MMTSB/CTBP Workshop
August 4-9, 2009
;+"(<7=4"%,(>=$?%,-(<7=@$"/(
•  A=B(?="3(4+"(#7%/'78(."CD",&"(3#"&%E8(4+"(,'F6"(E=$?G(
9HI,3%,J(.&%",&"J(KLMN:(
MTYKLILNGK TLKGETTTEA
VDAATAEKVF KQYANDNGVD
GEWTYDDATK TFTVTE
!"#$%&'()*&+',-"(.'/#$%,-(
•  O"6%,4+'$P3(<'7'?=*Q(+=B(#7=4"%,(E=$?3(4+%3(E'34G(
0%',+',(1+",(
2',3'3(.4'4"(5,%6"73%48(
10 conformations per residue,
10-11 (10 ps) per state
!fold < 1 second
1060 states for a 60-residue protein,
>1040 years for random search !
9&:(0%',+',(1+",(
9&:(0%',+',(1+",(
A=B(#7=4"%,3(E=$?G(
['#(%,(;%/"3&'$"3(
•  S1$'33%&'$T(D,?"734',?%,-3(
The Energy Landscape Theory
(arguably the prevailing theory)
–  U%VD3%=,W&=$$%3%=,(
–  A%"7'7&+%&'$(E=$?%,-(
–  H33"/@$8(=E(E=$?=,3(
Simulation Timescales
R(
Biological Timescales
(explicit water)
Protein Folding,
Conformational
Transitions
Peptides (~10 residues)
Small Proteins (<50 residues)
Diffusion and collision
Karplus and Weaver, Biopolymers., 18, 1421 (‘77).
Internal Dynamics
Large Proteins
(>200 residues)
Bond Vibrations
Folding via modular assembly
Ptitsyn and Rashin, Biophys. Chem., 3, 1 (‘75).
9&:(0%',+',(1+",(
X=$8,"3("4('$YJ(!"#$%"$(9KLLZ:Y(
N(
9&:(0%',+',(1+",(
\(
]/#$%&%4(;7"'4/",4(=E(.=$6'F=,(
^'77%"73J(;"/#"7'4D7"(',?(;%/"3&'$"3(
! = !0 exp("G /kT)!
#!0 ~ 10-12 s ~ ps!
H = H prot + H prot" wat + H wat
H = H prot + #Gsolv
!T = 300 K!
*!
"G : !1 kcal/mol, ! ~ 5 ps!
! !5 kcal/mol, ! ~ 4 ns!
10 kcal/mol, ! ~ 17 µs!
!
Protein energy landscape is highly complex and
rugged with numerous local minima.
9&:(0%',+',(1+",(
Z(
^'77%"73J(;"/#"7'4D7"(',?(;%/"3&'$"3(
!"#$%&'()*&+',-"(9!)a:(.'/#$%,-(
300 K
! = !0 exp("G /kT)!
#!0 ~
*!
10-12
_(
355 K
420 K
s ~ ps!
500 K
!T = 600 K!
REP1!
REP2!
REP3!
REP4!
MD/MC
"G : !1 kcal/mol, ! ~ 2 ps! 2x
! !5 kcal/mol, ! ~ 65 ps! 60x
10 kcal/mol, ! ~ 4 ns! 4000x
•  Increase temperature enhances barrier crossing.
•  The enhancement factor depends exponentially
on the barrier height.
Exchange criteria
?
?
REP2!
REP1!
REP3!
REP4!
REP2!
REP3!
REP1!
REP4!
?
MD/MC
MD/MC
Protein Energy Surface
*
Sugita and Okamoto, CPL (1999)!
M(
`(
T1, E2
T2, E1
T3, E3
T4, E4
REP2!
REP1!
REP3!
REP4!
REP2!
REP3!
REP1!
REP4!
?
W a = e" # 1 E 2 e" # 2 E1 e" # 3 E 3 e" # 4 E 4
U"4'%$"?(^'$',&"(7"CD%7"3Q(
!)a(D3%,-(dd;.^(;==$(."4(
T1, E2
T2, E3
T3, E1
T4, E4
•  H(3"4(=E((*rex.pl 3&7%#43(9aarex.pl, gorex.plJ("4&:(
•  eV"73(-7"'4(f"*%@%$%48(%,(3%/D$'F=,(3"4D#(91AH!dd(63(
H/@"7J(&+=%&"(=E(E=7&"(I"$?3J(&D34=/(3"4D#3J("4&:J(/'&+%,"(
'7&+%4"&4D7"(93+'7"?(/"/=78(3D#"7&=/#D4"7J($==3"$8(&=D#$"?(
O%,D*(&$D34"7J(=7(',8(&=/#D4"73($%,g"?(@8()4+"7,"4:J(h=@(
/=,%4=7%,-J(#=34(3%/D$'F=,(','$83%3(9CD%&g($==g(B%4+(
rexinfo.plJ("*47'&F,-(",3"/@$"J(&$D34"7%,-J(XAHd("4&:(((
STATE b
STATE a
!)a()*&+',-"(17%4"7%'(
W b = e" # 1 E 2 e" # 2 E 3 e" # 3 E1 e" # 4 E 4
W a Pa "b = W b Pb "a
Pa "b W b e# $ 1 E 2 e# $ 2 E1 e# $ 3 E 3 e# $ 4 E 4
=
= # $ 1 E 2 # $ 2 E 3 # $ 3 E1 # $ 4 E 4 = e#( $ 2 # $ 3 )(E1 #E 3 ) = e#%
Pb "a W a e
e
e
e
!
• (<7=#"7(4+"7/=?8,'/%&(",3"/@$"3('4('$$(4"/#"7'4D7"3Y(
• (c=(ED,?'/",4'$(7"CD%7"/",4(=,(4+"("*&+',-"(3&+"/"Y(
• (H,84+%,-(94"/#"7'4D7"J(A'/%$4=,%',J("4&:(&',(@"("*&+',-"?Y(
!
!
b(0%',+',(1+",(
aarex.pl –n 100 -mdpar dynsteps=100,param=22,gb,nocut \ !
–par equilruns=2,natpdb=1vii.exp.pdb -temp 4:298:400 \
1vii.{1,2,3,4}.pdb !
Runs 100 replica exchange MD simulation cycles with four exponentially
spaced temperature windows from 298 to 400K. The native PDB structure is
given as reference for calculation RMSD values. MD parameters are set to run
100 steps for each cycle, use CHARMM22 parameters with GB implicit solvent.
Initial conformations are taken from the files 1vii.?.pdb.
L(
b(0%',+',(1+",(
!)aWdU(.%/D$'F=,(=E(A"$%*(9HHjHH:N(
!)a(.%/D$'F=,(=E(9HHjHH:N(
aa8
Energy (kcal/mol)
Temperature (K) Energy (kcal/mol) RMSD (Å)
aa10
Ki(
Average Helicity
T=270 K
Number of REX Cycles (x 2ps)
Number of REX Cycles (x 2ps)
KK(
b(0%',+',(1+",(
KR(
A"$%&%48(=E(9HHjHH:N(
e#F/'$(."4D#(=E(!)a(
•  ;"/#"7'4D7"(7',-"(',?(?%347%@DF=,(
–  )*#=,",F'$$8(?%347%@D4"?(E=7(3834"/3(B%4+(&=,34',4(+"'4(&'#'&%48(
–  O=B"34(4"/#"7'4D7"Q(=k",(4+"(4"/#"7'4D7"(=E(%,4"7"34(9"Y-J(Nii(2:(
–  A%-+"34(4"/#"7'4D7"Q($"33(=@6%=D3J(@D4('(&7%F&'$(#'7'/"4"7(
•  cD/@"7(=E(7"#$%&'3((
–  U"#",?3(=,(4+"(3834"/(3%l"Q(m(3C749&:J(',?(4+"(4"/#"7'4D7"(7',-"(
–  0D?-"?(@8(4+"("*&+',-"('&&"#4',&"(7'F=(9=#F/'$(iYR(n(iYNG:(
–  ]/#$%&%4(3=$6",4(%3(#'7F&D$'7$8(3D%4'@$"(E=7(!)ao(
b(0%',+',(1+",(
e#F/'$(."4D#(=E(!)a(
1=,E=7/'F=,'$()CD%$%@7%'(=E($WA'%7#%,3(
•  ;"/#"7'4D7"(7',-"(',?(?%347%@DF=,(
–  )*#=,",F'$$8(?%347%@D4"?(E=7(3834"/3(B%4+(&=,34',4(+"'4(&'#'&%48(
–  O=B"34(4"/#"7'4D7"Q(=k",(4+"(4"/#"7'4D7"(=E(%,4"7"34(9"Y-J(Nii(2:(
–  A%-+"34(4"/#"7'4D7"Q($"33(=@6%=D3J(@D4('(&7%F&'$(#'7'/"4"7(
•  cD/@"7(=E(7"#$%&'3((
–  U"#",?3(=,(4+"(3834"/(3%l"Q(m(3C749&:J(',?(4+"(4"/#"7'4D7"(7',-"(
–  0D?-"?(@8(4+"("*&+',-"('&&"#4',&"(7'F=(9=#F/'$(iYR(n(iYNG:(
–  ]/#$%&%4(3=$6",4(%3(#'7F&D$'7$8(3D%4'@$"(E=7(!)ao(
•  )*&+',-"('p"/#4(E7"CD",&8(
–  E'34(@D4(,=4(4==(E'34(9"Y-YJ(KWR(#3:(
•  O",-4+(=E(3%/D$'F=,(
.%/D$'F=,3('7"(
7'7"$8(4==($=,-o(
–  !"#$%&'%#(%)&',(@"(47%&g8(4=(hD?-"Q(#$'4"'D(q(&=,6"7-",&"o(
–  U"#",?3(=,(4+"(4'7-"4(#7=#"7F"3Q(E=$?%,-(4'g"3(6"78(6"78(6"78($=,-(
–  dD$F#$"(%,?"#",?",4(3%/D$'F=,3(=k",(+"$#ED$(%,(4"3F,-(&=,6"7-",&"(
b(0%',+',(1+",(
KZ(
K\(
U="3(!)a(!"'$$8(X=7gG(
U="3(!)a(!"'$$8(X=7gG(
9<"#F?"(3%/D$'F=,(@",&+/'7g3:(
Standard deviations of folded fraction: (Periole and Mark, JCP, 2007)
800 ns MD runs
Helicity auto-correlation functions (Zhang et al, JCP, 2005)
REX-MD with 20 replicas
(REX-MD)
System: Fs-21, A5(AAARA)3, peptide in GB implicit solvent
A $-heptapeptide in explicit solvent.
Observation: enhancement of 35X at 300K and 72X at 270K.
Enhancement is even larger if considering the full temperature
range. Also note some caveat with auto-correlation analysis.
b(0%',+',(1+",(
KM(
U="3(!)a(!"'$$8(X=7gG(
Observation: approximately 10X more efficient (than a single 800
ns conventional MD at 275 K); only about 2-4X at 300 K. If the
goal is to determine the temperature dependence, >30X.
b(0%',+',(1+",(
K`(
A=B(4=(jD',FE8(S.'/#$%,-T(
•  HD4=W&=77"$'F=,(','$83%3(
•  .4'F3F&'$(4"343(
•  1=,E=7/'F=,'$(3#'&"(','$83%3(
•  ;+"7/=?8,'/%&3(#7=#"7F"3(
•  ;7',3%F=,("6",43(
•  )V"&F6"(3'/#$"(3%l"(4+7=D-+((
(((((347D&4D7'$(?%347%@DF=,(','$83%3((
(((((9rD&g"7/',J(01<(RiiM:(
Refinement of NMR Structures: protein
G B1 in GBSW implicit solvent. REX
traces from single replicas are shown.
Brooks et al, Science (2001)
•  H$$(4+"3"(','$83%3($%/%4"?(@8(S3'/#$%,-T(9%Y"YJ(g,=B$"?-"(=E(4+"(
47D"(&=,E=7/'F=,'$(3#'&":o(
Chen et al., JACS (2004)
9&:(0%',+',(1+",(
KL(
b(0%',+',(1+",(
Ri(
U="3(!)a(!"'$$8(X=7gG(
]/#=74',&"(=E(4+"(d'*%/D/(;"/#"7'4D7"(
•  H,FWH77+",%D3(@"+'6%=7(=E(#7=4"%,(E=$?%,-Q(+"'4(=E('&F6'F=,(
?%3'##"'73(=7("6",(@"&=/"3(,"-'F6"('4(+%-+(4"/#"7'4D7"Y((
•  ;+"=7"F&'$(&=,3%?"7'F=,3(@'3"?(=,(3%/#$"(g%,"F&(/=?"$(
3834"/3Q(",+',&"/",4(#=33%@$"('3($=,-('3(4+"7"(%3('(#=3%F6"(
+"'4(=E('&F6'F=,Y(
ku
Arrhenius kf
Number of
transition events as
a function of Tmax
Anti-Arrhenius kf
Zhang et al, (2007, 2008)
Also see: Zuckerman (2006)
b(0%',+',(1+",(
Nymeyer (2008)
RK(
b(0%',+',(1+",(
!)a()*4",3%=,3(',?(s'7%',43(9!)a(l==G:(
5/@7"$$'(.'/#$%,-'
Apply series of overlapping harmonic functions (umbrellas):
•  c=(ED,?'/",4'$(7"CD%7"/",4(=,(4+"("*&+',-"(3&+"/"Y(
•  H,84+%,-(94"/#"7'4D7"J(A'/%$4=,%',J("4&:(&',(@"("*&+',-"?(
•  [='$3('7"(-","7'$$8(4=(
•  *#+,#(%)-%./%&,-0&%)&,#1".)2,34)9"*&+',-"("t&%",&8:Q(7"?D&"(4+"(
,D/@"7(=E("*&+',-%,-(?"-7""3(=E(E7""?=/(93=$D4"(4"/#"7%,-J($=&'$(
!)aJ(!)a("33",F'$(?8,'/%&3J("4&:J(-$=@'$(7"'33%-,/",4(9;][)!(u(
;][)!R:J(?8,'/%&(3&'$%,-J(v(
•  *#+,#(%)5,67#)+"//7#'Q(A'/%$4=,%',(!)a(9$%g"(',8('&&"$"7'4"?(dUJ(%4(
%3(6"78(47%&g8(4=(I,?(#7=#"7(3&+"/"(E=7(/=?%E8%,-(4+"(#=4",F'$w(4+"7"(
'7"(/',8(6"73%=,3(=E(4+%3(48#":J(/D$F3&'$"(!)a(97"3=$DF=,("*&+',-":((
•  !".57#%)27-+)57,6%1)6,./37#'Q(RU(!)a(9/=34$8(E=7([=W/=?"$%,-:(
•  8-+%&6Q(3"7%'$(!)aJ(/D$F#$"*(!)a(9,=(38,&+7=,%l'F=,(7"CD%7"/",4:J(v((
E
%#
Need to know good reaction coordinate to find reasonable path.
Poorly chosen reaction coordinate might result in high barriers.
Simple temperature REX still appears to be the most applicable
in general. There is no substitution for serious sampling?
b(0%',+',(1+",(
Zhang et al., PNAS (2007).
RN(
U8,'/%&3(',?(],4"7'&F=,3(=E(<7=4"%,3(',?(cD&$"%&(H&%?3J(^d^L_Kx1)dL`Mx<Ay`NRJ(>'$$(RiiMJ(d%&+'"$(>"%-(
RR(
X"%-+4"?(A%34=-7'/(H,'$83%3(d"4+=?(9XAHd:'
Multiple umbrellas result in free energy profiles that are
determined only within a constant Ci. They need to be stitched
together to get profile for entire path!
H,'$83%3(=E(!)a(!"3D$43(
•  [","7'$$8(&=,&"7,3(4+"7/=?8,'/%&3(
–  d"4+=?3("*%34(E=7(7"&=6"7%,-(3=/"(g%,"F&(%,E=7/'F=,(9"Y-YJ(3""(
^D&+"4"(',?(AD//"7J(Rii`:(
•  U%7"&4(+%34=-7'/(9E7""(","7-8:(',?(&$D34"7%,-(','$83%3(=E(
347D&4D7'$(",3"/@$"3('4(4"/#"7'4D7"3(=E(%,4"7"34(
–  1=/@%,"(B%4+(47',3%F=,(34'4"(','$83%3(
•  ;WXAHd(94"/#"7'4D7"(B"%-+4"?(+%34=-7'/(','$83%3(/"4+=?:(
%#
ci’s are determined from
minimizing statistical variance at
each histogram bin
! ci = f(Ci)
but Ci = f(p(%))
need to solve iteratively
U8,'/%&3(',?(],4"7'&F=,3(=E(<7=4"%,3(',?(cD&$"%&(H&%?3J(^d^L_Kx1)dL`Mx<Ay`NRJ(>'$$(RiiMJ(d%&+'"$(>"%-(
–  1=/@%,"(3'/#$%,-(E7=/('$$(4"/#"7'4D7"3(
–  RU(=7(+%-+"7(?%/",3%=,(+%34=-7'/3(7"CD%7"($'7-"(,D/@"7(=E(3,'#3+=43((
–  d=7"(D3"ED$(E=7(3/'$$(3834"/3(B%4+(/=?"7'4"(7',-"(=E(","7-8(
fD&4D'F=,(93/'$$(#"#F?"3(',?x=7(7"?D&"?(/=?"$3:Q(?=(,=4("6",(
'p"/#4(E=7("*#$%&%4(3=$6",4(!)a(
–  ]/#$"/",4"?(%,(dd;.^(93""(4D4=7%'$:(
Gallicchio et al, JPCB (2005); Chodera et al, JCTC (2007)
b(0%',+',(1+",(
Tallgrass Prairie National Reserve, Sept 2007
R_(
9*:);//37(,<"#)*=,./3%)>?)
!"I,"/",4(=E(d'$4=3"W^%,?%,-(<7=4"%,(9d^<:(
(!)ax[^(!"I,"/",4(=E(cd!(.47D&4D7"3(
•  370 residues, 42 kDa
•  1943 NOE
•  45 hydrogen bonding
•  555 dihedral angle restraints.
•  Average backbone RMSD to
X-ray structure is 5.5 Å (a).
•  Improved to 3.3 Å with 940
additional dipolar coupling
based restraints (b).
Mueller et al., JMB 300, 197 (2000)!
b(0%',+',(1+",(
RL(
!)ax[^(!"I,"/",4(!"3D$43(
!
•  All NOE and dihedral angle
restraints were used.
•  48 replicas were simulated at
300 to 800 K until “converged”.
•  Total of 1.0 ns REX/GB
simulation.
!
!
!
!
!Initial
RMSD to X-ray (Å) a!
Global !
!
!
!
!4.3±4.1
N-domain !
!
!
!2.5±2.1
C-domain
!
!
!
!3.0±3.2
&/' space: residues (%)!
Most favored
!
!
!72.2 !
Additionally allowed !
!22.8 !
Generously allowed !
!3.8 !
Disallowed !
!
!
!1.2 !
Violation statistics!
RMSD of NOEs (Å) !
!0.0047
NOE violations ( > 0.2Å)
!2.85 !
RMSD of angles (in degrees) !0.53 !
b(0%',+',(1+",(
!"#7"3",4'F6"(.47D&4D7"3Q(d^<(
!Final!
(52%)"
!2.3±2.6!
!2.2±1.4!
!2.0±1.9!
!84.3!
!13.3!
!1.6!
!0.8!
5.8 Å
2.9 Å
5.7 Å
3.5 Å
(28%)!
!0.014!
!4.42!
!6.25!
Backbone RMSD with respect to PDB:
1dmb shown. Global: residues 6-235 and
241-370; N-domain: 6-109 and 264:309; Cdomain: 114-235, 241-258 and 316-370.
a
b(0%',+',(1+",(
RMSD values: from X-ray (PDB:1dm); backbone atoms of residues 6-235 and 241-370!
9*:);//37(,<"#)*=,./3%)@?)
!)ax[^(!"I,"/",4(&',(@"(D3"?(4=(=@4'%,((
,'F6"W$%g"(/=?"$3(E7=/($%/%4"?(cd!(?'4'Y(
!)ax[^(!"I,"/",4(=E(<7"?%&4"?(.47D&4D7"3(
Target TMR04 from CASPR Refinement Experiment
RMSD (Å)
2.18 (2.04)
1.88 (1.26)
1.57 (0.98)
GDT_TS
76.1
85.7
90.0
Chen and Brooks, Proteins (2006)
Cost: ~12h wall time using 16 Intel 2.4GHz CPUs!
b(0%',+',(1+",(
9*:);//37(,<"#)*=,./3%)A?)
<7"W"*%34",&"(=E(>=$?WO%g"((
1=,E=7/'F=,3(%,(4+"(>7""(#ZN(<"#F?"((
>7""(),"7-8(=E(#ZNx.Kii^9$$:(],4"7'&F=,(
•  .Kii^9$$:(@%,?3(#ZN(%,('(1'RzW?"#",?",4(/',,"7(
•  ],+%@%43(4+"(#+=3#+=78$'F=,(=E(1W4"7/%,'$(,"-'F6"(7"-D$'4=78(
?=/'%,(97"3%?D"3(N_MWN``:(',?(#7"6",43(#ZN('&F6'F=,(
•  H,(',FW&',&"7(?7D-(4'7-"4(
9R+\h:(((((((((((((((((((((((((((9K+R_:((((((((((((((((((((((((((((((((((((((((((9Kh3#:((((((((((((((((9K?4M:(
p53 (22 a.a.)
s100B($$)
(94 a.a.)
!D34',?%("4('$YJ(c.^(9Riii:Y(
NZ(
;)060,3)606/%(-)
"B)
("#B"&.,<"#,3)
6%3%(<"#C)
"&)#"-D))
c=4"Q('(7',?=/%l"?(3"CD",&"(?="3(,=4(-%6"(7%3"(4=(E=$?"?W$%g"(&=,E=7/'F=,3Y(
N_(
;+"(#ZN("*47"/"(1W4"7/%,D3(^%,?3(4=(.Kii^9$$:((
4+7=D-+(],?D&"?(>=$?%,-x>$8W1'3F,-(
!)a(%3(/=7"(9=7($"33:($%/%4"?(4+',(B+'4(8=D(
/%-+4(@"$%"6"Y(
;+"(&=/#$"*%48(=E(&=,E=7/'F=,'$(3#'&"(3+=D$?(
,"6"7(@"(D,?"7W'##7"&%'4"?Y(
;+"7"(%3(7"'$$8(,=(B'8('7=D,?(%4Y((
97"?D&"?(/=?"$3(/%-+4(+"$#(@D4(B%4+(&=/#7=/%3"3:(
;+"(","7-8(ED,&F=,(%3(%/#=74',4(%,(3'/#$%,-Y(
1+",J(0H1.(9RiiL:Y(
NM(
9&:(0%',+',(1+",(
N`(