bioenergetica 2007 i

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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 energíapotencial 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 larespiración

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 denominadasreacciones oscuras. Este es

un ejemplo de

transformación de energíaradiante en energía

química.



El ATP participa en una serie de

reacciones acopladas



Diversas moléculasbiológicas requieren la

capacidad de

„moverse‟ para cumplir sus funciones… Por lo

tanto hace falta energía

para realizar estafunción.



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



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´

Thermodynamics



Thermodynamics

A more useful concept is: ENTHALPY (H)

H = E + PV

At constant

pressure… PVVPwVP-qH p

E

00

Only P-V work involved… w´ = 0

(as in most biological systems)

So…

pqH

At constant pressure, the enthalpy change in a process is

equal to amount of heat exchanged in the process by the

system.

Thermodynamics



Thermodynamics

We have…

H = E + PV

H = E + PV + VPP = 0

V 0

in biological

systems

0 0

H E

at 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:

Thermodynamics



Thermodynamics

Second Law: Entropy and Disorder

Energy conservation is not a criterion to decide if a process willoccur 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 thesesystems

Let us study a simpler case…

tossing 4 coins

Thermodynamics



Thermodynamics

All permutations of tossing 4 coins…

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

Macroscopic states… H T T H H H T T

H T H T

T H H T

T T H H T H T H

2!2!

4!6

Microscopic states…

1

4

6

4

14 H, 0 T

3 H, 1 T

2 H, 2 T

1 H, 3 T

0 H, 4 T

The most probable

state is also the

most disordered

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 mostdisordered, i.e. ability to predict the microscopic outcome

is the poorest.

Thermodynamics

Thermodynamics



Thermodynamics

A measure of how disordered is the final state is also a measure of

how probable it is:

166 P 2T2H,

Entropy provides that measure

(Boltzmann)…

ln Wk 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 (NS BAvogadroR (gas constant)

Therefore: the most probable

outcome maximizes entropyof isolated systems

S > 0 (spontaneous)

S < 0 (non-spontaneous) Criterion for Spontaneity:

Thermodynamics



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



Thermodynamics

S dq

rev

T initial

fina l

(Carried through a reversible path)

S C

P

T initial

fina l

dT (If process occurs at contant pressure

S C

V

T initial

fina l

dT (If process occurs at const ant volume

Spontaneity Criteria

In these equat ions, the equal sign applies for reversible

processes. The inequalities apply for ir reversible, spontaneous, processes :

S ( system) S ( surroundings) 0

S (isolated system) 0

Thermodynamics



Thermodynamics

Free-energy…

•Provides a way to determine spontaneity whether system is

isolated or not

•Combining enthalpic and entropic changes

ST-HG

What are the criteria for spontaneity?

Take the case of H = 0:

ST-G

< 0 > 0G > 0

G < 0

G = 0

non-spontaneous process

spontaneous process

process at equilibrium

(Gibbs free energy)

Thermodynamics



Thermodynamics

Free energy and chemical equilibrium…

Consider this rxn:

A + B C + DSuppose 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]lnRTGG o

is the Standard Free Energy of reaction

o

G

i.e. G when A, B,

C, D are mixed in

their standard state:Biochemistry: 1M,

25oC, pH = 7.0

11

11lnRTGG o

Rxn

o

Rxn GG

Thermodynamics



Thermodynamics

Now… Suppose we start with equilibrium concentrations:

Reaction will not proceed forward or backward…

0GRxn

Then…

eqeq

eqeqo

[B][A]

[D][C]lnRTG0

eqeq

eqeqo

[B][A]

[D][C]lnRT-G

eq

o KlnRT-G

RT

oST-oH

eq eK

R

oSRT

oH

eeKeq

RT

oG

eq eK

R e a r r a n g i n g

Thermodynamics



Thermodynamics

R

oSRT

oH

eeKln eq

Graph:

R

S

RT

H -Kln

oo

eq

1-o K

T

1

eqKln

R

So

-Ho

R

Slope =

Van‟t Hoff Plot

Thermodynamics



Thermodynamics

1) Change in potential

energy stored in bonds

and interactions

2) Accounts for T-dependenceof Keq

3) Reflects: #, type, and

quality of bonds

4) If Ho < 0: T Keq

If Ho > 0: T Keq

1) Measure of disorder

S = R ln (# of microscopic ways of

macroscopic states can be attained)

2) T-independent contributionto Keq

3) Reflects order-disorder in

bonding, conformational

flexibility, solvation

4) So Keq

Rxn is favored

Summary: in chemical processes

Ho So

Thermodynamics



y

Examples:

A B

Consider the Reaction… [A]initial = 1M [B]initial = 10-5M

Keq = 1000

eq

o KlnRT-G

Free energy change

when products and

reactants are present at

standard conditions

1000lnK2981.98-G Kmolca lo

molKcalo 4.076-G Spontaneous rxn

How about GRxn…

[A]

[B]

lnRTGG

o

Rxn

1

10lnK298101.984.076-G

-5

Kmol

Kcal3-

mol

Kcal

Rxn

molKcal

Rxn 10.9-G Even more spontaneous

Thermodynamics



y

Another question… What are [A]eq and [B]eq?

1M101[B]A][-5

[B]-1A][

1000

[A]

[B] K

eq

eq

eq

eqeq [B]-11000B][

1000B][1001 eq

1M0.999M1001

1000 B][ eq

0.001MA][ eq

Thermodynamics



y

Another 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

Thermodynamics



y

CH3 – COOH + H2O CH3 – COO- + H3O+

K eq [CH3 COO

-][H 3O

]

[CH3 COOH]=

[CH3

COO-][H3O ]

[CH 3 COOH]T2

[CH3 COOH]T [CH3 COO-]

[CH 3 COOH]T 2

K eq

2[CH3 COOH]T

1

with [CH3 COO

-]

[CH 3 COOH]T

and =-K eq K

2eq + 4[CH 3 COOH]T K eq

2[CH3

COOH]T

Thermodynamics



CH3 -COOH total

y

Thermodynamics



y

Third Example… Amine Reactions

R – N – H + H2O R – NH2 + H3O+

H

H+

So 0

molKcalo 14H

-10

eq 10K not favorable

Backbone Conformational Flexibility



y

NC

R

HO

N

H

H

C

For the process… folded unfolded(native) (denatured)

folded

unfoldedoconf. backbone

WWlnRS

How many ways to form the unfolded state?…




y

degrees of freedom = 2

Assume 2 possible values for each degree of freedom. Then…

residueisomers onalconformati 4of 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 accessibleconfigurations for the chain is quite a bit smaller…

Wunfolded ~ 1016 conformations




y

Thermodynamic considerations…

16o

conf. backbone 10lnRS 2.303161.987

Kmolca l 73

C25at22-ST-Go

molKcaloo

conf. backbone

In addition other degrees of freedom may be quite important,

for example…

N

C

R

HO

N

H

H

C

We will see this

later in more detail

Ionization of Water



]][OHO[HK -

3w

•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

-

3eq

Since in the cell, [H2

O] ~ 55M, and ionization is very weak, then

[H2O] ~ constant, so se can define… “the ionic

product of

water”

Ionization of Water



]O[Hlog-]O[H

1 logpH 3

3

10

From the previous equation…

]][OHO[HK -

3w

-14

w 10K For pure water…

M10][OH]O[H][H -7-

3

i.e. in a neutral soln: M10]O[H -7

3 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 logpH

7-10 So, in fact for

pure water:

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 logpKpH

-

a rearrange… Henderson-Hasselbalch

equation

where, pKa = - logKa




Fraction of deprotonated acid is…

[AH]]A[][A

A

f Also… AAH 1 f f

A

Aa

-1

logpKpH

f

f

pH

0.5A f

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




Based on the previous page…

90%11

10

; 1pKpH Aa f

9% ; 1pKpHAa f

etc.0.9%, ; 2pKpHAa f

If…

Morever… the lower the pK a, the stronger the acid

pH

0.5A f

1.0

0

stronger

acid

weaker

acid

A

Aa

-1 logpKpH

f

f




Some useful relationships…

f AH AH

A AH

H

K a H

f A-

Ka

f AH

Ka

f A A

A AH

K a

K a H

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

( f r a c t i o n

d e p r o t o n a t e d )

m L o f b a s e a d d e d

Macroscopicexperiment shows

2 inflection points

(2 pKs)

Please correct in your

notes




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?




f HAH

f COOH f

NH3

H

K a1

H

H

K a2

H

f HA

f

COO f

NH3

K a1

K a 1 H

H

K a 2 H

f AH f COOH f NH2

H

K a 1 H

K a 2

K a 2 H

f A

f COO

f NH2

K a1

K a1 H

K a 2

K a 2 H

1AAHHAHAH

f f f f

bioenergetica 2007 i

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