Overview of Dynamics

1
Overview of Dynamics

• Judith Klein-SeetharamanCo-Course Director
• jks33_at_pitt.edu

2
Objectives of this Lecture

• What is dynamics?
• Time scales of dynamics
• Methods to study dynamics
• What data do you get typically?
• Example DNA binding

3
What is dynamics?
4
What is dynamics?

• Definition
• changes in the position of the atoms in a
  molecule relative to each other or relative to an
  outside reference point.

http//www.bioc.aecom.yu.edu/labs/girvlab/nmr/cour
se/relaxdyn
Proteins and other biological molecules are
dynamic.
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What are the time scales?
6
Example Time-scales in rhodopsin
Time-scales here from fs to min
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Time scales of protein motions
Overall tumbling
Libration
Slow loop reorientation
Fast loop reorientation
Side chain rotation/reorient.
Vibration
S-S flipping
Aromatic ring flips
10-9
10-12
10-6
103
10
10-3
seconds
minutes-hours-days
ms
ms
ns
ps
fs
ms-days proton exchange
ns-ps fast internal motions
ms-ms slow internal motions
Time scales from ps to days
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What are the methods to study dynamics?
9
NMR parameters and time-scales
Overall tumbling
Librations
Slow loop reorientation
Fast loop reorientation
Side chain rotation/reorient.
Vibration
S-S flipping
Aromatic ring flips
10-9
10-12
10-6
103
10
10-3
seconds
minutes-hours-days
ms
ms
ns
ps
fs
ms-days proton exchange
ns-ps fast internal motions
ms-ms slow internal motions
T2, T1r
T1, T2, NOE
HN exchange
Chemical shift
J
Except to some degree in ms-ms range, NMR can
report on all time-scales
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Other methods and time-scales
Overall tumbling
Librations
Slow loop reorientation
Fast loop reorientation
Side chain rotation/reorient.
Vibration
S-S flipping
Aromatic ring flips
10-9
10-12
10-6
103
10
10-3
seconds
minutes-hours-days
ms
ms
ns
ps
fs
ms-days proton exchange
ns-ps fast internal motions
ms-ms slow internal motions
Fluorescence
IR, Raman
HN exchange with mass spec
Some biophysical measurements are fast
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Trapping of conformations
Overall tumbling
Librations
Slow loop reorientation
Fast loop reorientation
Side chain rotation/reorient.
Vibration
S-S flipping
Aromatic ring flips
10-9
10-12
10-6
103
10
10-3
seconds
minutes-hours-days
ms
ms
ns
ps
fs
ms-days proton exchange
ns-ps fast internal motions
ms-ms slow internal motions
NMR, x-ray
Rapid Mixing
Light
Some biophysical measurements take a long time
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Functions of dynamics and the time-scales
Blue types of motions
Red functional categorization
Allosteric regulation / global conformational
changes
Ligand/protein binding
Chemical kinetics
Catalysis
Overall tumbling
Local folding
global
Libration
Slow loop reorientation
Fast loop reorientation
Side chain rotation/reorient.
Vibration
S-S flipping
Aromatic ring flips
10-9
10-12
10-6
103
10
10-3
seconds
minutes-hours-days
ms
ms
ns
ps
fs
ms-days proton exchange
ns-ps fast internal motions
ms-ms slow internal motions
Internal motions are needed to provide flexiblity
for functional motions.
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Need for protein dynamics in rhodopsin?
Dark state structure
Ligand 11-cis retinal, no clashes
Light-activated structure?
Dark state structure
Ligand all-trans retinal, steric clashes
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Example Function in Rhodopsin
Definition and Function
Example Rhodopsin Function in Signal
Transduction requires conformational changes
Dark (inactive) Rhodopsin 11-cis retinal does
not bind to G protein
hn Light-activated Rhodopsin All-trans
retinal does bind to G protein
involves protein-ligand and protein-protein
interactions
Biomolecular motions are needed for function.
Example for function biomolecular interaction.
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The type of data you can expect
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Atomic resolution method - example X-ray
Gives you snap shots of diffraction patterns in
different states
2bcc
1bcc
Zhang, Z.,  Huang, L.,  Shulmeister, V.M.,  Chi,
Y.I.,  Kim, K.K.,  Hung, L.W.,  Crofts,
A.R.,  Berry, E.A.,  Kim, S.H. Electron
transfer by domain movement in cytochrome bc1.
Nature v392 pp.677-684 , 1998
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More snap shots
1up5 calmodulin Ca-bound
1ctr calmodulin free
http//www.molmovdb.org/
http//www.bmb.psu.edu/faculty/tan/lab/gallery/cal
modulin.jpg
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Any problems?
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Any problems?No information on time-scales.
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Time-resolved spectroscopy
Intrinsic Trp fluorescence
Quenching by iodine
Binding of ANS
Dobson,et.al. 1994
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Any problems?
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Any problems?Not atomic level information.
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NMR parameters and time-scales
Overall tumbling
Librations
Slow loop reorientation
Fast loop reorientation
Side chain rotation/reorient.
Vibration
S-S flipping
Aromatic ring flips
10-9
10-12
10-6
103
10
10-3
seconds
minutes-hours-days
ms
ms
ns
ps
fs
ms-days proton exchange
ns-ps fast internal motions
ms-ms slow internal motions
T2, T1r
T1, T2, NOE
HN exchange
Chemical shift
J
Except to some degree in ms-ms range, NMR can
report on all time-scales
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Chemical Exchange
http//www.oci.unizh.ch/group.pages/zerbe/NMR.pdf
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H/D exchange can be measured in several ways

• Slow exchange lifetimes (from mins to days)
• by following the loss of HN signal intensity
  of a protein dissolved in D2O.
• Faster exchange lifetimes (5500 ms)
• by following the exchange of HN
  magnetization with that of water protons.
• At high pH
• directly measure the timescale of rate limiting
  conformational openings

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HD Exchange and NMR
Hernandez, G., Jenney, F.E.J., Adams, M.W.
LeMaster, D.M. Proc. Natl. Acad. Sci. USA 97,
31663170 (2000).
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Relaxation and the NOE
http//www.oci.unizh.ch/group.pages/zerbe/NMR.pdf

• Longitudinal relaxation (T1) return of
  longitudinal (z-component) to its equilibrium
  value
• Transverse relaxation (T2) decay of transverse
  (x,y-component)
• Heteronuclear NOE
• Due to dipole interactions between different
  nuclei

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From experiments to dynamics data
Palmer, A.G., 3rd, M. Rance, and P.E. Wright,.J
Amer Chem Soc, 1991
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Dynamics in folded/unfolded lysozyme
Unfolded
Arrows indicate oxidized (all disulfide bonds
present) lysozyme
Folded
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NMR parameters and time-scales
Overall tumbling
Librations
Slow loop reorientation
Fast loop reorientation
Side chain rotation/reorient.
Vibration
S-S flipping
Aromatic ring flips
10-9
10-12
10-6
103
10
10-3
seconds
minutes-hours-days
ms
ms
ns
ps
fs
ms-days proton exchange
ns-ps fast internal motions
ms-ms slow internal motions
T2, T1r
T1, T2, NOE
HN exchange
Chemical shift
J
Except to some degree in ms-ms range, NMR can
report on all time-scales
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Amplitudes and Frequencies
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Popular approach to quantify motions

• Measure R1, R2, heteronuclear NOE
• model free approach
• Get order parameter S2 ,te, tm

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Lipari-Szabo Model Free Approach
http//www.oci.unizh.ch/group.pages/zerbe/NMR.pdf
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Lipari Szabo
http//www.oci.unizh.ch/group.pages/zerbe/NMR.pdf

• Order parameters S2
• te, effective correlation function time for
  internal motions
• tm, overall tumbling correlation time for global
  motions

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LipariSzabo model-free approach

• Estimate (tm) from R2/R1 for a selected subset of
  the residues
• fits to the observed relaxation data using
  various regression variables
• model-selection criteria are used to decide which
  choice is appropriate for each residue
• Reoptimize using the selected models.
• Uncertainties in the optimized parameters were
  obtained by Monte Carlo simulation.

Michael Andrec, Gaetano T. Montelione, Ronald M.
Levy Journal of Magnetic Resonance 139, 408421
(1999)
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Example DNA binding
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Example GCN4 Leucine Zipper

• Low S2 indicates high flexibility. S2 can be used
  to estimate energetics.

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Energetic Components of Protein-DNA Interactions
Adapted from Jen-Jacobson L., Biopolymers (1997)
The observed free energy (green arrow) for
specific binding is the net of large opposing
energies.
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Sources of Entropy and Enthalpy in Protein-DNA
Interactions
Favorable Unfavorable
?Ho Attractive interactions (H-bonds, charge-charge, nonpolar) Molecular strain Repulsive interactions
?So Water release Counterion release Restriction of translational and rotational freedoms Restriction of configurational freedom Loss of vibrational freedom of water
?Go?HoT?So
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Molecular Strain
When atoms, functional groups or residues
(sidechains, bases) adopt positions that are not
their own positions of minimum potential
energy Can result from Bond bending Bond
rotation Steric repulsion Electrostatic
repulsion Strain energy The energetic cost of
strain
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Thermodynamic parameters

• H Enthalpy
• measure of heat energy
• S Entropy
• measure of disorder
• G Gibbs Free Energy
• G ? H TS
• C Heat capacity
• measure of the ability of a body to store
  heat
• ?CoP(??Ho/?T)P
• T(??So/?T)P

Using ?CoP we can calculate ?Ho, ?So, and ?GT at
any temperature.
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Factors affecting ?CoP
free protein specific DNA ? protein-DNA complex
?CoP is made more positive by Burial and
desolvation of polar surface Molecular
strain ?CoP is made more negative by Burial and
desolvation of nonpolar surface Losses of
configurational/vibrational freedom (Interface
restrains sidechains, bases, backbone) Restricted
freedom of interfacial H2O Linked equilibria
(e.g. protonation, ion binding)
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Proposal of Spolar Record (1994)
hydrophobic effect and conformational change

• Compared the measured heat capacity changes and
  the calculated changes in nonpolar ASA and polar
  ASA
• ?CoP is much more negative than predicted.
• The excess ?CoP could be accounted for by local
  folding coupled to binding.
• The observed ?CoP and ?So could be used to
  estimate the number of protein residues that fold
  upon DNA binding.
• Equation estimates -1.2 kJ K-1 mol-1 for DSconf

Conformational changes in the protein that
buried large amounts of nonpolar surface are
coupled to binding.
Spolar ad Record, Science (1994)
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Example GCN4 Leucine Zipper

• Low S2 indicates high flexibility. S2 can be used
  to estimate energetics.

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From order parameter to entropy
Sum of the order paramaters in bound form
in free form
Result DS -0.6 kJ K-1 mol-1

• Calorimetric data estimates -1.2 kJ K-1 mol-1
• MD simulations suggest that 40-45 of total
  conformational entropy loss arises from backbone
  chain entropy, rest from side-chain
• NMR result fits well with calorimetric experiment

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Specific vs. non-specific complexesof the
Lac-repressor
Kalodimos et al, Science(2004)
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Contacts of Lac repressor protein with
nonspecific and specific DNA
Kalodimos et al, Chem.Rev.(2004)
The same set of residues can switch roles from a
purely electrostatic interaction with the DNA
backbone in the nonspecific complex to a highly
specific binding mode with the base pairs of the
cognate operator sequence.
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Summary of this Lecture

• Study of biomolecular interactions and dynamics
  are important to understand function of
  biomolecules.

Biomolecular interactions
Dynamics
Function