Judith Klein-Seetharaman Co-Course Director

Judith Klein-Seetharaman Co-Course Director jks33@pitt.edu
Overview of Dynamics Judith Klein-Seetharaman Co-Course Director

Objectives of this Lecture
What is dynamics? Time scales of dynamics Methods to study dynamics What data do you get typically? Example: DNA binding 1/17/2019 Molecular Biophysics 3: Lecture 6

Molecular Biophysics 3: Lecture 6
What is dynamics? 1/17/2019 Molecular Biophysics 3: Lecture 6

Proteins and other biological molecules are dynamic.
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. Proteins are dynamic molecules, they often undergo conformational changes while performing thir specific functions. NMR can be used to monitor the dynamic behavior on a broad range of timescales. Typically, 3 types, fast internal motions, slow internal motions and proton exchange. These motions are reported by measurement parameters. • rotational diffusion (τc) • translational diffusion (D) • internal dynamics of backbone and sidechains (τi) • degree of order for backbone and sidechains (S2) • conformational exchange (Rex) • interactions with other molecules (kon,koff) Proteins and other biological molecules are dynamic. 1/17/2019 Molecular Biophysics 3: Lecture 6

What are the time scales?
1/17/2019 Molecular Biophysics 3: Lecture 6

Example: Time-scales in rhodopsin
Time-scales here from fs to min 1/17/2019 Molecular Biophysics 3: Lecture 6

Time scales of protein motions
Overall tumbling Libration Fast loop reorientation Slow loop reorientation Vibration Side chain rotation/reorient. S-S flipping Aromatic ring flips 10-12 10-9 10-6 10-3 10 103 fs Proteins are dynamic molecules, they often undergo conformational changes while performing thir specific functions. NMR can be used to monitor the dynamic behavior on a broad range of timescales. Typically, 3 types, fast internal motions, slow internal motions and proton exchange. These motions are reported by measurement parameters. • rotational diffusion (τc) • translational diffusion (D) • internal dynamics of backbone and sidechains (τi) • degree of order for backbone and sidechains (S2) • conformational exchange (Rex) • interactions with other molecules (kon,koff) ps ns ms ms seconds minutes-hours-days ns-ps: fast internal motions ms-days: proton exchange ms-ms: slow internal motions Time scales from ps to days 1/17/2019 Molecular Biophysics 3: Lecture 6

What are the methods to study dynamics?

NMR parameters and time-scales
Overall tumbling Librations Fast loop reorientation Slow loop reorientation Vibration Side chain rotation/reorient. S-S flipping Aromatic ring flips 10-12 10-9 10-6 10-3 10 103 fs ps ns ms ms seconds minutes-hours-days ns-ps: fast internal motions ms-days: proton exchange ms-ms: slow internal motions Proteins are dynamic molecules, they often undergo conformational changes while performing thir specific functions. NMR can be used to monitor the dynamic behavior on a broad range of timescales. Typically, 3 types, fast internal motions, slow internal motions and proton exchange. These motions are reported by measurement parameters. • rotational diffusion (τc) • translational diffusion (D) • internal dynamics of backbone and sidechains (τi) • degree of order for backbone and sidechains (S2) • conformational exchange (Rex) • interactions with other molecules (kon,koff) T1, T2, NOE T2, T1r HN exchange J Chemical shift Except to some degree in ms-ms range, NMR can report on all time-scales 1/17/2019 Molecular Biophysics 3: Lecture 6

Other methods and time-scales
Overall tumbling Librations Fast loop reorientation Slow loop reorientation Vibration Side chain rotation/reorient. S-S flipping Aromatic ring flips 10-12 10-9 10-6 10-3 10 103 fs ps ns ms ms seconds minutes-hours-days ns-ps: fast internal motions ms-days: proton exchange Proteins are dynamic molecules, they often undergo conformational changes while performing thir specific functions. NMR can be used to monitor the dynamic behavior on a broad range of timescales. Typically, 3 types, fast internal motions, slow internal motions and proton exchange. These motions are reported by measurement parameters. • rotational diffusion (τc) • translational diffusion (D) • internal dynamics of backbone and sidechains (τi) • degree of order for backbone and sidechains (S2) • conformational exchange (Rex) • interactions with other molecules (kon,koff) ms-ms: slow internal motions IR, Raman Fluorescence HN exchange with mass spec Some biophysical measurements are fast… 1/17/2019 Molecular Biophysics 3: Lecture 6

Trapping of conformations
Overall tumbling Librations Fast loop reorientation Slow loop reorientation Vibration Side chain rotation/reorient. S-S flipping Aromatic ring flips 10-12 10-9 10-6 10-3 10 103 fs ps ns ms ms seconds minutes-hours-days ns-ps: fast internal motions Proteins are dynamic molecules, they often undergo conformational changes while performing thir specific functions. NMR can be used to monitor the dynamic behavior on a broad range of timescales. Typically, 3 types, fast internal motions, slow internal motions and proton exchange. These motions are reported by measurement parameters. • rotational diffusion (τc) • translational diffusion (D) • internal dynamics of backbone and sidechains (τi) • degree of order for backbone and sidechains (S2) • conformational exchange (Rex) • interactions with other molecules (kon,koff) ms-days: proton exchange ms-ms: slow internal motions Light Rapid Mixing NMR, x-ray Some biophysical measurements take a long time… 1/17/2019 Molecular Biophysics 3: Lecture 6

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 Fast loop reorientation Slow loop reorientation Vibration Side chain rotation/reorient. S-S flipping Aromatic ring flips Proteins are dynamic molecules, they often undergo conformational changes while performing thir specific functions. NMR can be used to monitor the dynamic behavior on a broad range of timescales. Typically, 3 types, fast internal motions, slow internal motions and proton exchange. These motions are reported by measurement parameters. • rotational diffusion (τc) • translational diffusion (D) • internal dynamics of backbone and sidechains (τi) • degree of order for backbone and sidechains (S2) • conformational exchange (Rex) • interactions with other molecules (kon,koff) 10-12 10-9 10-6 10-3 10 103 fs ps ns ms ms seconds minutes-hours-days ns-ps: fast internal motions ms-days: proton exchange ms-ms: slow internal motions Internal motions are needed to provide flexiblity for functional motions. 1/17/2019 Molecular Biophysics 3: Lecture 6

Need for protein dynamics in rhodopsin?
Dark – state structure Trp265 Ala169 Ligand: 11-cis retinal, no clashes Light-activated structure? Trp265 Ala169 Dark – state structure Ligand: all-trans retinal, steric clashes 1/17/2019 Molecular Biophysics 3: Lecture 6

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. 1/17/2019 Molecular Biophysics 3: Lecture 6

The type of data you can expect

Atomic resolution method - example X-ray
Gives you snap shots of diffraction patterns in different states 1bcc 2bcc 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 v pp , 1998 1/17/2019 Molecular Biophysics 3: Lecture 6

More snap shots 1ctr – calmodulin free 1up5 – calmodulin Ca-bound 1/17/2019 Molecular Biophysics 3: Lecture 6

Any problems? 1/17/2019 Molecular Biophysics 3: Lecture 6

Any problems? No information on time-scales.

Time-resolved spectroscopy
Intrinsic Trp fluorescence Quenching by iodine Binding of ANS Dobson,et.al. 1994 1/17/2019 Molecular Biophysics 3: Lecture 6

Any problems? 1/17/2019 Molecular Biophysics 3: Lecture 6

Any problems? Not atomic level information.

Chemical Exchange 1/17/2019 Molecular Biophysics 3: Lecture 6

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 (5–500 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 1/17/2019 Molecular Biophysics 3: Lecture 6

HD Exchange and NMR Amide exchange measurements were carried out on 15N-labeled P. furiosus rubredoxin at pH values from 7.17 to 12.51, for 3°C, 28°C, and 53°C. (Right) indicate the 1H-15N amide cross peaks for which the initial 1H magnetization starts at the amide resonance and remains there during the pulse sequence. (using eight CLEANEX-PM mixing periods ranging from5.19 ms to ms in even increments) In contrast, (Left) indicate magnetization that initially resides in the 1H2O resonance and subsequently transfers to the amide resonance during the mixing sequence. As illustrated, nearly all of the amide positions in the protein exhibit magnetization transfer from 1H2O in one of these three spectra. That means the native hydrogen bonding is disrupted for all amide hydrogens logKex: pH dependence of amide exchange for residues at 28°C. Conclusion: the native hydrogen bonding is disrupted for all amide hydrogens of this protein, and water plus the hydroxide catalyst gain direct access in less than a sec. Hernandez, G., Jenney, F.E.J., Adams, M.W. & LeMaster, D.M. Proc. Natl. Acad. Sci. USA 97, 3166–3170 (2000). 1/17/2019 Molecular Biophysics 3: Lecture 6

Relaxation and the NOE 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 1/17/2019 Molecular Biophysics 3: Lecture 6

From experiments to dynamics data
From compare the signal intensity use these formulas , we can get R1, R2, and NOE. For rate constant, we compare a set of T ( evolution time?) For NOE, we compare intensities with or without Proton saturation. This is an example of measure rate constant of Xfin-31 Cross sections were taken from the two-dimensional spectra parallel to the w2 axis through the C" resonance of Glu12. from the zinc finger DNA-binding domain Xfin-3 1 I∞, is the intensity corresponding to the steady-state value of the magnetization under the given experimental conditions For measurements of R, and R2, a relaxation delay of 5.0 s, which is twice the longest 'H longitudinal relaxation time of the methine I2C isotopomers, was used between scans to ensure sufficient recovery of IH magnetization. For measurements of the NOE, a relaxation delay of 4.6 s, which is greater than 10/Rl for the methine carbon nuclei, was used between scans to ensure that maximal NOE enhancements have developed before acquisition. Palmer, A.G., 3rd, M. Rance, and P.E. Wright,.J Amer Chem Soc, 1991 1/17/2019 Molecular Biophysics 3: Lecture 6

Dynamics in folded/unfolded lysozyme
Arrows indicate oxidized (all disulfide bonds present) lysozyme Folded: 1/17/2019 Molecular Biophysics 3: Lecture 6

Amplitudes and Frequencies

Popular approach to quantify motions
Measure R1, R2, heteronuclear NOE “model free” approach Get order parameter S2 ,τe, τm This is the strategies to get dynamic information from experiment. First, then… 1/17/2019 Molecular Biophysics 3: Lecture 6

Lipari-Szabo Model Free Approach

Lipari Szabo Order parameters S2 τe, effective correlation function time for internal motions τm, overall tumbling correlation time for global motions 1/17/2019 Molecular Biophysics 3: Lecture 6

Lipari–Szabo “model-free” approach
Estimate (τm) 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. Model free approach is the most popular analytical methods, the name “model free” means it doesn’t depend on a specific physical model. Assuming that the global and internal motions are separable. It is a good approximation if the internal motions are sufficiently small. J(w); spectral density, is the fourier transform of the correlation function. (the function of correlation time) is a measure of amount of the motion present at different frequencies, ω, to cause the transitions (relaxation) S2 is the order parameter for the slow motion, Sf2 is the order parameter for the fast motion, and te is the effective correlation time for the slow motion, t-1 = te-1 + tm -1. Michael Andrec, Gaetano T. Montelione, Ronald M. Levy Journal of Magnetic Resonance 139, 408–421 (1999) 1/17/2019 Molecular Biophysics 3: Lecture 6

Example: DNA binding 1/17/2019 Molecular Biophysics 3: Lecture 6

Example: GCN4 Leucine Zipper
Ribbon diagram of GCN4-58 complexed with DNA. The section in blue is the binding domain. The section in red is the leucin zipper dimerization domain. The thicker and deeper purple regions indication the highest degree of disorder. Low S2 indicates high flexibility. S2 can be used to estimate energetics. 1/17/2019 Molecular Biophysics 3: Lecture 6

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. 1/17/2019 Molecular Biophysics 3: Lecture 6

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=∆Ho–T∆So 1/17/2019 Molecular Biophysics 3: Lecture 6

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 INTER-DEPENDENT Strain energy 1/17/2019 Molecular Biophysics 3: Lecture 6

Using ∆CoP we can calculate ∆Ho, ∆So, and ∆GT at any temperature.
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. 1/17/2019 Molecular Biophysics 3: Lecture 6

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) 1/17/2019 Molecular Biophysics 3: Lecture 6

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 Hydrophobic effect describes the transfer of nonpolar surface from water to a nonpolar environment. “Conformational changes in the protein that buried large amounts of nonpolar surface are coupled to binding.” Spolar ad Record, Science (1994) 1/17/2019 Molecular Biophysics 3: Lecture 6

Example: GCN4 Leucine Zipper
Ribbon diagram of GCN4-58 complexed with DNA. The section in blue is the binding domain. The section in red is the leucin zipper dimerization domain. The thicker and deeper purple regions indication the highest degree of disorder. Low S2 indicates high flexibility. S2 can be used to estimate energetics. 1/17/2019 Molecular Biophysics 3: Lecture 6

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 1/17/2019 Molecular Biophysics 3: Lecture 6

Specific vs. non-specific complexes of the Lac-repressor
Kalodimos et al, Science(2004) 1/17/2019 Molecular Biophysics 3: Lecture 6

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.” 1/17/2019 Molecular Biophysics 3: Lecture 6

Summary of this Lecture
Study of biomolecular interactions and dynamics are important to understand function of biomolecules. Biomolecular interactions Dynamics Function 1/17/2019 Molecular Biophysics 3: Lecture 6

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