Download H - Departamento de Física Geral

Princípios Físicos Aplicados à
Fisiologia (PGF5306-1)
14
Prof. Adriano Mesquita Alencar
Dep. Física Geral
Instituto de Física da USP
ENERGY TRANSFORMATION
B02
Energia
Aula 11
sábado, 5 de outubro de 13
Princípios Físicos Aplicados à
Fisiologia (PGF5306-1)
sábado, 5 de outubro de 13
Entalpia, H
H=
ON
U + RT n
R, é uma constante universal, 8.3145 J/K mol
Em um experimento dessa
bomba de calorímetro com
Etanol, a 298K e volume
constante, 1368 kJ/mol de
calor é liberado
Fig. 1.11 Schematic diagram of a bomb calorimeter. A sample is placed in the reaction
chamber. The chamber is then filled with oxygen at high pressure (>20 atm) to ensure
2 complete.
5 Electrical heating of a wire
2 initiates the reaction.
that the reaction is fast and
The increase in water temperature resulting from the combustion reaction is recorded,
and the temperature change is converted into an energy increase. The energy change is
sábado, 5 de outubro de 13
C H OH(`) + 3O (g) ! 2CO2 (g) + 3H2 O(`)
!1
!1
Entalpia, H
H=
U + RT n
H=
U + 298 · 8.3145 n
H=
U + 2478 n
C2 H5 OH(`) + 3O2 (g) ! 2CO2 (g) + 3H2 O(`)
n=2
H=
3=1
1368000
2478 (J/mol)
Se a variação de entalpia é negativo o processo é
exotérmico. Caso contrario o processo é
endotérmico
sábado, 5 de outubro de 13
Entalpia, H
C2 H5 OH(`) + 3O2 (g) ! 2CO2 (g) + 3H2 O(`)
H
H
H
C
C
H
H
H
O
+3( O
O
H
)
H
+ 2 (O
C
Liquido para Gas = 277
O)
+3(
O
H
Liquido para Gas = 41
((5*415+346+358+464)+277)+3*498
(2*2*805+6*464+(3*41))
ΔHο= -1113 (saindo do estado liquido)
1
ο
ΔH = -1267 (estado gasoso para todos)
C
ΔHο=
-1368 kJ/mol
(Valor de Tabela)
sábado, 5 de outubro de 13
C ! 346
C = C ! 602
C
H
H ! 415
H ! 436
O = O ! 498
C = O ! 1077 em Monoxido
C = O ! 805 em Dioxido
C O ! 358
O
H
H ! 464
Cl ! 432
)
C2 H5 OH(`) + 3O2 (g) ! 2CO2 (g) + 3H2 O(`)
H
H
H
C
C
H
H
H
+3( O
O
H
)
O
H
+ 2 (O
C
O)
+3(
O
H
)
6H + 2C + 7O
átomos
Entalpia
H
H
H
C
C
H
H
H
+3( O
O
H
H
H
C
C
H
H
O
H
O
H
C
C
H
H
gás
liquido
H
C
O
H
H
C
C
H
H
+3( O
O
O
O
+277
+3(
O
H
)
H
H
)
+ 2 (O
1
H
+3(
+ 2 (O
O
O
)
1
C
O)
+3(
-123
H
O)
C
+3(
O
gás
H
H
)
O)
-6004
H
1
sábado, 5 de outubro de 13
+ 2 (O
+4737
H
+3( O
H
H
)
gás
gás
H
1
O
H
H
)
H
)
gás
)
H
+ 2 (O
C
gás
O)
+3(
O
liquido
Bioquímica
• Aproximadamente 1/2 da massa seca do corpo
humano é de proteinas
• O estado nativo das proteínas é “folded”,
empacotado - uma espécie de cristal orgânico
• Mesmo nesse estado existe flutuação na
estrutura do caroço central.
• Estado empacotado - parecido com solido
• Estado desempacotado - parecido com liquido
sábado, 5 de outubro de 13
Table 2.2. Energetics of non-covalent interactions between
molecules
1 kcal
Type of interaction
Equation
Ion–ion
Ion–dipole
Dipole–dipole
Ion–induced dipole
Dispersion
E ¼ q1q2/Dr
E ¼ q„!/Dr2
E ¼ „1„2!0 /Dr3
2
2 4
E ¼ q fi/2Dr r
E ¼ 3h”fi2/4r6
a
= 4.18 kJ
Approximate
magnitude
!1
(kcal mol )
14
!2 to þ2
!0.5 to þ0.5
0.06
0 to 10
Charge q1 interacts with charge q2 at a distance r in medium of dielectric D.
b
Charge q interacts with dipole „ at a distance r from the dipole in medium of dielectric D. !
and !0 are functions of the orientation of the dipoles.
c
Dipole „1 interacts with dipole „2 at an angle q relative to the axis of dipole „2 and a
distance r from the dipole in medium of dielectric D.
d
Charge q interacts with molecule of polarizability at fi distance r from the dipole in medium
of dielectric D.
e
Charge fluctuations of frequency ” occur in mutually polarizable molecules of polarizability
fi separated by a distance r.
The data are from Table 1.1 of van Holde (1985).
sábado, 5 de outubro de 13
Charge q interacts with molecule of polarizability at fi distance r from the dipole in medium
of dielectric D.
e
Charge fluctuations of frequency ” occur in mutually polarizable molecules of polarizability
fi separated by a distance r.
The data are from Table 1.1 of van Holde (1985).
Bioquímica
Table 2.3. Characteristics of hydrogen bonds of biological importance
Bond type
Mean bond
distance (nm)
O–H . . . O
O–H . . . O!
...
O–H N
Nþ–H . . . O
N–H . . . O
N–H . . . N
...
HS–H SH2
0.270
0.263
0.288
0.293
0.304
0.310
—
!1
Bond energy (kJ mol )
!22
!15
!15 to !20
!25 to !30
!15 to !25
!17
!7
The data are from Watson (1965).
ideal case all amino acid side chains are completely exposed to
solvent (Table 2.4).
The
non-covalent interactions that stabilize folded protein strucsábado, 5 de outubro de
13
Table 2.4. Principal features of protein structure
Folded (native) state
Highly ordered polypeptide
chain
Intact elements of secondary
structure, held together by
hydrogen bonds
Intact tertiary structure contacts,
as in an organic crystal, held
together by van der Waals
interactions
Limited rotation of bonds in the
protein core
Desolvated side chains in protein
core
Compact volume
Unfolded (denatured)
state
Highly disordered chain
– “random coil”
No secondary structure
No tertiary structure
Free rotation of bonds
throughout polypeptide chain
Solvated side chains
Greatly expanded
volume
results from the concurrent breaking of a large number of weak
sábado, 5 de outubro de 13
SOME EXAMPLES FROM BIOCHEMISTRY
temperature at which a protein unfolds (or double-stranded
elts) is called the melting temperature, Tm. This temperature
s not only on the number and type of non-covalent bonds in
ed state but also on the pH and other solution conditions. Tm
pends on the pressure, but most biological science experire done at 1 atm pressure. In the case of proteins, changing
5 de outubrochanges
de 13
ofsábado,
solution
the net charge on the protein surface.
Fig. 2.7 Enthalpy of unfolding of hen
egg white lysozyme as a function of
transition temperature. Filled
symbols: intact lysozyme. Open
symbols: lysozyme in which one of
the four native disulfide bonds has
been removed. When folded, 3-SS
lysozyme closely resembles the
native state of intact lysozyme.
Change in transition temperature
was induced by a change of pH.
Note that 1H is approximately
linear in Tm. The data are from
Cooper et al. (1991).
45
Fig. 2.8 Isothermal titration
calorimeter. The temperature is
constant. There are two identical
chambers,
the sample cell and the
Isothermal
titration
reference cell. In most cases, the
ter. The
temperature is
sample cell will contain a
. Theremacromolecule,
are two identical
and the syringe/
stirrer is used
inject
a ligand into
s, the sample
cell toand
the
sample cases,
cell. Thethe
syringe is
e cell. the
In most
usually coupled to an injector
cell willsystem
contain
a
under software control and
olecule,rotated
and the
syringe/speed. The
at a constant
reference
is filledinto
with buffer;
used to
inject cell
a ligand
no reaction occurs there. 1T
ple cell.measures
The syringe
is
the temperature
oupleddifference
to an injector
between cells, which are
surroundedcontrol
by insulation
under software
andto
minimize heat exchange with the
at a constant speed. The
surroundings. Electronic (power
e cell isfeedback)
filled with
buffer;
circuitry
minimizes 1T
on a continuous
basis. If injection of
ion occurs
there. 1T
ligand results in binding, there will
s the temperature
ordinarily be a change in the
e between
cells, ofwhich
are The
temperature
the sample.
of the change
ded by sign
insulation
to will depend on
whether the reaction is exothermic
e heat exchange
with the
or endothermic. An experiment
dings. Electronic
(power injections
consists of equal-volume
from the
syringe into
the sample
k) circuitry
minimizes
1T
tinuouscell.
basis. If injection of
sults in binding, there will
y be a change in the
sábado,
outubro
de 13 The
ture
of5 de
the
sample.
What if we’re interested in the energetics of an enzyme binding
to its substrate? This can be measured if a suitable substrate analog
can be found or the enzyme can be modified. For instance, ITC has
been used to measure the enthalpy of binding of a small compound
called 20 -cytidine monophoshate (20 CMP) to ribonuclease A, which
hydrolyzes RNA to its component nucleotides. 20 CMP binds to and
inhibits the enzyme. If the enzyme of interest is, say, a protein
phosphatase with a nucleophilic cysteine in the active site, mutation of the Cys to Ser or Asn will abolish catalytic activity, as in the
What
if we’re interested in the energetics of an enzyme bind
N-terminal domain of the cytoskeleton-associated protein tensin,
to itsand
substrate?
Thisofcan
be measured
if a suitable
substrate ana
the energetics
binding
can be studied.
A deeper underof binding
be sought
in be
Chapters
5 and 7.For instance, ITC
can standing
be found
or thewill
enzyme
can
modified.
Fig. 2.10 Differential scanning
calorimetry. (A) Schematic diagram
of the instrument. In
this case the reference cell contains
buffer only, and the sample cell
contains the macromolecule
dissolved in buffer. Both cells are
!1
heated very slowly (e.g. 1 " C min )
in order to maintain equilibrium,
and feedback electronic circuitry is
used to add heat so that 1T # 0
throughout the experiment. Other
types of DSC have been used for
other purposes in biophysics, for
example, to investigate the
physiological limits of the freeze
tolerance and freeze-avoidance
strategies taken by different insect
species to survive subzero
temperatures. (B) Data. The heat
added to keep 1T # 0 can be
plotted as a function of
temperature. The endothermic
peak corresponds to heat absorbed,
for example, on protein
denaturation. The peak maximum
corresponds roughly to the
transition temperature, or melting
temperature. The area below the
peak is 1Hd(Tm). The heat capacity
of the unfolded state of a protein
minus the heat capacity of the
folded state is 1Cp,d. There is more
about DSC in Chapter 5.
sábado, 5 de outubro de 13
Hidratação e desidratação iônica ocorre
constantemente nos canais/bombas de íons e na
transmissão de impulsos nervosos.
Table 2.5. Standard ion hydration enthalpies
Hþ
þ
Li
Naþ
þ
K
—
NH4þ
#1090
#520
#405
#321
—
#301
Mg2þ
2þ
Ca
Ba2þ
2þ
Fe
2þ
Zn
Fe3þ
#1920
#1650
#1360
#1950
#2050
#4430
The data refer to Xþ(g) ! Xþ(aq) at 1 bar and are from Table 2.6c in Atkins (1998). 1 bar ¼ 10 5
Pa ¼ 105 N m#2 ¼ 0.987 atm. 1 Pa ¼ 1 pascal. Blaise Pascal (1623–1662) was a French scientist
and religious philosopher.
H. Heat capacity
sábado, 5 de outubro de 13
Energias
Energias mais relevantes para
sistemas biológicos:
1. Energia Química
2. Energia Mecânica
3. Energia Eletromagnética
4. Energia Térmica
sábado, 5 de outubro de 13
Fotossíntese
Energias
Energias mais relevantes para
sistemas biológicos:
1. Energia Química
2. Energia Mecânica
3. Energia Eletromagnética
4. Energia Térmica
Deterministicas
Movimento Browniano
Térmicas
A razão entre a escalas
derteminísticas e termicas é:
Forcas no interior da célula
sábado, 5 de outubro de 13
Edet /kB T
A razão entre a escalas
derteminísticas e termicas é:
Edet /kB T
kB T = 4.1 pN nm
= 0.6 kcal/mol
= 2.5 kJ/mol
= 25 meV
1010
Electrostatic energy
of a spherical shell
105
Bending of
a 20:1 rod
ENERGY ( joules)
100
10
Fracture of
a 20:1 rod
5
10
10
10
15
10
20
10
25
10
30
Proton
Nucleus
Chemical
bonds
Thermal energy
Binding energy of an
electron in a box
10
15
10
12
10
9
10
6
10
3
100
LENGTH (meters)
Maquinaria
molecular:
de Hidrogênio
(quadrado),
grupos
fosfato
emmechanical,
ATP (triângulo),
Figure 2. The
confluence Ligação
of energy scales
is illustrated in this
graph, which shows
how de
thermal,
chemical,
and
electrostatic
energies associated
with an
object scale
with
size. As the
characteristic
object de
size approaches
that
at which energia
moligações
covalentes
(círculo),
energia
de
torção
(azul),
energia
fratura
(verde),
lecular machines operate (shaded), all the energies converge. The horizontal line shows the thermal energy scale kT which, of
eletrostática
and
R. Quake,
Physics
Today (2006)]
course, does(laranja).
not depend[Rob
on an Phillips
object’s size.
We Stephen
estimate binding
energy (purple)
by considering
an electron in a box; for com-
parison, the graph shows measured binding energies for hydrogen bonds (square), phosphate groups in ATP (triangle), and cosábado, 5 de
outubro
de 13 (circle), along with characteristic energies for nuclear and subatomic particles. In estimating the bending energy
valent
bonds
OH
H
OH
H
A
A
A
A
Geração de Energias (Glicolise)
P P P
P P
P P P
2
2
2
A
P P P
A
N
P P
P P
2
N
A
4
Carbohydrate
Metabolism
A
151
A. Glycolysis: balance
O
O
O
8
P
O
C
HC
H
P
HC
H
2
O
O
C CH2
HO
2
P P
2
2
A
P
1
6
lucose 6-phosphate
omerase 5.3.1.9
-Phosphofructonase 2.7.1.11
ructose bisphosphate
dolase 4.1.2.13
riose-phosphate
omerase 5.3.1.1
-20
Glyceraldehyde3- P dehydrogenase 1.2.1.12
7
Phosphoglycerate
O 2.7.2.3
O
kinase
8
Phosphoglycerate
8
HC5.4.2.1
O P
mutase
C
H2C OH
Phosphopyruvate
hydratase 4.2.1.11
2 2-Phosphoglycerate
Pyruvate
kinase
10
2.7.1.40
9
sábado, 5 de outubro de 13
2 H 2O
A
H2C
P
O
CH2
O
A
OH
C
P
Glyceraldehyde2
3-phosphate
COO
COO
C
C
O
CH3
O
CH3
Glycerone
P P P
3-phosphate
Pyruvate
Pyruvate
O
CH2
H1
OH H
H
OH
2
P P
A
P P P
P P P
2
A
HC
H2C
O
P P
O
glycerate
A
2
P P
P
∆G' (kJ · mol-1)
N
A
7
3-Phospho2-80
A
P
4
OH
N
P P
A
P P
P P P
P P
3
-60C
P P P
A
P
A
A
A
CH2
OH
O
H HO
CH2 O
H
O
2
A
A
2
O
P
Pyruvate possui
H HO
2
3
grande valor
CH OH
H
OH H
OH H
energético e pode
ser utilizado para
2
2
4
produzir mais ATP.
Assim, uma
5
8
9
O
H
O
O
molécula
de glicose
C
C
H C OH
5 pode
6
HC OH
HC 6OH 7
C O gerar até 30
10 C O
H
HC O
O CH
ATPs.
2
Glycerone
1,3-BisphosphoGlyceraldehyde
P P P
P P
-40
Steps 1, 3 and 10
2
OHin
are CH
bypassed
O
gluconeogenesis
O
P
A
O OH
HO
Fructose
1,6-bisphosphate
Fructose
6-phosphate
A
A
9
H C O P
∆GOI = 2–35 kJ · mol–1
P
P P
H
P P P
exokinase 2.7.1.1
N
5
Glycolysis
2
H
H
H OH
Pyruvate
P P P
2
OH
0 Glucose
6-phosphate
Glucose
HO
A
C
C. Energy profile
CH3
spholpyruvate
2
H
HC
P
glycerate
Glucose
OH H
H2
O
A
6
O
CH HO O OH
10
P
N
H
OH
1,3-Bisphospho2 A
B. Reactions
O
P
2
OH
H2C
HO
glycerate
2 H 2O
O
OH H
2 3-Phospho-
hosphocerate
O OH
H7
O
O
C
CH2
HO
OH
H2C
OH
O
2
P
A
2
P
P
2
P
P P P
2
glycerate
3-phosphate
Pyruvate
C. Energy profile
3-phosphate
Koolman, Color Atlas of Biochemistry, 2nd edition © 2005 Thieme
Geração de Energias
sábado, 5 de outubro de 13
Armazenamento de Energias
kB T = 4.1 pN nm
= 0.6 kcal/mol
= 2.5 kJ/mol
ATP
= 25 meV
C
C ! 346 kJ/mol
C = C ! 602
C
H
H ! 415
H ! 436
O = O ! 498
Pi





AT P + H2 O ! ADP + Pi
sábado, 5 de outubro de 13
ADP
30.5 >
Go >
50 kJ/mol
A. ATP: structure
Phosphoric acid
ester bond
N
O
O
O
Pβ O
Pα O
O
O
O
CH2
O
H H
H
H
O
O
OH OH
Pβ O
Pα O
O
O
1. Formula
Mg
2. Mg2
C
N
Pγ O
O
C
HC
O
CH2
O
H
H
C
N
bond
N
CH
γ
β
Ribose
α
Phosphate residue
OH
-Complex
N-glycosidic
NH2
Adenine
Phosphoric acid
anhydride bonds
Adenosine
B. Hydrolysis energies
P
P
P
+
P
P
1. Hydrolysis energies
C. Types of ATP formation
+
Adenosine
AMP
+
-30
sábado, 5 de outubro de 13
4
P
ATP
-20
+
ADP
-10
3
P
ATP
∆G OI
kJ · mol-1
2
ATP
1
P
P
P
1
2
3
Positive
Neutral
Negative
2. ATP: charge density
Koolman, Color Atlas of Biochemistry, 2nd edition © 2005
Electrons
ATP-ADP ~ varias tipos de reações bioquímicas
ATP-ADP ~ 20 kBT
Ligação covalente típica ~ 150 kBT
NADP+
sábado, 5 de outubro de 13