FYTN05/TEK267 Chemical Forces and Self Assembly

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1 FYTN5/TEK267 Chemical Forces and Self Assembly CBB - victor.olariu@thep.lu.se CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 1

2 Introduction - Chapter 8 Reading material: Chapter 8 from Nelson Book, also subchapters 3.2.4, 6.6.2, 1.3.2, and Exercises: Exercises from Nelson: 8.2, 8.3, 8.5 and 8.6 Additional exercises from extra exercises file, addresses how to develop ODE models for different reactions. The course structure: Chemical otential Chemical Reaction Dissociation Self Assembly CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 2

3 Energy Release Energy is release when AT binds and lose a phosphate group Thermal energy 1 K B T can be used to move an object 1 nm opposing a force of 4 piconewtons CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 3

4 Cell Dynamics CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 4

5 Inside Cell Dynamics - Gene Regulatory Networks NANOG GATA6 SOX2 OCT4 SOX NANOG GATA OCT SOX2 CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 5

Inside Cell Dynamics - Signaling Cancer & Stem Cell Signaling athways Oxidative Stress, Infections, TNF-D, IL-1, Growth Factors I3K MAK/ERK JAK-STAT Cytokines & Survival Factors (IGFs, FGFs) Notch

RKI Apoptosis Smad4 E-Cat Gli NUMB p53 E-Cat BMR-II ActR-IIA ActR-IIB Smad1/5/8 Smad2/3 Intracellular Vesicle Ras GSK-3E ALK2 ALK3 ALK6 TGF-E RII Axin AC E-Cat STAT3 INB NF-NB INB TGF-E LGR Dsh Smo

6 Inside Cell Dynamics - Signaling Cancer & Stem Cell Signaling athways Oxidative Stress, Infections, TNF-D, IL-1, Growth Factors I3K MAK/ERK JAK-STAT Cytokines & Survival Factors (IGFs, FGFs) Notch J-Secretase BM ALK4 ALK7 Axin ActR-IIA ActR-IIB CK1 GSK-3E ALK1 ALK5 Smad2/3 Notch Intracellular Domain [NICD] RIN1 AKT Bad GSK-3E Ub Ub Ub Ub Smad6/7 SUFU Smad1/5/8 Degradation E Cat Raf MDM2 GSK-3E RKI Apoptosis Smad4 E-Cat Gli NUMB p53 E-Cat BMR-II ActR-IIA ActR-IIB Smad1/5/8 Smad2/3 Intracellular Vesicle Ras GSK-3E ALK2 ALK3 ALK6 TGF-E RII Axin AC E-Cat STAT3 INB NF-NB INB TGF-E LGR Dsh Smo roteolytic cleavage by J-Secretase & Metalloproteases STAT3 SHI1/TEN IKK R-spondin Frizzled Grb2 AKT Smo LR SOS atched JAK Frs2 Smad Activin/ Nodal Wnt Wnt Shh I2 I3 I3K Hedgehog Delta, Jagged EGFR LIFR gp13 IL-6R RTK RTK Notch Cytokines & Growth Factors (EGF, DGF, LIF, IL-6) Cytokines & Growth Factors (EGF, FGFs, DGF) Tra ns loc ati on NF-NB Adipogen International Schützenstrasse 12 t CH-441 Liestal t Switzerland TEL: t FAX: info@adipogen.com t E-Cat KA MAK/ERK E-Cat Smad2/3 NF-NB Smad4 NF-NB Family p5/p15 p52/p16 C-Rel, RelA, RelB Smad2/3 MK1-3 Stemness Maintenance, Survival, roliferation Smad1/5/8 MAML NICD Gli Smad4 CSL STAT3 STAT3 Smad1/5/8 E-Cat TCF/Lef C Y TO L A S M 4 Sm ad Sm 4 ad 1/5 /8 TF ad ad Stemness Maintenance, Survival, roliferation, Differentiation Sm Fos Sm Jun Ac TF MAK/ERK 2/3 NF-NB FYTN5/TEK267 Chemical Forces and Self Assembly AR 213 NUCLEUS CBB - victor.olariu@thep.lu.se 6

7 Inside Cell Dynamics - Signalling LIF BM4 15 OCT4 SOX2 NANOG LIF+BM4 15 OCT4 SOX2 NANOG 2i Concentration Time x Time x 1 4 CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 7

8 Introduction Chapter 8 Motivation: Even in a well-stirred environment the deviation from molecular concentration equilibrium gives rise to a chemical force. Chemical reactions take place and the system exchanges energy, particles with outside world or within the system To account for the exchange between different particles types one uses the chemical potential - µ CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 8

9 Chemical otential - µ We consider a system with: Energy E, Entropy S(E, {N α }) Number of particles of species α N α,α=1,2,... Temperature 1 T = ds de Nα Chemical otential µ α = T ds dn α E,Nβ,α β µ α represents the availability of particles of species α Temperature gradient characterizes the force driving energy transfer otential gradient characterizes the force driving particle type transfer Chemical Equilibrium µ α = µ β CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 9

10 Gradient Example - Free Energy FE = E T S A B.8 low T high T X C free energy.4 D X Y E X Free energy 2 2 Free energy Y X Y.5 X 1 1 CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 1

11 Chemical otential µ Ideal Gas Example total energy is fixed and molecules have internal energy ɛ E = E kin + N αɛ α α ds dn = ds E dn ɛ ds Ekin de kin N Sakur -Tetrode equation from 6.6 µ = k B T ln( c c ) + µ (T, ɛ,...) c reference concentration, µ standard chemical potential A molecular species is highly available if its concentration c is large or its internal energy ɛ is large CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 11

12 Chemical otential - µ Equilibrium between two containers A and B exchanging energy and particles T A = T B µ A = µ B > (c A = c B ) robability of a small system embedded in a big system to be in state j regardless of the big system is j = e ( (E j µn j ) k B T ) j e( (E j µn j ) k B T ) Gibbs grand canonical distribution. CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 12

13 Chemical Reactions Two state isolated system X 1 X 2 G = µ 2 µ 1 G < (µ 1 > µ 2 ) = 1 2 G > (µ 1 < µ 2 ) = 2 1 At equilibrium G = = k B T ln( c2 c ) + µ 2 k B T ln( c1 c ) µ 1 ln( c2 ) = µ 1 µ 2 c 1 k B T The equilibrium constant K eq c µ 1 µ 2 2 k c 1 = e B T reaction rates are proportional to concentration of reactants and depend on activation barriers equilibrium concentrations depend on potential differences CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 13

14 Chemical Reactions - Modelling For the reaction A + B k f k ba C Deterministic description: δc A δt Stochastic Description: = k f C A C B + k ba C C Gillespie algorithm: select randomly the reaction type and reaction time CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 14

15 Chemical Reactions - A + B k f k ba C Statistical equilibrium: forward rate equals backward rate CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 15

16 Chemical Reactions - Example for burning Hidrogen 2H 2 + O 2 2H 2 O In equilibrium, entropy should be at maximum: no change in S tot. G = 2µ H2 O 2µ H2 µ 2 For an isolated system S tot = G T =, thus the Gibbs free energy should be at minimum. Equilibrium condition : (2µ H 2 O 2µ H µ 2 ) 2 k where k eq = e B T T is small k eq >> 1 H 2, O (c H2 O)2 (c H2 ) 2 c O2 = k eq c if T is large k eq << 1 H 2, O 2 if CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 16

17 Chemical Reactions - Generalisation Consider k reactants and m k products then G < forward reaction G > backward reaction G = Equilibrium The standard free energy change [X ν k+1 νm k+1 ]...[Xm ] [X ν 1 1 ]...[X ν k = k k ] eq = e G k B T CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 17

18 Multiple Chemical Reactions - A k 1+ k 1 B k 2+ k 2 C The equilibrium constants: K eq c C ca K eq1 c B ca K eq2 c C cb = c Bk eq2 c B k eq1 = e = e G 1 k B T G 2 k B T ( G 1 + G 2 ) k = k eq1 k eq2 = e B T CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 18

19 THANK YOU! CBB - victor.olariu@thep.lu.se FYTN5/TEK267 Chemical Forces and Self Assembly 19

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