Transcript 1 - UPCH

Termodinámica
Biology is living soft matter
Self-assembly
Information
High specificity
Multi-component
Statistical description of random World
If everything is so random in the nano-world
of cells, how can we say anything predictive
about what’s going there ?
The collective activity of many randomly moving objects
can be effectively predictable, even if the individual
motions are not.
Interacciones Fundamentales
• Interacción Gravitacional (masa-masa)
• Interacción Electromagnética (carga-dipolo)
• Interacción Nuclear Débil (electronesnúcleo)
• Interacción Nuclear Fuerte (protonesneutrones)
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 Point
of Water
212F
100C
373 K
Freezing Point
of Water
32F
0C
273 K
Absolute Zero
-459F
-273C
0K
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)
F
F
P
A
Impact
A
Weight
Pressure
• What are the possible units for
pressure?
– N/m2
– Pascal
– atm
– psi
– mm Hg
1 Pa = 1 N/m2
1 atm = 1 × 105 Pa
1 psi = 1 lb/inch2
1 atm = 760 mm Hg
11.5 Density
• Density - mass per unit volume
• It has units of g/cm3
M

V
Low density
High density
11.6 States of Matter
Solid
Gas
Liquid
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
P2
V2
P1
V1
T = const
n = const
P2 V 1

P1 V 2
Charles’ Law
T2
V2
T1
V1
P = const n = const
V2 T2

V1 T1
Gay-Lussac’s Law
T2
P2
T1
P1
V = const n = const
P2 T 2

P1 T 1
Mole Proportionality Law
n2
V2
n1
V1
T = const
P = const
V2 n2

V1 n1
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
3
Pa·m
8.314
mol·K
atm·L
0.08205
mol·K
J
8.314
mol·K
cal
1.987
mol·K
Work
• Work = Force  Distance
•
W = F Dx
• 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
Dx
F
Mechanical Work
x2
W   F dx i.e., work is the area under the F vs. x curve
x1
x2
 F  dx (assume F is not a function of x)
x1
 F x 
x2
x1
 F x2  x1 
 F Dx
Hydraulic Work
W  FDx
F
 A Dx
A
 PDV
Dx
F
A
P
P F
P = const
DV
Joule’s Experiment
Joule showed that mechanical energy could be
converted into heat energy.
DT
M
H2O
Dx
F
W = FDx
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
1
2
KE  mv
2
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
Temperature
Profile in Rod
T = 0o C
Heat
Copper rod
Vibrating copper atom
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:
Heat-up the system
Cool-off the system
E
E
Do work on the system
Extract work from the system
DE = q + w
w
-PDV
w´
• Second Law of Thermodynamics
– naturally occurring processes are
directional
– these processes are naturally
irreversible
Heat into Work
W
Thot
Qhot
Heat
Engine
Qcold
Tcold
Entropy. The 2nd law of thermodynamics
Isolated system always evolve to thermodynamic
equilibrium.
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
For one molecule:
V – total volume
- “cell” volume (quantum uncertainty )
For N molecules:
Indistinguishablility
Free energy of ideal gas:
density:
Disordered Liquid
Ordered Solid
Hard-sphere liquid
Higher Entropy…
Hard-sphere freezing is driven
by entropy !
Lower Entropy…
Hard-sphere crystal
Entropy and Temperature
Isolated (closed) system:
Total energy:
System A
System B
Number of allowed states in A
Total number of allowed states
Total entropy
Ordering and 2nd law of thermodynamics
System in thermal contact with environment
Equilibration
Initially high
Cools to room
- Condensation into liquid (more ordered).
- Entropy of subsystem decreased…
- Total entropy increased! Gives off heat to room.
The first law of thermodynamics tells us that energy is conserved
The 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
or
energy stored = energy in – energy out
or
DE = E2 – E1
or
DE = Eproducts – Ereactants
(5-1)
(5-2)
(5-3) #Change in internal energy E
(5-4)
Enthalpy (H) – heat content– is the description of energy change during biological reactions.
H = E + PV
(P, pressure; V, volume) (5-5)
D H = DE + D( PV)  DE
DH = Hproducts – Hreactants
(Constant P &V)
(5-6)
(5-7)
Endothermic reaction: DH positive, products have higher
energy; the reaction needs energy
Exothermic reaction: DH 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. DSuniverse is always positive. For a particular
system, however, DS 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.
DG = DH - T DS
(T, temperature in Kelvin: K= oC + 273)
DG can be negative or positive depending on the change in
enthalpy (DH ) and entropy (DS).
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
kcal/mol)
Exergonic (-686
6CO2 + 6H2O + energy  C6H12O6 + 6O2
kcal/mol) (photosynthesis)
Endogonic (+686
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
DE = DH = 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 DH = 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
DS > 0 (spontaneous)
DS < 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
DS 
final

initial
DS 
final
(Carried thro ugh a reversib le path )

CP
dT (If pro cess occurs at co ntan t press ure)
T
final
CV
dT (If pro cess occurs at co nstant v olume)
T
initial
DS 
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 :
DS(system)  DS(surroundings)  0
DS(isolated system)  0
Thermodynamics
Free-energy…
•Provides a way to determine spontaneity whether system is
isolated or not
•Combining enthalpic and entropic changes
DG  DH - TDS
(Gibbs free energy)
What are the criteria for spontaneity?
Take the case of DH = 0:
DG  - TDS
<0
>0
DG > 0
DG < 0
DG = 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 DG is associated with this search and finding?:
[C][D]
o
DG  DG  RT ln
i.e. DG when A, B,
[A][B]
C, D are mixed in
o
DG is the Standard Free Energy of reaction
their standard state:
DG Rxn
11
 DG  RT ln
11
Biochemistry: 1M,
25oC, pH = 7.0
o
DG Rxn  DG o
Thermodynamics
Now… Suppose we start with equilibrium concentrations:
Reaction will not proceed forward or backward…
DG Rxn  0
Then…
DG  - RT ln
o
[C]eq [D] eq
[A]eq [B] eq
[C]eq [D] eq
[A]eq [B] eq
DG o  - RT ln K eq
K eq  e
Rearranging
0  DG  RT ln
o
K eq  e

o
G
 DRT
 DHo - TDSo 


RT
H
 DRT
 DRS 



K eq   e
 e 



o
o
Thermodynamics
Graph:
o
Ho
 DRT
 DRS 




ln K eq   e  e 




DH o DSo
ln K eq  
RT
R
DSo
R
Van’t Hoff Plot
DH o
Slope = R
ln K eq
1
T
K 
o
-1
Thermodynamics
Summary: in chemical processes
DHo
DSo
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) DSo  Keq
Rxn is favored
4) If DHo < 0: T  Keq
If DHo > 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
DG o  - RT ln K eq
DG o  - 1.98 molcalK 298 K  ln 1000
DG o  - 4.076 Kcal
mol
How about DGRxn…
Spontaneous rxn
[B]
DG Rxn  D G  RT ln
[A]
o

-3

DG Rxn  - 4.076 Kcal

1.98

10
mol
DG 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
DHo ~ 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
Third Example…
Amine Reactions
H
+
R – N – H + H2O  R – NH2 + H3O+
H
DSo  0
not favorable
DH 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)
DS
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…
DSobackbone conf.  R ln 1016
 1.987 16  2.303
 73 molcalK
o
DG obackbone conf.  - TDSo  - 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