Energetics of protein charge transfer and photosynthesis

Transcription

1 Energetics of protein charge transfer and photosynthesis Dmitry Matyushov Arizona State University, Center for Biological Physics Photochemistry, July 7, 2009

2 Respiratory chain Electron transport chain of oxidative phosphorylation: NADH + H+ + (1/2)O2 > NAD+ + H2O The entire reaction scheme is to snap a proton from solution!

3 Bacterial photosynthesis 0.25 ev lost in two electron hops! e

4 Energy loss to the phonon bath Moving electron with zero activation barrier requires losing (reorganization energy) at each electron hop.

5 Gaussian fluctuations of the thermal bath is the energetic parameter controlling the energetic efficiency of biological machines. Two questions for protein electron transfer: 1. Is this picture correct? 2. What is the typical magnitude of?

6 Expectation from redox chemistry: = 1 ev For proteins = ev is commonly expected 1.5 ev? Why does nature rely on multiple electron jumps if each of them is energetically unfavorable by the reorganization energy? Should we try to mimic this design if it does not provide energetic efficiency? Do molecules present a dead case for solar energy conversion?

7 Common explanation (paradigm): small! Results of long (ca. 15 ns) simulations: Charge transfer state according to traditional theories! From the Stokes shift From the parabola s curvature

8 Picture of crossing parabolas (Gaussian fluctuations) Stokes shift Reorganization energy This relation clearly breaks down for proteins!

9 GIGANTIC reorganization energy in proteins Breadth of fluctuations much exceeding that for typical small molecules (inset)?? Reorganization energy at the level of 5 ev Significant splitting between the reorganization energy and the Stokes shift/2 ~ ps is the scale of losing ergodicity

10 Electron transfer (half reaction) in plastocyanin Electrostatics facts: 9 /8 charge is made by 9 Glu and 6 Asp, 6 Lys, and Cu+ Dipole moment ~ 2400 D Observables:

11 Gigantic reorganization energy of electron transfer: non Gaussian electrostatic fluctuations Reorganization energy shoots up to its gigantic values from the «normal» magnitude seen at low temperatures?? The spectrum of electrostatic fluctuations is clearly non Gaussian at high (room) temperatures. The onset temperature is consistent with the temperature of dynamical transition in proteins ~ 200 K.

12 What do we see? Typical reorganization energy from the Stokes shift comes from fast solvent motions Gigantic reorganization energy from fluctuations arises from some collective modes which become dynamically arrested by either decreasing the observation time or by lowering temperature. The system loses ergodicity at short observation windows!

13 Nonergodic reorganization energy/nonergodicity factor Emission shift of triplet recombination Ito et al, J. Chem. Phys. 125, (2006). Ferrocene/ferrocenium on Cu electrode Khoshtaria et al, Chemistry 15, 5254 (2009)

14 Nonergodicity factor and dynamical transition in proteins THz absorption, Markelz and co workers, PRL 101, (2008). specifies the fraction of vibrational modes that are elastic Frauenfelder et al, PNAS 106, 5129 (2009)

15 Back to bacterial reaction center self consistent equation Nonergodicity reduces the driving force from 1.5 to 0.25 ev!

16 What have we learned? When the reaction is fast (ps), many slow protein modes are frozen, polar solvation (particularly of water) is frozen. There are collective nuclear modes that unfreeze on the time scale of ~100 ps and contribute to a gigantic reorganization energy Proteins are NOT non polar, they are SLOW!

17 What is the collective mode? Average number and variance of the number of first shell waters The hydration shell becomes softer and more noisy with increasing temperature! The change in the number of first shell particles is consistent with the mean squared displacements (Frauenfelder and Young). Does dynamical arrest implies the formation of the hydrophobic interface?

18 Length scale of fluctuations Dependence of the first and second cumulants on the cutoff distance from the protein surface. Different length scales for the first and second cumulants!

19 Terahertz spectroscopy of protein solutions Hydrated proteins: one needs a dramatic increase of an effective dipole of the protein to get experimental points. Protein polarizes water 20 A away from its surface (PNAS 07)! Matyushov, unpublished

20 Speculation: Water around protein is polarized to make an elastic ferroelectric bag which produces large electrostatic noise (gigantic reorganization energy). A part of the picture is lose density structure of the first solvation shell that allows more fluctuations.

21 How general is non Gaussianity? Reaction center again! Number of electron hops in the non Gaussian paradigm per one hop in the Gaussian picture:

22 Electron transport in molecular chains Parameter of energetic efficiency due to non Gaussian fluctuations: About 10 time higher energetic efficiency of biological machines in the picture of non Gaussian electrostatic fluctuations! LeBard and Matyushov, JPCB, accepted.

23 Conclusions Picture of Gaussian fluctuations (crossing parabolas) is inconsistent with the energetics of hopping charge transfer in biological energy chains. Transition in the breadth of electrostatic fluctuations coinciding with the dynamical transition of atomic displacements. Gigantic reorganization energy develops at high temperatures breaking down the picture of Gaussian fluctuations ( ferroelectric bag??). Two features are central to protein electron transfer and photosynthesis: Ergodicity breaking and small reorganization energy for fast reactions (ps) Significant decoupling of reorganization energy from the Stokes shift for slow reactions (ns) About 10 time higher energetic efficiency of biological machines in the picture of non Gaussian electrostatic fluctuations!

24 David LeBard JPCB 2008, 112, 5218 JPCB 2008, 112, PRE 2008, 78, Vitaliy Kapko JPCB 2009, accepted. $$ NSF, BES

25 Gigantic reorganization energy: other studies

26 Temperature dependence of protein's flexibility, dynamical transition at K The reason for the dynamical transition is either in the bulk (Widom line) or interfacial (hydrophobic interface) effects

27 Temperature dependence (10 ns observation window) Spike at 220 K: Crossing the Widom line? More likely a weak first order transition (Binder parameter).