FYTN05/TEK267
Chemical Forces and Self Assembly
Victor Olariu
CBBP - [email protected]
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
CBBP - [email protected]
1
Introduction - Chapter 8
Reading material: Chapter 8 from Nelson Book, also subchapters
3.2.4, 6.6.2, 10.3.2, 10.3.3 and 10.4.1
Exercises:
I
Exercises from Nelson: 8.2, 8.3, 8.5 and 8.6
I
Additional exercises from extra exercises file, addresses how to
develop ODE models for different reactions.
The course structure:
I
Chemical Potential
I
Chemical Reaction
I
Dissociation
I
Self Assembly
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
CBBP - [email protected]
2
Energy Release
Energy is release when ATP binds and lose a phosphate group
Thermal energy 1 KB T can be used to move an object 1 nm
opposing a force of 4 piconewtons
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
CBBP - [email protected]
3
Cell Dynamics
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
CBBP - [email protected]
4
Inside Cell Dynamics - Gene Regulatory Networks
NANOG
GATA6
SOX2
OCT4
1
SOX17
0.5
8
6
0
8
4
6
NANOG
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
GATA6
4
2
2
OCT4
0
0
SOX2
CBBP - [email protected]
5
Inside Cell Dynamics - Signaling
Cancer & Stem Cell Signaling Pathways
Oxidative Stress,
Infections,
TNF-D, IL-1,
Growth Factors
PI3K
MAPK/ERK
JAK-STAT
Cytokines &
Survival Factors
(IGFs, FGFs)
P
P
P
Notch
J-Secretase
BMP
ALK4
ALK7
P
P
Axin
ActR-IIA
ActR-IIB
CK1
P
GSK-3E
ALK1
ALK5
P
P
Smad2/3
Notch Intracellular
Domain [NICD]
RIN1
P
AKT
P
Bad
GSK-3E
Ub
Ub
Ub
Ub
P
P
P
P
Smad6/7
SUFU
Smad1/5/8
Degradation
ECat
Raf
MDM2
GSK-3E
RKIP
Apoptosis
Smad4
E-Cat
Gli
NUMB
P
p53
E-Cat
BMPR-II
ActR-IIA
ActR-IIB
Smad1/5/8
Smad2/3 P
Intracellular
Vesicle
Ras
GSK-3E
ALK2
ALK3
ALK6
TGF-E RII
P
Axin APC
E-Cat
P
STAT3
INB
NF-NB
INB
TGF-E
LGR
Dsh
Smo
Proteolytic cleavage
by J-Secretase &
Metalloproteases
STAT3
SHIP1/PTEN
IKK
R-spondin
Frizzled
P
Grb2
AKT
Smo
LRP
SOS
P
P
Patched
JAK
Frs2
P
P
Smad
Activin/
Nodal
Wnt
P
P
Wnt
Shh
PIP2 PIP3
PI3K
Hedgehog
Delta, Jagged
EGFR
LIFR
gp130
IL-6R
RTK
RTK
Notch
Cytokines &
Growth Factors
(EGF, PDGF, LIF, IL-6)
Cytokines &
Growth Factors
(EGF, FGFs, PDGF)
Tra
ns
loc
ati
on
NF-NB
Adipogen International
Schützenstrasse 12 t CH-4410 Liestal t Switzerland
TEL: +41-61-926-60-40 t FAX: +41-61-926-60-49
E-Mail: [email protected] t www.adipogen.com
E-Cat
PKA
MAPK/ERK
P
E-Cat
Smad2/3
NF-NB
Smad4
P
NF-NB Family
p50/p150
p52/p160
C-Rel, RelA, RelB
Smad2/3
MKP1-3
Stemness Maintenance,
Survival, Proliferation
P
Smad1/5/8
MAML
NICD
Gli
Smad4
P
CSL
STAT3
STAT3
Smad1/5/8
E-Cat
TCF/Lef
P
P
C Y TO P L A S M
4
Sm
ad
Sm 4
ad
1/5
/8
TF
ad
ad
Stemness Maintenance,
Survival, Proliferation,
Differentiation
Sm
Fos
Sm
Jun
Ac
TF
MAPK/ERK
2/3
P
P
NF-NB
www.adipogen.com
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
APR 2013
NUCLEUS
CBBP - [email protected]
6
Inside Cell Dynamics - Signalling
LIF
BMP4
150
2i
LIF+BMP4
OCT4−SOX2
150
Concentration
NANOG
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
NANOG
100
100
50
50
0
0
0.5
1
OCT4−SOX2
1.5
2
Time
2.5
3
0
0
3.5
4
x 10
0.5
1
1.5
Time
2
4
x 10
CBBP - [email protected]
7
Introduction Chapter 8
Motivation:
I
Even in a well-stirred environment the deviation from
molecular concentration equilibrium gives rise to a chemical
force.
I
Chemical reactions take place and the system exchanges
energy, particles with outside world or within the system
I
To account for the exchange between different particles types
one uses the chemical potential - µ
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
CBBP - [email protected]
8
Chemical Potential - µ
We consider a system with:
I
Energy E , Entropy S(E , {Nα })
I
Number of particles of species α Nα,α=1,2,...
dS 1
Temperature T = dE Nα
dS Chemical Potential µα = −T dNα I
I
E ,Nβ ,α6=β
µα represents the availability of particles of species α
I
Temperature gradient characterizes the force driving energy
transfer
I
Potential gradient characterizes the force driving particle type
transfer
I
Chemical Equilibrium µα = µβ
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
CBBP - [email protected]
9
Gradient Example - Free Energy
= E −T ·S
FE
A
B
0.08
low T
high T
free energy
X
C
X
Y
0
0
D
0.2
0.4
X
0.6
0.8
1
E
3
2
2
1
0
1
2
2
1
0
1
1
1
0.5
0.5
Y
3
4
Free energy
4
Free energy
0.04
0 0
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
X
0
0.5
Y
0.5
0 0
0
X
CBBP - [email protected]
10
Chemical Potential µ – Ideal Gas Example
total energy is fixed and molecules have internal energy E
=
Ekin +
X
Nα α
α
dS dN E
=
dS dS −
dN Ekin
dEkin N
Sakur -Tetrode equation from 6.6
µ = kB · T · ln(
c
) + µ0 (T , , ....)
c0
c0 reference concentration, µ0 standard chemical potential
A molecular species is highly available if its concentration c
is large or its internal energy is large
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
CBBP - [email protected]
11
Chemical Potential - µ
Equilibrium between two containers A and B exchanging energy
and particles
TA = TB
µA = µB − − > (cA = cB )
Probability of a small system embedded in a big system to be in
state j regardless of the big system is
Pj
=
e
P
(
−(Ej −µNj )
)
kB T
je
(
−(Ej −µNj )
)
kB T
Gibbs grand canonical distribution.
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
CBBP - [email protected]
12
Chemical Reactions
Two state isolated system X1 X2 ∆G = µ2 − µ1
I ∆G < 0(µ1 > µ2 ) =⇒ 1 → 2
I ∆G > 0(µ1 < µ2 ) =⇒ 2 → 1
At equilibrium ∆G = 0
ln(
0
=
kB · T · ln(
c2
)
c1
=
µ01 − µ02
kB · T
c2
c1
) + µ02 − kB · T · ln( ) − µ01
c0
c0
0
µ0
1 −µ2
The equilibrium constant Keq ≡ cc12 = e kB ·T
I reaction rates are proportional to concentration of reactants
and depend on activation barriers
I equilibrium concentrations depend on potential differences
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
CBBP - [email protected]
13
Chemical Reactions - Modelling
For the reaction A + B kkfba C
Deterministic description:
δCA
= −kf CA CB + kba CC
δt
Stochastic Description:
I
Gillespie algorithm: select randomly the reaction type and
reaction time
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
CBBP - [email protected]
14
Chemical Reactions - A + B kkfba C
Statistical equilibrium: forward rate equals backward rate
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
CBBP - [email protected]
15
Chemical Reactions - Example for burning Hidrogen
2H2 + O2 → 2H2 O
In equilibrium, entropy should be at maximum: no change in Stot .
∆G = 2µH2 O − 2µH2 − µ02
For an isolated system ∆Stot = − ∆G
T = 0, thus the Gibbs free
energy should be at minimum.
(cH
O )2
Equilibrium condition : (c 2)2 c
H2
O2
=
keq
c0
0
0
−(2µ0
H2 O −2µH2 −µ02 )
kB T
where keq = e
if T is large keq << 1 → H2 , O2 if
T is small keq >> 1 → H2 , O
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
CBBP - [email protected]
16
Chemical Reactions - Generalisation
Consider k reactants and m − k products then
I
I
I
∆G < 0 → forward − reaction
∆G > 0 → backward − reaction
∆G = 0 → Equilibrium
The standard free energy change
ν
k+1
[Xk+1
]...[Xmνm ]
ν
ν1
[X1 ]...[Xk k ]
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
= keq = e
−∆G 0
kB T
CBBP - [email protected]
17
k2+
Multiple Chemical Reactions - A kk1+
B
k2− C
1−
The equilibrium constants:
Keq ≡
cC
cA
=
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
Keq1 ≡
cB
cA
=e
∆G10
kB ·T
Keq2 ≡
cC
cB
=e
∆G20
kB ·T
cB keq2
cB
keq1
= keq1 keq2 = e
−(∆G10 +∆G20 )
kB ·T
CBBP - [email protected]
18
THANK YOU!
Victor Olariu
FYTN05/TEK267 Chemical Forces and Self Assembly
CBBP - [email protected]
19