optimization of protein force-field parameters€¦ · optimization of protein force-field...

Optimization of Protein Force-Field Parameters

Yuko OKAMOTO （岡本祐幸） Department of Physics and

Structural Biology Research Center

Graduate School of Science

and Center for Computational Science

Graduate School of Engineering

and Information Technology Center

NAGOYA UNIVERSITY （名古屋大学） e-mail: okamoto{a}phys.nagoya-u.ac.jp

URL: http://www.tb.phys.nagoya-u.ac.jp/

Seminar at the Basque Center for Applied Mathematics

July 14, 2014

cano

E

PB(E) = n(E)WB(E)

Canonical Probability Distribution

E

WB(E) = exp(- E )

Boltzmann Factor

E

n(E)

Density of States

Canonical Ensemble at

Temperature T

SA-2

P B

(E)

E E

P B

(E) = n(E)W B

(E)

High T

P B

(E)

E

E min

Low T

Canonical Distributions of Potential Energy

Intermediate T

30

20

10

0

-10

E

200000150000100000500000

MC Sweeps

Canonical 1000K

30

20

10

0

-10

E

200000150000100000500000

MC Sweeps

Canonical 600K

30

20

10

0

-10

E

200000150000100000500000

MC Sweeps

Canonical 50K

Generalized-Ensemble Algorithm（拡張アンサンブル法） Generic Term for Simulation Methods that Greatly Enhance

Conformational Sampling [e.g., Multicanonical Algorithm, Wang-Landau, Simulated Tempering, Replica-Exchange Method, etc.]

Based on Non-Boltzmann Weight Factors

Realize random walks in potential energy and/or any other physical quantities (OR their conjugate parameters)

Histogram Reweighting Techniques

Can obtain thermodynamic quantities for a wide range of temperature

and/or other parameter values from a single simulation run REVIEWS: U.H.E. Hansmann & Y.O., in Ann. Rev. Comput. Phys. VI, D. Stauffer (ed.) (World Scientific, Singapore, 1999) pp. 129-157;

A. Mitsutake, Y. Sugita, & Y.O., Biopolymers 60, 96 (2001); Y.O., J. Mol. Graphics Modell. 22, 425 (2004);

Y. Sugita, A. Mitsutake, & Y.O., in Lecture Notes in Physics,

W. Janke (ed.) (Springer-Verlag, Berlin, 2008) pp. 369-407; H. Okumura, S.G. Itoh, & Y.O., in Practical Aspects of Computational Chemistry II: An Overview of the Last Two Decades and Current Trends,

J. Leszczynski and M.K. Shukla (eds.) (Springer, Dordrecht, 2012) pp. 69-101;

A. Mitsutake, Y. Mori, and Y.O, in Biomolecular Simulations: Methods and Protocols,

L. Monticelli and E. Salonen (eds.) (Humana Press, New York, 2012) pp. 153-195;

H. Kokubo, T. Tanaka, & Y.O., in Advances in Protein Chemistry and Structural Biology,

T. Karabencheva-Christova (ed.) (Elsevier, Amsterdam, 2013) pp. 63-91.

P mu

(E) = n(E)W mu

(E) = const

E

E min

Multicanonical Algorithm

uniform (flat) distribution in energy

W mu

(E) = n(E) -1

Random Walk in Potential Energy Space

MC: B. Berg & T. Neuhaus, Phys. Lett. B267, 249 (1991); Phys. Rev. Lett. 68, 9 (1992).

MD: U. Hansmann, Y.O. & F. Eisenmenger, Chem. Phys. Lett. 259, 321 (1996);

N. Nakajima, H. Nakamura & A. Kidera, J. Phys. Chem. B 101, 817 (1997).

Cf: Wang-Landau method where the weight is dynamically updated

F. Wang & D.P. Landau, Phys. Rev. Lett. 86, 2050 (2001);

Phys. Rev. E 64, 056101 (2001).

Canonical Ensemble

MC version:

Multicanonical Ensemble

MC version:

Generalized-Ensemble Algorithms have been

developed in MC algorithms

Canonical Ensemble MD version:

MD version:

22

03

mu mui i i i

i

i B

i

E Es sm m m

s E s

sQs s m Nk T Q

s

q q f qq

q

0

1( ) exp( ( ))

( )mu muW E E E

n E

Multicanonical Ensemble

22 3

i i i i

i

i B

i

E s sm m m

s s

sQs s m Nk T Q

s

q q f qq

q

U. Hansmann, Y.O. & F. Eisenmenger, Chem. Phys. Lett. 259, 321 (1996);

N. Nakajima, H. Nakamura & A. Kidera, J. Phys. Chem. B 101, 817 (1997).

MULTICANONICAL ALGORITHM

B. Berg & T. Neuhaus, Phys. Lett. B267, 249 (1991).

B. Berg & T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992).

Step 1: Iterations of Short Preliminary Runs to

Determine the Multicanonical Weight Factor Wmu (E)

Step 2: One Long Production Run

Step 3: Analyze the Data to Obtain:

* Global-Minimum Energy Configuration

* Thermodynamic Quantities for Desired Temperatures

(by Ferrenberg-Swendsen Single-Histogram

Reweighting Techniques)

;;

B

C mu

mu

W E TP E T P E

W E

30

20

10

0

-10

E

200000150000100000500000

MC Sweeps

Multicanonical

Canonical 50K

Canonical 1000K

Single-Histogram Reweighting Techniques

, where ( ) ( .(

)( )

)mu m

u

mu

um N E n E W

N En E

W EE

A. Ferrenberg & R. Swendsen, Phys. Rev. Lett. 61, 2635 (1988).

( ) ; ( )

;

E

C

E ET E

C

E E

n EA E P E T A E e

AP E T en E

Here, the density of states n(E) is obtained from the histogram of the

energy distribution Nmu(E) that was obtained from the production run of

the multicanonical simulation:

Enk-ave

Single-Histogram Reweighting Techniques

A. Mitsutake, Y. Sugita & Y.O., J. Chem. Phys. 118, 6664 (2003).

When the physical quantity A cannot be written as

a function of E, we use the following equation:

fast movie

17-Residue Helical Peptide (120000-300000 MC Sweeps)

Simulation and movie by A. Mitsutake

Canonical MC: T = 200 K Multicanonical MC

ST( ; ) exp( ( ))W E T E a T

ST ( )exp( ( )) const( ) dEn E E a TP T

ST( ; ) exp( )m m mW E T E a

exp(am) dEn(E) exp(mE)

am : Dimensionless Helmholtz free energy at temperature Tm

Random Walk in Temperature Space

→ Random Walk in Energy Space

is determinded by iterations of short ST runs am

Discretize Temperature:

A.P. Lyubartsev, et al., J. Chem. Phys. 96, 1776 (1992).

E. Marinari and G. Parisi, Europhys. Lett. 19, 451 (1992).

Temperature is a dynamical variable： Sample temperature uniformly

Simulated Tempering （焼き戻し法）

See also: A. Irback & F. Potthast, J. Chem. Phys. 103, 10298 (1995).

U. Hansmann & Y.O., J. Comput. Chem. 18, 920 (1997).

Step 1: Canonical MC/MD Simulations at Temperature Tm

for a Few Steps

Step 2: Temperature is Updated to a Neighboring Value Tm±1

a la Metropolis with Conformations Fixed

where

Repeat These 2 Steps

Canonical Distribution at Any Temperature

by Multiple Histogram Reweighting Techniques (WHAM)

A.P. Lyubartsev, et al., J. Chem. Phys. 96, 1776 (1992).

E. Marinari and G. Parisi, Europhys. Lett. 19, 451 (1992).

Simulated Tempering （焼き戻し法）

Multiple-Histogram Reweighting Techniques

(Weighted Histogram Analysis Method: WHAM)

n E

Nm(E)m1

M

nmefm mE

m1

M

, where e

fm n E E

e mE .

A. Ferrenberg & R. Swendsen, Phys. Rev. Lett. 63, 1195 (1989).

S. Kumar, D. Bouzida, R. Swendsen, P. Kollman & J. Rosenberg, J. Comput. Chem. 13, 1011 (1992).

A T

A(E)n E E

e E

n E E

e E

Given M set of histograms Nm(E), which were obtained at Tm, the

following WHAM equations are solved iteratively for density of states n(E)

and dimensionless Helmholtz free energy f m : (nm are the total number

of samples obtained at Tm)

A. Mitsutake, Y. Sugita & Y.O., J. Chem. Phys. 118, 6664 (2003).

When the physical quantity A cannot be written as

a function of E, we first obtain the dimensionless

Helmholtz free energy fm (m = 1, …, M) by solving

the WHAM equations. We then use the following

equation:

Multiple-Histogram Reweighting Techniques

(Weighted Histogram Analysis Method: WHAM)

See also: M. R. Shirts and J. D. Chodera, J. Chem. Phys. 129, 124105 (2008).

Replica-Exchange Method (also referred to as Parallel Tempering)

1. System

M Non-Interacting Replicas of the Original System at M Different Temperatures

2. Replica-Exchange

Step 1: Independent Canonical Simulations Performed for Each Replica

Step 2: A Pair of Replicas (i and j) Corresponding to Neighboring

Temperatures (Tm and Tn) (i.e., n=m+1) are Exchanged a la Metropolis

Repeat These 2 Steps

3. Canonical Distribution at Any Temperature

by Multiple Histogram Reweighting Techniques (WHAM)

MC: K. Hukushima & K. Nemoto, J. Phys. Soc. Jpn. 65, 1604 (1996).

MD: Y. Sugita & Y.O., Chem. Phys. Lett. 314, 141 (1999).

From Multidimensional REM to

Multidimensional MUCA and ST

MMUCA: random walk in multidimensional energy

MST: random walk in multidimensional parameter

MREM: random walk in multidimensional parameter

e.g.,

WHAM eqns.

,

,

,( ), 1

( ) ,

,, 1

( , )

, where ., , m nm n

m n

m n

M

m nE Vm n

ME V EV

m nm n

f

f

N E V

en E V n eE

n

V

e

A. Mitsutake & Y.O., Phys. Rev. E 79, 047701 (2009);

J. Chem. Phys. 130, 214105 (2009); A. Mitsutake, J. Chem. Phys. 131, 094105 (2009).

Examples of Multidimensional REM, MUCA, and ST

T. Nagai & Y.O., Phys. Rev. E 86, 056705 (2012).

1. Simulated Tempering and Magnetizing

random walk in temperature T and external field h

＊Ising Model

＊3-state Potts Model

= h = external field

V = M = magnetization

T. Nagai, Y.O., & W. Janke,

J. Stat. Mech. (2013) P02039.

A. Mitsutake & Y.O., Phys. Rev. E 79, 047701 (2009);


Examples of Multidimensional REM, MUCA, and ST A. Mitsutake & Y.O., Phys. Rev. E 79, 047701 (2009);


2. Isobaric-Isothermal Ensemble（定圧定温アンサンブル）

＊ MUCA: Multibaric-Multithermal Algorithm (MUBATH) random walk in potential energy E and volume V H. Okumura & Y.O., Chem. Phys. Lett. 383, 391 (2004). (MC version) H. Okumura & Y.O., Chem. Phys. Lett. 391, 248 (2004). (MD version)

＊ REM: random walk in temperature T and pressure P Y. Sugita & Y.O., in Lect. Notes in Computational Science & Engineering,

ed. by T. Schlick and H.Gun (2002) pp. 304-332; cond-mat/0102296.

T. Okabe, M. Kawata, Y.O. & M. Mikami, Chem. Phys. Lett. 335, 435 (2001).

Also, see D. Paschek & A. Garcia, Phys. Rev. Lett. 93, 238105 (2004).

＊ ST: random walk in temperature T and pressure P Y. Mori & Y.O., J. Phys. Soc. Jpn. 79, 074003 (2010).

Examples of Multidimensional REM, MUCA, and ST A. Mitsutake & Y.O., Phys. Rev. E 79, 047701 (2009);


3. Umbrella Sampling

＊ REM: Replica-Exchange Umbrella Sampling (REUS) random walk in reaction coordinate x Y. Sugita, A. Kitao & Y.O., J. Chem. Phys. 113, 6042 (2000).

＊ ST: Simulated Tempering Umbrella Sampling (STUS) random walk in reaction coordinate x Y. Mori & Y.O., Phys. Rev. E 87, 023301 (2013). Cf.

＊ MUCA: Metadynamics (Wang-Landau in reaction coordinate) random walk in reaction coordinate x A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. USA 99, 12562 (2002).

Hk q, p K p E0 q lVl q

l1

L

, where Vl x Kl x q dl 2

.

Challenging the prediction of the 3-dimensional structure

of a small protein by MUCAREM.

Villin headpiece subdomain

(36 amino acids; 596 atoms)

sphere of water with radius 30 Å (3513 water molecules);

Total number of atoms = 11,135

Folding of a Small Globular Protein T. Yoda, Y. Sugita & Y.O., Biophys. J. 99, 1637 (2010).

helix1 helix2

MLSDEDFKAVFGMTRSAFANLPLWKQQNLKKEKGLF 1 10 20 30

helix3

Primary Sequence of HP-36

T. Yoda, Y. Sugita & Y.O., Proteins 82, 933-943 (2014).

Computational Details

(Force Field = CHARMM22/CMAP for protein

& TIP3P for water)

(1) REMD with 96 replicas in implicit solvent (GB/SA);

initial conformation was fully extended

(2) Unfolded protein w/o any secondary structures was

soaked in a sphere of radius 30Å (with 3513 TIP3P water molecules)

(3) REMD with 128 replicas (T = 250 K ～ 700 K) (4) Determine multicanonical weight factors by WHAM

(iterate several times to refine weight)

(5) Two production runs of MUCAREM with 8 replicas

(MUCAREM1: 1.127 ms in total covering T = 269 K ～ 699 K MUCAREM2: 1.157 ms in total covering T = 289 K ～ 699 K)

T. Yoda, Y. Sugita & Y.O., Biophys. J. 99, 1637 (2010).



in sphere of water of radius 30 Å (3513 water molecules);

altogether 11,135 atoms

MUCAREM simulation

MUCAREM2 (Replica 5)

Simulation and movie by T. Yoda

Native-Like Structures Obtained from MUCAREM

Main-Chain RMSD = 1.1 Å (residues 2 to 35) [Replica 5] 灰色：自然の構造（PDB ID: 1YRF）、緑色：シミュレーションの結果

T. Yoda, Y. Sugita & Y.O., Biophys. J. 99, 1637 (2010).

Challenging the prediction of the 3-dimensional structure

of a small protein by MUCAREM.



sphere of salted water with radius

30 Å (3494 water molecules,

11 K+, 13 Cl- ≈ 0.2 M KCl);

Salt Effects on Folding of a Small Globular

Protein T. Yoda, Y. Sugita & Y.O., Proteins 82, 933-943 (2014).

helix1 helix2

MLSDEDFKAVFGMTRSAFANLPLWKQQNLKKEKGLF 1 10 20 30

helix3

Primary Sequence of HP-36

Native-Like Structure (Global Minimum in Free

Energy) Obtained from MUCAREM Simulation

(Left)

Main-Chain RMSD = 1.25 Å Experimental Structure

(PDB ID: 1YRF)


Free Energy Landscape

in Pure Water in 0.2 M Salted Water


T. Hiroyasu, M. Miki, M. Ogura, & Y. O., J. IPS Japan 43, 70 (2002).

Combinations with Genetic Crossover

Simulated Annealing

Y. Sakae, T. Hiroyasu, M. Miki, K. Ishii & Y. O., J. Phys.: Conf. Ser. 487,

012003 (2014).

Y. Sakae, T. Hiroyasu, M. Miki, K. Ishii & Y. O., in preparation.

Metropolis

Y. Sakae, T. Hiroyasu, M. Miki & Y. O., J. Comput. Chem. 32, 1353 (2011).

High T A B C D F E

GA crossover

GA crossover

GA crossover

GA crossover

Low T

Y. Sakae, T. Hiroyasu, M. Miki & Y. O., J. Comput. Chem. 32, 1353 (2011).

Parallel Simulated Annealing MD with Genetic Crossover

(PSAMD/GAc2)

Step 1. Parallel simulated annealing simulations for a certain MD steps

Step 2. Genetic crossover Repeat these two steps. P

aral

lel

Sim

ula

ted A

nnea

lin

g S

imula

tions

All dihedral angles in randomly selected

consecutive amino-acid residues

are exchanged.

Structure A

Structure B

Dihedral Angle

Exchange a Randomly Chosen Pair of Dihedral Angle Sets

Genetic Crossover (2-Point Crossover)

1. All dihedral angles in randomly selected n (2-10)

consecutive amino-acid residues are exchanged.

2. A short (say, 20 ps) MD simulation with

H = H0 + Hconstr where Hconstr is a harmonic constraint potential that

constrains the corresponding main-chain dihedral

angles (f, y).

3. A short (say, 20 ps) equilibration MD with

H = H0 4. Selection rule is imposed with respect to the final

conformations in Step 3.

After Genetic Crossover Operation,

two children will have large energies;

side chains bump into each other.


012003 (2014).

Detailed Balance Conditions

1. All dihedral angles in randomly selected n (2-10)

consecutive amino-acid residues are exchanged.

2. A short (say, 20 ps) MD simulation with

H = H0 + Hconstr where Hconstr is a harmonic constraint potential that

constrains the corresponding main-chain dihedral

angles (f, y).

3. A short (say, 20 ps) equilibration MD with

H = H0 4. Accept or reject a la Metropolis criterion.

Detailed Balance Condition is satisfied just as in

Hybrid Monte Carlo method, provided that we use a

volume-preserving and time-reversal MD integrator.

Metropolis with Genetic Crossover Combined

Example 1

Trp-Cage (PDB ID: 1L2Y)

20 residues

method: MD (Langevin dynamics)

temperature: 282 K

solvent: GB/SA

force field: AMBER ff03

no. of individuals: 16

simulation time per individual: 100ps×100（10ns）

Simulation（Individual No.2） PDB Structure（NMR）

RMSD : 0.809 Å

Y. Sakae, T. Hiroyasu, M. Miki, K. Ishi & Y.O., in preparation.

Example 2

Villin Headpiece (PDB ID: 1YRF)

36 residues

PDB Structure (X-ray)

RMSD : 2.234 Å

Simulation（Individual No. 11）


temperature: 300 K

solvent: GB/SA



simulation time per individual: 200ps×100（39.4ns）

Y. Sakae, T. Hiroyasu, M. Miki, K. Ishi & Y.O., in preparation.

Example 3

Protein A (PDB ID: 1BDD)

46 residues (10-55 out of 60)

RMSD : 1.707 Å Simulation（Individual No. 5）

PDB Structure（NMR）


temperature: 300 K

solvent: GB/SA



simulation time per individual: 1.0ns×90（90ns）


012003 (2014).

2-Dimensional ST Simulation

in Isobaric-Isothermal Ensemble

temperature and pressure become dynamical

variables.

2-dimensional random walk

in temperature and pressure

Y. Mori & Y.O., J. Phys. Soc. Jpn. 79, 074003 (2010);

in preparation.

Pressure-Induced Unfolding of Ubiquitin

R. Kitahara et al. (2005)

30 bar – 3000 bar

NMR Experiments

• 76 amino acids

• 6232 water molecules

• 19985 atoms

PDB: 1V80

Simulated System

Time series of pressure P, potential energy E, and volume V for ubiquitin

Y. Mori & Y.O., in preparation.

Large structural fluctuations

Amino Acid Residues

f [Å]

• Fluctuations of distance d between pairs of Ca atoms.

Large fluctuations observed in agreement with experiments.

http://maru.bonyari.jp/texclip/texclip.php?s=/begin{align*}f /equiv /sqrt{/langle d^2 /rangle - /langle d /rangle^2}/end{align*}

Structural changes under high pressure

r

r [Å]

distribution [Å-1]

r

Ubiquitin and water molecules

at low pressure at high pressure

Simulation and movie by Y. Mori

Experiments:

R. Kitahara & K. Akasaka,

PNAS 100, 3167 (2003).

N

H

Calculation of chemical shifts • We calculated 15N chemical shifts for all the amino acid residues

and show the distributions of several calculated chemical shifts.

• Program: CamShift (ver. 1.35)

• Pressure: 1bar (blue) to 4,000 bar (red)

Residue 70

Residue 68 Residue 69

Residue 71 Residue 72

low pressure

high pressure

Y. Mori et al., in preparation.

Prediction of Protein-Ligand Binding Structures by

Replica-Exchange Umbrella Sampling H. Kokubo, T. Tanaka & Y.O., J. Comput. Chem. 32, 2810-2821 (2011).

Replica-Exchange Umbrella Sampling (REUS)

Potential of Mean Force

Hk q, p K p E0 q lVl q

l1

L

, where Vl x Kl x q dl 2

.

W x 1

ln P ,0 x .

P , E,x Nm(E,x)e

EV x

m1

M

nmef m m EVm x

m1

M

,

e f m P

m , mE,x

x

E

.WHAM

Y. Sugita, A. Kitao & Y.O., J. Chem. Phys. 113, 6042 (2000).

See also:

E.M. Boczko & C.L. Brooks, J. Phys. Chem. 97, 4509 (1993).

B. Roux, Comp. Phys. Commun. 91, 275 (1995).

Five test systems [ligand (protein)] (T = 300 K, P = 1 atm)

benzodiazepine

(protein: MDM2)

deoxythymidine 3’,5’-bisphosphate (pdTp)

(protein: staphylococcal nuclease)

tyrosine

(protein: aldolase)

cytidylic acid (2’-CMP)

(protein: ribonuclease A)

2-aminopyrimidine

(protein: heat shock protein HSP90)

PDB code

PDB code

H. Kokubo, T. Tanaka & Y.O., J. Comput. Chem. 32, 2810-2821 (2011).

Umbrella Potentials (24 Replicas)

dm : 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5, 10.0, 10.5, 11.0,

12.0, 13.0, 14.0, 15.0, 16.0, 17.5, 19.0, 20.5, 22.0, 23.5, 25.0

km : 1.0 for dm < 13.5 Å, 0.5 for dm > 13.5 Å

MD simulation: 110-220 nsec per replica


The initial structures of five protein-ligand complexes

53

The space-filled molecules, which do not actually exist in these

simulations, show the correct ligand binding positions (from

PDB) as references. The ligands are in bulk water and far

away from the binding pockets. 53

Simulation and movie by H. Kokubo

MDM2 and benzodiazepine: REUS simulation

Snapshots of MDM2 protein system

Protein surface is fluctuating

Simulation and movie

by H. Kokubo

heat shock protein and

2-aminopyrimidine

Asp-78 and ligand

Results: REUS with 24 replicas

• Starting from configurations in which protein and ligand are far away from

each other in each system, our method predicted the ligand binding

structures as the global minima in free energy (or, potential of mean force)

in excellent agreement with the experimental data from PDB.

potential of mean force shows

the most stable distance

crystal

predicted

We remark that for 1ROB and 1SNC, there

are attempts by a popular existing docking

program, GOLD, but they failed in the

predictions (classified as significant errors).


Kinase systems we tested

JNK3

1PMV 150 nM

2O2U 3.0 uM

P38

1OVE 0.74nM

1OZ1 6.5 nM

*240ns REUS simulations were performed for four systems:

1PMV, 2O2U, 1OVE, and 1OZ1.

H. Kokubo, T. Tanaka & Y.O., J. Chem. Theor. Comput. 9, 4660-4671 (2013).

Potential of Mean Force

59

1OZ1 1OVE

1PMV 2O2U

150 nM 3000 nM

0.74nM 6.5 nM

p38 p38

JNK3 JNK3


The comparison of the predicted global minimum free

energy structures and PDB structures

1PMV

1OVE

2O2U

JNK3 JNK3

p38 p38

1OZ1 crystal predicted


Movie for 1PMV

Simulation and movie by H. Kokubo

Necessity of protein flexibility

P38 & dihydroquinolinone (PDB ID: 1OVE)

Without flexibility With flexibility


Prediction of Protein-Ligand Binding Structures by

2-dim H-REMD: Replica-Exchange Umbrella

Sampling (REUS) and Replica-Exchange Solute

Tempering (REST)

H. Kokubo, T. Tanaka & Y.O., J. Comput. Chem. 34, 2601-2614 (2013) .

Potential Energy:

[ ] [ ] [ ]] [

0

[ ]

0

( ) ( ) () )( ( )ni i i imn ll ls ss mn iE q U q U qU Vq q

l: ligand

s: protein/water

REST: P. Liu, B. Kim, R.A. Friesner, & B.J. Berne, PNAS 102, 13749 (2005).

REUS: Y. Sugita, A. Kitao & Y.O., J. Chem. Phys. 113, 6042 (2000).

Total no. of replicas: M × N REST parameters (n=1, 2, …, N)

REUS parameters, i.e., umbrella potentials

(m=1, 2, …, M)

2-dim H-REMD: REUS (M=24) + REST (N=8)

(192 replicas)

REUS (1T4E) REUS/REST (1T4E)

No. of

Random Walk

Cycles

H. Kokubo, T. Tanaka & Y.O., J. Comput. Chem. 34, 2601-2614 (2013) .

Force field refinement for all-atom

protein models

with Yoshitake Sakae

REVIEW:

Y. Sakae & Y.O.,

in Computational Methods to Study the Structure and Dynamics of Biomolecules and

Biomolecular Processes – from Bioinformatics to Molecular Quantum Mechanics

A. Liwo (ed.) (Springer-Verlag, Berlin Heidelberg, 2014) pp. 195-247.

Force-field parameters for all-atom models

2

2

12 6

( )

( )

[1 cos( )]2

332

r eq

eq

n

ij ij i

conf

bonds

angles

dihedrals

i j j

j

i ij ij

K r

K

E r

Vn

A q q

R R

B

R

f

Bond-stretching

Bond-bending

Dihedral angle

Non-bonding interactions

(Lennard-Jones and electrostatic)

These energy terms include some force-field parameters (blue color)

Commonly used conformational potential energy

The existing force fields have different force-field parameters

Force-field dependency of secondary-structure properties

C-peptide

(13 residues)

AMBER parm94

AMBER parm96

AMBER parm99

CHARMM22

OPLS-AA/L

GROMOS96

α-h

elix

T. Yoda, Y. Sugita & Y.O.,

Chem. Phys. Lett. 386, 460 (2004).

Helicity of C-peptide

Typical example of folding simulations using different force fields

AMBER ff94 AMBER ff96

C-peptide

(13 residues) Lys-Glu-Thr-Ala-Ala-Ala-Lys-Phe-Glu-Arg-Gln-His-Met

Method：Simulated annealing, Simulation time : 1.0 nsec, Temperature : 700～200 K, Solvent model : GB/SA

70

Conformational Energy

nonbondtorsionBABLconf EEEEE

rest

n

nn

torsion

EE

nV

E

),(

)]cos(1[2

y

Backbone-torsion energy term

backbone dihedral

angles φ and ψ

rest of the torsion terms

Φ : all dihedral angles

n : number of waves

γn : phase

Vn : Fourier coefficient

Side chain

Backbone-torsion energy surfaces of some force fields

-180

-90

0

90

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180

90

0

-90

-180f

y

-180

-90

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90

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180

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0

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-180f

y-180

-90

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180

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-180f

y

-180

-90

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180

90

0

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-180f

y -180

-90

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180

90

0

-90

-180f

y-180

-90

0

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180

90

0

-90

-180f

y

AMBER parm94 AMBER parm96 AMBER parm99

CHARMM22 OPLS-AA OPLS-AA/L

72

m n

nn

mm n

Vm

VE )]cos(1[

2)]cos(1[

2),( yy

resttorsion EE ),( y

)sinsincossin yy nminnh mnmn

1 1

11

sincoscoscos(

)sincos()sincos(),(

m n

mnmn

n

nn

m

mm

nmgnmf

nendmcmba

yy

yyy

Y. Sakae and Y.O., J. Phys. Soc. Jpn. 75, 054802 (9 pages) (2006).

1. Proposal of new functional form

conventional energy term

New torsion energy term

New backbone-torsion-energy term

a,bm,cm,dn,en,fmn,gmn,hmn,imn

: Fourier coefficient

Ramachandran plot

タンパク質の構造入門第2版

Example of the application of new backbone-torsion energy term

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y-180

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y-180

-90

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y

a-helix region -structure region

Energy surface of new energy term can represent Ramachandran space directly

74

-180

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90

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180

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-90

-180f

y

-180

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180

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-90

-180f

y

~

~

~

~

~

~

~

~

AMBER parm94

AMBER parm96

Application to AMBER parm94 and AMBER parm96

αhelix βstructure

αhelix βstructure

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AMBER parm94 AMBER parm96

Original Original

a-helix region a-helix region

-structure region -structure region

Results of folding simulations C-peptide

Simulated annealing simulation Simulation time : 1ns (1,000,000 MD steps × 1.0fs × 60 times) Temperature : 2,000K to 250K (Berendsen’s method)

Solvent : GB/SA model

76


G-peptide

Simulation time : 1ns (1,000,000 MD steps × 1.0fs × 60 times) Temperature : 2,000K to 250K (Berendsen’s method)


Results of folding simulations

Original Original

a-helix region a-helix region

-structure region -structure region

Simulated annealing simulation

mN

mif

2

1 1

1 m

m

m

NN

i

m im

F fN

m

m

i

m

toti

x

Ef

}{

}{m

totEmi

fAtom i

Molecule m

Optimization method of force-field parameters

Y. Sakae and Y.O., Chem. Phys. Lett. 382, 626-636 (2003)

Number of atoms in molecule m

Force acting on atom i

Total potential energy for molecule m

If force-field parameters are of ideal values, all native structures

are stable without any force acting on each atom in molecules.

(we expect F=0)

In reality, F≠0, and because F ≥0, we can optimize the force-field

parameters by minimizing F with respect to these parameters.

Structures of selected 100 proteins

Resolution: >= 2.0Å, Sequence similarity of amino acid: >= 30%, Number of residue: < 200

Results: Optimized force-field parameters and its energy surface

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y-180

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y


Optimized ff

yy

yy

yy

yy

y

sinsin603.0cossin114.0

sincos247.0coscos427.0

2sin054.02cos019.0

sin160.0cos287.0

2sin100.02cos088.0

sin327.0cos835.0),(

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-90

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180

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-90

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y

80

C-peptide

(13 residues)

blocked by COCH3- and –NH2

G-peptide

(16 residues)

Test simulations

Y. Sugita and Y.O., Chem. Phys. Lett. 314, 141-151 (1999)

Replica Exchange Molecular Dynamics (REMD) simulation

Simulation time : 5.0 ns (32 replica)

Temperature : 700K to 250K (Nosé-Hoover method)


Program : Modified TINKER program package

C-peptide

300K

Comparison of helicity and strandness

G-peptide

300K

Comparison of helicity and strandness

C-peptide

),(ln),( yfyf BB PTkG

Optimized ff

AMBER ff96 AMBER ff94 300K

Potential of mean force

G-peptide

),(ln),( yfyf BB PTkG

Optimized ff

AMBER ff96 AMBER ff94 300K

Potential of mean force

COLLABORATORS Ayori MITSUTAKE [IMS Keio Univ.]

Yuji SUGITA [IMS Univ. Tokyo RIKEN]

Takao YODA [IMS Nagahama Inst. Bio-Science]

Yoshitake SAKAE [IMS Hiroshima Univ. Nagoya Univ.]

Yoshiharu MORI [Nagoya Univ. IMS]

Tetsuro NAGAI [Nagoya Univ. Ritsumeikan Univ.]

Hironori KOKUBO [IMS Univ. of Houston Takeda Pharm.]

Toshimasa TANAKA [Takeda Pharm.]

Takeshi NISHIKAWA [IMS AIST FOCUS]

Yasuyuki ISHIKAWA [Univ. Puerto Rico]

Ryo KITAHARA [Ritsumeikan Univ.]

Kazuyuki AKASAKA [Kinki Univ.]

Wolfhard JANKE [Univ. Leipzig]

Giovanni LA PENNA [ICCOM, CNR, Firenze]

Michele VENDRUSCOLO [Univ. of Cambridge]

Christopher M. DOBSON [Univ. of Cambridge]

optimization of protein force-field parameters€¦ · optimization of protein force-field...

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