la termodinámica y la vida prof. mirko zimic [email protected]
TRANSCRIPT
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La Biología está basada en la materia ´suave´ viviente
Auto-ensamblaje
Alta especificidadInformación
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“Los objetos vivientes están compuestos por moléculas inertes”
Albert Lehninger
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El problema es:
Cómo estas moléculas confieren la admirable combinación de características que denominamos vida???
Cómo es que un organismo vivo aparece ser más que la suma de sus partes inanimadas???
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La Física procura entender y reducir la Biología en leyes fundamentales
Pero este es un problema muy complicado !
Son demasiadas las variables y resulta imposible describir un sistema de un
número tan grande de partículas
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SOLUCIÓN:Descripción estadística del mundo ´aleatorio´
La ACTIVIDAD COLECTIVA de ‘muchos’ objetos de Movimiento aleatorio puede ser predicho, aun cuando el movimiento exacto de un sólo objeto es desconocido
Si todo en el nano-mundo de las células es aleatorio, cómo podemos realizar predicciones?
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TERMODINÁMICA
• Permite predecir la ACTIVIDAD COLECTIVA de ‘muchos’ objetos de movimiento aleatorio, aun cuando el movimiento exacto de un sólo objeto es desconocido
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Todo en el Universo esta compuesto por Materia y Energía
• Materia: - Medida de la ‘inercia’
• Energía: - Energía cinética (movimiento)
- Energía potencial (reposo)
E = M C2
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Trabajo
• Trabajo = Fuerza Distancia
• W = F x
• La unidad del trabajo es el Newton-metro conocido también como Joule.
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Trabajo mecánico
F
Fx
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Kinetic Energy
• Kinetic Energy is the energy of motion.
• Kinetic Energy = ½ mass speed2
2mv2
1KE
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Potential Energy
• The energy that is stored is called potential energy.
• Examples: – Rubber bands– Springs– Bows– Batteries– Gravitational Potential PE=mgh
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Conversión entre la Energía cinética y la Energía potencial
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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
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Interacciones Fundamentales
• Interacción Gravitacional (masa-masa)
• Interacción Electromagnética (carga-dipolo)
• Interacción Nuclear Débil (electrones-núcleo)
• Interacción Nuclear Fuerte (protones-neutrones)
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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
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Enlace Covalente
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Las interacciones Iónicas se dan entre partículas cargadas
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PUENTE DE HIDRÓGENO
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Participación de los Puentes de Hidrógeno:Replicación, Transcripción y Traducción
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Las interacciones débiles dirigen el proceso de ‘docking’ molecular
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El efecto hidrofóbico colabora en el plegamiento de las proteínas
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Revisión de algunos conceptos Termodinámicos
• Sistemas termodinámicos
• Equilibrio termodinámico
• Temperatura
• Calor
• Entalpía
• Energía Libre
• Entropía
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Clasificación de los sistemas termodinámicos
• Sistemas Abiertos– Intercambian materia y energía con el exterior
• Sistemas Cerrados– Sólo intercambian energía con el exterior
• Sistemas Aislados– No tienen ningun tipo de intercambio con el
exterior
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Equilibrio Termodinámico
Un sistema se encuentra en equilibrio termodinámico cuando la distribución espacial y temporal de la materia y la
energía es uniforme
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En el equilibrio termodinámico se reducen las gradientes y con ello se
reduce la energía potencial
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Qué esta más frío?
El metal o la madera?
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Temperatura
Es la medida de la energía cinética interna de un sistema molecular
Ek = N K T /2
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Cool Hot
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Qué es el “cero absoluto”?
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Escalas de temperatura
Fahrenheit Celsius Kelvin
Boiling Pointof Water
Freezing Pointof Water
Absolute Zero
212F
32F
-459F
100C
0C
-273C
373 K
273 K
0 K
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Los estados de la materia
Sólido Líquido
Gas Plasma
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Calor
Es la energía cinética que se propaga debido a
un gradiente de temperatura, cuya
dirección es de mayor temperatura a menor
temperatura
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El flujo del calor
T = 100oC
T = 0oC
Temperature Profile in Rod
HeatVibrating copper atom
Copper rod
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Reversibilidad
• Reversibility is the ability to run a process back and forth infinitely without losses.
• Reversible Process – Example: Perfect Pendulum
• Irreversible Process – Example: Dropping a ball of clay
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Procesos reversibles
• Examples: – Perfect Pendulum– Mass on a Spring– Dropping a perfectly elastic ball– Perpetual motion machines– More?
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Procesos irreversibles
• Examples:– Dropping a ball of clay– Hammering a nail– Applying the brakes to your car– Breaking a glass– More?
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Primera Ley de la Termodinámica
“ La energía no se crea ni se destruye, sólo se transforma”
Q = W + dE
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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:
E
Heat-up the system
Do work on the system
E
Cool-off the system
Extract work from the system
E = q + ww
-PV
w´
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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
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Entropía
S = K Ln(W)
La entropía es la medida del grado de desorden de un sistema molecular
S1 > S2
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La entropía es la medida del grado de desorden de un sistema
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Ordered Solid
Disordered Liquid
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Hard-sphere crystal
Hard-sphere liquid
Hard-sphere freezing is driven by entropy !
Higher Entropy…
Lower Entropy…
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Segunda Ley de la Termodinámica
“En todo sistema aislado, la entropía siempre aumenta hasta alcanzar el estado de equilibrio”
dS>=0 (dS>=dQ/T)
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Ordering and 2nd law of thermodynamics
- Condensation into liquid (more ordered).
- Entropy of subsystem decreased…
- Total entropy increased! Gives off heat to room.
System in thermal contact with environment
Equilibration
Initially high Cools to room
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Algunos eventos bioquímicos contradicen la segunda ley de la termodinámica?
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• Second Law of Thermodynamics– naturally occurring processes are
directional
– these processes are naturally irreversible
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Energía Libre de Gibbs
G=H-TSLa energía libre es
la fracción de la energía que se
puede utilizar para realizar trabajo en
condiciones de presion, volumen y
temperatura constante
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Lo importante es la variación de la energía libre…
dG<0 proceso exergónico (espontáneo)
dG>0 proceso endergónico
dG<0 perder capacidad de hacer trabajo == perder energía potencial == aumentar el desorden (entropía)
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∆G= ∆H - T ∆S∆G+ (exergónico) ∆H +(endotérmico) ∆G – (endergónico)∆H- (exotérmico)
∆S +(sube entropía) ∆S – (baja entropía)
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Table 3.2
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La paradoja del ¨Demonio de Maxwell¨
Segunda ley: Entropía y desorden
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Las Enzimas o biocatalizadores, reducen la Energía de Activación
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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
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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
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La síntesis de ATP ocurre durante la
glicólisis y la respiración celular en la mitocondria usualmente
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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.
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El ATP participa en una serie de reacciones acopladas
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Diversas moléculas biológicas requieren la
capacidad de ‘moverse’ para cumplir sus funciones… Por lo tanto hace falta energía
para realizar esta función.
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La fuente de energía para el movimiento
molecular es fundamentalmente el
ATP
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El ATP contribuye a diversos tipos de reacciones
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El ATP suele participar en el correcto plegamiento de las
proteínas
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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:
E
Heat-up the system
Do work on the system
E
Cool-off the system
Extract work from the system
E = q + ww
-PV
w´
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Thermodynamics
A more useful concept is: ENTHALPY (H)
H = E + PV
At constant pressure…PV VP w VP - q H p
E
00
Only P-V work involved… w´ = 0 (as in most biological systems)
So…
pq H
At constant pressure, the enthalpy change in a process is equal to amount of heat exchanged in the process by the
system.
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Thermodynamics
We have…
H = E + PV
H = E + PV + VP
P = 0V 0
in biological systems
0 0
H Eat P = 0 and since V 0
Q: How is this energy stored in the system?
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
A:
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Thermodynamics
Second Law: Entropy and Disorder
Energy conservation is not a criterion to decide if a process will occur or not:
Examples…
q
HotT ColdT T T
E = H = 0
This rxn occurs in one direction and not in the opposite
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
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Thermodynamics
All permutations of tossing 4 coins…
1 way to obtain 4 heads4 ways to obtain 3 heads, 1 tail6 ways to obtain 2 heads, 2 tails4 ways to obtain 1 head, 3 tails1 way to obtain 4 tails
Macroscopic states…
H T T HH H T TH T H TT H H TT T H HT H T H
2!2!
4! 6
Microscopic states…
1
4
6
4
14 H, 0 T
3 H, 1 T2 H, 2 T
1 H, 3 T
0 H, 4 T
The most probable state is also the most disordered
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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 mostprobable 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
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ThermodynamicsA measure of how disordered is the final state is also a measure of how probable it is:
16
6 P 2T 2H,
Entropy provides that measure (Boltzmann)…
ln W k S B Number of microscopic ways in which a particular outcome (macroscopic state) can be attained
Boltzmann Constant
Molecular Entropy
For Avogadro number’s of molecules…
ln W )k(N S BAvogadro
R (gas constant)
Therefore: the most probable outcome maximizes entropy of isolated systems
S > 0 (spontaneous)S < 0 (non-spontaneous)
Criterion for Spontaneity:
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Thermodynamics
The macroscopic (thermodynamic) definitionof entropy:
dS = dqrev/T
i.e., for a system undergoing a change from an initial stateA 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.
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Thermodynamics
S dqrev
Tinitial
final
(Carried through a reversible path)
S CP
Tinitial
final
dT (If process occurs at contant pressure)
S CV
Tinitial
final
dT (If process occurs at constant volume)
Spontaneity Criteria
In these equations, the equal sign applies for reversible
processes. The inequalities apply for irreversible, spontaneous, processes :
S(system) S (surroundings) 0
S(isolated system) 0
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Thermodynamics
Free-energy…•Provides a way to determine spontaneity whether system is isolated or not•Combining enthalpic and entropic changes
ST - H G
What are the criteria for spontaneity?
Take the case of H = 0:
ST - G
< 0 > 0G > 0G < 0G = 0
non-spontaneous processspontaneous process process at equilibrium
(Gibbs free energy)
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ThermodynamicsFree 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?:
[A][B]
[C][D]ln RT G G o
is the Standard Free Energy of reactionoG
i.e. G when A, B, C, D are mixed in their standard state:Biochemistry: 1M, 25oC, pH = 7.0
1 1
1 1ln RT G G o
Rxn
o
Rxn G G
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Thermodynamics
Now… Suppose we start with equilibrium concentrations:
Reaction will not proceed forward or backward…
0 GRxn Then…
eqeq
eqeqo
[B][A]
[D][C]ln RT G 0
eqeq
eqeqo
[B][A]
[D][C]ln RT - G
eqo Kln RT - G
RT
oST - oH
eq e K
R
oSRT
oH
ee Keq
RT
oG eq e K
Rea
rran
ging
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Thermodynamics
R
oSRT
oH
ee K ln eq
Graph:
R
S
RT
H - Kln
oo
eq
1-o K T
1
eqKln
R
So
- Ho
RSlope =
Van’t Hoff Plot
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Thermodynamics
1) Change in potential energy stored in bonds and interactions
2) Accounts for T-dependence of Keq
3) Reflects: #, type, and quality of bonds
4) If Ho < 0: T Keq If Ho > 0: T Keq
1) Measure of disorderS = R ln (# of microscopic ways of macroscopic states can be attained)
2) T-independent contribution to Keq
3) Reflects order-disorder in bonding, conformational flexibility, solvation
4) So Keq Rxn is favored
Summary: in chemical processes
Ho So
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Thermodynamics
Examples:
A BConsider the Reaction… [A]initial = 1M
[B]initial = 10-5MKeq = 1000
eqo Kln RT - G
Free energy change when products and reactants are present at standard conditions
1000ln K 2981.98 - G K molcalo
molKcalo 4.076- G Spontaneous rxn
How about GRxn…
[A][B]
ln RT G G oRxn
1
10ln K298101.98 4.076 - G
-5
K molKcal3-
molKcal
Rxn
molKcal
Rxn 10.9- G Even more spontaneous
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Thermodynamics
Another question… What are [A]eq and [B]eq?
1M 10 1 [B] A][ -5
[B] - 1 A][
1000 [A]
[B] K
eq
eqeq
eqeq [B] - 1 1000 B][
1000 B][ 1001 eq
1M 0.999M 1001
1000 B][ eq
0.001M A][ eq
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ThermodynamicsAnother Example… Acetic Acid Dissociation
Ho ~ 0
CH3 – COOH + H2O CH3 – COO- + H3O+
5-
3
3-
3eq 10 ~
COOH][CH
]O][HCOO[CH K
Creation of charges Requires ion solvation Organizes H2O around ions
At 1M concentration, this is entropically unfavorable. Keq ~ 10-5
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
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Thermodynamics
CH3 – COOH + H2O CH3 – COO- + H3O+
Keq [CH3 COO
-][H3O
]
[CH3 COOH] =
[CH3 COO-][H
3O ]
[CH 3 COOH] T2
[CH3 COOH] T [CH3 COO-]
[CH3 COOH]
T2
Keq 2
[CH3 COOH] T1
with [CH3 COO
-]
[CH 3 COOH] T
and =-Keq K
2eq + 4[CH3 COOH] T Keq
2[CH3 COOH]
T
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CH3 -COOH total
Thermodynamics
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ThermodynamicsThird Example… Amine Reactions
R – N – H + H2O R – NH2 + H3O+
H
H+
So 0
molKcalo 14 H
-10eq 10 K
not favorable
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Backbone Conformational Flexibility
NC
R
HO
N
H
H
C
For the process…
folded unfolded(native) (denatured)
folded
unfoldedoconf. backbone W
Wln R S
How many ways to form the unfolded state?…
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Backbone Conformational Flexibility
degrees of freedom = 2
Assume 2 possible values for each degree of freedom. Then…
residueisomers onalconformati 4 of Total
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
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Backbone Conformational FlexibilityThermodynamic considerations…
16oconf. backbone 10ln R S
2.303 16 1.987
K molcal 73
C25at 22- ST- G omolKcaloo
conf. backbone
In addition other degrees of freedom may be quite important, for example…
NC
R
HO
N
H
H
C
We will see this later in more detail
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]][OHO[H K -3w
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.
H2O + H2O H3O+ + OH-
Here we concern ourselves with its ionization properties:
O][H
]][OHO[H K
2
-3
eq
Since in the cell, [H2O] ~ 55M, and ionization is very weak, then [H2O] ~ constant, so se can define…
“the ionic product of water”
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]O[H log- ]O[H
1 log pH 3
310
Ionization of Water
From the previous equation…
]][OHO[H K -3w
-14
w 10 K For pure water…
M10 ][OH ]O[H ][H -7-3
i.e. in a neutral soln: M10 ]O[H -73 M10 ][OH -7-
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…
7 10
1 log pH
7-10 So, in fact for pure water:
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Weak Acids and Bases
All biological acids and bases belong to this category
Consider acetic acid…
AH A- + H+
The Dissociation Constant…
AH][]A][[H
K-
a
[AH]
][A log pK pH
-
a rearrange…Henderson-Hasselbalch equation
where, pKa = - logKa
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Fraction of deprotonated acid is…
[AH] ]A[
][A
A
f
Weak Acids and Bases
Also… AAH 1 ff
A
Aa - 1
log pK pHf
f
pH
0.5Af
1.0
0
pKa
i.e. pKa is the pH at which the acid is 50% ionized
So, we can re-write the
Henderson-Hasselbalch
equation
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Weak Acids and Bases
Based on the previous page…
90% 11
10 ; 1 pK pH
Aa f
9% ; 1 pK pHAa f
etc. 0.9%, ; 2 pK pHAa f
If…
Morever… the lower the pKa, the stronger the acid
pH
0.5Af
1.0
0
stronger acid
weaker acid
A
Aa - 1
log pK pHf
f
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Weak Acids and Bases
Some useful relationships…
fAH AH
A AH
H Ka H
fA-
Ka
fAH
Ka
fA
A
A AH
K a
K a H
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Multiple Acid-Base Equilibria
Consider Alanine…
NH3+
CH3
CH COOH
Titrate a solution of ala, using a gas electrode (pH meter), and a buret to add a strong base of known concentration:
= 2
.3
= 9
.7
pK1 pK2 pH
(fra
ctio
n de
prot
onat
ed)
mL
of
base
add
ed
Macroscopic experiment shows 2 inflection points (2 pKs)
Please correct in your notes
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Multiple Acid-Base Equilibria
N+
CH3
CH COOH
H
H
H
N+
CH3
CH COO –
H
H
H
N
CH3
CH COO –
H
H
Cation Zwitterion Anion
If we assume that the ionization of a given group is independent of the state of ionization of the others, then…
As we vary the pH of the solution from low to high:
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?
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Multiple Acid-Base Equilibria
f HAH fCOOH fNH3
H
Ka1 H
H
Ka 2 H
f HA fCOO fNH3
K a1
Ka 1 H
H
K a 2 H
fAH fCOOH fNH2 H
Ka 1 H
Ka 2
K a 2 H
fA fCOO fNH2 K a1
Ka 1 H
Ka 2
Ka 2 H
1 AAHHAHAH
ffff
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