Cell Biology
Chapter 8
Free Energy

Life is Antentropic
o Life is thermodynamically improbable:
 Highly ordered and anti-entropic
o Life obtains energy from Sun, directly or indirectly from energy bound up
in carbohydrates, lipids, proteins, etc.
o Life creates order using:
 Information encoded in DNA
 Energy

Law of thermodynamics and ΔG
o 1st Law:
 Energy neither created nor destroyed.
 Energy is conserved
nd
o 2 Law:
 Every conversion increases entropy.
 This energy bleeds off as random molecular motion leaving less
energy available to do work.
o Calculations of energy available to cell to do work use these laws to
determine the change in free energy, ΔG
 ΔG = ΔH – TΔS
o –ΔG:
 Energy released, exergonic, less free energy in system after
reaction has taken place
o +ΔG
 Energy required to make reaction proceed, endergonic, more free
energy in system after reaction has occurred

Equilibrium Coefficient, K eq
o –ΔG means a reaction can go, but does not indicate if it will go. Reaction
needs a mechanism/pathway as well, and often activation energy. Examine
this later in kinetics
o Simple reaction:
 A B
o A and B, at equilibrium, each have a certain concentration expressed as
molarity. This relationship can be described by an equilibrium constant, K
eq.
 K eq = B eq / A eq

Free Energy Lowest at Equilibrium
o K eq = 0.5:

o
o
o
o
At equilibrium, concentration of fructose-6-phosphate is ½ of
glucose-6-phosphate
 K eq = F-6-P eq / G-6-P eq = 0.5
Ratio < 0.5, low fructose-6-phosphate, A  B
Ratio > 0.5, low glucose-6-phosphate, A  B
Free energy lowest at equilibrium, increases with imbalance in either
direction:
 Therefore ΔG a measure of how far reaction is from equilibrium
Tendency towards equilibrium is the driving force behind chemical
reactions in the cell

Calculations of ΔG
o With K eq and actual cellular concentrations of A, B it is possible to
determine whether A  B or A  B, how much free energy involved. ΔG
a measure of how far from equilibrium reaction is under specified
conditions

Multispecies Reactions
o For two reactants and two products, with stoichiometry integers a, b, c, d
 aA + bB  cC + dD
o This can be expanded to any number of reactants and products in any
reaction

Cellular Free Energy Calculations
o Most cells operate under similar conditions, for most organisms. Can use
these conditions for most calculations.
o Can also compare relative energies of different reactions at standard state
o These together allow calculation of free energy changes under cellular
conditions

“Standard State” ΔG°’
o Defined as 1 atmosphere pressure, 298 K, pH 7. When concentrations are
assumed to be 1 mole/liter, this provides standard free energy change,
ΔG°’
o Under standard conditions:
 Product / reactant = 1
o ln1 = 0, ΔG°’ = 0 – RT lnK’ eq = -RT lnK’ eq
o ΔG°’ can be calculated directly from K’ eq

Cellular Free Energy: ΔG’
o ΔG’
 Free energy at pH 7 under real-cell concentration conditions

Cellular Thermodynamics
o With stable known temperature, pressure, and pH, and knowing the
equilibrium constant for any given reaction at standard concentrations,
it is possible to calculate the energy change involved in the reaction at
standard concentrations
o ΔG°’ is useful for comparing various substrates to each other in terms
of the quantity of energy then can yield
o This value is used in calculating ΔG’, the free energy change under
cellular conditions

Spontaneous or Nonspontaneous?
o If ΔG’ is negative, reaction can occur as written for what is product and
what is reactant, and is thermodynamically favored or spontaneous
o If ΔG’ is positive, reaction will not go in direction written, and is
thermodynamically unfavored or nonspontaneous. It may be possible
to make it favorable by changing concentrations of products or reactants.
Adding energy to drive the reaction in a particular direction will also
cause it to proceed.

Equilibrium
o All reactions tend towards equilibrium
o Cells specialize in maintaining reactants in dynamic non-equilibrium but
steady-state conditions and using that drive towards equilibrium to power
cellular functions
o A cell at equilibrium is a dead cell
o Cellular processes always move toward equilibrium, but never reach it.
Cells maintain a steady-state, far away from equilibrium conditions.
Energy is used to maintain this non-equilibrium steady state.