We measure the rate (constant) But compute the ac0va0on free energy d d[4p] − = = k dt dt 0.69 t1/2 = k The connecGon is Transi0on State Theory k≈ kBT − ΔG ≠ / RT h e ( 10 -1 −1 = 2.1 × 10 s K T ⋅ e − ΔG ≠ / RT ) ( k ≈ 10 s 10 13 -1 ) − ΔG ≠ /1.4 (room T, ΔG in kcal/mol)
To compute the rate constant we need to ﬁnd the transi0on state Image: h4p://en.wikipedia.org/wiki/TransiGon_state_theory
Since bonds are broken/formed we must use quantum mechanics to ﬁnd the TS (methods like B3LYP/6-‐31G(d) and PM3) Source: Patrick Rydberg Finding the TS is much trickier than ﬁnding the reactant and product (minima) structures Finding minima: minimize E along all degrees of freedom Finding TS: maximize E along one* degree of freedom and minimize along rest *but which one? h4p://en.wikipedia.org/wiki/Saddle_point
The free energy has two contribuGons: PotenGal (electronic) energy and vibraGonal free energy Approximate TS as maximum on Minimum (PotenGal) Energy Path (MEP) G X ≈ Eele + Gvib X XPoten0al energy E
Approximate TS as maximum on Reac0on Coordinate scan the Poten0al Energy Surface (PES) G X ≈ Eele + Gvib X XPoten0al energy E O-‐C Distance O-‐C distance is kept ﬁxed during energy minimizaGon
Approximate TS can then serve as a starGng point for ﬁnding the real transi0on state This requires an (expensive) frequency calcula0on G X ≈ Eele + Gvib X XPoten0al energy E
Once the real transiGon state is found the vibraGonal free energy can be calculated to yield the ac0va0on free energy This requires another (expensive) frequency calculaGon G X ≈ Eele + Gvib X X
Building a TransiGon State: The movie h4p://molecularmodelingbasics.blogspot.com/2009/06/building-‐transiGon-‐state.html h4p://molecularmodelingbasics.blogspot.com/search/label/transiGon%20state
Modeling Chemical Reac0ons in Enzyme Ac0ve Sites Enzymes are too large to be treated quantum mechanically image: 10.1080/01442350903495417 Source: Patrick Rydberg Image: 10.1021/jp805137x
image: 10.1080/01442350903495417 One opGon is to make a small (gas phase) model of the acGve site Problems: Key interacGons missing System is too ﬂoppy Can by ﬁxed by going to larger models but expensive Image: 10.1021/jp805137x
image: 10.1080/01442350903495417 Another opGon is QM/MM Red: QM region Yellow & Green: MM Problems: QM/MM Boundary Set-‐up is diﬃcult Schrodinger’s QM/MM: Qsite Source: 10.1021/jp805137x
Ques0ons Now? Ques0ons Later? Leave a comment on h4p://proteinsandwavefuncGons.blogspot.com/2011/02/modeling-‐chemical-‐reacGons-‐in-‐enzyme.html
A particular slide catching your eye?
Clipping is a handy way to collect important slides you want to go back to later.