Hybrid Quantum Mechanics / Molecular Mechanics (QM/MM) Approaches - Examples of Applications (and troubles ) - Mauro Boero Institut de Physique et Chimie des Matériaux de Strasbourg University of Strasbourg - CNRS, F-67034 Strasbourg, France and @Institute of Materials and Systems for Sustainability, Nagoya University - Oshiyama Group, Nagoya Japan 1
Example 1: Charge localization and transport in DNA • Is the spin (and the charge) moving along the DNA coupled to the proton transfer process (proton coupled electron transfer) as proposed by B. Giese at al., Chem. Comm. 2108 (2001); Nature 412 318 (2001) [Basel Universität] ? • Or is it rather a polaron: charge coupled to the tilting of the G-bases (as suggested by P. T. Henderson et al. Proc. Natl. Acad. Sci. USA 96 , 8353 (1999) [Georgia Inst. of Technology] and J. Rudnick at al. Phys. Rev. Lett. 85 , 4393 (2000) [UCLA] ? • Or are the two events occurring simultaneously in a concerted way. i.e. the bases tilt and in doing so they favor the proton transfer that, in turn, induces the spin localization and the charge transfer ? 2
DNA conducting properties have been very clearly unraveled in major journals… DNA is an insulatingmetalsemisuperconductor …all right, we are just kidding ! ;-) 3
QM/MM Double Stranded Hydrated B-DNA system G:C A:T G:C G:C G:C •Fully hydrated 38-base pair B-DNA •LSD-HCTH gradient corrected functional •MM: 20265 atoms (5902 solvent H 2 O) in a box of 38 x 49 x 154 Å 3 •QM: 819 e - , 238 atoms + 4 capping H E cut = 70 Ry (386625 PWs) •Cell = 22.6 x 48.6 x 38.5 Å 3 4
QM/MM + Metadynamics for N-H distance s ( t ) = | R ( N) – R( H Gua )| D F = 6.5 kcal/mol proton and spin transfer initial spin position 5
QM/MM + Metadynamics for N-H coordination number s ( t ) = N coord ( N ,H solute ) D F = 7.2 kcal/mol 6
Double proton shift mechanism: 7
Initial configuration: proton spin Final configuration: proton + spin on the same G-C site 8
The transition is such that the spin is transferred from a G-base to another one via backbone G -H :C +* (final) charge flow G:C z -axis (initial) This is however not the only possibility, since experiments have evidenced charge transfer also in case of broken backbone 9
Double proton shift: Acidification of G-base • The deprotonation is triggered by a transfer to G of a proton belonging to C • G (contrary to G +. ) is not acidic, making the single proton exchange highly unfavorable • A double proton exchange makes the final state energetically more favorable 10
C G h + C G N 1 + C G h +
Problem Workaround Electron spill-out Auxiliary bounding potential V bound ( x ) = A x 2 n MM MM QM 12
About the Workaround • The auxiliary bounding potential V bound ( x ) = A x 2 n can be simply added to the Kohn-Sham Hamiltonian • The power law 2 n can be adjusted to make the bounding walls more or less stiff • Contrary to a “ step function ”-like box, the force is not discontinuous at the boundaries and can be computed as V 2 n 1 bound A 2 n x x • Thus we do not need two different Hamiltonians inside the QM box and outside it. • But the force can become very large: use small A pre-factors ! 13
Conclusions about the DNA system: 1. The proton is transferred from the initial G base to the nearby paired C base and, in turn, this H + shift induces a charge transfer from the starting GGG site to this deprotonated G base . 2. This provides a clear indication that the deprotonation is essential and not accessory to the charge transfer along DNA and is triggered by a transfer to G of a proton belonging to C . 3. The double proton exchange makes the final state energetically more favorable than a single proton transfer since G is not acidic . 4. The charge displacement occurs via a flow that passes across the backbone. 5. The free energy profile in the same figure shows that an activation barrier of 6-7 kcal/mol has to be overcome in order to complete the charge transfer and this agrees rather well with the known experimental outcome. 6. Yet, experiments are not capable of catching the intimate details of the reaction and in this respect these results represent the first attempt ever to unravel the proposed mechanism. 14
Example 2: ATP to ADP conversion • ATP synthase: ATPase, short acronym for ATP synthase, is a reaction used by living organisms in a wealth of processes (see e.g. S. M. Wilbanks and D. B. McKay, Biochemistry 37 , 7456 (1988)). • It is the “gasoline” of molecular motors: converting chemical energy of Adenosin-triphosphate (ATP) into mechanical motion with metal ions (Mg 2+ /Ca 2+ , K + ) playing a still unclear role (W.D. Frash, Biochim. Biophys. Acta 1458 , 310 (2000)). • This process is ubiquitous in nature and is used by all living systems: “ The principal net chemical reaction occurring in the whole world ” (P. D. Boyer, Nobel Lecture in Chemistry , World Scientific Ed., Singapore, 2003) • Appealing applications as molecular machines and nanoscale batteries are now at a (very) pioneering stage. 15
Bovine heat shock cognate (Hsc70) protein ATPase T13G mutant system P a P b K 2 P g Mg K 1 • Representative of chaperones family • Accurate X-ray data available • Metal ions are crucial 16
Bovine heat shock cognate (Hsc70) protein ATPase: why is it interesting ? ...well because it is our exercise and • As a response to stress, cells produce a whole series of Heat Shock Proteins. • They protects the cell against stress. • Exert protein metabolism functions such as degradation, folding and synthesis • Act as stress sensing and help the cell to adapt to stress and development • Response to muscle disorders (atrophy, hypertropy) and injury • Response to heat shock • Response to ischemia • Response to fatigue and exercise in skeletal muscle See e.g. Y. Liu et al. Frontiers in Bioscience 11 , 2802-2827 (2006) 17
QM/MM hybrid 5 ps simulation (started after AMBER equilibration) System size: 50730 atoms (thin sticks) 5910 Hsc70 atoms + 14940 H 2 O molecules QM subsystem: 35 atoms (stick&balls) +1 H-capping link atom 142 electrons (LSD) DFT - HCTH functional PW basis set (194196 PWs) E cut-off = 80 Ry Martins-Troullier PPs NLCC for Mg, semicore for K s 1 =|P g – O water | QM cell = 17 x 17 x 17 Å 3 s 2 =|O 3 b – H water | 18
Bovine heat shock cognate (Hsc70) protein ATPase T13G mutant • Side chain main residues within 10 Å from the ATP site. • His has not a direct interaction being located at distances larger than 9-10 Å 19
QM/MM Metadynamics Simulation with s 1 =|P g – O water | s 2 =|O 3 b – H water | 20
Collective variables from metadynamics: breaking the P g -O 3 b bond upon H 2 O dissociation s 1 =| P g – O water | & s 2 =| O 3 b – H water | 21
Free energy landscape reconstruction 22
final: Penalty potential ADP V ( s 1 , s 2 ) = - F ( s 1 , s 2 ) V ( s 1 , s 2 ) (kcal/mol) 10 9 8 7 6 5 initial: 4 3 ATP 2 1 0 P g -O wat (Å) O b 3 -H wat (Å) 23
F ( s 1 , s 2 ) (kcal/mol) -2 ATP -4 -6 0 -8 -5 -10 ADP -10 valley of Mg 2+ solvation shell fluctuations 4.0 1.0 3.0 2.0 P g -O wat (Å) 2.0 3.0 4.0 3 -H wat O b 0 (Å) F ( s 1 , s 2 ) ATP -5 (kcal/mol) ADP -10 D F # = F ATP - F TS = 3.0 kcal/mol D F = F ATP - F ADP = 6.9 kcal/mol s 1 , s 2 (Å) 1 1.5 2 2.5 3 3.5 4 (exp. 7.1 kcal/mol)
Collective variables for metadynamics simulations Simulation using s ( t ) = N coord ( P g ,O wat ) coordination number of P g with any O wat of the solvent to check in an unbiased way which water molecule participate to the reaction No constraint is imposed on H wat atoms 25
Simulation with N coord (P g -O wat ) D F # = F ATP - F TS = 3.2 kcal/mol D F = F ATP - F ADP = 7.0 kcal/mol ATP ADP+P i 26
K 2 + OH - Mg-O wat K 1 -O wat No proton wire exchange of OH - between Mg 2+ and K + mechanism !
Problems Workarounds 1) Atoms spill-out: Reflecting (soft) QM walls: H 2 O molecules box_boundary_utils.mod.F90 escaping the QM in ./src activated by keyword box BOX WALLS 2) Coordination number Separate solute and solvent of the solvent (O wat ,H wat ) species in the CPMD input avoiding other O and H file QM atoms belonging to the solute 28
About the Workaround 1 • The reflecting box walls just reverse the motion of the escaping atoms when they go beyond a given distance from the QM box boundaries p M R p I I I I • Note that, although affecting the momentum , this does not affect the Hamiltonian, since momenta enter only as p I 2 , hence the energy conservation is preserved 2 2 p H I V R I M I I 29
Simulation with s ( t ) = N coord (P g , O wat ) ADP+P i ATP no reflecting walls reflecting walls 30
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