Biomolecules in solution: Computational studies & THz spectra (.3 3 THz)"

Transcription

1 Biomolecules in solution: Computational studies & THz spectra (.3 3 THz)" David Leitner (U. Nevada, Reno)" Martin Gruebele (U. Illinois)" Martina Havenith (Ruhr Universität Bochum)" Thanks to" Erik Bründermann" Simon Ebbinghaus" Ramachandran Gnanasekaran" Matthias Heyden" Udo Heugen" Seung Joong Kim" Konrad Meister" Gerhard Schwaab" Yao Xu THz Workshop, SLAC, Sept. 5-6, 2012"

2 " " " " "" " " " " "" Biomolecules in solution: THz spectra" " " " " "" " " " " "" " " " " "" " " " "" " " "" "1. THz vibrations of proteins. " "2. THz spectroscopy: Measure of hydration layer." " "" " " ""

3 Vibrational modes of myoglobin" 0.20" Mode" Density" (a.u.)" 0.10" " Mode Frequency (cm -1 ) Moritsugu, Miyashita & Kidera, PRL 85, 3970 (2000)."

4 How many residues participate in normal mode? Information entropy, S = - p r ln p r r ε residue" e S = 1 localization to 1 residue" e S = N vibration distributed over N residues p r = projection of mode" onto residue r " 100" 80" e S" 60" 40" 20" " frequency (cm -1 )" DML, PRL 87, (2001)."

5 Spectral dimension, d, from vibrational mode density: " ρ (ω) ω d log ρ(ω) d 1.30 GFP" 0.5 d 1.34 d = 3 Myoglobin" ω (cm -1 ) X. Yu and DML, J. Chem. Phys. 122, (2005); DML, Ann. Rev. Phys. Chem. 59, 233 (2008).

6 Mode damping rate Mode damping from cubic anharmonic interactions sum of decay + " collision terms:" ω β Decay :" ω α ω α = ω β + ω γ ω γ rate α, decay = (h π/8ω α )Σ ( Φ αβγ 2 /ω β ω γ )(1+n β +n γ )δ(ω α ω β ω γ ) β,γ V = potential energy function (from force field model) Q α = mass-weighted normal coordinate B. K. Ridley, Quantum Processes in Semiconductors (Oxford, 2000)

7 Mode damping rate Mode damping from cubic anharmonic interactions sum of decay + " collision terms:" ω β Decay :" ω α ω α = ω β + ω γ ω γ rate α, decay = (h π/8ω α )Σ ( Φ αβγ 2 /ω β ω γ )(1+n β +n γ )δ(ω α ω β ω γ ) β,γ Collision :" ω α ω γ ω γ = ω α + ω β ω β rate α, coll. = (h π/8ω α )Σ ( Φ αβγ 2 /ω β ω γ )(n β -n γ )δ(ω α + ω β ω γ ) β,γ n β = (e hω β /kt -1) 1 Mode damping rate independent of N (# of modes) B. K. Ridley, Quantum Processes in Semiconductors (Oxford, 2000)

8 Vibrational energy transfer rates in myoglobin ω β 3" T = 15 K 45 K 135 K ω α ω α ω γ ω γ Rate (ps -1 ) 2" ω β Amide I 0.5 ps -1 1" DML, Phys. Rev. Lett. 87, (2001);" " Frequency (cm -1 ) X. Yu & DML, J Phys Chem B 107, 1698 (2003)

9 Pump-probe measurements of amide I lifetimes" Same Result! Peterson, Rella, Engholm, Schwettman, J Phys Chem B 103, 557 (1999)"

10 Mode damping rates in GFP & PYP (300 K) Average mode damping rate independent of size of protein: expectation of theory, independent of force field model used. DML, Chem. Phys. Lett. 530, 102 (2012)"

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12 Terahertz spectra of proteins: Experiment" Ebbinghaus, Kim, Heyden, Yu, Heugen, Gruebele, Leitner, Havenith, PNAS 104, (2007)"

13 " " " " "" Biomolecules in solution: THz spectra" " " " " "" " " " " "" " " " " "" " " " "" " " "" "What can we learn from featureless spectra of solvated biomolecule?" " Study concentration dependence of THz absorbance." " " "" " " " " ""

14 Heugen, Schwaab, Bründermann, Heyden, Yu, Leitner, Havenith, PNAS 103, (2006)"

15 Sugar Molecule

16 Terahertz spectra of biomolecules: Simulations" I(ν ) = 1/ 2π dte i 2πνt M(0) M(t) " " " "M = total dipole moment of sample" "" α(ν ) = " 16π 4 ν[1 " e hν / k B T "]I(ν )/ 3hcn(ν " ) "IR absorption cross-section" Simulations Experiment Heugen, Schwaab, Bründermann, Heyden, Yu, Leitner, Havenith, PNAS 103, (2006)"

17 Terahertz spectra of proteins: Experiment" Ebbinghaus, Kim, Heyden, Yu, Heugen, Gruebele, Leitner, Havenith, PNAS 104, (2007)"

18 Terahertz spectra of proteins: Simulations" I(ν ) = 1/ 2π dte i 2πνt M(0) M(t) " " " "M = total dipole moment of sample" "" α(ν ) = " 16π 4 ν[1 " e hν / k B T "]I(ν )/ 3hcn(ν " ) "IR absorption cross-section" Ebbinghaus, Kim, Heyden, Yu, Heugen, Gruebele, Leitner, Havenith, PNAS 104, (2007)"

19 Terahertz spectra of simple solvated proteins" Concentration dependence of absorbance nonlinear in experiments and simulations." Experiments much more nonlinear & width of hydration layers inferred from data very different (> 20 Å from experiments, 10 Å from simulations)."

20 Terahertz spectra of proteins" 30 Å 20 C 5 C Antifreeze protein DAFP-1 Difference, Δα, in THz absorbance ( THz) of solvated DAFP-1 relative to water reference Long-range protein-water dynamics in hyperactive insect antifreeze proteins, K. Meister, S. Ebbinghaus, Y. Xu, J. G. Duman, A. L. DeVries, M. Gruebele, DML and M. Havenith (2012)

21 Is there any bulk water in the living cell?"

22 Protein thermodynamics and solvation" P. H. Yang and J. A. Rupley, Biochem (1979). C 1, pure water" Specific heat measured for lysozyme-water system" C p / J K -1 g -1 " C p = w 1 C 1 + w 2 C 2 C p (lyso) = 1.48 J K -1 g -1 " Weight fraction lysozyme" C p (lyso) = 1.26 J K -1 g -1 " 180 hydration water molecules" 1 solvation shell"

23 5 C (J/g K)" 4 3 Hydrated BPTI" (Computed by MD)" X. Yu, J. Park & DML, J. Phys. Chem. B. 107, (2003). Lots of bulk water in cell! solvation shell" Hydrated lysozyme" (Measured)" C 2, full hydration" C 2, pure protein" Yang & Rupley, Biochem. 18, 2654 (1979). protein, w 2 "

24 Terahertz spectra of proteins" 30 Å 20 C 5 C Antifreeze protein DAFP-1 Little bulk water in cell! Difference, Δα, in THz absorbance ( THz) of solvated DAFP-1 relative to water reference Long-range protein-water dynamics in hyperactive insect antifreeze proteins, K. Meister, S. Ebbinghaus, Y. Xu, J. G. Duman, A. L. DeVries, M. Gruebele, DML and M. Havenith (2012)