7.3 –

30.5 –4.0 –

16.7

Resonance Forms of Pi

–

–

–

–

P

O

OHO

O

P

O

OHO

O

P

O

OHO

O

P

O

OHO

O

So: resonance stabilization

etc...

P

O

OO

O

Phosphate Esters and Anhydrides

ROH + HO P

O

O

O

R O P

O

O

OH2O

H2OEsters:

R CO

OH

+ P

O

HO O

OH2O

H2O

R C

O

O P

O

O

O

Anhydrides:

= Hydrolysis

Hydrolysis of Glucose-6-Phosphate

∆Gº = –3.3 kcal/mol= –13.8 kJ/mol

O

CH2OP

O

O

HO

+ H2O O

CH2HO+ OHP

O

O

HOO

CH2OP

O

O

HO

+ H2O O

CH2HO+ OHP

O

O

HO

Ionization,resonance

Productstabilization