Interactions between proteins, DNA and RNA. The energy, length and time coordinate system to find your way in the cell

Transcription

1 Interactions between proteins, DNA and RNA The energy, length and time coordinate system to find your way in the cell

2 Scanning/atomic force microscope (SFM/AFM) mirror laser beam photo diode fluid cell fluid in fluid out O-ring sample piezo scanner

3 Movement of the SFM tip along the sample SFM tip superhelical DNA plasmid Path of SFM tip DNA double helix Mg 2+ Mg 2+ Mg 2+ Mg 2+ Mg 2+ Mg 2+ negatively charged mica surface

4 SFM image of a 6.8 kb superhelical plasmid

5 E. coli RNA polymerase at the promoter of a 1036 bp DNA

6 RNA polymerase finds its promoter by sliding along the DNA as visualized by SFM DNA E. coli RNA polymerase Guthold, M. et al. (1999). Direct observation of one-dimensional diffusion and transcription by escherichia coli RNA polymerase. Biophys J 77,

7 Synthesis of RNA by E.coli RNA polymerase immobilized on the surface, Example 1 E. coli RNA polymerase DNA Kasas, Guthold, Bustamante, C.

8 Synthesis of RNA by E.coli RNA polymerase immobilized on the surface, Example 2 E. coli RNA polymerase DNA Kasas, Guthold, Bustamante, C.

9 Synthesis of RNA by E.coli RNA polymerase immobilized on the surface, Example 3 E. coli RNA polymerase DNA Kasas, Guthold, Bustamante, C.

10 Different intermediates in the transcription initiation process

11 Reaction mechanism of transcription by yeast RNA polymerase II Cramer/Lab-Cramer-Publications/txnmovie.mov

12 Intermediate steps during transcription that could be rate limiting for gene expression Scheme: Michael Thomm

13 Why is it important to study kinetics? a) Thermodynamic versus kinetic control b) Understanding the reaction mechanism Reaction 1 (green) is the faster reaction since the activation energy is lower. => P1 is the kinetic product. Reaction 2 (blue) generates a more stable product => P2 is the thermodynamic product.

14 Kinetic analysis of two different promoters (McClure) lag time (sec) until RNA is detected promoter 1 promoter 2

15 Calculating reaction kinetics

16 A very, very simple reaction A d[a] dt k on B = k [A] d[a] [A] = k dt k on in s -1 is the reaction rate constant 1 k =τ decay time of the reaction rate equation for decrease of A over time separate variables 1 [A] d[a] = k dt integrate ln[a] = kt + constant succesful integration! but what about the constant?

17 A simple reaction, 2nd try [ A] t [ A] 0 1 [A] t 0 d[a] = k dt boundary condition: at t = 0 the initial concentration of A is [A]0 we already know the indefinite integral and we calculate it with our boundaries ln[a] = kt + constant ( ln[a] t ln[a] ) 0 = kt k0 and ln[a] t = kt ln[a] 0 ln [A] t [A] 0 and = kt [A] t = [A] 0 e kt hurray!

18 Irreversible bimolecular reaction A + B k on AB k on in M -1 s -1 or liter mol s d[ab] dt = k on [A] [B] separating three variables is not good... x = ([A] 0 [A] ) t = ([B] 0 [B] ) t but we can do a trick... 1 ( ) ln [B] [A] 0 t [A] 0 [B] 0 [A] 0 [B] t = kt to get something useful

19 Reversible bimolecular reaction AB k off k on A+B k off in s -1 is the reaction rate constant for dissociation k on in M -1 s -1 is the reaction rate constant for binding k off k on = K d 1 k off =τ relation to the equilibrium dissociation constant decay time of the complex d[ab] dt = k on [A] [B]-k off [AB] rate equation for complex formation, can be solved but it is already difficult

20 The simple Michaelis-Menten reaction k k E + S +1 ES +2 E + P k k -1-2 e 0 -x s 0 -x p x p dx dt = k +1 e 0 x ( ) s 0 x p ( ) k -1 x k +2 x+k -2 e 0 x ( ) p dp dt = k +2 x k -2 e 0 x ( ) p The second equation can be used to express x and dx/dt in dependence of p and dp but the resulting equation has no solution in p and t simplifications like s0 >> e0 or dx/dt = constant

21 But can you calculate how ATP consuming chromatin remodeling complexes translocate nucleosomes? transcription blocked blocked transcription ATP hydrolysis in vitro: 2-5 s nucleosome translocation (3-5 bp) in vitro: ~20 s

22 Chromatin remodeling complexes are diverse and abundant ATPase subfamilies with many members Diversity of chromatin remodeling complexes Different complexes different additional subunits MOTOR Motor exchange within the same ATPase subfamily Splice variants of complex subunits A B C A B C A B C adapted from Owen-Hughes, NAR 2006 Figure by Gernot Längst

23 Different chromatin remodeler position nucleosomes to different sites on the same substrate (hsp70 promoter) - Brg1 Chd1 ISWI Snf2H Mi-2 ACF NURF N1 N2 N3 N4 N4 DNA Rippe, Schrader, Riede, Strohner, Lehmann & Längst (2007). PNAS 104,

24 Nucleosome translocation as a Michaelis-Menten reaction E + S k +1 ES k +2 (or k cat ) E + P k -1 E: enzyme = remodeler S: substrate = nucleosome at initial position P: product = translocated nucleosome P could sever as the substrate for a new translocation cycle K M = k -1+k +2 k 1 = dissociation rates of ES formation rate of ES in mol liter concentration of substrate at which half the active sites of the enzyme are filled "reaction efficiency" = k cat K M = catalysis rate binding site saturation high kcat = good catalysis rate low KM = good binding of substrate to enzyme

25 Copasi ( to the rescue: Numerical simulations of binding kinetics (Question 2 and 3) Standard conditions R + N i-1 R + N i R + N i+1 k on,i-1 = k on,i = k on,i+1 = 10 8 M-1 s-1 K d,i-1 K d,i K d,i+1 k off,i-1 = k off,i = k off,i+1 = 0.1 s -1 RN i-1 RN i RN i+1 k i-1 k i+1 K d = k off /k on =10-9 M k i-1 = k i+1 =k -i = k i = 1 s -1 k i k -i N i = M R = M

26 Standard conditions: koff = 0.1 s -1 concentration (M) Ni Ni+1 Ni-1 time (s)

27 10x reduced binding affinity at Ni+1: koff,i+1 = 1 s -1 Ni Ni+1 concentration (M) Ni-1 time (s) this works perfect and is beautifully simple

28 Karsten s good and bad substrate model for nucleosome translocation E + S k +1 k -1 ES "reaction efficiency" = k cat K M = k +2 (or k cat ) E + P catalysis rate binding site saturation good nucleosome substrates: - high remodeler binding affinity (= low KM) - high translocation rate away from this position (= high kcat) => high kcat/km bad nucleosome substrates: - low substrate binding affinity (= high KM) - low translocation rate away from this position (= low kcat) => low kcat/km Hypothesis: The remodeler move good substrate nucleosomes (high kcat/km) to positions where they are bad substrates (low kcat/km)

29 Two mechanisms to time (sec) release model low remodeler binding affinity at position N i+1 N i+1 Concentration (nm) release model N i N i-1 N i+1 N i uniform binding affinity K d and rate k at N i, N i+1 and N i-1 Concentration (nm) uniform K d and k N i N i+1 N i-1 arrest model reduced translocation rate at position N i+1 N i+1 Concentration (nm) arrest model N i N i-1 N i time (sec)

30 Finding a nucleosme substrate: 3D search versus 1D sliding along the DNA