1. Biological Macromolecules
protein
DNA
tRNA

2. single-strand of DNA

4. double-stranded DNA
One helical turn = 3.4 nm

5. DNA is a long molecular thread that is wrapped up inside the nucleus of cells in the form of chromosomes

6. RNA is single-stranded

7. Secondary structure of tRNA

8. 3-dimensional (tertiary) structure of tRNA

9. Proteins are made up of a polypeptide chain that consists of 20 different types of building blocks (amino-acids)

10. Sequence of amino-acids determines the 3-dimensional structure of proteins

11. The molecular shape of a protein defines its function

12. Biological macromolecules maintain their shape as a result of intramolecular interactions consisting of weak, noncovalent bonds
thermal energy (kBT = 1/40 eV) ~0.6 kcal/mol
ionic bonds ~3 kcal/mol (in water)
hydrogen bonds ~1 kcal/mol
van der Waals interactions ~0.1 kcal/mol
hydrophobic interactions ~1-10 kcal/mol

13. Biomolecular recognition relies on shape (and charge) complementarity that maximizes noncovalent interactions
Weak interactions: ionic, hydrogen bonding, hydrophobic, and van der Waals interactions ~ thermal energy (kBT)

14. Crystal structure of the ribosome with bound tRNA

15. Thermal fluctuations in the “conformation” (molecular shape) facilitate stabilizing interactions
Dynamics plays a key role in the recognition mechanism

16. Chemical reactions involving biological molecules
unimolecular
bimolecular

17. Folding Problem
Protein RNA
Structural: Can we predict the three-dimensional structure from sequence?
Dynamical: What is the underlying energy landscape? What can we say about the dynamics of folding?

18. Protein-folding problem
Levinthal’s paradox
Proteins with N amino-acids (N=100)
Each amino-acid can be in 3 different orientations
Possible number of protein configurations is 3N = 3100 = 51047
If time to sample each configuration is approx. 1 ns
Folding time for each protein would be 51047 10-9 s = 51038 s > 1031 years
However, small globular proteins fold on sub-milliseconds to seconds time-scales
Can proteins find their lowest free energy structure by random search in configurational space?

19. Biased random-walk can reduce the folding time to biologically relevant times

20. RNA folding problem
Secondary structure forms rapidly (on time-scales of microseseoconds)
Complete folding of RNA on time-scales of milliseconds to tens-of-seconds
Kinetics measurements reveal time-scales for fundamental steps in various biological processes and give insights into the underlying energy landscape

21. Elementary step in RNA folding: hairpin formation
zipping
nucleation
What is the role of chain dynamics in the nucleation step?
Are there kinetic traps prior to nucleation?
Why do hairpins form so slowly?
What are the bottlenecks?

22. Review of thermodynamics
U: Internal energy of a system (Kinetic energy + potential energy)
S: Entropy (=kBln) where  is the number of accessible configurations
H: Enthaply (= U+PV)
G: Gibbs free energy (=U+PV-TS)
At constant T and P, system will minimize Gibbs free energy
Boltzmann probability of finding the system in a particular macrostate at temperature T is proportional to exp(-G/kBT)
At room temperature kBT  410-21 J  1/40 eV  0.6 kcal/mol

23. Unimolecular reactions: folding of protein or RNA molecules
GU: Free energy of an unfolded molecule
GF: Free energy of a folded molecule
Probability that molecule is unfolded ∞ exp(-GU/kBT)
Probability that molecule is folded ∞ exp(-GF/kBT)
Equilibrium constant for the reaction
where DG/kBT = GF-GU

24. Folding/unfolding of a ssDNA or RNA hairpin

25. Fluorescence Intensity
Equilibrium thermodynamics does not give any information about the dynamics of the system
Fluorescence Intensity
Time (microseconds)

26. A statistical mechanical model that includes all possible misfolded states is required for a complete description of the folding kinetics of nucleic acid hairpins

27. Spontaneous folding of RNA molecules
Local secondary structure in RNA forms rapidly (tens-to-hundreds of microseconds)
Complete folding of RNA on time-scales of milliseconds to tens-of-seconds
RNA molecule can get stuck is misfolded conformations along the folding pathway

28. Protein-DNA Interactions
Regulation of gene expression requires formation of protein-DNA complexes
Nonspecific binding (e.g. wrapping of DNA in the nucleosome)
Specific binding (e.g TATA-binding protein to initiate transcription)
Protein-DNA complexes involve bending, kinking or looping DNA.

29. How do site-specific DNA-binding proteins locate their target sites?
Random search in 3-dimensional space to locate the target site.
Diffusion-limited rate ~ kdiffusion[protein] 4Da [protein]
Smoluchowski, 1917
Experimental measurements of rate of target location are ~ times faster than this apparent theoretical limit!

30. Facilitated diffusion 3-dimensional diffusion to encounter the DNA
1-dimensional sliding of protein on DNA to rapidly scan neighboring sites
Hopping between different DNA segments to continue the search in an uncorrelated region of DNA
sliding
hopping
Binds to target site with fold higher affinity
DGbinding ~7-14 kBT

31. How do the proteins recognize their target site on DNA?
Direct read-out: proteins recognize specific sequences by making direct hydrogen bonds with the bases
Indirect read-out: proteins rely on the sequence-dependent flexibility of DNA

32. Conformational rearrangements in both protein and DNA lead to a tighter fit in the complex+
Protein
DNA
Non-specific complex
Specific complex
Kalodimos et al,Science. 2004
What are the times-scales for these concerted changes? 32

33. DNA-Bending Proteins
MutS: DNA repair protein binds to mismatches in DNA
IHF and HU: package DNA inside the cell
TATA binding protein (TBP) binds to promoter sequences to initiate transcription
EcoRV restriction enzyme protects the host bacterial cell by cutting foreign DNA at specific sites

34. b-ribbon arms of the protein wrap around the bound DNA
IHF (Integration Host Factor) is a prokaryotic protein that induces a large bend in DNA (~180o).
b-ribbon arms of the protein wrap around the bound DNA
Rice et al. (1996) Cell 87, 1295
Swinger et al. (2003), EMBO J. 14, 3749.

35. What role does the bendability of DNA play in the recognition mechanism?
DNA is a semiflexible polymer, with persistence length P = 50 nm (~150 base pairs)
Rigid rod on length scales L < P
Random coil on length scales L >> P

36. IHF bends ~12 nm long DNA by 180°
The energetic cost for bending a semiflexible polymer would be ~21 kBT
Crystal structure indicates that DNA is not uniformly bent but kinked at two sites spaced by about 9 bp
Swinger et al. (2003), EMBO J. 14, 3749.
Base-pair disruption or unstacking of bases can signifantly reduce the energetic cost of kinking/bending DNA (~ kBT)

37. What is the sequence of molecular rearrangements that lead from the nonspecific to the specific complex?
What are the bottlenecks in the transition pathway?
What are the time-scales for DNA bending?
Does the protein bend the DNA, or is the DNA able to bend spontaneously, from thermal fluctuations?
What des the transition state look like?
Need kinetics measurements to understand the mechanism

38. Dynamics of DNA bending observed with fluorescence resonance energy transfer (FRET)hn
High FRET
Low FRET
T-jump
Hillisch et al. (2001)

39. Measure time-scales for bending/unbending of DNA
TEMPERATURE (C)
Measure time-scales for bending/unbending of DNA

40. Experimental time-scales for single base-pair disruption from NMR measurements of imino proton exchange rates
Dhavan et al. (1999) JMB 288, 659
Coman and Russu (2005) Biophys. J. 89, 3285
The rates and activation energy of DNA bending, in complex with IHF, are similar to that of a single base-pair opening inside DNA

41. Spontaneous bending/kinking of DNA, from thermal fluctuations, may be the bottleneck in the recogntion process
In the transition state, the DNA is bent, but favorable interactions between protein and DNA have not yet been made
The protein captures the bent state and the complex is stabilized by specific protein-DNA interactions

42. Does recognition occur in a single step, that occurs on time-scales of few milliseconds?
At least two steps in the recognition process:
tfast ~ 100 ms
tslow ~ 10 ms

43. The fast kinetics may be the protein wrapping and unwrapping its arms around the DNA, in an attempt to recognize its binding site