Com omputer S Simulation ons of of Biol ologi ogical Function - - PowerPoint PPT Presentation

Com

• mputer S

Simulation

• ns of
• f Biol
• logi
• gical

Function

• ns ; F

From

• m E

Enzymes t to

• Molec

ecular M Machines es

Send nding ng i inf nformation n (Signa nals) in t n the c cell

No Enzyme Enzyme

Aha! I see!

12 1 2 3 4 5 6 7 8 9 10 11

How does that work?

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

• l 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

\Weizmann

1968-1970 Weizmann Institute

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 )

Product Reactant Reactant:

Force field-like functions describing the reactants’ bonding pattern

Product:

Force field-like functions describing the products’ bonding pattern

Ground State:

Eigenvalue of 2x2 Hamiltonian built from Reactant and Product energies and Off-diagonal function (H12).

The Ras/GAP complex catalyzes GTP hydrolysis

Calc

Exp

Water 27.9 (27.5) Ras 23.2 23.1, 22.2 RasGap 16.1 15.9

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 Reaction in protein

Spend a large amount of energy rotating the water molecules 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

g x z y

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

Computer Simulation of Protein Folding Michael Levitt and Arieh Warshel, Nature (1975) 253, 694-698

Very Early CG

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 i i i self self self self i

G U N U N U N ∆ = + +

∑

+ +

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

xconform(t) autocorrelation function

Long time dynamics, conform. coordinate

F1F0-ATP synthase – The smallest rotary motor

F1F0 are two coupled rotary motors; an ATPase and an ion-pump In presence of right ion-gradient F0 transports ion across the membrane and F1 synthesizes ATP In the opposite direction ATP hydrolysis

• ccurs in F1, while

F0 acts as an ion-pump

John Walker Movie The e 1997 N Nobel el P Prize i e in C Chem emis

Mechano-Chemical Coupling between the central stalk and the catalytic dimers in F1

Y asuda, R. et. al., Nature, 2001. Each 120 120° rot

• tation
• n of
• f the Stalk brok
• ken 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

• tation
• n

ATP catalysis

40

40° rot

• tation
• n

Kinosita movie

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

• tation
• n and con
• nfor
• rmation
• n change

ge of

• f c

catalytic subunits has

• S. Mukherjee and A.Warshel, Proc. Natl. Acad. Sci. USA ,108, 20550–20555 (2011)

The C e CG el elec ectrostatic free ee en ener ergy f for t the e 360° rot

• tation
• n
• f c

central al stal alk an and cat atal alytic s subunit conformat ation changes es

Centr tral S Sta talk rota tati tion Con

• nfor
• rmation
• n change

ge of

• f c

catalytic subunits

Simplifi fied s surfa face of f F1- ATPase function sh shows s the cou

• upling

g of

• f ATP hydrol
• lysis with central stalk rot
• tation
• n

Hig igh barrie ier r of 40° rotat ation an and cat atal alytic subunit changes bias the system towards A ATP TP hyd ydrolys ysis 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 very hig igh b barrie ier r and wil ill need mon

• nths to
• oc
• ccur

F1F0-ATP synthase – The smallest rotary motor

F1F0 are two coupled ATPase and ion-pump Consists of a rotary motor and a stator portion In presence of right ion- 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 H+ ADP + Pi ATP

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

• nfor
• rmation
• n)

Schematic func nctiona nal cycle of myosin n V sing ngle leg

Low

• w cos
• st of
• f w

walking f g for

• rward in M

Myos

• sin

High gh cos

• st of
• f w

walking g backwards i in M Myos

• sin V

Life T T ransistors

K

Ionic Strength Effect and External Potential

qi

g = qi + + qi −

i i

box box i

N e Q e q A A

βφ βφ

α ±

± ± ± ± ±

= =

 

ϕi = 332 qj

P

εeff

gpr ij j

∑

+ 332 qk

g

ε watr

ik k≠i

∑

+ Vi

ext

52

1 1 1 1 2 1 2 1 2 2

( ) / < = = ( ) / ( ) / ( ) / ( ) / ( ) / >

wat i i ext ideal wat mem wat mem wat

Z Z D Z Z V V Z Z D Z Z D Z Z Z Z Z D Z Z D Z Z D Z Z ε ε ε ε ε ε  − ⋅  − ⋅ + − ⋅ ≤ ≤   − ⋅ + − ⋅ + − ⋅ 

For protein-containing systems Need to approximate

Transloc

• con
• n a

and R Ribos

• som
• me Cou
• upling

g

White and von Heijne,

• Annu. Rev. Biophys.,

2008

Drug Resistance

Vitality diagram for double mutant

Ishikita & Warshel (2007)

) ( ) ( drug G TS G

M N bind M N bind → →

∆∆ + ∆∆ −

large e vita tality ty small vitality  preferable for virus

charged residue charged residue

Influence of the size of nonpolar residue on vitality value

Ishikita & Warshel (2007)

H

C H3 C H3

exp. calc.

) ( ) ( drug G TS G

bind M N bind

∆ + ∆∆ −

→

STR TRUCTU TURE- FUNC UNCTION R RELATIONS NSHIP

STRUCTURE SOLVATION BY PROTEIN + WATER ENERGY FUNCTION MAINLY ELECTROSTATIC!

Missing link

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

Mechano-Chemical Coupling between γ and α/β dimers : As revealed by numerous single-molecule studies

Binding dwell Catalytic dwell

Shimo-Kon, R. et. al., Biophys. J., 2010. Y asuda, , R. . et. . al., N ., Nature, 2 , 2001. .

Und nderstand nding ng t the action o n of p proton d n driven F n F0 mot

• tor
• r

A 2D schem ematic model el o

• f

F0 rot

• tation
• n c

cou

• upled to
• ion
• n transpor
• rt

The C e CG el elec ectrostatic free ee en ener ergy f for F F0 rot

• tation
• n

cou

• upled t

to

• prot
• ton
• n transpor
• rt acros
• ss m

membrane

Uptake of

• f prot
• ton
• ns f

from

• m

the he lo low pH pH side Release of

• f prot
• ton
• ns t

to

• the

he hi high h pH pH side

Free en ee ener ergy s surface e that c can ex explain unid idir irectio ional w walkin ing motio ion

Forward steps are p e pref efer erred ed by lower barri rriers rs

• r f

free ee en ener ergies es Backward steps are o e obstructed ed by hig igher b r barrie iers

• r free

ee en ener ergies es

Free Energy of the System

Voltage (volt) Closed (kcal) Open (kcal)

• 0.2
• 203
• 189

0.0

• 201
• 200

+0.2

• 202
• 218

The free energy at different regions

• f the conformation/voltage

landscape

Dryga A, Chakrabarty S, Vicatos S, & Warshel A (2011) Realistic simulation of the activation of voltage gated ion channels. PNAS (in press)

73

A General Cycle For Moving between Different Multiscale Leveles

JPC 2013 Systematic QM(ai)/MM PMFs

PNAS 2013

• A. Warshel & A. Bromberg, J. Chem. Phys., 1970
• A. Warshel & M. Karplus, J. Am. Chem. Soc., 1972

QM(VB) + MM QM(MO) + MM

Molecular Mechanics Quantum Mechanics cannot study chemistry very expensive

A General Thermodynamic CycleFor MultiScale Modeling

High level ab initio potential EVB potential Our Pradynamics ( since 1992 with different names )

CG en ener erget etics of a a s single e leg eg as i it b ben ends (change ges c con

• nfor
• rmation
• n)

Schematic func nctiona nal cycle of myosin n V sing ngle leg

Pontifical Academy 1983 Free energy perturbation in enzyme catalysis