Com omputer S Simulation ons of of Biol ologi ogical Function ons ; F From om E Enzymes t to o Molec ecular M Machines es
Send nding ng i inf nformation n (Signa nals) in t n the c cell
No Enzyme Enzyme
12 1 How 11 Aha! I does 10 2 that see! 3 work? 9 8 4 7 5 6
Bio iochemis istry –Disco covers t the cl clock ck Crys ystallography y –Sho hows all t the he pa parts Single le mo mole lecule les– Det eter ermines es h how fast the w e wheel eels rotate
Abstract Israel J. of Chem. Proceeding of the 34 Meeting V ol 4 1966 “On the interaction of chymotrypsin with ionized Substrate” A. Varshel and Y Shalitin During undergraduate work concluded that (since external salts have very small effect ) electrostatic is unlikely to be important
Impact parameter Asymptotic solution f for en enzymes es ( Thecnion 1965) 1965)- Eventially lly E EVB
Lifson ( Nir David)- - - - - Warshel (Sde Nahom ) about 3 km distance
1968-1970 Weizmann Institute \Weizmann Around 20 years latter
Early development of the general Cartesian Force field and prograrm ( 1966- 69) Energy , Structure and vibrations of general molecules and molecular crystals
A. Warshel & M. Karplus, J. Am. Chem. Soc. , 1972 QM(MO)+ M M
Back t to Enzymes es Adding the environment to the quantum mechanics(QM) part
QM/MM: To study enzymatic reactions, we divide the system in two parts (Warshel & Levitt, JMB 1976)
The Empirical Valence Bond (EVB) method ( JACS 1980 ) Reactant : Force field-like functions describing the reactants ’ bonding pattern Product : Force field-like functions describing the products ’ bonding pattern Product Reactant Ground State : Eigenvalue of 2x2 Hamiltonian built from Reactant and Product energies and Off-diagonal function (H 12 ).
The Ras/GAP complex catalyzes GTP hydrolysis
Calc Exp Water 27.9 (27.5) 23.1, 22.2 Ras 23.2 15.9 RasGap 16.1 Good Agreement between calculation and experiment
M. Roca, A. Vardi- Kilshtain and A. Warshel, Biochemistry , 48, 3046- 3056 (2009). Calculating effect of mutations
Warshel , PNAS (1978) • The secret of Enzyme catalysis is electrostatic preorganization
Reaction in water Spend a large amount of energy rotating the water molecules Reaction in protein The protein polar groups and charges are already pointing in the correct direction
Bridging time scales and length scales
For short time scales can use direct MD simulations to determine the exact time dependence on an atomistic level
z y x g
Simulated in Biochemistry 1988
What about reproducing the structural changes and their time dependence and long time dynamics Needs Free Eenrgy landscape and and efficient approach
Coarse Grained (CG) approaches
Very Early CG Computer Simulation of Protein Folding Michael Levitt and Arieh Warshel, Nature (1975) 253 , 694-698
Improved Coarse Grained Model PROTEINS , 78, 1212–1227 (2010 ) Ann Rev Phys Chem 62, 62, 41 41- 64 64 (201 2011) 1) Now focused ed on bet etter er trea eatmen ent of el elec ectrostatics f free ee en ener ergy Mai ainly self energy (solvat ation) an and c char arge- charge e inter eraction ( ) ( ) ( ) ( ) ∑ ∆ = + + np np p p mem mem G U N U N U N self self i self i self i i + + Nonpolar r res esidues es Polar r res esidues es Ionizable r e res esidues es
• Long time simulations
Newtonian Dynamics Brownian Dynamics
The Renormalization Model
Long time dynamics, conform. coordinate x conform (t) autocorrelation function
F 1 F 0 -ATP synthase – The smallest rotary motor The e 1997 N Nobel el P Prize i e in C Chem emis John Walker Movie F 1 F 0 are two coupled rotary motors; an ATPase and an ion-pump In presence of right ion-gradient F 0 transports ion across the membrane and F 1 synthesizes ATP In the opposite direction ATP hydrolysis occurs in F 1 , while F 0 acts as an ion-pump
Mechano-Chemical Coupling between the central stalk and the catalytic dimers in F 1 Each 120 120 ° rot otation on of of the Stalk brok oken in 80 ° and 40 40 ° step eps by t the e Catalytic Dwell Seq equen ence o e of E Even ents Ligand nd B Bind nding ng 8 80 ° rot otation on ATP catalysis 40 40 ° rot otation on Kinosita movie Y asuda, R. et. al., Nature, 2001.
The C e CG el elec ectrostatic free ee en ener ergy f for t the e 360 ° rot otation on of c central al stal alk an and cat atal alytic s subunit conformat ation changes es tion S. Mukherjee and A.Warshel, Proc. Natl. Acad. Sci. USA ,108, 20550–20555 (2011) tati talk rota Sta tral S Centr Con onfor ormation on change ge of of c catalytic subunits The l e lea east en ener ergy p path clea early shows the e 80 ° /40 40 ° substeps. The 8 e 80 ° rotat ation has as smal all electrostat atic b bar arrier. . The 4 e 40 ° rot otation on and con onfor ormation on change ge of of c catalytic subunits has
Simplifi fied s surfa face of f F 1 - ATPase function sh shows s the cou oupling g of of ATP hydrol olysis with central stalk rot otation on The functional al surfac ace reveal als w why cat atal alysis occurs af after 80 ° rota tati tion ATP hydro rolysis is in in water r has Hig igh barrie ier r of 40 ° rotat ation an and cat atal alytic very hig igh b barrie ier r and wil ill subunit changes bias the system need mon onths to o oc occur towards ATP A TP hyd ydrolys ysis
F1F0-ATP synthase – The smallest rotary motor F1F0 are two coupled ATPase and ion-pump ATP Consists of a rotary motor and a stator portion ADP + P i In presence of right ion- H + gradient across the membrane ATP synthesis occurs in the F1 In the opposite direction ATP hydrolysis occurs while the F0 acts as an ion-pump
What driv ives u unid idir irectio ional w walkin ing motio ion of myosin n V on a n actin f n filament nts Almost no no backsteps as myosinV nV walks over actin n filament nt
It is h hard to u und nderstand nd uni nidirectiona nal l movement nt, even i n in o n our daily ly li life !!!
CG en ener erget etics of a a s single e leg eg as i it b ben ends (change ges c con onfor ormation on) Schematic func nctiona nal cycle of myosin n V sing ngle leg
Low ow cos ost of of w walking f g for orward in M Myos osin High gh cos ost of of w walking g backwards i in M Myos osin V
Life T T ransistors
K
Ionic Strength Effect and External Potential α ± ± βφ ± βφ g = q i + + q i N e Q e i i ± = = − box box q q i ± ± i A A P g q j q k ∑ ∑ ϕ i = 332 + 332 + V i ext ε eff ε wat r gp r k ≠ i j ij ik − ⋅ ε ( Z Z ) D / Z < Z 0 0 wat 1 − ⋅ ε + − ⋅ ε ≤ ≤ i i V = V = ( Z Z ) D / ( Z Z ) D / Z Z Z ext ideal 1 0 0 wat 1 0 mem 1 2 − ⋅ ε + − ⋅ ε + − ⋅ ε ( Z Z ) D / ( Z Z ) D / ( Z Z ) D / Z > Z 1 0 0 wat 2 1 0 mem 2 0 wat 2 For protein-containing systems Need to approximate 52
Transloc ocon on a and R Ribos osom ome Cou oupling g White and von Heijne, Annu. Rev. Biophys., 2008
Drug Resistance
Vitality diagram for double mutant → → − ∆∆ + ∆∆ N M N M G ( TS ) G ( drug ) bind bind charged residue large e vita tality ty preferable for virus small vitality charged residue Ishikita & Warshel (2007)
Influence of the size of nonpolar residue on vitality value → − ∆∆ + ∆ N M G ( TS ) G ( drug ) bind bind calc. exp. H 3 C H 3 C H Ishikita & Warshel (2007)
STR TRUCTU TURE- FUNC UNCTION R RELATIONS NSHIP STRUCTURE FUNCTION Missing link ENERGY SOLVATION BY PROTEIN + WATER MAINLY ELECTROSTATIC!
A.Adamczyk M.Kato A.Reymer J.Aqvist I.Kim M.Roca J.Bentzien G.King E.Rosta J.Bertran M.Klahn R.Rucker M.Bohac B.Kormos S.Russel R.P .Bora M.Kosloff A.Rychkova S.Braun- Sand I.Kupchenko P .Schopf A.Burykin S.Kuwajima N.Schutz J.Cao J.Lameira T .Schweins S.Chakrabarty R.Langen Y.Sham Z.T .Chu F .Lee P .Sharma E.Chudyk N.Li A.Shurki A.Churg H.Liu M.K.Singh M.de Caceres V .Luzhkov N.Singh C.Deakyne L.Manna M.Strajbl A.Dryga R.Matute F .Sussman J.Florian J.Mavri H.T ao M.Fothergill B.Messer W.Thompson M.Frushicheva M.Mills N.Vaidehi M.Fuxreiter I.Muegge A.Vardi T .Glennon R.Mueller P .Varnai M.Haranczyk S.Mukherjee S.Vicatos G.Hong J.Na J.Villa J.- K.Hwang G.Naray- Szabo R.Weiss H.Ishikita P .Oelschlaeger T .Wesolowski C- Y.Jen M.Olsson H.Y.Woon L.Kamerlin A.Papazyan Y.Xiang M.Kato A.Pisliakov A.Yadav I.Kim N.Plotnikov
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