1. Optimization, Energy Landscapes, Protein Folding
V9: Energy Barriers
Where do energy barriers come from?
Why do reactions have activation barriers?
Different processes are characterized by similar energy barriers that are due to very different mechanisms.
Effects on energy barriers
Chemical reactions - temperature
protein:ligand association - pH
protein:protein association - D2O vs. H2O
protein:membrane association - viscosity
protein:DNA association
during protein folding
time scales of protein dynamics
vesicle budding
virus assembly
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

2. History of Energy Barriers of Chemical Reactions
1834 Faraday: chemical reactions are not instantaneous because there is an electrical barrier to reaction
1889 Arrhenius: reactions follow Arrhenius law
with an activation barrier Ea.
Bodenstein: reactions occur via a series of elementary steps where bonds break and form. Bodenstein showed that Arrhenius‘ law is applicable only to elementary reactions. Overall reactions often show deviations.
1935 Polanyi & Evans: bonds need to stretch during elementary reactions.
The stretching causes a barrier. Bonds also break.
Physical causes of barriers to chemical reactions
bond stretching and distortion
orbital distortion due to Pauli repulsions (not more than 2 electrons may occupy one orbital)
quantum effects
special reactivity of excited states
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

3. Energy Barriers of Chemical Reactions
When chemical bonds need to be „broken“,
- Nuclei need to move only over small distances,
- Electrons need to redistribute „settle down“ in different orbitals
Intermediate state has high energy
One can compute the energy barriers by quantum-chemistry methods.
However, these calculations do not explain why the barriers arises.
Chemists like to think in concepts and rules and like to separate these.
How fast can reaction proceed? E.g. within one bond vibration.
Such processes need to be activated.
E.g. bond length should stretch far beyond equilibrium distance.
Is possible by statistical fluctuations and by coupling with other modes (large energy becomes concentrated in this mode).
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

4. Energy Barriers of Protein:Ligand Interaction
Step 1: Protein and Ligand are independently solvated (left picture below)
Step 2: The Ligand may preorganize into its binding conformation (costs usually  3 kcal/mol)
Step 3: The Ligand approaches the binding pocket of the protein.
 System partly looses 6 degrees of freedom (CMS of ligand: 3 translation, 3 rotation)
Step 4: The Ligand enters the binding pocket of the protein  Waters are displaced from binding pocket.
Sometimes: simultaneous conformational changes of protein/receptor
No collective modes!
Bound and
associated H2O
Receptor
Ligand
Displaced
H2O
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

5. Energy Barriers of Protein:Protein Interaction
Steps involved in protein-protein association:
- random diffusion (1) + hydrodynamic interaction
- electrostatic steering (2)
- formation of encounter complex (3)
(Possible: large-scale conformational changes of
one or two proteins)
- dissociation or formation of final complex via TS (4)
Origin of Barrier (4):
System partly looses 6 degrees of freedom (CMS: 3 translation, 3 rotation)
Desolvation: large surface patches need to be partially cleared from water
Induced fit of side chains at interface  potential entropy loss
Effects of hydrodynamic
Interactions:
(left) effect of translation
(right) effect of rotation
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

6. Energy Barriers of Protein:Membrane Interaction
Membrane surface carries net negative charge (mixture of neutral and anionic lipids) or has a partially negative character.
Cloud of positive counter ions to compensate membrane charge.
Membrane surface is not well defined and quite dynamic, ondulations.
wikipedia.org
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

7. Energy Barriers of Protein:Membrane Interaction
Neutron scattering: four layers of ordered water molecules above membrane – also found by MD simulation.
Water layers significantly weaken membrane potential.
Lin, Baker, McCammon, Biophys J, 83, 1374 (2002)
Interaction potential of protein:membrane
systems is largely unknown.
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

8. Energy Barriers of Protein:DNA Interaction
DNA backbone carries strong permanent negative charge.
 surrounded by cloud of positive ions and coordinating water molecules
Protein must displace this cloud and must form very polar interactions with DNA backbone.
Spatial distribution functions of water, polyamine atoms and Na+ ions around a CA/GT fragment. View of the minor groove. Data are for systems with 30 diaminopropane2+ (A), 30 putrescine2+ (B), 20 spermidine3+ (C) and 60 Na+ (D), averaging the MD trajectories over 6 ns, with three decamers with three repeated CA/GT fragments in each decamer.
Water (oxygen, red; hydrogen, gray) is shown for a particle density >40 p/nm3 (except for the Na/15 system, where this value is 50 p/nm3);
Spherical distribution function of the polyamine N+ atoms (blue) and Na+ (yellow) ions are drawn for a density >10 p/nm3; polyamine carbon and hydrogen atoms not shown.
Korolev et al. Nucl Acid Res 31, 5971 (2003)
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

9. Energy Barriers of Protein:DNA Interaction
Recognition shows Faster-than-diffusion paradox (similar to Anfinsen paradox for protein folding).
Maximal rate achieveable by 3D diffusion: 108 M-1s-1
This would correspond to target location in vivo on a timescale of a few seconds, when each cell contains several tens of TFs.
However:
Experimentally found (LacI repressor and its operator on DNA): 1010 M-1s-1.
Suggests that dimensionality of the problem changes during the search process. While searching for its target site, the protein periodically scans the DNA by sliding along it. This is best done if the TF is only partially folded and only adopts its folded state when it recognizes ist binding site.
Slutsky, Mirny, Biophys J 87, 4021 (2004)
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

10. Time scales of protein dynamics
Motion
Spatial extent (nm)
Log10 of characteristic time (s)
Relative vibration of bonded atoms
0.02 to 0.05
-14 to –13
Elastic vibration of globular region
1 to 2
-12 to –11
Rotation of side chains at surface
0.5 to 1
-11 to –10
Torsional libration of buried groups
Relative motion of different globular regions (hinge bending)
1 to 2
-11 to –7
Rotation of medium-sized side chains in interior
0.5
-4 to 0
Allosteric transitions
0.5 to 4
-5 to 0
Local denaturation
0.5 to 1
-5 to 1
Protein folding
???
-5 to 2
Adapted from
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

11. Energy Barriers during protein folding
Peptide chain must organize into particular 3D fold: large entropy loss.
Formation of secondary structure elements  formation of hydrogen bonds.
This is almost cancelled by loss of hydrogen bonds with solvent molecules.
Burial of hydrophobic surface  free energy gain due to hydrophobic effect.
Charged active site residues must be buried in hydrophobic protein interior
 often electrostatically unfavorable
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

12. Energy Barriers during vesicle budding
Vesicle budding (right, above) does not occur spontaneously: would be too dangerous for cell.
Distorting plane membrane costs deformation energy  binding of coat proteins reduce energy cost and give natural membrane curvature (right, below).
SNARE proteins help to overcome energy cost for fusion of membranes.
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

13. Energy Barriers during formation of virus capsid
Many individual particles combine into one larger particle
 big loss of translational and rotational degrees of freedom
Much hydrophobic surface gets buried between assembling proteins
free energy gain according to hydrophobic effect (primarily solvent entropy)
Electrostatic attraction: probably not very significant for binding affinity but important for specificity.
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

14. What is the effect of temperature on energy barriers?
In general, higher temperature will enormously speed up activated processes.
However, we often need to consider free energy barriers instead of energy barriers. The free energy barriers often change considerably with temperature.
E.g. in a MD simulation of a protein at 500K, the protein residues will more easily overcome individual torsional energy barriers.
But, after a certain time, the whole protein will unfold.
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

15. What is the effect of pH on energy barriers?
At different pH, titratable groups will adopt different protonation states.
 e.g. at low pH, Asp and Glu residues will become protonated
 salt-bridges (Asp – Lys pairs) in which residues were involved will break up.
 proteins unfold at low and high pH.
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

16. What is the effect of D2O on energy barriers?
It is a common strategy to compare the speed of chemical reactions in H2O and in D2O.
The electronic energy profile of the barrier is the same.
But the deuteriums of D2O have a higher mass than the hydrogens of H2O.
 Their zero-point energies are lower  they need to overcome a higher effective energy barrier  all chemical reactions involving proton transfer will be slowed down, typically by a factor of 1.4
This is called the „kinetic isotope effect“ (KIE).
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding

17. What is the effect of viscosity on energy barriers?
Adding co-solvents in the solvent to increase the viscosity should, in principle, slow down conformational transitions.
It is often problematic that the co-solvent will also change the equilibrium, e.g. between folded and unfolded states of a protein.
9. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding