# Environmental Cycles of Metabolism

Mechanics

Oct 27, 2013 (4 years and 6 months ago)

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Environmental Cycles of
Metabolism

Carbon is fixed (incorporated) by
autotrophs (CO
2
) and heterotrophs
(complex such as carbohydrates)

Nitrogen (N
2
) is solely introduced into
biological systems through microbes

Also phosphate cycle, sulfur cycle, etc.

Modes of metabolism

Catabolism

nutrient breakdown

Anabolism

macromolecule synthesis

Both are linked via carriers of chemical
2

These sources of chemical energy allow
cells to perform “work” (synthesis, etc…)

Consider the cell a “system”

Isolated system

cannot exchange energy
or matter with its surroundings (not a cell)

Closed system

can exchange energy, but
not matter with its surroundings (still not a
cell)

Open system

can exchange energy and
matter in and out (A Cell!)

Internal energy is a state function

The thermodynamic state is defined by
prescribing the amounts of all substances
present, and two of these variables:
temperature (T), Pressure (P), and Volume
(V) of the system.

The internal energy (E) of the system
reflects all of the kinetic energy of motion,
vibration, and rotation and all of the energy
contained within chemical bonds and non
-
covalent interactions

How do cells make and use
chemical energy?

Bioenergetics must follow the laws of
thermodynamics

First Law: the total amount of energy in the
universe remains constant; energy may
change form or location, but cannot be
created or destroyed.

Second Law: Entropy is always increasing

First Law of Thermodynamics

D
E = q

w

q = heat; positive q indicates heat is absorbed
by the system, negative q indicates heat
given off by system

w = work; positive w means the system is
doing work, negative w means work is
being done on the system

Oxidation of palmitic acid

A “bomb” calorimeter allows reactions
to be carried out at constant volume

Because the reaction in (a) is carried out at
constant V, no work is done on the
surroundings

Therefore,
D
E = q

In this case,
D
E =
-
9941.4 kJ/mole

releases energy stored in chemical bonds
and transfers heat to the surroundings

Reactions at constant pressure

In reaction (b), the reaction proceeds at 1
atm pressure

The system is free to expand or contract, the
final state has contracted because the
amount of gas has changed from 23 moles
to 16

The decrease in volume means that work
has been done on the system by the
surroundings

PV work appears as extra heat
released

When volume is changed against a constant
pressure, w = P
D
V

Assumptions: constant T, gases are ideal,
which allows us to use PV = nRT

w =
D
nRT =
-
17.3 kJ/mol

SO
, under constant pressure q =
D
E + w =
D
E +
D
nRT =
-
9941.4 kJ/mol

17.3 kJ/mol

=
-
9958.7 kJ/mol

In (b) the surroundings
can do work on the system, this (PV) work
looks like extra heat

Most biochemical reactions occur under
constant pressure, not constant volume

Because q does not equal
D
E, we need to
account for PV work done

We define a new quantity, enthalpy (H)

H = E + PV

D
H =
D
E + P
D
V

When the heat of a reaction is measured at
constant pressure,
D
H is determined

D
E and
D
H measurements are
useful for biochemists

Although oxidation of palmitic acid occurs
very differently in the human body than in a
calorimeter, the values of
D
E and
D
H are
the same regardless of the pathway

Average human expends ~6000 kJ or
roughly 1500 kcal for bodily function, with
exercise that figure easily doubles

D
E,
D
H, is there a big
distinction?

For most chemical reactions the difference
between these two quantities is negligible

Typically, P
D
V is a tiny quantity

For instance, it’s about 0.2% difference for
palmitic acid oxidation

D
H is generally considered a direct measure
of the energy change in a process and is the
heat evolved in a reaction at constant P

Entropy and the second law

The minimal value

of entropy is a

perfect crystal at

absolute zero

Diffusion is an entropy driven
process

Increase in entropy can lead to
-
D
G

Thermodynamic quantities

D
H = enthalpy, the heat content of the system

exothermic = negative, endothermic =

positive; Units: Joules/mole

D
S = entropy, randomization of energy and

matter;

entropy;
Units: joules/mole(K)

D
G = Gibbs Free energy, amount of energy that is
available to do work at constant T and P; Units:
Joules/mole

Note 1 calorie = 4.184 Joule

Gibbs
-
Helmholtz equation

D
G =
D
H

T
D
S

Positive
D
G is endergonic, requires energy for
reaction to occur, this is unfavorable

Negative
D
G is exergonic, releases energy,
this is a favorable process; spontaneous but
not necessarily rapid

A decrease in energy (
-
D
H) and/or increase in
entropy (+
D
S) make favorable processes

D
G =0 indicates the system is at equilibrium

Thermodynamics of melting ice

Ice is a crystal lattice held together by H
-
bonds, bonds must be broken to form water

Energy for breakage of H
-
bonds is almost
entirely the
D
H for this reaction and this
term is positive

Entropy favors water over ice

But recall
D
G is also temperature dependent

Entropy and Enthalpy
contributions to melting ice

Biochemical reactions can have
different contributions

Why is
D
G called “free” energy?

D
G represents the portion of an energy change
D
H that is available or free to do useful
work.

T
D
S is amount of energy that is unavailable to
do work

D
G =
D
H

T
D
S

A
D
G Warning!

You will see many different
D
G’s

D
G

Gibbs Free Energy

D
G’
o
or
D
G
o

Standard State Free Energy

energy per mole in standard state (1M)

D
G
o

Standard state Free Energy of Activation

enzyme catalysis