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Bioenergética
Mirko Zimic
[email protected]
Qué es la Bioenergética?
• Es la disciplina que estudia los aspectos
energéticos en los sistemas vivos, tanto a
nivel molecular como a nivel celular.
– Interacciones moleculares
– ATP como biomolécula almacenadora de
energía
– Biocatálisis
– Reacciones acopladas
Conversión entre la Energía cinética y
la Energía potencial
Interacciones Fundamentales
•
•
•
•
Interacción Gravitacional (masa-masa)
Interacción Electromagnética (carga-dipolo)
Interacción Nuclear Débil (electrones-núcleo)
Interacción Nuclear Fuerte (protones-neutrones)
Los Sistemas Biológicos son guiados
fundamentalmente por Interacciones
Electromagnéticas
– Enlaces Covalentes
– Enlaces No-covalentes (Interacciones Débiles):
•
•
•
•
•
•
Puentes de Hidrógeno
Efecto Hidrofóbico
Interacciones Iónicas
Interacciones Ión-Dipolo
Interacciones Dipolo-Dipolo
Fuerzas de Van der Waals
Enlace Covalente
La Energía de Activación es el resultado
de la repulsión de las nubes electrónicas
Las interacciones Iónicas se dan
entre partículas cargadas
Participación de los Puentes de Hidrógeno:
Replicación, Transcripción y Traducción
Las interacciones débiles dirigen el
proceso de ‘docking’ molecular
El efecto hidrofóbico colabora en
el plegamiento de las proteínas
Temperatura
Es la medida de la energía cinética
interna de un sistema molecular
Ek = N K T /2
Calor
Es la energía cinética
que se propaga debido a
un gradiente de
temperatura, cuya
dirección es de mayor
temperatura a menor
temperatura
Entropía
S = K Ln(W)
La entropía es la medida del grado de
desorden de un sistema molecular
S1
>
S2
Entalpía
H=E+PV
La entalpía es la fracción de la energía
que se puede utilizar para realizar
trabajo en condiciones de presión y
volumen constante
dH<0 proceso exotérmico
dH>0 proceso endotérmico
Energía Libre
G=H-TS
La energía libre es la fracción de la energía
que se puede utilizar para realizar trabajo en
condiciones de presion, volumen y
temperatura constante
dG<0 proceso exergónico (espontáneo)
dG>0 proceso endergónico
Las Enzimas o biocatalizadores,
reducen la Energía de Activación
La molécula de ATP
Los seres vivos utilizan la
molécula de ATP como
medio principal para
almacenar energía
potencial proveniente de
la degradación de los
alimentos
La manera de utilizarse la energía en la
molécula de ATP es mediante la separación de
un grupo fosfato el cual está unido mediante
un enlace covalente de alta energía
La síntesis de
ATP ocurre
durante la
glicólisis y la
respiración
celular en la
mitocondria
usualmente
En las plantas, la síntesis
de ATP ocurre asistida por
luz durante la fotosíntesis,
la cual es luego empleada
en las denominadas
reacciones oscuras. Este es
un ejemplo de
transformación de energía
radiante en energía
química.
El ATP participa en una serie de
reacciones acopladas
Diversas moléculas
biológicas requieren la
capacidad de ‘moverse’
para cumplir sus
funciones… Por lo
tanto hace falta energía
para realizar esta
función.
La fuente de energía
para el movimiento
molecular es
fundamentalmente el
ATP
El ATP contribuye a diversos
tipos de reacciones
El ATP suele participar en el
correcto plegamiento de las
proteínas
Thermodynamics
First Law:
Energy conservation
Internal energy (E).- Total energy content of a system. It
can be changed by exchanging heat or work with the
system:
Heat-up the system
Cool-off the system
E
E
Do work on the system
Extract work from the system
E = q + w
w
-PV
w´
Thermodynamics
A more useful concept is: ENTHALPY (H)
H = E + PV
0
0
H  q p - PV  w   PV  VP
At constant
pressure…
E
Only P-V work involved… w´ = 0
(as in most biological systems)
So…
H  q p
At constant pressure, the enthalpy change in a process is
equal to amount of heat exchanged in the process by the
system.
Thermodynamics
We have…
H = E + PV
0
H = E + PV + VP
0
in biological
systems
P = 0
V  0
H  E
at P = 0 and since V  0
Q: How is this energy stored in the system?
A: 1) As kinetic energy of the molecules. In isothermal (T =
0) processes this kinetic energy does not change.
2) As energy stored in chemical bonds and interactions. This
“potential” energy could be released or increased in chemical
reactions
Thermodynamics
Second Law:
Entropy and Disorder
Energy conservation is not a criterion to decide if a process will
occur or not:
Examples…
THot TCold
T
q
E = H = 0
This rxn occurs in one
direction and not in the
opposite
T
these processes
occur because
the final state
( with T = T &
P = P) are the
most probable
states of these
systems
Let us study a simpler case…
tossing 4 coins
Thermodynamics
All permutations of tossing 4 coins…
Macroscopic states…
1 way to obtain 4 heads
4 ways to obtain 3 heads, 1 tail
6 ways to obtain 2 heads, 2 tails
4 ways to obtain 1 head, 3 tails
1 way to obtain 4 tails
6
4
The most probable
state is also the
most disordered
4
2 H, 2 T
1
4 H, 0 T
3 H, 1 T
1 H, 3 T
Microscopic states…
HTTH
HHTT
4!
HTHT
6
THHT
2! 2!
TTHH
THTH
1
0 H, 4 T
Thermodynamics
In this case we see that H = 0,
i.e.:
there is not exchange of heat between the system and its
surroundings, (the system is isolated ) yet, there is an
unequivocal answer as to which is the most
probable result of the experiment
The most probable state of the system is also the most
disordered, i.e. ability to predict the microscopic outcome
is the poorest.
Thermodynamics
A measure of how disordered is the final state is also a measure of
how probable it is:
6
P2H, 2T 
16
Entropy provides that measure
(Boltzmann)…
S  k B ln W
Molecular
Entropy
Boltzmann
Constant
Number of
microscopic
ways in which
a particular
outcome
(macroscopic
state) can be
attained
Criterion for Spontaneity:
For Avogadro number’s
of molecules…
S  (N Avogadrok B ) ln W
R (gas constant)
Therefore: the most probable
outcome maximizes entropy
of isolated systems
S > 0 (spontaneous)
S < 0 (non-spontaneous)
Thermodynamics
The macroscopic (thermodynamic) definition
of entropy:
dS = dqrev/T
i.e., for a system undergoing a change from an initial state
A to a final state B, the change in entropy is calculated
using the heat exchanged by the system between these
two states when the process is carried out reversibly.
Thermodynamics
S 
final

initial
S 
final
(Carried through a reversible path)

CP
dT (If process occurs at contant pres sure)
T
final
CV
dT (If process occurs at cons tant volume)
T
initial
S 
dqrev
T

initial
Spontaneity Criteria
In thes e equations, the equal s ign applies for revers ible
process es . The inequalities apply for irrevers ible, spontaneous, process es :
S(system)  S(surroundings)  0
S(isolated system)  0
Thermodynamics
Free-energy…
•Provides a way to determine spontaneity whether system is
isolated or not
•Combining enthalpic and entropic changes
G  H - TS
(Gibbs free energy)
What are the criteria for spontaneity?
Take the case of H = 0:
G  - TS
<0
>0
G > 0
G < 0
G = 0
non-spontaneous process
spontaneous process
process at equilibrium
Thermodynamics
Free energy and chemical equilibrium…
Consider this rxn:
A+B
C+D
Suppose we mix arbitrary concentrations of products and reactants…
•These are not equilibrium concentrations
•Reaction will proceed in search of equilibrium
•What is the G is associated with this search and finding?:
[C][D]
o
G  G  RT ln
i.e. G when A, B,
[A][B]
C, D are mixed in
o
G is the Standard Free Energy of reaction
their standard state:
G Rxn
1 1
 G  RT ln
1 1
Biochemistry: 1M,
25oC, pH = 7.0
o
G Rxn  G o
Thermodynamics
Now… Suppose we start with equilibrium concentrations:
Reaction will not proceed forward or backward…
G Rxn  0
Then…
G  - RT ln
o
[C]eq [D] eq
[A]eq [B] eq
[C]eq [D] eq
[A]eq [B] eq
Go  - RT ln Keq
K eq  e
Rearranging
0  G  RT ln
o
K eq  e

o
G
 RT
 Ho - TSo 


RT
H
 RT
 RS 



K eq   e
 e 



o
o
Thermodynamics
Graph:
o
Ho
 RT
 RS 




ln K eq   e  e 




H o So
ln K eq  
RT
R
So
R
Van’t Hoff Plot
H o
Slope = R
ln K eq
1
T
K 
o
-1
Thermodynamics
Summary: in chemical processes
Ho
So
1) Change in potential
energy stored in bonds
and interactions
2) Accounts for T-dependence
of Keq
1) Measure of disorder
3) Reflects: #, type, and
quality of bonds
3) Reflects order-disorder in
bonding, conformational
flexibility, solvation
4) So  Keq
Rxn is favored
4) If Ho < 0: T  Keq
If Ho > 0: T  Keq
S = R ln (# of microscopic ways of
macroscopic states can be attained)
2) T-independent contribution
to Keq
Thermodynamics
Examples:
Consider the Reaction…
A
Free energy change
when products and
reactants are present at
standard conditions
B
[A]initial = 1M
[B]initial = 10-5M
Keq = 1000
Go  - RT ln Keq
G o  - 1.98 molcalK 298 K  ln 1000
G o  - 4.076 Kcal
mol
How about GRxn…
Spontaneous rxn
[B]
G Rxn   G  RT ln
[A]
o

-3

G Rxn  - 4.076 Kcal

1.98

10
mol
G Rxn  -10.9 Kcal
mol
Kcal
mol K

10-5
298K  ln
1
Even more spontaneous
Thermodynamics
Another question…
What are [A]eq and [B]eq?
[A]  [B]  1  10-5  1M
[A]  1 - [B]
K eq 
[B] eq
[A]eq
 1000
[B]eq  1000 1 - [B]eq 
1001[B]eq  1000
1000
[B]eq 
 0.999M  1M
1001
[A]eq  0.001M
Thermodynamics
Another Example…
Acetic Acid Dissociation
Ho ~ 0
CH3 – COOH + H2O
CH3 – COO- + H3O+
Creation of charges  Requires ion solvation
 Organizes H2O around ions
At 1M concentration, this is entropically unfavorable.
Keq ~ 10-5
[CH 3  COO- ][H 3O  ]
K eq 
~ 10-5
[CH 3  COOH]
If [CH3 – COOH]total ~ 10-5  50% ionized
Percent ionization is concentration dependent. We can favor
the forward rxn (ionization) by diluting the mixture
If [CH3 – COOH]total ~ 10-8  90% ionized
Thermodynamics
CH3 – COOH + H2O
CH3 – COO- + H3O+
[CH  COO- ][H O  ]
3
3

2
[CH 3  COO ][H 3 O ]
[CH 3  COOH]T
K eq 
=
[CH 3  COOH]
[CH 3  COOH]T  [CH 3  COO ]
2
[CH  COOH]
3
T
2
 [CH 3  COOH]T
[CH 3  COO ]
K eq 
with  
1 
[CH 3  COOH]T
and  =
2
-K eq  K eq + 4[CH 3  COOH]T K eq
2[CH  COOH]
3
T
Thermodynamics

CH3 -COOH total
Thermodynamics
Third Example…
Amine Reactions
H
+
R – N – H + H2O  R – NH2 + H3O+
H
So  0
not favorable
H o  14 Kcal
mol
K eq  10-10
Backbone Conformational Flexibility
 R

H
C
N
N
C
H
H
O
For the process…
folded
unfolded
(native)
(denatured)
S
o
backbone conf.
Wunfolded
 R ln
Wfolded
How many ways to form the unfolded state?…
Backbone Conformational Flexibility

degrees of freedom = 2

Assume 2 possible values for each degree of freedom. Then…
Total of 4 conformati onal isomers residue
For 100 amino acids…
4100 ~ 1060 conformations
These results do not take into account excluded volume effects.
When these effects are considered the number of accessible
configurations for the chain is quite a bit smaller…
Wunfolded ~ 1016 conformations
Backbone Conformational Flexibility
Thermodynamic considerations…
Sobackbone conf.  R ln 1016
 1.987 16  2.303
 73 molcalK
o
G obackbone conf.  - TSo  - 22 Kcal
at
25
C
mol
In addition other degrees of freedom may be quite important,
for example…
R 
H
C
N
N
C
H
H
O
We will see this
later in more detail
Ionization of Water
•Water is the silent, most important component in the cell
•Its properties influence the behavior and properties of all other
components in the cell.
Here we concern ourselves with its ionization properties:
H2O + H2O
H3O+ + OH-
[H 3O  ][OH - ]
K eq 
[H 2 O]
Since in the cell, [H2O] ~ 55M, and ionization is very weak, then
[H2O] ~ constant, so se can define…
“the ionic
product of
K w  [H 3O  ][OH - ]
water”
Ionization of Water
From the previous equation…
K w  [H 3O  ][OH - ]
K w  10-14
For pure water…
[H  ]  [H 3O  ]  [OH - ]  10-7 M
i.e. in a neutral soln: [H 3O  ]  10-7 M
[OH- ]  10-7 M
The overall acidity of the medium greatly affects many biochemical
reactions, because most biological components can function either
as bases or acids.
A measure of acidity is given by the pH scale, defined as…
1

pH  log 10

log
[H
O
]
3

[H 3O ]
1
So, in fact for
pH  log 10 -7  7
10
pure water:
Weak Acids and Bases
All biological acids and bases belong to this category
Consider acetic acid…
AH
A- + H+
The Dissociation Constant…
Ka
rearrange…
[H ][A- ]

[AH]
[A - ] HendersonpH  pK a  log
Hasselbalch
[AH]
equation
where, pKa = - logKa
Weak Acids and Bases
Fraction of deprotonated acid is…
f A
[A  ]
 
[A ]  [AH]
So, we can re-write the
Henderson-Hasselbalch
equation
Also… f AH  1  f A 
pH  pK a  log
f A
1 - f A
1.0
fA
0.5
pKa
0
pH
i.e. pKa is the pH at
which the acid is
50% ionized
Weak Acids and Bases
Based on the previous page…
pH  pK a  1 ; f A 
If…
pH  pK a  1 ; f A 
10
  90%
11
 9%
pH  pK a  2 ; f A   0.9%, etc.
Morever… the lower the pKa, the stronger the acid
1.0
fA
stronger
acid
0.5
weaker
acid
0
pH
pH  pK a  log
f A
1 - f A
Weak Acids and Bases
Some useful relationships…
f AH

H
 
AH
 

A  AH
Ka  H 
fAH
Ka
f A
A
Ka
 

A  AH
K a  H 
fA-
Ka
Multiple Acid-Base Equilibria
Consider Alanine…
CH3
NH3+
CH
COOH
= 9.7
Please correct in your
notes
= 2.3
(fraction deprotonated)
mL of base added
Titrate a solution of ala, using a gas electrode (pH meter), and a
buret to add a strong base of known concentration:
pK1
pK2
pH
Macroscopic
experiment shows
2 inflection points
(2 pKs)
Multiple Acid-Base Equilibria
As we vary the pH of the solution from low to high:
H
CH3
N+
H
CH
H
H
COOH
CH3
N+
H
CH
H
COO –
H
Cation
Zwitterion
CH3
N
COO –
CH
H
Anion
So, in fact the two inflection points seen correspond to the
deprotonation of the carboxylic group (at low pH) and then
to the deprotonation of the amine group (at high pH).
So, How can we estimate the fraction of these different species in solution?
If we assume that the ionization of a given group is independent
of the state of ionization of the others, then…
Multiple Acid-Base Equilibria
f  HAH   fCOOH  fNH 3






H
H
 

 
Ka1  H Ka 2  H 
 K




a
H
1


f  HA   fCOO   fNH 3   
Ka 1  H  K a 2  H  

 K



a
H
2


f AH  fCOOH  fNH 2  


Ka 1  H K a 2  H 
 K
 K


a
a
1
2
 

f A  f COO  fNH 2  
Ka 1  H  Ka 2  H  
f  HAH  f  HA  f AH  f A   1