Moil: Milestoning, NAIS Workshop

Moil:
Milestoning
Alfredo
Cardenas
Ins3tute
for
Computa3onal
Engineering
and
Science
University
of
Texas
at
Aus3n
Mo3va3on
•  The
reac3on
paths
techniques
can
provide
mechanis3c
informa3on
but
they
can
not
answer
the
ques3on:
How
long
it
takes?
•  Normal
MD
simula3ons
are
also
bound
to
study
events
shorter
than
~
1
microsecond.
•  Milestoning
is
a
method
that
can
be
used
to
address
these
problems.
The
theory
will
be
described
later.
Here
we
focus
on
the
determina3on
of
the
quan33es
needed
to
compute
the
rate.
Problems
with
reac3on
path
R
P
Minimum
energy
path
Real
trajectories
at
the
temperature
of
interest
Timescale
problem
with
MD
R
P
If
we
are
interested
to
study
slow
biomolecular
processes
(millisecond
or
longer)
the
individual
MD
trajectories
will
not
reach
the
Product
state
The
Milestoning
solu3on
R
P
1
3
4
5
Compute many trajectory fragments starting at different milestones and
ending at neighbor milestones
Milestoning
features
•  Trajectories
between
milestones
are
a
lot
shorter
than
trajectories
connec3ng
R
and
P
•  Typical
3mes
of
the
individual
milestone
trajectories
range
from
500
fs
to
tens
of
ps
•  Trajectories
between
milestones
are
computed
by
straighRorward
MD
algorithms
•  The
typical
number
of
trajectories
ini3ated
at
each
milestone
ranges
from
100
to
1000
•  The
set
of
trajectories
star3ng
at
milestone
i
can
be
run
independently
of
the
set
of
trajectories
ini3ated
at
milestone
j
How
to
construct
a
set
of
configura3ons
in
each
milestone?
Umbrella Sampling
(
dij ( X ) ! d X, X j
R
i
)
2
" d ( X, Xi ) + # i2
2
j
In the easiest case ! i2 = 0
P
U ! ( X ) = U ( X ) + U ij1 ( X ) + U ij2 ( X )
$ K1dij ( X )2
&
2
&
1
U ij ( X ) = % K1 dij ( X ) + "
&
&'0
$& K d ( X, X ) # d
2
k
U ij ( X ) = % 2
&'0
(
(
if dij ( X ) > 0
)
if dij ( X ) < # "
otherwise
(
X, X j
))
2
(
if d ( X, X k ) < d X, X j
otherwise
)
How
to
construct
a
set
of
configura3ons
in
each
milestone?
With constraints
i
R
j
k
P
(X ! X )"e
j
j
=0
X ! Xi
ej # k
X k ! Xi
This constraint is enforced with
Lagrange s multiplier. Additional constraints
are needed to fix the overall rotation and
translation of the molecule of interest
West et al., J. Chem. Phys. 126, 145104 (2007)
Next
step:
First
hiUng
point
distribu3on
Once a set of configurations has been obtained for a milestone need to determine
a set of configurations and velocities that correspond to a first hitting of that
Milestone
i
j
k
A set of position and velocities
correspond to a first hitting point
of milestone j if the system has
arrived for the first time at j
coming from i or k
The red point are first hitting point. Their positions and the negative of their
velocities are saved for the final step.
The green points are not first hitting point. Don t save their positions or velocities
Final
step:
compute
trajectories
star3ng
from
the
first
hiUng
point
i
j
k
Notice the forward trajectories
are not stopped when they
cross the originated milestone (j).
They are only stopped when
they hit for the first time a
neighbor milestone (i or k)
What
informa3on
is
needed
to
compute
kine3cs
with
Milestoning?
i
j
k
Milestone
hit
+me
k
10
i
12
i
14
i
15
i
12
k
14
Lifetime of milestone:
Transition probabilities:
Kji = 4/6 = 0.67
Kjk = 2/6 = 0.33
t
j
=
10 + 12 + 14 + 15 + 12 + 14
= 12.8
6
The overall Mean First Passage Time (MFPT or ! if ) from milestone i to the final
milestone f is:
!
= p i # [ I " K ]ij t
"1
if
j
j
How
to
prepare
a
reac3on
path
for
Milestoning?
The
main
steps
are
the
following:
–  Pick
the
individual
structures
of
the
pack
for
prepara3on
(ccrd)
–  Solvate
every
structure
in
the
path
with
a
water
box
(solvatecrd)
–  Add
ions
if
needed
to
have
a
neutral
box
(addion)
–  Run
MD
simula3on
on
each
structure
(dyna)
–  Reconstruct
the
solvated
reac3on
path
(ccrd)
Pick
individual
structures
in
the
path
Pick
ccrd
<
ccrd.inp
>
ccrd.log
ccrd.inp:
file
conn
name=(aladp.wcon)
read
file
rcrd
name=(aladp_sdp_30.pth)
bina
read
file
wcrd
name=(aladp_1.crd)
wovr
ctyp=(CHARM)
fpth
tchr
lpst=1
lpen=1
ac3on
Solvate
the
structure
./solvatecrd
<
solvate_1.inp
>
solvate_1.out
solvate_1.inp:
file
conn
name=(aladp.wcon)
read
file
rcrd
name=(aladp_1.crd)
read
file
wcrd
name=(aladp_s1.crd)
wovr
file
rwbx
name=(watbox.crd)
read
file
wpol
name=(aladp_s1.poly)
wovr
xwbx=26.2
ywbx=26.2
zwbx=26.2
ac3on
Add
ions
(no
needed
for
alanine
dipep3de)
./addion
<
addion.inp
>
addion.log
addion.inp:
file
conn
name=(apep_s1.wcon)
read
file
rcrd
name=(apep_s1.crd)
wovr
file
wcrd
name=(apep_ion1.crd)
wovr
file
poly
name=(apep_ion1.poly)
wovr
iona=(CL)
ionm=(CL)
#ion=4
ac3on
Run
MD
in
the
structure
./dyna
<
dyna.inp
>
dyna.out
dyna.inp:
file
conn
name=(aladp_solv.wcon)
read
file
rcrd
name=(aladp_s1.crd)
read
file
wcrd
name=(aladp_s1.dcd)
bina
wovr
#ste=80000
#equ=40000
info=200
#crd=20000
#lis=10
rand=3151187
step=0.0005
tmpi=3
tmpf=300
relx=9.
rvmx=8.
symm
xtra=27.5
ytra=27.5
ztra=27.5
sym2
xtr2=25.45
ytr2=25.45
ztr2=25.45
ewald
dtol=1.e‐9
grdx=32
grdy=32
grdz=32
ac3on
Sampling
and
first
hiUng
points
./dim_sampleS
<
sample.inp
>
sample.log
sample.inp:
file
conn
name=(aladp_solv.wcon)
read
file
rint
name=(2.crd)
read
file
rcrd
name=(aladp_centers.PTH)
bina
read
2.crd
file
wcrd
name=(2_3.PTH)
bina
wovr
file
wvel
name=(vel2_3.PTH)
bina
wovr
#ste=15000
#pri=40
#lis=10
step=0.001
grid=30
#sav=50
#scl=50.0
umbr=0.5
appr=2.0
K1_U=100.0
K2_U=100.0
cell=2
cel2=3
symm
xtra=25.45
ytra=25.45
ztra=25.45
ewald
dtol=1.e‐9
grdx=32
grdy=32
grdz=32
relx=8.5
rvmx=8
sele
rand=2413
cpth
TORS
atm1=7
atm2=9
atm3=11
atm4=17
TORS
atm1=5
atm2=7
atm3=9
atm4=11
ac3on
pick
#prt
5
5
|
#prt
7
7
|
#prt
9
9
|
#prt
11
11
|
#prt
17
17
done
Computa3on
of
forward
trajectories
./dim_run
<
run.inp
>
run.log
run.inp:
file
conn
name=(aladp_solv.wcon)
read
file
rint
name=(2_3.PTH)
bina
read
file
rcrd
name=(aladp_centers.PTH)
bina
read
file
rvel
name=(vel2_3.PTH)
bina
read
file
wcrd
name=(output.PTH)
bina
wovr
file
wfpt
name=(output.fpt)
wovr
#ste=15000
#pri=40
#lis=10
step=0.001
grid=30
#sav=50
#scl=50.0
cell=2
cel2=3
nInt=1
nEnd=10
symm
xtra=25.45
ytra=25.45
ztra=25.45
ewald
dtol=1.e‐9
grdx=32
grdy=32
grdz=32
relx=8.5
rvmx=8
sele
rand=2413
cpth
TORS
atm1=7
atm2=9
atm3=11
atm4=17
TORS
atm1=5
atm2=7
atm3=9
atm4=11
ac3on
pick
#prt
5
5
|
#prt
7
7
|
#prt
9
9
|
#prt
11
11
|
#prt
17
17
done
Applica3ons:
Coil
to
Helix
Path
unfolding
+me
(ns)
elementary
step
(ps)
1
280
455
2
7000
1580
3
86000
8900
J. Phys. Chem. A, 113, 7461 (2009)
Solute
permea3on
in
membrane
•  About
20000
milestoning
trajectories
run
for
a
total
simula3on
3me
of
~
1
microsecond
•  The
computed
permea3on
3me
of
several
hours
agree
with
experiment
z
J. Phys. Chem. B, 116, 2739 (2012)
Milestoning
as
an
analysis
tool:
Early
Events
in
Helix
Unfolding
CFMD
126-residue helix, 49605 water
Molecules
60 ns of simulation time
Flux
network
as
a
func3on
of
load
Average Milestone lifetime as a function of load
Kreuzer, Elber, and Moon, J. Phys. Chem. B (in press)
MOIL
team
Current Code developers:
Alfredo Cardenas, Ron Elber, Serdal Kirimizialtin,
Mauro Mugnai, Michele di Pierro, Peter Ruymgaart
Previous Code developers:
Avijit Ghosh, Robert Goldstein, Chen Keasar, Haiying
Li, Peter Májek, Jaroslaw Meller, Debasisa Mohanty,
Roberto Olender, Felicia Pitici, Adrian Roitberg, Amena
Siddiqi, Carlos Simmerling, Ileana Stoica, Alex Ulitsky,
Gennady Verkhivker, Yael Weinbach, Anthony West,
Veaceslav Zaloj
GUI developers:
Thomas Blom, Baohua Wang, Avijit Ghosh