SL22015 Molecular Biochemistry Lecture 6 PDF

SL22015 Molecular Biochemistry 6. Electron transfer reactions, quantum tunnelling (More physics…) Dr Fiona Dickinson, WH1.18. v1.0 October 2024  Rate enhancement kcat κcat ΔΔ‡G...

SL22015 Molecular Biochemistry 6. Electron transfer reactions, quantum tunnelling (More physics…) Dr Fiona Dickinson, WH1.18. v1.0 October 2024  Rate enhancement kcat κcat ΔΔ‡G rate enhancement = = e RT knon-cat κnon-cat kBT −Δ‡G kTS = κ e RT ΔΔ‡G = Δ‡Gnon-cat − Δ‡Gcat h The enh ncement is due to di erences in v1.0 fd287@b th. c.uk the tr nsmission coe icient nd the di erence between the Gibbs free energy of the tr nsition st te Enh ncements of 1012 - 1015 re typic l for enzyme c t lysed re ctions ff a a a a a a a a a a ff a a ff a  Transition States C t lysts work by lowering the energy of the tr nsition st te ES‡ The re ction p sses through the s me tr nsition st te (structure) ES‡c Δ‡G t The Gibbs’ free energy of ctiv tion is t ken from re ct nts not from the ES ΔG Δ‡Gc t complex proti ted deuter ted E+S v1.0 fd287@b th. c.uk ΔG0 ES Some re ctions go to ‘f st’ to be p ssing E+P through even this enzyme c t lysed EP tr nsition st te… why??? reaction coordinate a a a a a a a a a a a a a a a a a a a a a a a a a Electron transfer reactions Reactions which don’t involve the making and breaking of bonds Electron transfer reactions The simplest cl ss of re ction re electron tr nsfer or electron exch nge re ctions Ψ* D + A D+ + A− Ψ Ψ* Ψ v1.0 fd287@b th. c.uk Ψ* Ψ* D− + A D + A− Ψ Ψ a a a a a a Marcus Theory A new theory of kinetic rates 2π | V(r) |2 1 − (ΔG + λ)o 2 ket = e 4λk T B h 4πλkBT o − β(r −2 r0) | V(r) | = | V(r) | e v1.0 fd287@b th. c.uk ket is the r te of electron tr nsfer |V(r)|º is the electronic coupling element t closest sep r tion |V(r)| is the overl p integr l between the donor nd cceptor r is the centre to centre sep r tion of the donor nd cceptor h is Pl nck’s const nt ro is the closest possible centre to centre dist nce kB is Boltzm n’s const nt β is the dist nce dependence sc ling f ctor (how well the T is the bsolute temper ture medium couples the donor nd cceptor w vefunctions) Gº is the driving force of the re ction λ is the reorg niz tion energy of the system a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a  Marcus Theory A new theory of kinetic rates M rcus theory introduces the concept of the ‘reorg nis tion energy’, λ Electron tr nsfers re ‘f st’ (~10−15 s) so the environment is poorly minimised λ fter the electon tr nsfer v1.0 fd287@b th. c.uk 2|V(r)| -ΔGº a a a a a a a a a a Marcus Theory Where ΔGº is the difference in Gibbs energy of the reactions and ΔG‡ is the free energy difference between the reactants λ and the transition state D- + A ΔGº = 0 −ΔGº < λ −ΔGº = λ −ΔGº > λ D + A- Potential λ v1.0 fd287@b th. c.uk -ΔGº a a  Marcus Theory λ We c n now consider re ctions th t D- + A −ΔGº = λ h ve no reorg nis tion energy (or free D + A- energy of ctiv tion Or even c ses where re ction becomes so f vour ble the r te slows down v1.0 fd287@b th. c.uk a a a a a a a a a a a a a a a a Quantum Tunneling Going through the barrier  Anomalies in kinetic observations Sometimes the kinetic isotope e ect is much bigger th n expected C nnot be due to di erences in zero point energies of the isotopes Some re ctions show n Arrhenius pref ctor, A, which is sm llest for proti ted re ct nts nd biggest for triti ted Some re ctions proceed despite unf vour ble temper tures v1.0 fd287@b th. c.uk Why? a a a a a a a a a ff a ff a a a a Wave Particle Duality Electrons can be considered to be particles and/or waves v1.0 fd287@b th. c.uk h λ= mv λ is the w velength of w ve/p rticle h is Pl nck’s const nt m is the m ss of the p rticle v the velocity of the p rticle a a a a a a a a a a Tunneling Quantum Mechanics v1.0 fd287@b th. c.uk The mplitude of the oscill tion is represent tive of the prob bility. a a a a a  Tunneling Quantum Mechanics 12 ES‡ 10 log k / s−1 8 6 4 2 0 5 10 15 20 25 ΔG D-A separation / Å E+S v1.0 fd287@b th. c.uk ΔG0 Tunneling re ctions re very dist nce depend nt E+P reaction coordinate a a a a a a  Tunneling Tunneling occurs when there is prob bility the p rticle c n exist Kinetic Isotope E ects in product potenti l well (when the w ve function exists in the product potenti l well). Qu ntum tunneling is seen with: Electrons Isotopes of protons v1.0 fd287@b th. c.uk light isotope Isotopes of hydrogen he vy isotope Isotopes of hydrides re ct nt product a a a a a a a a a a a ff a a Tunneling In enzymes There is v st mounts of current liter ture on electron nd hydrogen tunnelling in enzyme c t lysed re ctions… v1.0 fd287@b th. c.uk a a a a a a a a The end… so far In summary  Different models of kinetics Moved from Arrhenius to more dv nced models TST (for re ctions where bonds re m de nd broken) M rcus (for electron tr nsfer) M rcus like for tunnelling of protons v1.0 fd287@b th. c.uk Also looked t thermodyn mics nd structure of binding a a a a a a a a a a a a a a