b termodinamica bioenergetica ciencias 2008

8/12/2019 B Termodinamica Bioenergetica Ciencias 2008

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La Termodinmica y la Vida

Prof. Mirko Zimic

[email protected]


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La Biologa est basada en lamateria suaveviviente

Auto-ensamblaje

Alta especificidadInformacin


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Los objetos vivientes estn

compuestos por molculas inertesAlbert Lehninger


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El problema es:

Cmo estas molculasconf ieren la admirable

combinacin de

caractersticas que

denominamos vida???

Cmo es que unorganismo vivo aparece

ser ms que la suma de

sus partes inanimadas???


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La Fsica procura entender y reducir la

Biologa en leyes fundamentales

Pero este es un problema muycomplicado !

Son demasiadas las variables y resultaimposible describir un sistema de un

nmero tan grande de partculas


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SOLUCIN:Descripcin estadstica del mundo aleatorio

La ACTIVIDAD COLECTIVA de muchos objetos deMovimiento aleatorio puede ser predicho, aun cuando elmovimiento exacto de un slo objeto es desconocido

Si todo en el nano-mundo de las clulas es aleatorio,cmo podemos realizar predicciones?


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TERMODINMICA

Permite predecir la ACTIVIDADCOLECTIVA de muchos objetos de

movimiento aleatorio, aun cuando elmovimiento exacto de un slo objeto esdesconocido


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Todo en el Universo estacompuesto por Materia y Energa

Materia: - Medida de la inercia

Energa: - Energa cintica (movimiento)- Energa potencial (reposo)

E = M C2


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Trabajo

Trabajo = Fuerza Distancia

W = F Dx

La unidad del trabajo es el Newton-metroconocido tambin como Joule.


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Trabajo mecnico

F

FDx


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Kinetic Energy

Kinetic Energy is the energy of motion.

Kinetic Energy = mass speed2

2mv2

1KE


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Potential Energy

The energy that is stored is calledpotential energy.

Examples:Rubber bands

Springs

Bows

Batteries

Gravitational Potential PE=mgh


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Conversin entre la Energa cintica yla Energa potencial


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Qu es la Bioenergtica?

Es la disciplina que estudia los aspectosenergticos en los sistemas vivos, tanto a

nivel molecular como a nivel celular.Interacciones moleculares

ATP como biomolcula almacenadora de

energaBiocatlisis

Reacciones acopladas


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Interacciones Fundamentales

Interaccin Gravitacional (masa-masa)

Interaccin Electromagntica (carga-dipolo)

Interaccin Nuclear Dbil (electrones-ncleo)

Interaccin Nuclear Fuerte (protones-neutrones)


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Enlace Covalente


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Las interacciones Inicas se dan

entre partculas cargadas


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PUENTE DE

HIDRGENO


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Participacin de los Puentes de Hidrgeno:Replicacin, Transcripcin y Traduccin


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Las interacciones dbiles dirigen elproceso de docking molecular


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El efecto hidrofbico colabora enel plegamiento de las protenas


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Revisin de algunos conceptosTermodinmicos

Sistemas termodinmicos

Equilibrio termodinmico

Temperatura

Calor

Entalpa

Energa Libre

Entropa


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Clasificacin de los sistemastermodinmicos

Sistemas AbiertosIntercambian materia y energa con el exterior

Sistemas CerradosSlo intercambian energa con el exterior

Sistemas AisladosNo tienen ningun tipo de intercambio con el

exterior


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Equilibrio Termodinmico

Un sistema se encuentra en equilibriotermodinmico cuando la distribucin

espacial y temporal de la materia y laenerga es uniforme


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En el equilibrio termodinmico sereducen las gradientes y con ello se

reduce la energa potencial


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Qu esta ms fro?El metal o la madera?


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Temperatura

Es la medida de la energa cinticainterna de un sistema molecular

Ek= N K T /2


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Cool Hot


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Qu es el cero absoluto?


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Escalas de temperatura

Fahrenheit Celsius Kelvin

Boiling Point

of Water

Freezing Point

of Water

Absolute Zero

212F

32F

-459F

100C

0C

-273C

373 K

273 K

0 K


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Los estados de la materia

Slido Lquido

Gas Plasma


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Calor

Es la energa cinticaque se propaga debido a

un gradiente de

temperatura, cuyadireccin es de mayortemperatura a menor

temperatura


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El flujo del calor

T= 100oC

T= 0oC

TemperatureProfile in Rod

HeatVibrating copper atom

Copper rod


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Reversibilidad

Reversibilityis the ability to run a processback and forth infinitely without losses.

Reversible ProcessExample: Perfect Pendulum

Irreversible ProcessExample: Dropping a ball of clay


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Procesos reversibles

Examples:Perfect Pendulum

Mass on a SpringDropping 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 Termodinmica

La energa no se crea ni se destruye, slo

se transforma

Q = W + dE


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First Law: Energy conservation

Internal energy (E).-Total energy content of a system. Itcan be changed by exchanging heat or work with thesystem:

EHeat-upthe system

Do work onthe system

ECool-offthe system

Extract work fromthe system

DE = q + ww

-PDV

w


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Entalpa

H=E+PVLa entalpa es la fraccin de la energa

que se puede utilizar para realizar

trabajo en condiciones de presin yvolumen constante

dH0 proceso endotrmico


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Entropa

S = K Ln(W)La entropa es la medida del grado de

desorden de un sistema molecular

S1 > S2


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La entropa es la medida del gradode desorden de un sistema

Di d d Li id


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Ordered Solid

Disordered Liquid

H d h li id


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Hard-sphere crystal

Hard-sphere liquid

Hard-sphere freezing is drivenby entropy !

Higher Entropy

Lower Entropy

S d d l di i


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Segunda Ley de la Termodinmica

En todo sistema

aislado, la entropasiempre aumenta

hasta alcanzar elestado de equilibrio

dS>=0 (dS>=dQ/T)


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Ordering and 2ndlaw 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

Algunos eventos bioqumicos contradicen


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Algunos eventos bioqumicos contradicenla segunda ley de la termodinmica?

Second La of Thermod namics


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Second Law of Thermodynamicsnaturally occurring processes are

directionalthese processes are naturally irreversible

E Lib d Gibb


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Energa Libre de Gibbs

G=H-TSLa energa libre esla fraccin de la

energa que sepuede utilizar pararealizar trabajo en

condiciones depresion, volumen y

temperaturaconstante


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Lo importante es la variacin de la

energa libre

dG0 proceso endergnico

dG


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G= H - T SG+ (exergnico) H +(endotrmico)

G (endergnico) H- (exotrmico)S +(sube entropa)S (baja entropa)


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Table 3.2


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La paradoja del Demonio de Maxwell


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La paradoja del Demonio de Maxwell

Segunda ley: Entropa y desorden


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Las Enzimas o biocatalizadores


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Las Enzimas o biocatalizadores,reducen la Energa de Activacin


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La molcula de ATP

Los seres vivos utilizan lamolcula de ATP comomedio principal para

almacenar energapotencial proveniente dela degradacin de los

alimentos


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La manera de utilizarse la energa en la


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La manera de utilizarse la energa en lamolcula de ATP es mediante la separacin deun grupo fosfato el cual est unido mediante

un enlace covalente de alta energa


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La sntesis deATP ocurredurante la

gliclisis y larespiracincelular en lamitocondria

usualmente


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En las plantas, la sntesis

de ATP ocurre asistida porluz durante la fotosntesis,la cual es luego empleada

en las denominadasreacciones oscuras. Este esun ejemplo de

transformacin de energaradiante en energaqumica.

El ATP participa en una serie de


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El ATP participa en una serie dereacciones acopladas


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Diversas molculasbiolgicas requieren lacapacidad de moverse

para cumplir susfunciones Por lotanto hace falta energa

para realizar estafuncin.


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La fuente de energapara el movimiento

molecular esfundamentalmente el

ATP


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El ATP contribuye a diversos

tipos de reacciones

El ATP suele participar en el


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El ATP suele participar en elcorrecto plegamiento de las

protenas


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Thermodynamics


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First Law: Energy conservation

Internal energy (E).-Total energy content of a system. Itcan be changed by exchanging heat or work with thesystem:

EHeat-upthe system

Do work onthe system

ECool-offthe system

Extract work fromthe system

DE = q + ww

-PDV

w

Thermodynamics


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A more useful concept is: ENTHALPY (H)

H = E + PVAt constant

pressurePVVPwVP-qH p DDDD

DE

00

Only P-V work involved w= 0(as in most biological systems)

So

pqHD

At constant pressure, the enthalpy change in a process isequal to amount of heat exchanged in the process by the

system.

Thermodynamics


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We have

H = E + PV

DH = DE + PDV + VDPDP = 0DV 0

in biologicalsystems

0 0

DH DEat DP = 0 and since DV 0

Q:How is this energy stored in the system?

1) As kinetic energyof the molecules. In isothermal (DT =0) processes this kinetic energy does not change.

2) As energy stored in chemical bonds and interactions. Thispotential energy could be released or increased in chemical

reactions

A:

Thermodynamics


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Second Law: Entropy and Disorder

Energy conservation is nota criterion to decide if a process willoccur or not:

Examples

q

HotT ColdT T T

DE = DH = 0This rxn occurs in onedirection and not in theopposite

these processesoccur because

the final state( with T = T &P = P) are themost probable

states of thesesystems

Let us study a simpler case

tossing 4 coins

Thermodynamics


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All permutations of tossing 4 coins

1way to obtain 4 heads4ways to obtain 3 heads, 1 tail6ways to obtain 2 heads, 2 tails4ways to obtain 1 head, 3 tails

1way to obtain 4 tails

Macroscopic states

HT THH HT TH THTTH HT

T TH HTHTH

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 themost disordered

Thermodynamics


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In this case we see that DH = 0,i.e.:

there is not exchange of heat between the system and itssurroundings, (the system is isolated ) yet, there is an

unequivocal answer as to which is the mostprobableresult of the experiment

The most probable state of the system is also the mostdisordered, i.e. ability to predict the microscopic outcomeis the poorest.

Thermodynamics


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A measure of how disordered is the final state is alsoa measure ofhow probable it is:

16

6P 2T2H,

Entropyprovides that measure(Boltzmann)

ln WkS B Number ofmicroscopicways in whicha particularoutcome(macroscopic

state) can beattained

BoltzmannConstant

MolecularEntropy

For Avogadro numbers

of molecules

ln W)k(NS BAvogadroR (gas constant)

Therefore: the most probable

outcome maximizes entropyof isolated systems

DS > 0 (spontaneous)DS < 0 (non-spontaneous)

Criterion for Spontaneity:

Thermodynamics


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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 thesetwo states when the process is carried out reversibly.

Thermodynamics


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DS dq

rev

Tinitial

fina l

(Carried through a reversible path)

DS C

P

Tinitial

fina l

dT (If process occurs at contant pressure

DS C

V

Tinitial

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 irreversible, spontaneous, processes :

DS(system) DS(surroundings) 0

DS(isolatedsystem) 0

Thermodynamics


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Free-energyProvides a way to determine spontaneity whether system is

isolated or not

Combining enthalpic and entropic changes

ST-HG DDD

What are the criteria for spontaneity?

Take the case of DH = 0:

ST-G DD

< 0 > 0 DG > 0DG < 0DG = 0

non-spontaneous processspontaneous process

process at equilibrium

(Gibbs free energy)

Thermodynamics


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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 DG is associated with this search and finding?:

[A][B]

[C][D]lnRTGG o DD

is the Standard Free Energyof reactionoGD

i.e. DG when A, B,C, D are mixed intheir standard state:Biochemistry: 1M,25oC, pH = 7.0

11

11lnRTGG oRxn

DD

o

Rxn GG DD

Thermodynamics


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Now Suppose we start with equilibrium concentrations:

Reaction will not proceed forward or backward

0GRxnD

Then

eqeq

eqeqo

[B][A]

[D][C]lnRTG0 D

eqeq

eqeqo

[B][A]

[D][C]lnRT-G D

eq

o KlnRT-G D

RT

oST-oH

eq eK

DD

DD R

oSRT

oH

eeKeq

RT

oG

eq eKD

Rearranging

Thermodynamics


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DD

R

oS

RT

oH

eeKln eq

Graph:

R

S

RT

H-Kln

oo

eq

D

D

1-o KT

1

eqKln

R

SoD

-DHo

R

Slope =

Vant Hoff Plot

Thermodynamics


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1) Change in potentialenergy stored in bondsand interactions

2) Accounts for T-dependenceof Keq

3) Reflects: #, type, andquality of bonds

4) If DHo< 0: T Keq

If DHo> 0: T Keq

1) Measure of disorderS = R ln (# of microscopic ways ofmacroscopic states can be attained)

2) T-independent contributionto Keq

3) Reflects order-disorder inbonding, conformational

flexibility, solvation4) DSoKeq

Rxn is favored

Summary: in chemical processes

DHo DSo

Thermodynamics


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Examples:

A B

Consider the Reaction [A]initial= 1M[B]initial= 10-5MKeq= 1000

eq

o KlnRT-G D

Free energy changewhen products andreactants are present atstandard conditions

1000lnK2981.98-G Kmolca lo

DmolKcalo 4.076-G D Spontaneous rxn

How about DGRxn

[A]

[B]lnRTGG oRxn

D

D

1

10lnK298101.984.076-G

-5

Kmol

Kcal3-

mol

Kcal

Rxn D

molKcal

Rxn 10.9-G D Even more spontaneous

Thermodynamics


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Another question What are [A]eqand [B]eq?

1M101[B]A][

-5

[B]-1A][

1000

[A]

[B]K

eq

eq

eq

eqeq [B]-11000B][

1000B][1001 eq

1M0.999M1001

1000B][ eq

0.001MA][ eq

ThermodynamicsA h E l A i A id Di i i


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Another Example Acetic Acid Dissociation

DHo~ 0

CH3COOH + H2O CH3COO-+ H3O+

5-

3

3

-

3eq 10~

COOH][CH

]O][HCOO[CHK

Creation of charges Requires ion solvationOrganizes H2O around ions

At 1M concentration, this is entropically unfavorable.

Keq~ 10-5

If [CH3COOH]total~ 10-5

50% ionizedPercent ionization is concentration dependent. We can favorthe forward rxn (ionization) by diluting the mixture

If [CH3

COOH]total

~ 10-890% ionized

Thermodynamics


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CH3COOH + H2O CH3COO-+ H3O+

Keq [CH3 COO

-][H 3O

]

[CH3 COOH] =

[CH3

COO-][H3O ]

[CH 3COOH]T2

[CH3 COOH]T [CH3 COO-]

[CH 3COOH]T2

Keq

2[CH3COOH]T

1 with

[CH3 COO-

]

[CH 3COOH]T

and =-Keq K

2eq + 4[CH 3COOH]T Keq

2[CH3

COOH]T

Thermodynamics


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CH3 -COOH total

ThermodynamicsThi d E l A i R ti


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Third Example Amine Reactions

RNH + H2O RNH2+ H3O+

H

H+

DSo0

molKcalo 14H D

-10

eq 10K not favorable

Backbone Conformational FlexibilityR H


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NC

R

HO

N

H

H

C

For the process folded unfolded(native) (denatured)

folded

unfoldedo

conf.backboneW

W

lnRS D

How many ways to form the unfolded state?

Backbone Conformational Flexibility


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degrees of freedom = 2

Assume 2 possible valuesfor each degree of freedom. Then

residueisomersonalconformati4ofTotal

For 100 amino acids4100~ 1060conformations

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~ 1016conformations

Backbone Conformational FlexibilityTh d i id ti


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Thermodynamic considerations

16o

conf.backbone 10lnRS D2.303161.987

Kmolca l73

C25at22-ST-G

o

mol

Kcaloo

conf.backbone DDIn addition other degrees of freedom may be quite important,for example

NC

R

HO

N

H

H

C

We will see thislater in more detail

Ionization of Water


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]][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[HK

2

-

3eq

Since in the cell, [H2O] ~ 55M, and ionization is very weak, then

[H2O] ~ constant, so se can definethe ionic

product ofwater


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Weak Acids and BasesAll bi l i l id d b b l hi


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All biological acids and bases belong to this category

Consider acetic acid

AH A-+ H+

The Dissociation Constant

AH]

[

]

A

][

[HK

-

a

[AH]][AlogpKpH

-

a rearrange Henderson-Hasselbalchequation

where, pKa= - logKa

F i f d d id i

Weak Acids and Bases


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Fraction of deprotonated acid is

[AH]]A[

][AA

f Also AAH 1 ff

A

Aa

-1

logpKpH

f

f

pH

0.5Af

1.0

0

pKa

i.e. pKais the pH at

which the acid is50% ionized

So, we can re-write theHenderson-Hasselbalch

equation

Weak Acids and BasesB d th i


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Based on the previous page

90%11

10;1pKpH

Aa

f

9%;1pKpHAa

f

etc.0.9%,;2pKpHAa

f

If

Morever the lower the pKa, the stronger the acid

pH

0.5Af

1.0

0

strongeracid

weakeracid

A

Aa

-1logpKpH

f

f

Weak Acids and Bases


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Some useful relationships

fAH AH

A AH

H

Ka H

fA-

Ka

fAH

Ka

fA A

A AH Ka

Ka H

Multiple Acid-Base EquilibriaC id Al i


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Consider Alanine

NH3+

CH3

CH COOH

Titrate a solution of ala, using a gas electrode (pH meter), and aburet to add a strong base of known concentration:

=

2.3

=9.7

pK1 pK2 pH

(fractio

ndeprotonated)

mLo

fbaseadded

Macroscopicexperiment shows2 inflection points(2 pKs)

Please correct in yournotes

Multiple Acid-Base Equilibria


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N+CH3CH COOH

H

HH

N+CH3CH COO

H

HH

NCH3CH COO

H

H

Cation Zwitterion Anion

If we assume that the ionization of a given group is independentof 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 thedeprotonation of the carboxylic group (at low pH) and thento the deprotonation of the amine group (at high pH).

So, How can we estimate the fraction of these different species in solution?

Multiple Acid-Base Equilibria


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fHAH

fCOOH fNH3

H

Ka1 H

H

Ka2 H

fHA

f

COO f

NH3 K a1

Ka 1H

H

Ka 2H

fAH fCOOH fNH2

H

Ka 1 H

Ka 2

K a 2 H

fA

fCOO

fNH2

Ka1

Ka1 H

Ka 2

Ka 2 H

1AAHHAHAH

ffff


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