BCMB308: Bioenergetic
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Some important questions about life
Are living systems stable?
 What are the energetic costs of cellular
functions?
 How can cellular energy be stored and made
available when required?
 To what extent do cells equilibrate with
their surroundings?
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Bioenergetics- Biochemical Thermodynamics
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Quantitative study of the energy transductions that occur in living
cells, and of the nature and function of the chemical processes
underlying these transductions
Provides underlying principles to explain why:
 Some reactions may occur while others do not
 Non-biological systems may use heat energy to perform work,
whereas biological systems are essentially isothermic and use
chemical energy to power living processes
Basic question in bioenergetics is:
 How is biological energy coupling carried out at the molecular
level?
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Biomedical Importance
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Fuel is required to provide energy for normal processes, so
understanding energy production and utilization is
fundamental to understanding normal nutrition and
metabolism
Starvation - occurs when available energy reserves are
depleted
Certain forms of malnutrition are associated with energy
imbalance e.g. marasmus- wasting disease due to
insufficient energy and protein intake
Excess storage of surplus energy results in obesity which
can have negative effects on health
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Thermodynamics
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Central theme in bioenergetics is Thermodynamics
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Thermodynamics
Is originates from Greek meaning therme, heat +
dynamis, power.
 Is the branch of physical science that deals with
energy changes
 Describes the relationship among various forms
of energy
 Concerns with how energy affects matter on the
macroscopic as opposed to molecular level
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Open, closed and isolated systems
Open system: It exchanges both matter and
energy with its surroundings.
 Closed system: It exchanges only energy with its
surroundings but not matter.
 Isolated system (adiabatic): Neither matter nor
energy is exchanged between the system and its
surroundings.
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State and non-state functions
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State functions: Internal energy, enthalpy, entropy
and Gibbs free energy.
Non-state functions: Heat, work
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Laws of Thermodynamics
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The First Law:
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It is a mathematical statement of the law of conservation
of energy.
It states that the total energy of the universe is conserved.
i. e. energy is neither created nor destroyed in a process.
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Mathematical expression

For isolated systems, the change in internal energy
during any process must be zero.
DU = 0
DU = U final – U initial, DU = 0 and U final = U initial

For closed or open systems, energy can be
exchanged with surroundings.
DU (system) = -DU (surroundings)
DU (system) + DU (surroundings) = 0
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Energy

This is the total energy content of a system.
Symbol: U or E.

Originates from translational and vibrational
energies of the molecules in matter.
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Its value depends on the heat absorbed or evolved
by a system and work done on or by a system.
Mathematically, U = q + w
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
Work (denoted, w) is the energy associated with
the orderly movement of objects e. g. expansion
of a piston.

Heat (denoted q) is the energy associated with
disorderly movement of objects e. g. molecular
motion of liquids and gasses. It is the flow of
internal energy down a temperature gradient.
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
If work w was done on the system by the
surroundings and heat q absorbed by the system
from the surrounding. The internal energy would
increase by
DU = q + w
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Note that: work could either be done on or by a
system and heat could be absorbed or released
by a system.
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Property
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Process
Sign
q
Heat is transferred to the system.
+ve
q
Heat is given off by the system.
-ve
w
Work is done on the system by the
surrounding.
+ve
w
Work is done by the system on the
surrounding.
-ve
q = -ve, exothermic process
q = +ve, endothermic process
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Heat (q) and Work (w)
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They are both forms of energy
They are related forms of energy: one can be
converted to the other
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Steam engine
Heat generated in rubbing hands together
Specific heat: the heat required to raise one (1)
gram of a material by one (1) degree Celsius.
Specific heat, given by the symbol "C", is
generally defined as:
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Problem: If a 2.34 g substance at 22 degrees
Celsius with a specific heat of 3.88 cal/g°C is
heated with 124 cal of energy, what is the new
temperature of the substance?
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Work energy in chemical systems
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The work done by an object is exactly equal to:
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the loss in energy that the object experiences while
doing that work.
The energy that the object being acted on gains.
Work energy unlike the heat term, can assume many
different forms:
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The mechanical work performed by muscle
Electrical work required to move an ion through an
electric field gradient.
Work of expansion
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The most common source of work in chemical
reactions is changes in volume (V) during the reaction.

The work done against a pressure P is given by;
v2
w = ∫ PDV
v1
w = P(V2 – V1)
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If expansion is the only form of work energy exchange
between the system and the surroundings, as is always the
case for most chemical reactions in solution, then from the
first law;
DUp = qp - P (V2 – V1)
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Therefore,
DUp = qp- P (V2 – V1)
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For reactions in solution, DV is very small and so the work
associated with expansion is also very small. Therefore;
DUp = qp
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The Concept of Enthalpy, H
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Enthalpy is an interesting concept
It is defined by its change rather than a single entity.
It is a state property,
The word enthalpy originates from Greek “ethalpein”
"heat inside".
It is equal to the heat output of a body at constant
pressure
Recall, if heat, q is absorbed by a system and work, w
done on the system, then internal energy change is given
as; DU = q + w
But Dw = PDV
Therefore, DU = q + PDV
At constant volume, DV = 0, PDV = 0
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Implies, DU = qv at constant volume. Thus, the
heat change at constant volume gives the
internal energy change of the system.
However, if the heat is absorbed by the system
at constant pressure,
DU = Dqp + PDV
Dqp = DU - PDV
The heat change, Dqp is different from internal
energy change and is called enthalpy change,
DH.
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That is if expansion is the only form of work
energy exchange between the system and the
surroundings, then DH equals the heat absorbed at
constant pressure.
The heat change, qp is the enthalpy change, DH.
Implies;
DH = DU + PDV
DH = DU – (-PDV)
DH = Change in total energy – Energy available
for expansion
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However, most biochemical processes occur in
solution; in these cases volume changes are
negligible, and thus DH = DU.
Note that PDV = DnRT
Problem: The DU values for oxidation of glucose
(C6H12O6) and stearic acid (C18H36O2) are -2.9 x 103
kJmol-1 and -11.36 x 103 kJmol-1, respectively.
(a) Calculate DH for the processes;
(b) Which of the two substances is more useful as
energy store in the body?
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Calculations involving state functions
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Enthalpy
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DH = qp and qp can be determined by measuring
the change in temperature of the system caused by
the reaction (a technique called Calorimetry)
For some processes the Hess’s law of constant heat
summation is employed.
This is because enthalpy is an extensive state
function.
This law is often written as:
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DH° reaction = SDHof products - SDHof reactants
Note: DHf for elements is 0.
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Problem: Calculate the standard enthalpy of
formation (DHof) of glucose from graphite,
Hydrogen and Oxygen giving the following
enthalpy changes:
C(graphite) + O2(g) = CO2(g), DHo = -393.1 kJmol-1
H2(g) + 1/2O2(g) = H2O(l), DHo = -285.5 kJmol-1
C6H12O6(s) + 6O2(g) = 6CO2(g) + 6H2O(l)
DHo = -2821.5 kJmol-1
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Limitations of the first law
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The first law only deals with energy balance of a system
It is unable to predict the direction of a reaction
 Enthalpy change during a reaction does not give us any
information on whether the reaction is likely to occur or not
 Dissolution of NaNO3 in water
spontaneous
DH = +ve
 Dissolution of NaOH in water
spontaneous
DH = -ve
 Diffusion of Na+ ions down a concentration gradient
DH = 0
spontaneous
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Naturally
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Chemical reactions proceed in one direction,
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Heat only flows from high to low temperature but
never in the opposite direction, even though this
would not violate the First Law
Joule expansion
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Why the first law is unable to predict direction
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Available energy, work and change
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Changing a system from one state to another is an orderly
process
Work is the energy involved in orderly movement and the
driving force for change.
The work energy can come from within the system itself, in
which case the system is unstable and will change
spontaneously.
The work energy can come from the surroundings, for example
a stable system can be forced to change by input of energy.
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Because the first law deals with the sum of
heat and work and not work on its own, it is
unable to predict the direction of a reaction.
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Second Law
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Most natural processes show a universal trend toward
increased randomisation, or dissipation of energy.
Thus, in order to predict whether a reaction will occur we
need to consider something other than the total energy
change in the system.
It is the purpose of the Second Law of Thermodynamics
to express this tendency in a unifying, quantitative
manner.
Definition: The law states that the universe (i.e. all
systems) tends to the greatest degree of randomization or
disorderliness and that spontaneous changes are those
that can do work.
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Degree of disorderliness
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In order to calculate whether there is any available work
energy in a system, we have to introduce another
thermodynamic quantity, the entropy.
Entropy: Is the measure of disorder or freedom or
randomness of a system.
It is denoted S.
The more disorganized a system the higher the entropy
(S) or vice versa.
Therefore, according to the second law, for a chemical or
physical change to occur, the total entropy change must be
greater than zero (DStotal > 0).
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DStotal = DSsystem + DSsurrounding

That is:
 Spontaneous processes are characterized by
the conversion of order to disorder.
 Disordered states are much more probable
than ordered states
 The driving force for all processes is the
tendency to seek the position of maximum
entropy (S).
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Mathematical expression of Entropy
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Disorder is defined as the number of energetically
equivalent ways, W, of arranging the components
of a system.
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That is, S = kb lnW, where kb is the Boltzmann
constant.
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Alternative expression of the second law
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Input of heat energy increases disorder
Therefore, TS, is a measure of the amount of heat
energy, present in the system
Note that w = U – q, that is the difference
between the heat absorbed and internal energy
gives the amount of work energy in a system
For a system, at equilibrium, no work energy is
being used and so the change in heat energy in the
system equals the amount of heat energy, q,
added to the system
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That is;
TDS = q
During spontaneous change, work energy is being
released and converted to heat energy in the
system.
Therefore, TDS > q
Thus the entropy change of a process can be
experimentally determined from measurements of
heat.
The second law can then be expressed by the
equation TDS > q
The difference between TDS and q gives the
amount of work energy that has been released
during a change.
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Limitation of the second law
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The spontaneity of a process cannot be predicted
under defined conditions from knowledge of
the system’s entropy change alone.
H 2 + O2
H2O
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What then, is the thermodynamic criterion
for a spontaneous process under a defined
condition
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Gibbs Free Energy
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Recall, DS > q/T
The expression, DS = q/T stands for
reversible equilibrium processes. They
are however not common in nature.
DS > q/T stands for spontaneous
irreversible processes.
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Therefore, for spontaneous irreversible processes,
DS > q/T………………………(1)
Multiplying through by T;
TDS > q…………..(2)
At constant temperature and pressure, q = qp = DH,
Implies;
TDS > DH………………(3)
Rearranging, DH – TDS < 0, -ve………………..(4)
Conversely, for non-spontaneous irreversible processes;
DH – TDS > 0, +ve
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The expression DH – TDS is a measure of the extent to
which the reaction can proceed and it represents another
state function called the Gibbs free energy.
Therefore, DG = DH – TDS………………(5)
Thus, DG < 0 or = -ve, for spontaneous processes.

Josiah Gibbs articulated the concept of free energy
(Sometimes called Gibbs free energy or Gibbs free
function).
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Rearranging equation (5) gives, DH = DG + TDS
Thus, DH = total energy change.
 DG = change in available energy of a system.
 DS = change in unavailable energy.
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That is; available energy = total energy – unavailable
energy.
A simple analogy is:
Total cash = Free cash + Assets
 Or Free cash = Total cash – Assets
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Note
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There are two kinds of useful energy.
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Free energy is the kind of energy that can do work
at constant temperature and pressure.
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Heat energy can do work only through a change
in temperature. Since temperature is constant in
living systems, the only useful energy in living
system is free energy.
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Spontaneous process
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A spontaneous process is a chemical reaction in
which a system releases free energy (most often as
heat) and moves to a lower, more thermodynamically
stable, energy state.
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The sign convention of changes in free energy
follows the general convention for thermodynamic
measurements, in which a release of free energy from
the system corresponds to a negative change in free
energy, but a positive change for the surroundings.
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Summary
DH
DS
DG
-ve
+ve
-ve
+ve
+ve
-ve at high temperature
-ve
-ve
-ve at low temperature
+ve
-ve
+ve for forward process but –ve
for reverse process
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Summary
Type of system
Exchange with surroundings
Criterion for equilibrium
Criterion for spontaneous
change
Isolated system
None
DS = 0
DS > 0
Closed system
Energy
DG = 0
DG < 0
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Standard States in Biochemistry
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Standard states are the reference points from
which energy changes are measured and are
defined as follows:
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Solid
Liquid
Solutes
Gas
pure solid
pure liquid
concentration of 1 M
pure gas at a pressure of 1 atm
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Standard states can be defined at any temperature,
although if a temperature is not specified it is
usually assumed to be 25 oC or 298 K.
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Many biological processes involve hydrogen ions.
By definition, the standard state of H+ solution is 1
M, which will give a pH of 0.
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This is however incompatible with most forms of life.
Therefore a new standard state must be defined for
biological system.
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Biochemical standard state is when all solutes are at 1 M
concentration except H+ which is present at 10-7 M, which
will give a pH of 7 as in most living systems.
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The standard state thermodynamic parameters in
biochemistry are denoted DGo, DHo and DSo to distinguish
them from chemistry standard state functions.
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Problems
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Why is that the free energy change (DG/) of most
biochemical reactions in an intact cell is frequently
different from the standard free energy change (DGo/) of
the same reaction?
Which of the following is true about the change in
enthalpy (DH) of a reaction that is spontaneous at room
temperature.
1.
It is equal to TDS
2.
It is positive and the reaction is exothermic
3.
It is negative and the reaction is endothermic
4.
It must be equal to zero
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5.
It can be either positive or negative.
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Pyruvate kinase transfers a phosphate group from
phosphoenolpyruvate to ADP forming ATP. The
reaction catalysed by this enzyme is essentially
irreversible. Which of the following is the best
explanation for the irreversible nature of the reaction?
A.
B.
C.
D.
E.
The binding of pyruvate to the active site is very weak
relative to the binding of phosphoenolpyruvate.
The reaction is coupled to pyruvate dehydrogenase
reaction.
The hydrolysis of ATP is highly favourable.
The change in free energy for the overall reaction is large
and negative.
There is a different enzyme in the cell which catalyses
phosphoenolpyruvate.
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