9. Lecture SS 20005

Optimization, Energy Landscapes, Protein Folding 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

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

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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 InteractionStep 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

Receptor

Ligand

Bound and associated H2O

Displaced H2O

No collective modes!

9. Lecture SS 20005

Optimization, Energy Landscapes, Protein Folding 5

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

Energy Barriers of Protein:Protein Interaction

Effects of hydrodynamicInteractions:(left) effect of translation(right) effect of rotation

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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

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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:membranesystems is largely unknown.

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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)

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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 0.5 to 1 -14 to –13

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 http://www.dbbm.fiocruz.br/class/Lecture/d22/kolaskar/ask-11june-4.ppt

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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

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Optimization, Energy Landscapes, Protein Folding 12

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.

Energy Barriers during vesicle budding

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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.

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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.

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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.

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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).

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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.