Photosynthetic and Protein Electron Transfer: Is Biology (Thermo) Dynamic?

Transcription

1 Photosynthetic and Protein Electron Transfer: Is Biology (Thermo) Dynamic? University of Calgary, December 13, 2014 Dmitry Matyushov Department of Physics/Chemistry Center for Biological Physics Arizona State University Dr#Daniel#Mar*n $$"NSF"

2 Bacterial reaction center

3 Questions What is the spectrum of fluctuations of the protein-water interface? What are the time-scales involved? What is the mechanism of activation of electron transport? Is it thermodynamics only? Can we view biological energy flow as a canonical ensemble problem? There is a mechanism of dynamical control that nature (again!) had discovered and we are still missing in our theories of activated events.

4 Energy conversion machinery Reaction center bc1 complex

5 Biology s energy chains RC BC1 ADT ATP 22 electron hops in mitochondria s membrane over the free energy span of 1.1 ev 8-9 electrons per one ATP produced ~25 kg of ATP produced daily in a human body

6 Mitochondria s Complex I (a) FMN Nqo1 Nqo2 Nqo3 (b) FMN 13.5 (12.3) N1a 22.3 (19.4) N (7.6) 14.2 (11.1) 13.9 (10.7) N4 NADH N1b 24.2 (20.5) N7 = Nqo15 N5 Nqo5 Nqo9 N6a 12.2 (8.5) 16.9 (14.1) 12.2 (9.4) Nqo6 N6b Nqo4 Q H1 N2 Efremov and Sazanov, Curr. Opinion Struct. Biol. 2011, 21: (10.5) a Potential energy (V) NADH/ Flavin Fe 4Fe Fe 4Fe 4Fe Fe Quinone + p Experimental profile Corrected with ε = 20 Corrected with ε = Fe 1 J. Hurst, Annu. Rev. Biochem :551 75

7 Energy balance of electron transport e D e e e D e A input catalitic reaction 22 hops Q: How does biology produce energy? A: By reducing the grip of thermodynamics!

8 Two NON s of protein electron transfer Non-ergodicity: reactions are faster than the medium (protein) relaxation Globally non-gaussian free energies of electron transfer Bacterial reaction center Bacterial bc1 complex

9 Ergodicity P e βh(p,q), β =1/(k B T ) p {p,q} q Mathema*cal#abstrac*on:# τ obs 9

10 Canonical ensemble: All the fast things have happened and all the slow things have not - R. Feynman p observation time q distribution slow fast part of phase space reached! on the observation time-scale biology Relaxation time Biology: dynamically restricted ensemble (only a part of phase space is available on the time of the reaction) 10

11 Dynamically restricted ensemble frozen sub-space p q Canonical#(Gibbs)#average#over#mo*ons# faster"than"the"rate canonical ensemble 11

12 Nonergodic kinetics (first NON ) Ac*va*on#barrier#depends#on#the#rate F(X) gas F a (k) F a X 12

13 Electron tunneling (hopping conductivity) gas condensed matter D A e e Reorganization energy (extent of medium deformation)

14 F X 1 X 2 X 1 X=0 X 2 X

15 Marcus theory:

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17 Reaction free energy & activation barrier 1 2 from MD of redox proteins

18 Consequences for activation 1 2 Reac*on#barrier#is#decreased#without#the#need#in#a#nega*ve# reac*on#free#energy.# 18

19 Dynamics vs thermodynamics Stokes-shift time correlation function: e C i (t) = δx(t)δx(0) i χ i (ω) =(βω/2)c i (ω) e D HA - QA -> HA-QA - k exp k CS D e A , GHz

20 Bacterial photosynthesis: Energetics e P 0.25 ev P + B L P + H L 3 P ev 0 P traditional theory

21 Bacterial charge separation (3 ps reaction time!)

22 Spectroscopy in super-cooled liquids (T) butyronitrile MTHF calc. quinoxaline dye, R. Richert, ASU T/T g Freezing out of nuclear degrees of freedom on the time-scale of phosphorescence

23 Population dynamics Fokker-Planck operator depending on LeBard, Kapko, DVM, JPCB 112 (2008) 10322

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25 State χ G All Flexible 25 Protein frozen 11 Protein and chromophore frozen water protein coupled fluctuations , ns -1 Low-frequency motions of the protein move both the ionized surface residues and the water shells polarized by them.

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27 Protein-Water Interface Water structure is locally broken: surface polarization is determined by the residue Frustration of surface polarized domains: long propagation into the bulk Heterogeneous dynamics of the interfacial polarization

28 Dipolar domains in the protein-water Interface Phenomenology of relaxor ferroelectrics!

29 CS k CS HA - QA -> HA-QA - k exp e , GHz 1.2 k exp var, ev k, ps -1 Chem. Sci. 4 (2013) 4127.

30 bc1 complex Reaction rate ~ 1 ms Izrailev et al., Biophys. J. 99 Martin, LeBard, DVM, JPCL 4 (2014) 3602.

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32 bc1 complex: lambda(k) 200 ns simulation

33 Time arrow of biological electron transport 100ns 100 ps Gaussian picture non-gaussian picture!! energetically! energetically! inefficient! efficient! transport transport 10 ps non-ergodic energetically! efficient! transport

34 What did we learn? Combination of flexibility and surface charges -> intense electrostatic noise. Barriers of biological reactions depend on relaxation time (nonergodicity of biology). ( there s plenty of room at the bottom of time-scales) Energetic bottlenecks of biological energy production are eliminated by restricting the rules of thermodynamics. 34

35 Why are enzymes big? We are all familiar with the systems like software (or government legislation) can grow rapidly in size over a number of years. Enzyme evolution is a great deal slower - but it has been going for million of years From Enzyme Models to Model Enzymes, Kirby & Hollfelder Maybe because slow reactions require slower elastic deformations of the interface HA - QA -> HA-QA - k exp k CS , GHz

36 bc1 complex: 15 microseconds MD (Anton)

37 The laws of nature that we care about emerge through collective self-organization and really do not require knowledge of their component parts they owe their reliability to principles of organization rather than to microscopic rules. - Robert Laughlin the advancement of science depends on the discovery and development of exact ideas to warrant the deductions we may draw by the application of mathematical reasoning. - J. C. Maxwell

38 Dissipative Electro-Elastic Network Model (DENM) Atomic#charges res i res j active site Spring#Constant t 0 ζ(t t ) q m (t )dt + λ m q m = F(t)+R(t) Hessian#Matrix JCP#137#(2012)#165101

39 CytB: potential response DENM MD ( ) /ns -1 Elastic deformations of the protein shape 39

40 Does sequence matter? e 2 ( ) W+P W P metmb /ns CytC /ns -1 λ s = λ w + λ p + λ pw (δx w + δx p ) 2 Protein λ p, ev λ w, ev λ s,ev Myoglobin Cytochrome c Protein-water compensation depends on the surface charge (sequence+folding). critical term

41 Lambda: dynamical transition k B T var, ev MD (GFP protein) T/K Standard#picture: Proteins: JPCB 116 (2012)

42 Glassy kinetics 1 2 High-temperature rate constant: Fogel-Fulcher-Tammann high-temperature kinetics

43 Average electrostatic potential + + P Fe W P ( ) Gaussian fit W P+W cytochrome c P / Protein and water contributions tend to compensate each other