V9: Energy Barriers

1. 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 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 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). 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 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 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 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. 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) 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) Optimization, Energy Landscapes, Protein Folding

10. Time scales of protein dynamics Adapted from http://www.dbbm.fiocruz.br/class/Lecture/d22/kolaskar/ask-11june-4.ppt 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 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. 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. 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. 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. 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). 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. Optimization, Energy Landscapes, Protein Folding