Termodinámica

Biology is living soft matter

Self-assembly

High specificityMulti-componentInformation

Statistical description of random World

The collective activity of many randomly moving objectscan be effectively predictable, even if the individual motions are not.

If everything is so random in the nano-worldof cells, how can we say anything predictive about what’s going there ?

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

Which is colder?

Metal or Wood?

Temperatura

Es la medida de la energía cinética interna de un sistema

molecular

Ek = N K T /2

11.3 Temperature

• Measured in Fahrenheit, Celsius, and Kelvin

• Rapidly moving molecules have a high temperature

• Slowly moving molecules have a low temperature

Cool Hot

What is “absolute zero”?

Temperature Scales

Fahrenheit Celsius Kelvin

Boiling Pointof Water

Freezing Pointof Water

Absolute Zero

212F

32F

-459F

100C

0C

-273C

373 K

273 K

0 K

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

11.4 Pressure

• Pressure - force per unit area• It has units of N/m2 or Pascals (Pa)

A

FP

F

A

Impact Weight

Pressure

• What are the possible units for pressure?– N/m2

– Pascal 1 Pa = 1 N/m2

– atm 1 atm = 1 × 105 Pa– psi 1 psi = 1 lb/inch2

– mm Hg 1 atm = 760 mm Hg

11.5 Density

• Density - mass per unit volume

• It has units of g/cm3

V

M

High densityLow density

11.6 States of Matter

Solid Liquid

Gas Plasma

Questions

• Is it possible to boil water at room temperature? – Answer: Yes. How?

• Is it possible to freeze water at room temperature? – Answer: Maybe. How?

Gas Laws

• Perfect (ideal) Gases

• Boyle’s Law

• Charles’ Law

• Gay-Lussac’s Law

• Mole Proportionality Law

Boyle’s Law

2

12

1 V

V

P

P

T = const n = const

P1

V1

P2

V2

Charles’ Law

1

2

1

2

T

T

V

VT1

V1

T2

V2

P = const n = const

Gay-Lussac’s Law

1

2

1

2

T

T

P

PT1

P1

T2

P2

V = const n = const

Mole Proportionality Law

1

2

1

2

n

n

V

V

T = const P = const

n1

V1

n2

V2

Perfect Gas Law

• The physical observations described by the gas laws are summarized by the perfect gas law (a.k.a. ideal gas law)

PV = nRT• P = absolute pressure• V = volume• n = number of moles• R = universal gas constant• T = absolute temperature

Table 11.3: Values for R

mol·Katm·L

mol·KPa·m3

08205.0

314.8

mol·K

cal

mol·K

J

1.987

314.8

Work

• Work = Force Distance

• W = F x

• The unit for work is the Newton-meter which is also called a Joule.

Types of Work

Work Driving Force

Mechanical Force (Physical)

Shaft work Torque

Hydraulic Pressure

Electric Voltage

Chemical Concentration

Mechanical Work

F

Fx

Mechanical Work

xF

xxF

xF

dxF

dxFW

xx

x

x

x

x

12

2

1

2

1

2

1

(assume F is not a function of x)

i.e., work is the area under the F vs. x curve

Hydraulic Work

VP

xAA

F

xFW

x

P PFA

V

P = const

F

Joule’s ExperimentJoule showed that mechanical energy could beconverted into heat energy.

F

M

xH2O

T

W = Fx

11.11 Energy

• Energy is the ability to do work.

• It has units of Joules.

• It is a “Unit of Exchange”.

• Example– 1 car = $20k– 1 house = $100k– 5 cars = 1 house =

11.11 Energy Equivalents

• What is the case for nuclear power?– 1 kg coal » 42,000,000 joules– 1 kg uranium » 82,000,000,000,000 joules– 1 kg uranium » 2,000,000 kg coal!!

11.11 Energy

• Energy has several forms: – Kinetic– Potential– Electrical– Heat– etc.

Kinetic Energy

• Kinetic Energy is the energy of motion.

• Kinetic Energy = ½ mass speed2

2mv2

1KE

Potential Energy

• The energy that is stored is called potential energy.

• Examples: – Rubber bands– Springs– Bows– Batteries– Gravitational Potential PE=mgh

Conversión entre la Energía cinética y la Energía potencial

11.11.3 Energy Flow

• Heat is the energy flow resulting from a temperature difference.

• Note: Heat and temperature are not the same.

Heat Flow

T = 100oC

T = 0oC

Temperature Profile in Rod

HeatVibrating copper atom

Copper rod

11.12 Reversibility

• 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

Reversible Process

• Examples: – Perfect Pendulum– Mass on a Spring– Dropping a perfectly elastic ball– Perpetual motion machines– More?

Irreversible Processes

• Examples:– Dropping a ball of clay– Hammering a nail– Applying the brakes to your car– Breaking a glass– More?

Example: Popping a Balloon

Not reversible unless energy is expended

Sources of Irreversibilities

• Friction (force drops)

• Voltage drops

• Pressure drops

• Temperature drops

• Concentration drops

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´

• Second Law of Thermodynamics– naturally occurring processes are

directional

– these processes are naturally irreversible

Heat into Work

Thot TcoldHeat

Engine

W

QhotQcold

Entropy. The 2nd law of thermodynamics

Isolated system always evolve to thermodynamicequilibrium.

In equilibrium isolated system has the greatest possible ENTROPY (disorder*) allowed by the physical constraints on the system.

Entropy as measure of disorder

Number of allowed states in A: Number of allowed states in B:

Number of allowed states in joint system A+B:

Entropy:

Entropy is additive:

Entropy of ideal gas

Indistinguishablility

For N molecules:

For one molecule:

- “cell” volume (quantum uncertainty )V – total volume

Free energy of ideal gas: density:

Ordered Solid

Disordered Liquid

Hard-sphere crystal

Hard-sphere liquid

Hard-sphere freezing is driven by entropy !

Higher Entropy…

Lower Entropy…

Entropy and Temperature

System A System B

Total energy:

Isolated (closed) system:

Number of allowed states in A

Total number of allowed states

Total entropy

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

The first law of thermodynamics tells us that energy is conservedThe law of conservation of energy: in every physical or chemical change, the total amount of energy in the universe remains constant, although the form of energy may change. In other words, convertible but not creatable or destroyable

For an open system like a cell: energy out = energy in – energy stored (5-1)

or energy stored = energy in – energy out (5-2)or E = E2 – E1 (5-3) #Change in internal energy Eor E = Eproducts – Ereactants (5-4)

Enthalpy (H) – heat content– is the description of energy change during biological reactions.

H = E + PV (P, pressure; V, volume) (5-5) H = E + ( PV) E (Constant P &V) (5-6)

H = Hproducts – Hreactants (5-7)

Endothermic reaction: H positive, products have higher energy; the reaction needs energy

Exothermic reaction: H negative, products have lower energy; the reaction releases energy

Thermodynamic spontaneity is a measure of whether a reaction or process can go, but says nothing about whether it will go.

The second law of thermodynamics or the law of thermodynamic spontaneity tells us that reactions have directionality: in every physical or chemical change, the universe always tends toward greater disorder or randomness.

The second step in glycolysis to break down glucose

Entropy and free energy are two alternative means of assessing thermodynamic spontaneity:

Entropy (S) is a measure of randomness or disorder, such as when ice melts the volume becomes larger and there is more randomness for the water molecules.

For the whole universe, all processes or reactions that occur spontaneously result in an increase in the total entropy of the universe, i.e. Suniverse is always positive. For a particular system, however, S can be positive or negative. Due to the conservative of energy, the surroundings have to be considered when using entropy to describe a biological system.

Free energy is one of the most useful thermodynamic concepts in biology, a better way to describe thermodynamic spontaneity of a reaction based solely on the properties of the system.

G = H - T S (T, temperature in Kelvin: K= oC + 273)

G can be negative or positive depending on the change in enthalpy (H ) and entropy (S).

Interpretation of the second thermodynamic law in free energy is: all processes or reactions that occur spontaneously result in a decrease in the free energy content of the system.

C6H12O6 + 6O2 6CO2 + 6H2O + energy Exergonic (-686 kcal/mol)

6CO2 + 6H2O + energy C6H12O6 + 6O2 Endogonic (+686 kcal/mol) (photosynthesis)

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

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

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

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:

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.

Thermodynamics

Sdqrev

Tinitial

final

(Carried through a reversible path)

SCP

Tinitial

final

dT (If process occurs at contant pressure)

SCV

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

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)

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

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

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

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

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

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

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

ThermodynamicsThird Example… Amine Reactions

R – N – H + H2O R – NH2 + H3O+

H

H+

So 0

molKcalo 14 H

-10eq 10 K

not favorable

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?…

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

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